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Therapeutic Apheresis and Blood Fractionation



Centrifugal Devices • Membrane Plasmapheresis


Plasma Perfusion

Andrew L. Zydney



University of Delaware



Apheresis is the process in which a specific component of blood (either plasma, a plasma component, white cells, platelets, or red cells) is separated and removed with the remainder of the blood returned to the patient (often in combination with some type of replacement fluid). Donor apheresis is used for the collection of specific blood cells or plasma components from blood donors, resulting in a much more effective use of limited blood-based resources. Donor apheresis developed during World War II as a means for increasing the supply of critically needed plasma, and clinical trials in 1944 demonstrated that it was possible to safely collect donations of a unit of plasma (approximately 300 ml) on a weekly basis if the cellular components of blood were returned to the donor. Therapeutic apheresis is used for the treatment of a variety of diseases and disorders characterized by the presence of abnormal proteins or blood cells in the circulation which are believed to be involved in the progression of that particular condition. Therapeutic apheresis thus has its roots in the ancient practice of bloodletting, which was used extensively well into the 19th century to remove “bad humors” from the patient’s body, thereby restoring the proper balance between the “blood, yellow bile, black bile, and phlegm.”

The term plasmapheresis was first used by Abel, Rowntree, and Turner in 1914 in their discussion of a treatment for toxemia involving the repeated removal of a large quantity of plasma, with the cellular components of blood returned to the patient along with a replacement fluid [Kambic & Nose, 1993]. The first successful therapeutic applications of plasmapheresis were reported in the late 1950s in the management of macroglobulinemia (a disorder characterized by a large increase in blood viscosity due to the accumulation of high-molecular-weight globulins in the blood) and in the treatment of multiple myeloma (a malignant tumor of the bone marrow characterized by the production of excessive amounts of immunoglobulins).

By 1990, there were well over 50 diseases treated by therapeutic apheresis [Sawada et al., 1990] with varying degrees of success. Plasmapheresis is used in the treatment of: (1) protein-related diseases involving excessive levels of specific proteins (e. g., macroglobulins in Waldenstrom’s syndrome and lipoproteins in familial hypercholesterolemia) or excessive amounts of protein-bound substances (e. g., toxins in hepatic failure and thyroid hormone in thyrotoxicosis), (2) antibody-related or autoimmune diseases (e. g., glomerulonephritis and myasthenia gravis), and (3) immune-complex-related diseases (e. g., rheumatoid arthritis and systemic lupus erythematosus).

Cytapheresis involves the selective removal of one (or more) of the cellular components of blood, and it has been used in the treatment of certain leukemias (for the removal of leukocytes) and in the treatment of polycythemia. Table 132.1 provides a more complete listing of some of the diseases and blood com­ponents that are removed during therapeutic apheresis. This list is not intended to be exhaustive, and there is still considerable debate over the actual clinical benefit of apheresis for a number of these diseases.

The required separation of blood into its basic components (red cells, white cells, platelets, and plasma) can be accomplished using centrifugation or membrane filtration; the more specific removal of one (or more) components from the separated plasma generally involves a second membrane filtration or use of an appropriate sorbent. The discussion that follows focuses primarily on the technical aspects of the different separation processes currently in use. Additional information on the clinical aspects of thera­peutic apheresis is available in the references listed at the end of this chapter.


The therapeutic application of plasmapheresis can take one of two forms: plasma exchange or plasma perfusion. In plasma exchange therapy, a relatively large volume of plasma, containing the toxic or immunogenic species, is separated from the cellular components of blood and replaced with an equivalent volume of a replacement fluid (either fresh frozen plasma obtained from donated blood or an appropriate plasma substitute). In plasma perfusion, the separated plasma is treated by an adsorptive column or second membrane filtration to remove a specific component (or components) from the plasma. This treated plasma is then returned to the patient along with the blood cells, thereby eliminating the need for exogenous replacement fluids. The different techniques that can be used for plasma perfusion are discussed subsequently.

The reduction in the concentration (C) of any plasma component during the course of a plasma­pheresis treatment can be described using a single compartment pharmacokinetic model as

V—^ □□□ QC DG (132.1)

P dt i p i i

Where Vp is the volume of the patient’s plasma (which is assumed to remain constant over the course of therapy through the use of a replacement fluid or through the return of the bulk of the plasma after a plasma perfusion), Qp is the volumetric rate of plasma collection, Gt is the rate of component generation, and □i is a measure of the effectiveness of the removal process. In membrane plasmapheresis, □i, is equal to the observed membrane sieving coefficient, which is defined as the ratio of the solute concentration in the filtrate collected through the membrane to that in the plasma entering the device; □i is thus equal to 1 for a small protein that can pass unhindered through the membrane but can be less than 1 for large proteins and immune complexes. In plasma perfusion systems, □i is equal to the fraction of the particular component removed from the collected plasma by the secondary (selective) processing step. The gener­ation rate is typically negligible over the relatively short periods (fewer than 3 hours) involved in the actual plasmapheresis; thus the component concentration at the end of a single treatment is given as

C ^ a. Qt□ □ □ y □

—- □ expo – i p □□ expo – i exc□ (132.2)

Coo □ yp □ □ yp □

Where Vexc = Qpt is the actual volume of plasma removed (or exchanged) during the process. Plasma exchange thus reduces the concentration of a given component by 63% after an exchange of one plasma volume (for □i = 1) and by 86% after two plasma volumes. This simple single compartment model has been verified for a large number of plasma components, although immunoglobulin G actually appears to have about 50% extravascular distribution with the re-equilibration between these compartments occurring within 24-28 hr following the plasmapheresis.


Components Removed



AntiFactor VIII Ab

Idiopathic Thrombocytopenia Purpura

Antiplatelet Ab, immune complexes

Thrombotic Thrombocytopenia Purpura

Antiplatelet Ab, immune complexes


Antilymphocyte Ab, immune complexes

Autoimmune Hemolytic Anemia

Anti-red cell Ab, red cells

Rh Incompatibility

Anti-Rh Ab



Hyperviscosity Syndrome

Macroglobulins, immunglobulin M

Waldenstrom’s Syndrome

Immunoglobulin M



Sickle Cell Anemia

Red blood cells




Systemic Lupus Erythematosus

Anti-DNA Ab, immune complexes

Progressive Systemic Sclerosis

Antinonhistone nuclear Ab

CREST Syndrome

Anticentromere Ab

Sjorgen Syndrome

Antimitochondrial Ab

Rheumatoid Arthritis

Rheumatoid factor, cryoglobulins, immunoglobulins

Periarteritis Nodosa

Cryoglobulins, immune complexes

Raynaud’s Disease

Cryoglobulins, macroglobulins


Immune complexes

Mixed Connective Tissue Diseases



Myasthenia Gravis

Antiacetylcholine receptor Ab, cryoglobulins

Multiple Sclerosis

Antimyelin Ab

Guillain-Barre Syndrome

Antimyelin Ab


Cryoglobulins, macroglobulins



Lambert-Eaton Syndrome



Chronic Active Hepatitis

Antimitochondrial Ab

Hepatic Failure

Protein-bound toxins

Primary Biliary Cirrhosis

Protein-bound toxins, antimitochondrial Ab


Goodpasture’s Syndrome

Antiglomerular basement membrane Ab


Immune complexes

Lupus Nephritis

Immune complexes

Transplant Rejection

Immune complexes, anti-HLA Ab

Malignant diseases


Tumor-specific Ab, immune complexes

Multiple Myeloma





Addison’s Disease

Antiadrenal Ab

Autoimmune Thyroiditis

Antimicrosomal Ab

Chronic Ulcerative Colitis

Anticolonic epithelial cell Ab

Diabetes Mellitus

Antiinsulin receptor Ab

Hashimoto’s Disease

Antithyroglobulin Ab

Insulin Autoimmune Syndrome

Antiinsulin Ab


Antiepidermal cell membrane Ab

Ulcerative Colitis

Anticolonic lipopolysaccharide Ab


Immunoglobulin E


Cholesterol, lipoproteins


Low – and very low density lipoproteins


Thyroid hormone

There is still considerable variability in the frequency and intensity of the plasmapheresis used in different therapeutic applications, and this is due in large part to uncertainties regarding the metabolism, pharmacokinetics, and pathogenicity of the different components that are removed during therapeutic apheresis. The typical plasma exchange therapy currently involves the removal of 2-3 L of plasma (approximately one plasma volume) at a frequency of 2-4 times per week, with the therapy continued for several weeks. There have also been a number of studies of the long-term treatment of several diseases via plasmapheresis, with the therapy performed on a periodic basis (ranging from once per week to once every few months) over as much as 5 years (e. g., for the removal of cholesterol and lipoproteins in the treatment of severe cases of hypercholesterolemia).

Centrifugal Devices

Initially, all plasmapheresis was performed using batch centrifuges. This involved the manual removal of approximately one unit (500 ml) of blood at a time, with the blood separated in a centrifuge so that the target components could be removed. The remaining blood was then returned to the patient before drawing another unit and repeating the entire process. This was enormously time-consuming and labor­intensive, requiring as much as 5 hours for the collection of only a single liter of plasma. Batch centrif­ugation is still the dominant method for off-line blood fractionation in most blood-banking applications, but almost all therapeutic plasmapheresis is performed using online (continuous) devices.

The first continuous flow centrifuge was developed in the late 1960s by IBM in conjunction with the National Cancer Institute, and this basic design was subsequently commercialized by the American Instrument Co. (now a division of Travenol) as the Aminco Celltrifuge [Nose et al., 1983]. A schematic diagram showing the general configuration of this, and most other continuous flow centrifuges is shown in Fig. 132.1. The blood is input at the bottom of the rotating device and passes through a chamber in


1 White Cells

Red Cells

Therapeutic Apheresis and Blood Fractionation


I Feed Blood



FIGURE 132.1 Schematic diagram of a generic continuous flow centrifuge for fractionation of blood into red cells, white cells/platelets, and plasma.

Which the actual separation into plasma, white cells/platelets, and red cells occurs. Three separate exit ports are located at different radial positions to remove the separated components continuously from the top of the chamber using individual roller pumps. The position of the buffy coat layer (which consists of the white cells and platelets) is controlled by adjusting the centrifugal speed and the relative plasma and red cell flow rates to obtain the desired separation. Probably the most difficult engineering problem in the development of the continuous flow centrifuge was the design of the rotating seals through which the whole blood and separated components must pass without damage. The seal design in the original NCI/IBM device used saline lubrication to prevent intrusion of the cells between the contacting surfaces.

In order to obtain effective cell separation in the continuous flow centrifuge, the residence time in the separation chamber must be sufficiently large to allow the red cells to migrate to the outer region of the device. The degree of separation can thus be characterized by the packing factor

GV t

P □ (132.3)


Where G is the g-force associated with the centrifugation, Vsed is the sedimentation velocity at 1 g, t is the residence time in the separation chamber, and h is the width of the separation chamber (i. e., the distance over which the sedimentation occurs). The packing factor thus provides a measure of the radial migration compared to the width of the centrifuge chamber, with adequate cell separation obtained when P > 1. The residence time in the separation chamber is inversely related to the blood flow rate (QB) as


T □ (132.4)


Where L and A are the length and cross-sectional area of the chamber, respectively.

Rotational speeds in most continuous flow centrifuges are maintained around 1500 rpm (about 100 g) to obtain a relatively clean separation between the red cells and buffy coat, to avoid the formation of a very highly packed (and therefore highly viscous) region of cells at the outer edge of the chamber, and to minimize excessive heating around the rotating seals [Rock, 1983]. The width of the separation chamber must be large enough to permit effective removal of the different blood components from the top of the device, while minimizing the overall extracorporeal blood volume. For example, a packing factor of 10 requires a residence time of about 20 s for a device operated at 100 g with a 0.1-cm-wide separation chamber. The blood flow rate for this device would need to be maintained below about 120 ml/min for a chamber volume of 40 ml. Most of the currently available devices operate at QB □ 50 ml/min and can thus collect a liter of plasma in about 30-40 minutes.

More recent models for the continuous flow centrifuge have modified the actual geometry of the separation chamber to enhance the cell separation and reduce the overall cost of the device [Sawada et al., 1990]. Examples include tapering the centrifuge bowl to improve flow patterns and optimizing the geometry of the collection region to obtain purer products. The IBM 2997 (commercialized by Cobe Laboratories) uses a disposable semirigid plastic rectangular channel for the separation chamber, which eliminates some of the difficulties involved in both sterilizing and setting up the device. Fenwal Labora­tories developed the CS-3000 Cell Separator (subsequently sold by Baxter Healthcare), which uses a continuous J-shaped mulitchannel tubing connected directly to the rotating element. This eliminates the need for a rotating seal, thereby minimizing the possibility of leaks. The tubing in this device actually rotates around the centrifuge bowl during operation, using a “jump rope” principle to prevent twisting of the flow lines during centrifugation.

In addition to the continuous flow centrifuge, Haemonetics has developed a series of intermittent flow centrifuges [Rock, 1983]. Blood flows into the bottom of a separation chamber similar to that shown in Fig. 132.1, But the red cells simply accumulate in this chamber while the plasma is drawn to the center of the rotating bowl and removed through an outlet port at the top of the device. When the process is complete, the pump action reverses, and the red cells are forced out of the bowl and reinfused into the patient (along with any replacement fluid). The entire process is then automatically repeated to obtain the desired level of plasma (or white cell) removal. This device was originally developed for the collection of leukocytes and platelets, but it is now used extensively for large-scale plasmapheresis as well. Maximum blood flow rates are typically about 70-80 ml/min, and the bowl rotates at about 5000 rpm. The device as a whole is more easily transported than most of the continuous flow centrifuges, but it requires almost 50% more time for the collection of an equivalent plasma volume due to the intermittent nature of the process. In addition, the total extracorporeal volume is quite high (about 500 ml compared to only 250 ml for most of the newer continuous flow devices) due to the larger chamber required for the red cell accumulation [Sawada et al., 1990].

All these centrifugal devices have the ability to carry out effective plasma exchange, although the rate of plasma collection tends to be somewhat slower than that for the membrane devices discussed in the next section. These devices can also be used for the collection of specific cell fractions, providing a degree of flexibility that is absent in the membrane systems. The primary disadvantage of the centrifugal units is the presence of a significant number of platelets in the collected plasma (typically about 105 platelets per □). Not only can this lead to considerable platelet depletion during repeated applications of plasma exchange, it can also interfere with many of the secondary processing steps employed in plasma perfusion.

Membrane Plasmapheresis

The general concept of blood filtration using porous membranes is quite old, and membranes with pores suitably sized to retain the cellular components of blood and pass the plasma proteins have been available since the late 1940s. Early attempts at this type of blood filtration were largely unsuccessful due to severe problems with membrane plugging (often referred to as fouling) and red cell lysis. Blatt and coworkers at Amicon recognized that these problems could be overcome using a cross-flow configuration [Solomon et al., 1978] in which the blood flow was parallel to the membrane and thus perpendicular to the plasma (filtrate) flow as shown schematically in Fig. 132.2. This geometry minimizes the accumulation of retained cells at the membrane surface, leading to much higher filtration rates and much less cell damage than could be obtained in conventional dead-end filtration devices [Solomon et al., 1978]. This led to the development of a large number of membrane devices using either flat sheet or hollow-fiber membranes made from a variety of polymers including polypropylene (Travenol Laboratories, Gambro, Fresenius), cellulose diacetate (Asahi Medical), polyvinyl alcohol (Kuraray), polymethylmethacrylate (Toray), and polyvinyl chloride (Cobe Laboratories).

Therapeutic Apheresis and Blood Fractionation

Plasma Filtrate Flux, J(z)

FIGURE 132.2 Schematic diagram of a parallel plate device for cross-flow membrane plasmapheresis.

Therapeutic Apheresis and Blood Fractionation

FIGURE 132.3 Experimental data for the filtrate flux as a function of the applied transmembrane pressure drop in a parallel plate membrane plasmaphersis device. Red cell hemolysis, defined as a filtrate hemoglobin concentration exceeding 20 mg/dl, occurs to the right of the dashed line. Data have been adapted from Zydney and Colton [1987].

These membrane devices all produce essentially cell-free plasma with minimal protein retention using membranes with pore sizes of 0.2-0.6 Dm. In addition, these devices must be operated under conditions that cause minimal red cell lysis, while maintaining a sufficiently high plasma filtrate flux to reduce the cost of the microporous membranes. Typical experimental data for a parallel plate membrane device are shown in Fig. 132.3 [Zydney & Colton, 1987]. The results are plotted as a function of the mean trans­membrane pressure drop (□□□□ ) at several values of the wall shear rate (Hy, where is directly propor­tional to the inlet blood flow rate (QB). The filtrate flux initially increases with increasing □□□□ reaching a maximum pressure independent value which increases with increasing shear rate. The flux under all conditions is substantially smaller than that obtained when filtering pure (cell-free) saline under identical conditions (dashed line in Fig. 132.3). No measurable hemolysis was observed at low □□□□ even when the flux was in the pressure-independent regime. Hemolysis does become significant at higher pressures, with the extent of hemolysis decreasing with increasing and with decreasing membrane pore size [Solomon et al., 1978]. The dashed diagonal line indicates the pressure at which the filtrate hemoglobin concentration exceeds 20 mg/dl.

The pressure-independent flux at high □Onn generally has been attributed to the formation of a concentration polarization boundary layer consisting of a high concentration of the formed elements in blood, mainly the red blood cells, which are retained by the microporous membrane (Fig. 132.2). This dynamic layer of cells provides an additional hydraulic resistance to flow, causing the flux to be substan­tially smaller than that obtained during filtration of a cell-free solution. At steady-state, this boundary layer is in dynamic equilibrium, with the rate of convection of formed elements toward the membrane balanced by the rate of mass transport back into the bulk suspension. There has been some debate in the literature over the actual mechanism of cell transport in these devices, and the different models that have been developed for the plasma flux during membrane plasmapheresis are discussed elsewhere [Zydney & Colton, 1986].

Zydney and Colton [1982] proposed that cell transport occurs by a shear-induced diffusion mechanism in which cell-cell interactions and collisions give rise to random cell motion during the shear flow of a concentrated suspension. This random motion can be characterized by a shear-included diffusion coef­ficient, which was evaluated from independent experimental measurements as


подпись: (132.5)D □ a2U f ([

Where □ is the local shear rate (velocity gradient), a is the cell radius (approximately 4.2 Dm for the red blood cells), and C is the local red cell concentration. The function f(C), which reflects the detailed concentration dependence of the shear-induced diffusion coefficient, is approximately equal to 0.03 for red cell suspensions over a broad range of cell concentrations.

The local filtrate flux can be evaluated using a stagnant film analysis in which the steady-state mass balance is integrated over the thickness of the concentration boundary layer yielding [Zydney & Colton, 1986]

J( □□ km ln – w (132.6)


Where z is the axial distance measured from the device inlet, and Cw and Cb are the concentrations of formed elements at the membrane surface and in the bulk suspension, respectively. The bulk mass transfer coefficient (km) can be evaluated using the Leveque approximation for laminar flow in either a parallel plate or hollow fiber device

Rf/3 □ a4 ri/3

Km □ 0516 □ “□ □ °.°47 ppn (I32.7)

z □ □ z □

Where the second expression has been developed using the shear-induced diffusion coefficient given by Eq (132.5) with f(C) = 0.03. The wall shear rate is directly proportional to the blood flow rate with


□ —^ (132.8)


For a hollow-fiber device with N fibers of inner radius R and

W □ 0 (132.9)


For a parallel plate device with channel height h and total membrane width w.

At high pressures, Cw approaches its maximum value which is determined by the maximum packing density of the cells (about 95% under conditions typical of clinical plasmapheresis). The plasma flux under these conditions becomes independent of the transmembrane pressure drop, with this pressure – independent flux varying linearly with the wall shear rate and decreasing with increasing bulk cell concentration as described by Eqs. (132.6) and (132.7). A much more detailed numerical model for the flux [Zydney & Colton, 1987], which accounts for the concentration and shear rate dependence of both the blood viscosity and shear-induced cell diffusion coefficient as well as the compressibility of the blood cell layer that accumulates at the membrane, has confirmed the general behavior predicted by Eqs. (132.6) and (132.7).

The volumetric filtrate (plasma) flow rate (0p) in a hollow-fiber membrane filter can be evaluated by integrating Eqs. (132.6)-(132.8) along the length of the device accounting for the decrease in the blood flow rate (and thus H^) due to the plasma removal [Zydney & Colton, 1986]. The resulting expression for the fractional plasma yield is

^ □ n 2 rf2/3 □

0 1-1 n a 2 t r c n


подпись: (132.1°)0a 1 – expо°.62lOT ln qH

An analogous expression can be evaluated for a parallel plate device with the channel height h replacing R and the coefficient 0.62 becoming 0.84. Even though the development leading to Eq. (132.10) neglects the detailed variations in the bulk cell concentration and velocity profiles along the fiber length, the final expression has been shown to be in good agreement with experimental data for the plasma flow rate in actual clinical devices [Zydney & Colton, 1986]. Equation (132.10) predicts that the volumetric plasma flow rate is independent of the number of hollow fibers (or the membrane width for a parallel plate membrane device), a result which is consistent with a number of independent experimental investigations.

According to Eq. (132.10), the plasma flow rate increases significantly with decreasing fiber radius. There are, however, a number of constraints on the smallest fiber radius that can actually be employed in these hollow-fiber membrane devices. For example, blood clotting and fiber blockage can become unacceptable in very narrow bore fibers. The blood flow in such narrow fibers also causes a very high bulk shear stress, which potentially can lead to unacceptable levels of blood cell damage (particularly for white cells and platelets). Finally, the hollow-fiber device must be operated under conditions which avoid hemolysis.

Zydney and Colton [1982] developed a model for red cell lysis during membrane plasmapheresis in which the red cells are assumed to rupture following their deformation into the porous structure of the membranes. A given red cell is assumed to lyse if it remains in a pore for a sufficient time for the strain induced in the red cell membrane to exceed the critical strain for cell lysis. Since the red cell can be dislodged from the pore by collisions with other cells moving in the vicinity of the membrane or by the fluid shear stress, the residence time in the pore will be inversely related to the wall shear rate.

The tension (□) in the red cell membrane caused by the deformation in the pore is evaluated using Laplace’s law [Zydney & Colton, 1987]

□Pn, Rp



Where Rp is the pore radius. Hemolysis is assumed to occur at a critical value of the strain in the red cell membrane (S); thus the time required for lysis is given implicitly by

S □□ #[}[□□ j 0.0010 □ 0.0012 [ □ exp(8l[ 4.5 10-6l} (132.12)

The function g(t) represents the temporal dependence of the lytic phenomenon and has been evaluated from independent experimental measurements [Zydney & Colton, 1982]. Cell lysis occurs when S □ 0.03 in Eq. (132.12) where □ is given in dyne/cm and 1 is in sec. This simple model has been shown to be in good agreement with experimental data for red cell lysis during cross-flow membrane plasmapheresis [Zydney & Colton, 1987].

This physical model for red cell lysis implies that hemolysis can be avoided by operating at sufficiently high shear rates to reduce the residence time in the membrane pores. However, operation at high shear rates also causes the inlet transmembrane pressure drop to increase due to the large axial pressure drop associated with the blood flow along the length of the device [Zydney & Colton, 1982]:

Ptm ([□□Ptm (□ 2D$L (132.13)


Where □Dcn(0) and □Ocn(L) are the inlet and exit transmembrane pressure drops, respectively, and D is the average blood viscosity. □Ocn(L) is typically maintained at a small positive value (about 20 mmHg) to ensure that there is a positive transmembrane pressure drop along the entire length of the device.

Since the increase in □0CD(0) with increasing has a greater effect on hemolysis than the reduction in

Therapeutic Apheresis and Blood Fractionation

FIGURE 132.4 Schematic representation of the safe operating regime for a clinical membrane plasmapheresis device.

The residence time for the red cells in the membrane pores, there is also an upper bound on the shear rate for the safe operation of any given clinical device.

The predicted safe operating regime for a clinical membrane plasmapheresis device can be determined using Eq. (132.11), with the maximum transmembrane pressure drop occurring at the device inlet, Eq. (132.13). The results are shown schematically in Fig. 132.4. HEmolysis occurs at very low shear rates due to the long residence time in the membrane pores, whereas lysis at high shear rates is due to the large value of the inlet transmembrane pressure drop associated with the axial flow. Note that there is a critical fiber length [at fixed values of the fiber radius and Шш (L)] above which there is no longer any safe operating condition.

To avoid some of the constraints associated with the design of both parallel plate and hollow-fiber membrane devices. Hemasciences developed a rotating membrane filter for use in both donor and therapeutic plasmapheresis. A nylon membrane is placed on an inner cylinder and rotated at about 3600 rpm inside a concentric outer cylindrical chamber using a magnetic coupling device. The rotating membrane causes a very high shear rate (on the order of 10,000 s-1) in the narrow gap between the cylinders. However, these high shear rates do not result in a large axial pressure drop, as found in the parallel plate and hollow-fiber devices, due to the decoupling of the axial blood flow and the shear rate in this system (the shear is now due almost entirely to the membrane rotation). The fluid flow in this rotating cylinder system also leads to the development of fluid instabilities known as Taylor vortices, and these vortices dramatically increase the rate of cell mass transport away from the membrane and back into the bulk suspension. This leads to a dramatic increase in the plasma filtrate flux and a dramatic reduction in the required membrane area. The Autopheresis-C (the rotating filter currently sold by Baxter Healthcare) uses only 70 cm2 of membrane, which is more than an order of magnitude less than that required in competitive hollow-fiber and parallel plate devices. The mathematical analysis of the plasma filtrate flux and the corresponding design equations for the rotating cylinder plasma filter are provided by Zeman and Zydney [1996].

Plasma Perfusion

In repeated applications of plasma exchange, it is necessary to use replacement fluids that contain proteins to avoid the risks associated with protein depletion. One approach to minimizing the cost of these protein – containing replacement fluids (either albumin solutions, fresh frozen plasma, or plasma protein fraction) is to use a saline or dextran solution during the initial stages of the process and to then switch to a protein-containing replacement fluid toward the end of the treatment. Alternatively, a number of tech­niques have been developed to selectively remove specific toxic or immunogenic components from the plasma, with this treated plasma returned to the patient along with the cellular components of blood. This effectively eliminates the need for any expensive protein-containing replacement fluids.

Plasma perfusion (also known as online plasma treatment) is typically performed using either mem­brane or sorbent-based systems. Membrane filtration separates proteins on the basis of size and is thus used to selectively remove the larger molecular weight proteins from albumin and the small plasma solutes (salts, sugars, amino acids, and so on). A variety of membranes have been employed for this type of plasma fractionation including cellulose acetate (Terumo), cellulose diacetate (Asahi Medical and Teijin), ethylene vinyl alcohol (Kuraray), and polymethylmetharcrylate (Toray). These membranes are generally hydrophilic to minimize the extent of irreversible protein adsorption, with pore sizes ranging from 100-600 A depending on the specific objectives of the membrane fractionation.

The selectivity that can be obtained with this type of plasma filtration can be examined using available theoretical expressions for the actual sieving coefficient (Sa) for a spherical solute in a uniform cylindrical pore:

Therapeutic Apheresis and Blood Fractionation

Where # is the ratio of the solute to pore radius. Equation (132.14) is actually an approximate expression which has been shown to be in good agreement with more rigorous theoretical analyses. This expression for the actual sieving coefficient, where Sa is defined as the ratio of the protein concentration in the filtrate to that at the upstream surface of the membrane, is valid at high values of the plasma filtrate flux, since it implicitly assumes that the diffusive contribution to protein transport is negligible. To avoid excessive albumin loss, it is desirable to have Sa > 0.8, which can be achieved using a membrane with an effective pore size greater than about 160 A (albumin has a molecular weight of 69,000 and a Stokes­Einstein radius of 36 A). This membrane would be able to retain about 80% of the immunglobulin M (which has a molecular weight of about 900,000 and a Stokes-Einstein radius of 98 A), but it would retain less than 40% of the immunglobulin G (with MW = 155,000 and a radius of 55 A).

The protein retention obtained during an actual plasma filtration is substantially more complex than indicated by the above discussion. The polymeric membranes used in these devices actually have a broad distribution of irregularly shaped (noncylindrical) pores. Likewise, the proteins can have very different (nonspherical) conformations, and their transport characteristics also can be affected by electrostatic, hydrophobic, and van der Waals interactions between the proteins and the polymeric membrane, in addition to the steric interactions that are accounted for in the development leading to Eq. (132.14). Protein-protein interactions can also significantly alter the observed protein retention. Finally, the partially retained proteins will tend to accumulate at the upstream surface of the membrane during filtration (analogous to the concentration polarization effects described previously in the context of blood cell filtration).

This type of secondary plasma filtration, which is generally referred to in the literature as cascade filtration, is primarily effective at removing large immune complexes (molecular weight of approximately 700,000) and immunglobulin M (MW of 900,000) from smaller proteins such as albumin. Several studies have, however, found a higher degree of albumin-immunoglobulin G separation than would be expected based on purely steric considerations [Eq. (132.14)]. This enhanced selectivity is probably due to some type of long-range (e. g., electrostatic) interaction between the proteins and the membrane.

A number of different techniques have been developed to enhance the selectivity of these plasma filtration devices. For example, Malchesky and coworkers at the Cleveland Clinic [Malchesky et al., 1980] developed the process of cryofiltration in which the temperature of the plasma is lowered to about 10°C prior to filtration. A number of diseases are known to be associated with the presence of large amounts of cryo – (cold-) precipitable substances in the plasma, including a number of autoimmune diseases such as systemic lupus erythematosus and rheumatoid arthritis. Lowering the plasma temperature causes the aggregation and/or gelation of these cryoproteins, making it much easier for these components to be removed by the membrane filtration. About 10 g of cryogel can be removed in a single cryofiltration, along with significant amounts of the larger-molecular-weight immune complexes and IgM. The actual extent of protein removal during cyrofiltration depends on the specific composition of the plasma and thus on the nature as well as the severity of the particular disease state [Sawada et al., 1990]. There is thus considerable uncertainty over the actual components that are removed during cryofiltration under different clinical and/or experimental conditions. The cryogel layer that accumulates on the surface of the membrane also affects the retention of other plasma proteins, which potentially could lead to unacceptable losses even of small proteins such as albumin.

It is also possible to alter the selectivity of the secondary membrane filtration by heating the plasma up to or even above physiologic temperatures. This type of thermofiltration has been shown to increase the retention of low- (LDL) and very low (VLDL) density lipoproteins, and this technique has been used for the online removal of these plasma proteins in the treatment of hypercholesterolemia. LDL removal can also be enhanced by addition of a heparin/acetate buffer to the plasma, which causes precipitation of LDL and fibrinogen with the heparin [Sawada et al., 1990]. These protein precipitates can then be removed relatively easily from the plasma by membrane filtration. The excess heparin is subsequently removed from the solution by adsorption, with the acetate and excess fluid removed using bicarbonate dialysis.

An attractive alternative to secondary membrane filtration for the selective removal of plasma com­ponents is the use of sorbent columns such as: (1) activated charcoal or anion exchange resins for the removal of exogenous toxins, bile acids, and bilirubin; (2) dextran sulfate cellulose for the selective removal of cholesterol, LDL, and VLDL; (3) immobilized protein A for the removal of immunoglobulins (particularly IgG) and immune complexes; and (4) specific immobilized ligands like DNA (for the removal of anti-DNA Ab), tryptophan (for the removal of antiacetylcholine receptor antibodies), and insulin (for the removal of anti-insulin antibodies). These sorbents provide a much more selective separation than is possible with any of the membrane processes; thus they have the potential to signifi­cantly reduce the side effects associated with the depletion of needed plasma components. The sorbent columns generally are used in combination with membrane plasmaphersis, since the platelets that are present in the plasma collected from available centrifugal devices can clog the columns and interfere with the subsequent protein separation.

The development of effective sorbent technology for online plasma treatment has been hindered by the uncertainties regarding the actual nature of the plasma components that must be removed for the clinical efficacy of therapeutic apheresis in the treatment of different disease states. In addition, the use of biologic materials in these sorbent systems (e. g., protein A or immobilized DNA) presents particular challenges, since these materials may be strongly immunogenic if they desorb from the column and enter the circulation.


Cytapheresis is used to selectively remove one (or more) of the cellular components of blood, with the other components (including the plasma) returned to the patient. For example, leukocyte (white cell) removal has been used in the treatment of leukemia, autoimmune diseases with a suspected cellular immune mechanism (e. g., rheumatoid arthritis and myasthenia gravis), and renal allograft rejection. Erythrocyte (red cell) removal has been used to treat sickle cell anemia, severe autoimmune hemolytic anemia, and severe parasitemia. Plateletapheresis has been used to treat patients with thrombocythemia.

Most cytapheresis is performed using either continuous or intermittent flow centrifuges, with appro­priate software and/or hardware modifications used to enhance the collection of the specific cell fraction. It is also possible to remove leukocytes from whole blood by depth filtration, which takes advantage of the strong adherence of leukocytes to a variety of polymeric materials (e. g., acrylic, cellulose acetate, polyester, or nylon fibers). Leukocyte adhesion to these fibers is strongly related to the configuration and the diameter of the fibers, with the most effective cell removal obtained with ultrafine fibers less than

Dm in diameter. Available leukocyte filters (Sepacel, Cellsora, and Cytofrac from Asahi Medical Co.) have packing densities of about 0.1-0.15 g fiber/cm3 and operate at blood flow rates of 20-50 ml/min, making it possible to process about 2 L of blood in 1.5 hr.

Leukocyte filtration is used most extensively in blood-banking applications to remove leukocytes from the blood prior to transfusion, thereby reducing the likelihood of antigenic reactions induced by donor leukocytes and minimizing the possible transmission of white-cell associated viral diseases such as cytomegalovirus. The absorbed leukocytes can also be eluted from these filters by appropriate choice of buffer solution pH, making it possible to use this technique for the collection of leukocytes from donated blood for use in the subsequent treatment of leukopenic recipients. Depth filtration has also been considered for online leukocyte removal from the extracorporeal circuit of patients undergoing cardio­pulmonary bypass as a means to reduce the likelihood of postoperative myocardial or pulmonary rep­erfusion injury which can be caused by activated leukocytes.

A new therapeutic technique that involves online cytapheresis is the use of extracorporeal photochemo­therapy, which is also known in the literature as photopheresis. Photopheresis can be used to treat a variety of disorders caused by aberrant T-lymphocytes [Edelson, 1989], and it has become an established therapy for the treatment of advanced cutaneous T-cell lymphoma in the U. S. and several European countries. In this case, the therapy involves the use of photoactivated 8-methoxypsoralen, which blocks DNA replication causing the eventual destruction of the immunoactive T-cells. The psoralen compound is taken orally prior to the phototherapy. Blood is drawn from a vein and separated by centrifugation. The white cells and plasma are collected, diluted with a saline solution, and then pumped through a thin plastic chamber in which the cells are irradiated with a high-intensity UV light that activates the psoralen. The treated white cells are then recombined with the red cells and returned to the patient. Since the photoactivated psoralen has a half-life of only several microseconds, all its activity is lost prior to reinfusion of the cells, thereby minimizing possible side effects on other organs. The removal of the red cells (which have a very high adsorptivity to UV light) makes it possible to use a much lower energy UV light, thereby minimizing the possible damage to normal white cells and platelets.

Photopheresis has also been used in the treatment of scleroderma, systemic lupus erythematosus, and pemphigus vulgaris. The exact mechanism for the suppression effect induced by the photo-therapy in these diseases is uncertain, although the T-cel! destruction seems to be highly specific for the immuno – active T-cells [Edelson, 1989]. The response is much more involved than simple direct photoinactivation of the white cells; instead, the photo-treated cells appear to undergo a delayed form of cell death which elicits an immunologic response possibly involving the production of anti-idiotypic antibodies or the generation of clone-specific suppressor T-cells. This allows for an effective “vaccination” against a par­ticular T-cell activity without the need for isolating or even identifying the particular cells that are responsible for that activity [Edelson, 1989].

Phototherapy has also been used for virus inactivation, particularly in blood-banking applications prior to transfusion. This can be done using high-intensity UV light alone or in combination with specific photoactive chemicals to enhance the virus inactivation. For example, hematoporphyrin derivatives have been shown to selectively destroy hepatitis and herpes viruses in contaminated blood. This technique shows a high degree of specificity toward this type of enveloped virus, which is apparently due to the affinity of the photoactive molecules for the lipids and glycolipids that form an integral part of the viral envelope.

Another interesting therapeutic application involving cytapheresis is the ex vivo activation of immu­nologically active white cells (lymphokine-activated killer cells, tumor-infiltrating lymphocytes, or acti­vated killer macrophages) for the treatment of cancer. The detailed protocols for this therapy are still being developed, and there is considerable disagreement regarding its actual clinical efficacy. A pool of activated cells is generated in vivo by several days of treatment with interleukin-2. These cells are then collected from the blood by centrifugal cytapheresis and further purified using density gradient centrif­ugation. The activated cells are cultured for several days in a growth media containing additional interleukin-2. These ex-vivo activated cells are then returned to the patient, where they have been shown to lyse existing tumor cells and cause regression of several different metastatic cancers.


Apheresis is unique in terms of the range of diseases and metabolic disorders which have been successfully treated by this therapeutic modality. This broad range of application is possible because apheresis directly alters the body” s immunologic system though the removal or alteration of specific immunologically active cells and/or proteins.

Although there are a number of adverse reactions that can develop during apheresis (e. g., fluid imbalance, pyrogenic reactions, depletion of important coagulation factors, and thrombocytopenia), the therapy is generally well tolerated even by patients with severely compromised immune systems. This has, in at least some instances, led to the somewhat indiscriminate use of therapeutic apheresis for the treatment of diseases in which there was little physiologic rationale for the application of this therapy. This was particularly true in the 1980s, where dramatic advances in the available technology for both membrane and centrifugal blood fractionation allowed for the relatively easy use of apheresis in the clinical milieu. In some ways, apheresis in the 1980s was a medical treatment that was still looking for a disease. Although apheresis is still evolving as a therapeutic modality it is now a fairly well-established procedure for the treatment of a significant number of diseases (most of which are relatively rare) in which the removal of specific plasma proteins or cellular components can have a beneficial effect on the progression of that particular disease. Furthermore, continued advances in the equipment and procedures used for blood fractionation and component removal have, as discussed in this chapter, provided a safe and effective technology for the delivery of this therapy.

The recent advances in sorbent-based systems for the removal of specific immunologically active proteins and in the development of treatment for the activation or inactivation of specific cellular components of the immune system has provided exciting new opportunities for the alteration and even control of the body’s immunologic response. This includes: (1) the direct removal of specific antibodies or immune complexes (using membrane plasmapheresis with appropriate immunosorbent columns), (2) the inactivation or removal of specific lymphocytes (using centrifugal cytapheresis in combination with appropriate extracorporeal phototherapy or chemotherapy), and/or (3) the activation of a disease – specific immunologic response (using cytapheresis and ex vivo cell culture with appropriate lymphokines and cell stimuli). New advances in our understanding of the immune system and in our ability to selectively manipulate and control the immunologic response should thus have a major impact on therapeutic apheresis and the future development of this important medical technology.

Defining Terms

Autoimmune diseases: A group of diseases in which pathological antibodies are produced that attack

The body’s own tissue. Examples include glomerulonephritis (characterized by inflammation of the capillary loops in the glomeruli of the kidney) and myasthenia gravis (characterized by an inflammation of the nerve/muscle junctions).

Cascade filtration: The combination of plasmapheresis with a second online membrane filtration of

The collected plasma to selectively remove specific toxic or immunogenic components from blood based primarily on their size.

Cytapheresis: A type of therapeutic apheresis involving the specific removal of red blood cells, white

Cells (also referred to as leukapheresis), or platelets (also referred to as plateletapheresis).

Donor apheresis: The collection of a specific component of blood (either plasma or one of the cellular

Fractions), with the return of the remaining blood components to the donor. Donor apheresis is used to significantly increase the amount of plasma (or a particular cell type) that can be donated for subsequent use in blood banking and/or plasma fractionation.

Immune complexes: Antigen-antibody complexes that can be deposited in tissue. In rheumatoid arthri­

Tis this deposition occurs primarily in the joints, leading to severe inflammation and tissue damage. Photopheresis: The extracorporeal treatment of diseases characterized by aberrant T-cell populations

Using visible or ultraviolet light therapy, possibly in combination with specific photoactive chemicals. Plasma exchange: The therapeutic process in which a large volume of plasma (typically 3 L) is removed

And replaced by an equivalent volume of a replacement fluid (typically fresh frozen plasma, a plasma substitute, or an albumin-containing saline solution).

Plasma perfusion: The therapeutic process in which a patient’s plasma is first isolated from the cellular

Elements in the blood and then subsequently treated to remove specific plasma components. This secondary treatment usually involves a sorbent column designed to selectively remove a specific plasma component or a membrane filtration designed to remove a broad class of plasma proteins. Plasmapheresis: The process in which plasma is separated from the cellular components of blood using

Either centrifugal or membrane-based devices. Plasmapheresis can be employed in donor applica­tions for the collection of source plasma for subsequent processing into serum fractions or in therapeutic applications for the treatment of a variety of disorders involving the presence of abnormal circulating components in the plasma.

Therapeutic apheresis: A process involving the separation and removal of a specific component of the

Blood (either plasma, a plasma component, or one of the cellular fractions) for the treatment of a metabolic disorder or disease state.


Edelson RL. 1989. Photopheresis: A new therapeutic concept. Yale J Biol Med 62:565.

Kambic HE, Nose Y. 1993. Plasmapheresis: Historical perspective, therapeutic applications, and new frontiers. Artif Organs 17(10):850.

Malchesky PS, Asanuma Y, Zawicki I, et al. 1980. On-line separation of macromolecules by membrane filtration with cryogelation. Artif Organs 400:205.

Nose Y, Kambic HE, Matsubara S. 1983. Introduction to therapeutic apheresis. In Y Nose, PS Malchesky, JW Smith, et al. (eds), Plasmapheresis: Therapeutic Applications and New Techniques, pp 1-22, New York, Raven Press.

Rock G. 1983. Centrifugal apheresis techniques. In Y Nose, PS Malchesky, JW Smith, et al. (eds), Plas­mapheresis: Therapeutic Applications and New Techniques, pp 75-80, New York, Raven Press. Sawada K, Malchesky P, Nose Y. 1990. Available removal systems: State of the art. IN UE Nydegger (ed), Therapeutic Hemapheresis in the 1990s, pp 51-113, New York, Karger.

Solomon BA, Castino F, Lysaght MJ, et al. 1978. Continuous flow membrane filtration of plasma from whole blood. Trans AM Soc Artif Intern Organs 24:21.

Zeman LJ, Zydney AL. 1986. Microfiltration and Ultrafiltration: Principles and Applications, pp. 471-489, New York, Marcel Dekker.

Zydney AL, Colton CK. 1982. Continuous flow membrane plasmaphersis: Theoretical models for flux and hemolysis prediction. Trans Am Soc Artif Intern Organs 28:408.

Zydney AL, Colton CK. 1986. A concentration polarization model for filtrate flux in cross-flow micro­filtration of particulate suspensions. Chem Eng Commun 47:1.

Zydney AL, Colton CK. 1987. Fundamental studies and design analyses of cross-flow membrane plas­mapheresis. In JD Andrade, JJ Brophy, DE Detmer (eds), Artificial Organs, pp 343-358, VCH Publishers.

Further Information

Several of the books listed above provide very effective overviews of both the technical and clinical aspects of therapeutic apheresis. In addition, the Office of Technology Assessment has published Health Tech­nology Case Study 23: The Safety Efficacy, and Cost Effectiveness of Therapeutic Apheresis, which has an excellent discussion of the early clinical development of apheresis. Several journals also provide more detailed discussions of current work in apheresis, including Artificial Organs and the Journal of Clinical Apheresis. The abstracts and proceedings from the meetings of the International Congress of the World Apheresis Association and the Japanese Society for Apheresis also provide useful sources for current research on both the technology and clinical applications of therapeutic apheresis.

Galletti, P. M., Jauregui, H. O. “Liver Support Systems.” The Biomedical Engineering Handbook: Second Edition. Ed. Joseph D. Bronzino Boca Raton: CRC Press LLC, 2000

Peritoneal Dialysis Equipment

Therapy Format

Fluid and Solute Removal

The Peritoneal Membrane: Physiology and

Transport Properties

Transport Modeling

Emerging Developments

Peritoneal Dialysis Equipment

Michael J. Lysaght

Brown University

John Moran

Vasca, Inc.


Irreversible end-stage kidney disease occurs with an annual frequency of about 1 in 5000 to 10,000 in general population, and this rate is increasing. Until the 1960s, such disease was universally fatal. In the last four decades various interventions have been developed and implemented for preserving life after loss of all or most of a patient’s own kidney function. Continuous ambulatory peritoneal dialysis (CAPD), the newest and most rapidly growing of renal replacement therapies, is one such process in which metabolic waste products, electrolytes, and water are removed through the peritoneum, an intricate membranelike tissue that lines the abdominal cavity and covers the liver, intestine, and other internal organs. This review begins with a brief summary of the development of CAPD and its role in the treatment of contemporary renal failure. The therapy format and its capacity for solute removal are then described in detail. Bioengineering studies of peritoneal transport, in which the peritoneum is described in terms analogous to the mass transfer properties of a planar membrane separating well-mixed pools of blood and dialysate, are then reviewed. The transport properties of the equivalent peritoneal membrane are summa­rized and compared to those of hemodialysis membranes. Models to describe and predict fluid and solute removal rates are examined. Finally, current developments and emerging trends are summarized.

The early history of peritoneal dialysis, as reviewed by Boen [1985], is contemporaneous with that of hemodialysis (HD). Small-animal experiments were reported in the 1920s and 1930s in the United States and Germany. Earliest clinical trials in acute reversible cases of kidney failure began in the late 1930s in the form of a continuous “lavage” in which dialysate was continuously infused and withdrawn from dual trochar access sites. Acute treatments were continued through the 1940s, and about 100 case reports appeared in the literature by 1950; sequential inflow, dwell, and withdrawal was increasingly favored over continuous flow. Chronic therapy was introduced in the early 1960s, followed shortly by indwelling peritoneal catheters. From 1960 onward, peritoneal dialysis clearly lagged behind HD, as the latter became more streamlined, efficient, and cost-effective. Although endorsed by a small group of enthusiasts and proponents, peritoneal dialysis had evolved into a specialized or niche therapy. This changed dramatically in 1976 when Popovich, a biomedical engineer, and Moncrief, a clinical nephrologist, announced the development of a new form of peritoneal dialysis in which ambulatory patients were continuously treated by two liters of dialysis dwelling in the peritoneal cavity and exchanged four times daily [Popovich et al., 1976]. Two years later Baxter began to offer CAPD fluid in flexible plastic containers, along with necessary ancillary equipment and supplies. The rapid subsequent growth of the process is tabulated in Fig. 131.1.


Peritoneal Dialysis Equipment

1978 1982 1986 1990

FIGURE 131.1 The growth of peritoneal dialysis. Line and points refer to the total estimated worldwide peritoneal dialysis population; the numbers adjacent to the points are PD patients as a percent of total dialysis population. At the end of 1993, 14,000 of the 90,000 peritoneal dialysis patients utilized some version of APD; the remainder were treated with CAPD. Data compiled taken from various patient registries and industrial sources.

At this writing, approximately 90,000 patients are treated by CAPD (versus 490,000 by HD and 130,000 with kidney transplants). A more recent development is the introduction of automated peritoneal dialysis (APD), in which all fluid exchanges are performed by a simple pump console, usually while the patient sleeps. About one peritoneal dialysis patient in six now receives some form of APD; this approach is discussed more fully in a later section on emerging developments.

Both CAPD and HD have advantages and disadvantages, and neither therapy is likely to prove better for all the patients all the time. The principal attraction of CAPD is that it frees the patient from the pervasive life-style invasions associated with thrice weekly in-center HD. CAPD is particularly popular with patients living in rural areas distant from a hemodialysis treatment center. The continuous nature of CAPD eliminates fluctuations in the concentrations of uremic metabolites and avoids the sawtooth pattern of hemodialysis peak toxin concentrations. Fluid and dietary constraints are less restrictive for patients on CAPD than those on HD. A major complication of CAPD is peritonitis. Th rate of peritonitis was initially around 2 episodes per patient year; this has fallen to fewer than 0.5 episodes per patient year due to advances in administration set design and use. The morbidity of peritonitis has also decreased with increased experience in its treatment. In most cases, detected early and treated promptly, peritonitis can be managed without requiring hospitalization. Peritonitis caused by certain organisms including Staphylococcus aureus, Pseudomonas, and fungi remains a clinical problem. Other drawbacks of CAPD include the daily transperitoneal administration of 100-150 g of glucose providing D600 calories, and the tedium of the exchanges. APD and new solution formulations are being developed to address both issues. Little doubt now exists that risk-adjusted survival and morbidity for patients treated by CAPD is equivalent to that for patients treated with HD. On balance, the therapy seems well suited to many patients, and it continues to grow more rapidly than alternative treatment modalities.

Therapy Format

The process of CAPD is technically simple. Approximately 2 L of a sterile, nonpyrogenic, and hypertonic solution of glucose and electrolyte are instilled via gravity flow into the peritoneal cavity through an indwelling
Catheter 4 times per day. A single exchange is illustrated in Fig. 131.2. I Ntraperitoneal fluid partially equili­brates with solutes in the plasma, and plasma water is ultrafiltered due to osmotic gradients. After 4-5 hours, except at night where the exchange is lengthened to 9-11 hours to accommodate sleep, the peritoneal fluid is drained and the process repeated. Patients perform the exchanges themselves in 20-30 minutes, at home or in the work environment after a training cycle which lasts only 1-2 weeks. In APD, 10-15 L are automatically exchanged overnight; 2 L remain in the peritoneal cav­ity during the day for a “long dwell” exchange.

FIGURE 131.2 Illustration of the three steps involved in a single CAPD exchange: fluid infusion, dwell, and drain. Some administration sets require the bag to stay connected during dwell (it is rolled and fits in a girdle around the waist); others allow it to be disconnected. Drain and infusion take about 10 minutes each; three daytime dwells are 4-6 hours each; the overnight dwell lasts 8-10 hours.

figure 131.2 illustration of the three steps involved in a single capd exchange: fluid infusion, dwell, and drain. some administration sets require the bag to stay connected during dwell (it is rolled and fits in a girdle around the waist); others allow it to be disconnected. drain and infusion take about 10 minutes each; three daytime dwells are 4-6 hours each; the overnight dwell lasts 8-10 hours.
As will be discussed in more detail below, the drained fluid contains solute at concentrations around 90-100% of plasma for urea, 65-70% for creatinine, and 15-25% for inulin and D2 microglobulin. Net fluid removal ranges up to 1000 ml per exchange. CAPD generally removes the same quantity of toxins and fluid as HD ( a little thought will show that this is a require­ment of steady state, provided that generation is unal­tered between the two treatment formats); however,

CAPD requires a higher plasma concentration as the driving force for this removal. Steady-state concentra­tions during CAPD are typically close to the peak, i. e., pretreatment, concentrations of small solutes during HD but much lower than the corresponding peaks for larger species.

Access to the peritoneum is usually via a double-cuff Tenchkhoff catheter, essentially a 50-100 cm length of silicone tubing with side holes at the internal end, a Dacron mesh flange at the skin line, and connector fittings at the end of the exposed end. Several variations have evolved, but little hard evidence supports the selection of one design format over another [Dratwa et al., 1986]. Most are implanted in a routine surgical procedure requiring about 1 hour and are allowed to heal for 1-2 weeks prior to routine clinical use. Sterile and nonpyrogenic fluid is supplied in 2-L containers fabricated from dioctyl phthalate plasti­cized polyvinyl chloride. The formulation is essentially potassium-free lactated Ringers to which has been added from 15-42.5 g/L of glucose (dextrose monohydrate). The solution is buffered to a pH of 5.1-5.5, since the glucose would caramelize during autoclaving at higher pH levels. Several different exchange protocols are in use. In the original design, the patient simply rolls up the empty bag after instillation and then drains into the same bag following exchange. The bag filled with drain fluid is disconnected and a fresh bag is reconnected. Patients are trained to use aseptic technique to perform the connect and discon­nect. Many ingenious aids were developed to assist in minimizing breaches of sterility including enclosed ultraviolet-sterilized chambers and heat splicers. More recent approaches, known as the “O” set and “Y” set or more generically as “flush before fill” disconnect, invoke more complex tubing sets to allow the administration set to be flushed (often with antiseptic) prior to installation of dialysate and generally permit the patient to disconnect the empty bag during the dwell phase. Initial reports of the success of the protocols in reducing peritonitis were regarded with skepticism, but definite improvement over earlier systems has now been documented in a well-designed and carefully controlled clinical trials [Churchill et al., 1989].

Fluid and Solute Removal

The rate at which solutes are removed during peritoneal dialysis depends primarily upon the rate of equilibration between blood and instilled peritoneal fluid. This is usually quantified as the ratio of



подпись: o

< ■ “—“—x

Q 0.00 —1 1 ‘ 1 1 1 1 1 1—1—1—1—1—■—1—1 ‘ ’—

0 60 120 180 240 300 360

< ■ “—“—x
q 0.00 —1 1 ' 1 1 1 1 1 1—1—1—1—1—■—1—1 ' ’—
0 60 120 180 240 300 360
FIGURE 131.3 Ratio of plasma to dialysate concentration for urea (60 daltons), creatinine (113 daltons), uric acid (158 daltons), and Q2 microglobulin (012,000 daltons). Data were obtained by withdrawing and analyzing a sample of dialysate at each time point and comparing it to plasma concentration. Each point is the average of two determi­nations on five patients. Error bars are standard error of the mean [Lysaght, 1989].

Dialysate to plasma concentration as a function of dwell time, often in graphs called simply “D over P” (dialysate over plasma) curves. A typical plot of dialysate-to-plasma ratio for solutes of various molecular weight is given in Fig. 131.3. Smaller species equilibrate more rapidly than do larger ones, because diffusion coefficient varies in inverse proportion to the square root of a solute’s molecular weight. Dialysate equilibrium rates vary considerably from patient to patient; error bars on the plot represent standard error of the mean for duplicate determinations with five patients.

The rate of mass removal during dialysis, □, is simply the volume of fluid, VD, removed from the peritoneal cavity at the end of a dwell period lasting time t, multiplied by the concentration CD of the solute in the removed fluid

= VDCD (131.1)

The whole blood clearance, Cl, is the rate of mass removal divided by the solute concentration in blood CB

Cl □ —□ (131.2)


In Eqs. (131.1) and (131.2), time conventionally is reported in minutes, volume in milliliters, and concentration in any consistent units. Equations (131.1) and (131.2) are based on mass balances; they are thus general and unaffected by the complexity of underlying phenomena such as bidirectional selective connective transport and lymphatic uptake. Equation (131.2) requires that solute concentration in the denominator be reported as whole blood concentration, rather than as plasma concentration, which is

Often reported clinically. With many small solutes (urea, creatinine, and uric acid), only small error is

Introduced by considering blood and plasma concentration as interchangeable. With larger solutes,

Peritoneal Dialysis Equipment

FIGURE 131.4 Volume of fluid in the peritoneal cavity versus time during an exchange with 02.5% glucose dialysis fluid. Solid line is actual volume. Dotted line represents estimate of the volume in the absence of lymphatic flow. Results represent an average of duplicate determinations on five patients. Volume was estimated by dilution of radiolabeled tracers (too large to diffuse across the peritoneal membrane) added to dialysate prior to installation; lymphatic flow was calculated from a mass balance on net recovered marker. Each point is the average of two determinations on five patients. Error bars are standard error of the mean [Lysaght, 1989].

Especially those excluded from the red blood cell, care must be taken to correct for differences in plasma and blood concentrations.

Since urea is nearly completely equilibrated during CAPD, i. e., cD/cB = 01.0, urea clearance is commonly equated with total drainage volume. Four 2-L exchanges and 2 L of ultrafiltration would thus result in a continuous urea clearance of 10 L/day or 07 ml/min. The situation is more complex with APD, which involves several (4-6) short exchanges at partial equilibrium and one very long exchange. In any case, no meaningful direct or a priori comparison of clearance with hemodialysis is possible because one therapy is intermittent and the other continuous.

The volume of fluid in the peritoneal cavity increases during an exchange but at a decreasing rate. The driving force for fluid transfer from the blood to the peritoneal cavity is the osmotic pressure of the glucose in the infused dialysate. Typical CAPD solutions contain 01.5%, 02.5%, or 04.25% by weight of glucose monohydrate, leading to an initial maximum osmotic force (across an ideally semipermeable membrane) of approximately 1000-5000 mmHg. In the first few minutes of an exchange, the rate of ultrafiltration may be as high as 10-30 ml/min. The driving force rapidly dissipates as glucose diffuses from the peritoneal cavity into the bloodstream. After the first hour, rates of 1.0-2.0 ml/min are common. Throughout the exchange, the peritoneal lymphatics are draining fluid from the peritoneal cavity at a rate of 0.5-2.0 ml/min. Fluid balance is thus the difference between removal by a time-dependent rate of ultrafiltration and return via a more constant lymphatic drainage. Net fluid removal is very easily determined in the clinical setting simply by comparing the weight of fluid drained to that instilled. Instantaneous rates of ultrafiltration may be estimated in study protocols by a series of tedious mass balances around high-molecular-weight radiolabled markers added to the dialysate fluid. The results of a typical study are plotted in Figs. 131.4 and 131.5 Showing both the instantaneous rate of ultrafiltration and the net intraperitoneal volume as a function of time. On average, these patients removed 500 ml of fluid in a single 6-hour exchange or roughly 2 L/day, which permits far more liberal fluid intake than

Peritoneal Dialysis Equipment

FIGURE 131.5 Comparisons of rates of ultrafiltration of fluid into the peritoneal cavity (open circles) and lymphatic drainage of fluid from the peritoneal cavity back to the patient (dotted line). Same study and methods as in Fig. 131.4.

Is possible with patients on HD. But here again patient variation is high. Commercial CAPD fluid is available in a variety of solute concentrations; physicians base their prescription for a particular patient on his or her fluid intake and residual urine volume.

The Peritoneal Membrane: Physiology and Transport Properties

In contrast to synthetic membranes employed during HD, the peritoneum is not a simple selective barrier between two phases. As implied by its Latin root (peritonere = to stretch tightly around), the primary physiologic function of the peritoneum is to line the walls of the abdominal cavity and encapsulate its internal organs (stomach, liver, spleen, pancreas, and parts of the intestine). Most CAPD literature, including this review, uses the terms peritoneum and peritoneal membrane interchangeably and conve­niently extends both expressions to include underlying and connective tissue. Overall adult peritoneal surface is approximately 1.75 □ 0.5 m2, which generally is considered equal on an individual basis to skin surface area. The peritoneum is not physically homogenous. The visceral portion (080%) covering the internal organs differs somewhat from the parietal portion overlaying the abdominal walls, which in turn is different from the folded or pleated mesentery connecting the two.

The physiology of the peritoneum, its normal ultastructure, and variations induced by CAPD have been increasingly elucidated over the past decade. Morphologically, the peritoneum is a smooth, tough, somewhat translucent sheath. Its thickness ranges from under 200 to over 1000 microns. The topmost layer, which presents to the dialysate during CAPD, is formed from a single layer of mesothelial cells, densely covered by microvilli (hairlike projections), although the latter tend to disappear gradually during the first few weeks of CAPD. Immediately underneath is the interstitium, a thick sheath of dense mucopolysaccharide hydrogel interlaced with collagenous fibers, microfibrillar structures, fibroblasts, adipocytes, and granular material. Most important for CAPD, the interstitium is perfused with a network of capillaries through which blood flows from the mesenteric arteries and the vasculature of the abdominal wall to the portal and systemic venous circulations. Blood-flow rate has been estimated to be in the range of 30-60 ml/min, but this is not well established. The interstitial layer is a hydrogel; its water content, and thus its transport properties, will vary in response to the osmolarity of the peritoneal dialysate.

Peritoneal mass transfer characteristics are most commonly obtained by back-calculating basic mem­brane properties from results in standard or modified peritoneal dialysis. Three membrane parameters will be described: Lp, the hydraulic permeability; R, the rejection coefficient; and KoA, the mass transfer coefficient ( = area A □ diffusive permeability Ko). The formal definitions of these parameters are given in Eqs. (131.3) through (131.5), with R and KoA defined for the limiting conditions of pure convection and pure diffusion.

LP □ Fillrali°n rate =, (131.3)

Area ^pressure driving force A(P □ □□Q)

^, m Concentration in bulk filtrate m □ CD D

R □ 1 □ = (131.4)

Concentration in bulk retentate C„ fl

Y B MudD 0

K0A □ Solute transport = Dd □ (131.5)

Concentration driven force nC„ □ Cn M

Y B D Mifr□ 0

Where JF = filtration rate, A = area, □ = Staverman reflection coefficient, □ = osmotic pressure, and other terms are as defined previously.

At the onset of a CAPD exchange using 4.25% dextrose, the ultrafiltration rate is 10-30 ml/min. Relative to a perfectly semipermeable membrane, the glucose osmotic pressure of the solution is 4400 mmHg. Overall membrane hydraulic permeability is the quotient of these terms and is thus of the order of 0.2 ml/hr-mmHg, in the units commonly employed for HD membranes. This estimate needs to be corrected for the osmotic back-pressure, which is primarily due to urea in the blood (conc 0 1.3 g/L) as well as the fact that the membrane is only partially semipermeable. The best results are not obtained from a single point measurement but either from curve fitting to the ultrafiltration profile during the entire course of dialysis or from data taken at different osmotic gradients. A review [Lysaght & Farrell, 1989] of reports from several different investigators suggests an average value of 0 2 ml/hr-mmHg or, roughly, 2 gal/ft2/day (GSFD) at 100 PSI. This is higher than desalination membranes, just slightly lower than conventional regenerated cellulose hemodialysis membranes, and much lower than anisotropic ultrafiltration membranes.

Rejection coefficients, R, numerically equal to unity minus sieving coefficient are obtained either from kinetic modeling as described below or experimentally by infusing a hypertonic solution into the peri­toneum with a permeant concentration equal to that in the plasma. After a suitable period of ultrafil­tration, the ration of solute to water flux is calculated from the dilution of the recovered solution. Both methods are approximate and results from different investigators may vary substantially. Reported values are observed average rejection coefficients. These are often described as the Staverman rejection coeffi­cient, □, which is somewhat overreaching, since filtration velocity is not recorded and differences between bulk and wall concentrations are not known. Representative values, from a review of the literature [Lysaght & Farrell, 1989], are summarized in Table 131.1. Thus the membrane appears quite tight, possibly rejecting about 10-20% of urea and other small molecules, about 50% of intermediate-molec – ular-weight species, and over 99% of plasma proteins.

The diffusive permeability of the membrane is obtained by back calculation from measurements of blood and dialysate concentration versus time during an exchange, as will be further elaborated below. Values are given as the product of membrane permeability and estimated peritoneal area (KA), and the results of various investigators have been reasonably consistent. Critical values from a review of the literature are summarized in Table 131.1. A KoA value of about 20 ml/min for urea is around one order of magnitude less than comparable values for contemporary hollow-fiber hemodialyzers. If the area of the peritoneum is taken as 1.75 m2, then urea transfers through the peritoneum analogously to urea diffusing through a stagnant film of water roughly a centimeter thick. Alternatively, given a peritoneal

Permeant Species, MW

Rejection Coefficient, dimensionless

KjA cm3/min

Urea, 60

0.26 □ 0.08

21 □ 4

Creatinine, 113

0.35 □ 0.07

10 □ 2

Uric acid, 158



B-12, 1355


Inulin, 5200

0.5 □ 0.2

4 □ 1.5

□2microglobulin, 12,000

0.8 □ 0.4

Albumin, 69,000


Note: SD not given if n < 3. Equivalent ultrafiltration coefficient is D2.0 ml/min- m2-mmHg. Data taken from a review by Lysaght and Farrell [1989].

Thickness range of 200-2000 microns, the diffusion of urea inside the membrane is about 20% of what would be found in a film of stagnant water of the same thickness.

It should once more be noted that the physiologic peritoneum is a complex and heterogeneous barrier, and its transport properties would be expected to vary over different regions of its terrain. For example, studies in animal models have suggested that transport during peritoneal dialysis is little affected when large segments of the visceral membrane are surgically excised. It is also repeated for emphasis that the terms Lp, R, and KA do not describe this membrane itself but rather a hypothetical barrier that is functionally and operationally equivalent and thus capable of producing the same mass transfer charac­teristics in response to the same driving forces.

Transport Modeling

Several investigators have developed mathematic models to describe, correlate, and predict relationships among the time-course of solute removal, fluid transfer, treatment variables, and physiologic properties [Lysaght & Farrell, 1989; Vonesh et al., 1991; Waniewski et al., 1991]. Virtually all kinetic studies start with the model illustrated in Fig. 131.6. THe patient is considered to be a well-mixed compartment with a distribution volume VB set equal to some fraction of total body weight. (For example, urea distributes over total body water, which is □ 0.58 times body weight.) Dialysate occupies a second, much smaller compartment, VD = 2-3 L, which is also considered well-mixed but which changes in size during the

Lymph Flow











J v°






Fixed Volume Variable Volume

Peritoneal Membrane (Lp, a-, KoA)

FIGURE 131.6 Single pool model for peritoneal dialysis. Solute diffuses across a planar selective membrane from a large well-mixed plasma space at constant volume and concentration to a smaller well-mixed space in which concentration and volume both increase with time. Fluid and solute are selectively ultrafiltered across the peritoneal membrane from plasma to dialysate; they are also nonselectively transported by the lymphatics from the dialysate to the body compartment.

Course of exchange. These two compartments are separated by a planar membrane capable of supporting bidirectional transport and characterized by the terms Lp, R, and KoA previously defined by Eqs. (131.3)—(131.5). Fluid drains from the peritoneum to the blood at a rate of QL. From this point forward, the complexity and appropriate utility of the models depend upon the investigators’ choices of simplifying assumptions. The simplest model, proposed by Henderson and Nolph [1969], considers ultrafiltration rate and lymphatic flow to be negligible and treats all parameters except dialysate concen­tration as constant with time. The basic differential equation describing this model is

Peritoneal Dialysis Equipment


Peritoneal Dialysis Equipment

K0 A □-

подпись: k0 a □-Equation 131.6 may be readily solved, either to obtain KoA from a knowledge of concentration versus time data Eq. (131.7), or to predict dialysate concentration from a knowledge of mass transfer coefficient, blood concentration, and initial dialysate concentration Eq. (131.8) where:


□ K 0At

Peritoneal Dialysis Equipment


In these equations, the superscript t represents the value at time t, and the superscript 0 designates the

Value at t = 0. This model provides a very easy way of measuring K0A if it is applied during the isovolemic interval that often occurs □ 30-90 min after the beginning of an exchange.

Several years later, investigators at the University of New South Wales [Garred et al., 1983] proposed a slightly more complex model that included ultrafiltration, subject to the assumptions that: (1) blood concentration was constant, (2) the membrane was nonselective (R = O), and (3) lymphatic involvement could be ignored. The appropriate differential equation is now:

Peritoneal Dialysis Equipment


Peritoneal Dialysis EquipmentThis equation can be solved in two ways. Over either relatively short time intervals or small differences in dialysate volume, an average volume VD is obtained as the mean of initial and final volumes. In that case K0A is given by


Where variables overlined with a solid diachrin are treated as constant during the integration of Eq. (131.9). The similarity of Eqs (131.9) and (131.10) to Eqs. (131.7) and (131.8) should be noted. Where a series of data points for blood and dialysate concentrations are available at various times during the treatment, Eq. (131.10) may be rewritten as

□□ KaAt □

Peritoneal Dialysis Equipment


Infc ( □ CD) ln[ ( □ CD) ]


Data in the form of this equation may be readily regressed to obtain K0A from a knowledge of VD, CB, and CD at various times in an exchange. The values for peritoneal volume VD may be obtained experi­mentally from tracer dilution studies, calculated from an algorithm, in which case it varies with time, or simply averaged between initial and final values, in which case it is assumed constant. Equations (131.11) and (131.12) are recommended for routine modeling of patient kinetics.

Several investigators, reviewed by Lysaght and Farrell [1989], have produced far more elaborate models which incorporate lymphatic drainage, deviations from ideal semipermeability of the peritoneal mem­brane, time-dependent ultrafiltration rates, and coupling between bidirectional diffusive and connective transport. Although potent in the hands of their developers, none of the numerical models has been widely adopted, and the current trend is toward simpler approaches. In comparative studies [Lysaght, 1989; Waniewski et al., 1991], only small differences were found between the numeric values of transport parameters calculated from simple analytic models [Eqs. (131.6)—(131.12)] and those we obtained by far more complex numerical methods. In peritoneal dialysis, solute is being exchanged through an inefficient membrane between a large body compartment through an inefficient membrane and a second compart­ment only 5% as large, and treatment times have been chosen so that the smaller compartment will reach saturation. These physical circumstances, and the very forgiving nature of exponential asymptotes, perhaps explain why simple analytic solutions perform nearly as well as their more complex numeric counterparts.

Emerging Developments

Modified therapy formats and new formulations for exchange solutions constantly are being proposed and evaluated. APD is the most successful of the new formats; at the end of 1993, about one in six peritoneal dialysis patients received some variant of automated overnight treatment. APD is carried out by a small console (Fig. 131.7) Which automatically instills and drains dialysate at 1.5—3-hour intervals while the patient sleeps, typically over 8—10 hours each night. The peritoneum is left full during the day. Since the short exchanges do not permit complete equilibration even for urea, the process is somewhat wasteful of dialysate. However, reference to Fig. 131.3 wIll readily demonstrate that small-solute removal is most efficient in the early portion of an exchange; for example, two 2-hour exchanges will provide 75% more urea clearance than one 4-hour exchange. As currently prescribed, APD requires 84—105 L per week of dialysate (versus 56 for CAPD) and increases total small-solute clearance per 24 hours by up to 50% over that achieved by CAPD. The number of patients on APD is increasing by half every year, a phenomenon driven by two main factors. The first relates to quality of life; APD is far-and-away the least invasive of the maintenance dialysis protocols. The patient performs one connection at night and one disconnection in the morning and is thereby freed from the tedium and inconvenience of daily exchanges or the need to spend a significant portion of 3 days per week at an HD treatment facility. In addition, small-solute clearance is higher than in other continuous peritoneal therapies, which helps address increasing concern about the adequacy of the standard four 2-L CAPD exchanges per day, especially with large muscular patients and those with no residual renal function. A group of patients who may benefit from APD are those who have rapid transport of glucose across the peritoneal mem­brane; because of the consequent loss of the osmotic gradient, they have difficulty achieving adequate ultrafiltration. The short dwell times of ADP circumvent this problem. The counterbalancing disadvan­tage of APD is increased expense associated with the larger fluid consumption and the fluid cyclers.

Virtually all solution development comprises attempts to replace glucose with an alternative osmotic agent, preferably one which diffuses more slowly and thus provides a more stable osmotic gradient and one which obviates the obligatory load of about 600 calories of sugar. However glucose is cheap and safe, and it will be difficult to find a satisfactory alternative. A competing osmotic agent must be safe to

Peritoneal Dialysis Equipment

FIGURE 131.7 Contemporary equipment module for APD (Home Choice, Renal division, Baxter Healthcare) which automatically controls and monitors the delivery of 10-15 L of dialysate from 5-L bags via a multipronged disposable administration set. The console incorporates a diaphragm pump used to emulate gravity, and a derivative of the ideal gas law measures fluid volume, eliminating the need for scales. Setup and operation are designed to be straightforward and convenient.

Administer in amounts of tens of grams per day over years to patients who have little or no ability to clear accumulated material via the kidney—but an osmotic agent which is readily metabolizable provides no caloric “advantage” over glucose. A glucose polymer, termed polyglucose, has been recently introduced in England [Mistry & Gokal, 1993]. This disperse oligodextrin has a weight-averaged MW of 18,700 daltons and number-averaged molecular weight of 7300 daltons. At a concentration of 7.5% (i. e., 30 g per 2-L exchange), it provides more stable ultrafiltration during long dwell exchanges; however, admin­istration is limited to one exchange per day because of the accumulation of maltose and higher MW polysaccharides; an alternative approach, recently introduced in Europe and in clinical trials in the United States, is a solution in which glucose is replaced with 1.1% amino acids, enriched for essential amino acids [Jones et al., 1992]. This solution also improves nitrogen balance, a significant feature, since dialysate patients are frequently malnourished. Concern about excessive nitrogen intake, however, limits its use to one or two exchanges per day, and the amino acid solution is necessarily more expensive than glucose.

Defining Terms

Automated peritoneal dialysis (APD): A recent variant of CAPD in which fluid exchanges are per­

Formed by simple pumps, usually at night while the patient sleeps.

Clearance: The rate of mass removal divided by solute concentration in the body. Clearance represents

The virtual volume of blood or plasma cleared of a particular solute per unit time.

Continuous ambulatory peritoneal dialysis (CAPD): A continuous process for the treatment of

Chronic renal failure in which metabolic waste products and excess body water are removed through the peritoneum with four exchanges of up to 3 L every 24 hours.

Diffusion: The molecular movement of matter from a region of greater concentration to lesser con­

Centration at a rate proportional to the difference in concentration.

Hemodialysis (HD): Intermittent extracorporeal therapy for chronic renal failure. See Chapter 130.

Mass transfer coefficient: The proportionality constant between the rate of solute transport per unit

Area and the driving force.

Membrane: A thin barrier capable of providing directional selective transport between two phases.

Peritoneal cavity: A topologically closed space in the abdomen which is surrounded by the peritoneum.

Peritoneum: An intricate, vascularized, membranelike tissue that lines the internal abdominal walls

And covers the liver, intestine, and other internal organs. Used interchangeably with the expression peritoneal membrane.


Boen ST. History of peritoneal dialysis.1985. In KD Nolph (ed), Peritoneal Dialysis, pp 1—22, The Hague, Martinus Nijhoff.

Churchill DN, Taylor DW, Vas SI, et al. 1989. Peritonitis in continuous ambulatory peritoneal dialysis (CAPD): A multi-centre randomized clinical trial comparing the Y connector disinfectant system to standard systems. Perit Dial Int 19:159.

Dratwa M, Collart F, Smet L. 1986. CAPD peritonitis and different connecting devices: A statistical comparison. In JF Maher, JF Winchester (eds), Frontiers in Peritoneal Dialysis, pp 190—197, New York, Field Rich.

Garred LJ, Canaud B, Farrell PC. 1983. A simple kinetic model for assessing peritoneal mass transfer in chronic ambulatory peritoneal dialysis. ASAIO J 6:131.

Henderson LW, Nolph KD. 1969. Altered permeability of the peritoneal membrane after using hypertonic peritoneal dialysis fluid. J Clin Invest 48:992.

Jones MR, Martis L, Algrim CE, et al. 1992. Amino acid solutions for CAPD: Rationale and clinical experience. Miner Electrolyte Metab 18:309.

Lysaght MJ. 1989. The Kinetics of Continuous Peritoneal Dialysis. PhD thesis, Center for Biomedical Engineering, University of New South Wales.

Lysaght MJ, Farrell PC. 1989. Membrane phenomena and mass transfer kinetics in peritoneal dialysis. J Mem Sci 44:5.

Mistry CD, Gokal R. 1993. Single daily overnight (12-h dwell) use of 7.5% glucose polymer (Mw 18700;

Mn 7300) + 0.35% glucose solution: A 3-month study. Nephrol Dial Transplant 8:443.

Popovich RP, Moncrief JW, Decherd JF, et al. 1976. The definition of a novel portable/wearable equilib­rium peritoneal technique. Abst AM Soc Artif Intern Organs 5:64.

Vonesh EF, Lysaght MJ, Moran J, et al. 1991. Kinetic modeling as a prescription aid in peritoneal dialysis. Blood Purif 9:246.

Waniewski J, Werynski A, Heimburger O, et al. 1991. A comparative analysis of mass transport models in peritoneal dialysis. ASAIO Trans 37:65.

Further Information

The literature on continuous peritoneal dialysis is abundant. Among several reference texts the most venerable and popular is Peritoneal Dialysis edited by K. Nolph and published by Kluwer; this is regularly updated. Also recommended is Continuous Ambulatory Peritoneal Dialysis edited by R Gokal and pub­lished by Churchill Livingston. The journal Peritoneal Dialysis International (published by MultiMed; Toronto) is published quarterly and is devoted exclusively to CAPD. The continuing education depart­ment of the University of Missouri-Columbia organizes a large annual conference on peritoneal dialysis with plenary lecture and submitted papers. The International Society of Peritoneal Dialysis holds its conference biannually and usually publishes proceedings. Peritoneal dialysis is also discussed in the meeting and journals of the other major artificial organ societies (American Society of Artificial Internal Organs; European Dialysis and Transplant Association; Japanese Society of Artificial Organs) and the American and International Societies of Nephrology. Blood Purification (published by Karger; Basel) attracts many outstanding papers dealing with engineering and transport issues in peritoneal dialysis. For the insatiable, Medline now contains over 10,000 citations to CAPD and peritoneal dialysis.

Zydney, A. L. “Therapeutic Apheresis and Blood Fractionation.” The Biomedical Engineering Handbook: Second Edition.

Ed. Joseph D. Bronzino

Boca Raton: CRC Press LLC, 2000

130.1 130.2 130.3 130.4 130.5 130.6 130.7 130.8 Pierre M. Galletti 130.9 (deceased) 130.10 130.11 Clark K. Colton 130.12 Massachusetts Institute 130.13 Of Technology Michael J. Lysaght 130.14 Brown University 130.15 Artificial Kidney

Structure and Function of the Kidney Kidney Disease Renal Failure

Treatment of Renal Failure Renal Transplantation Mass Transfer in Dialysis Clearance Filtration Permeability Overall Transport Membranes Hemofiltration Pharmacokinetics

Glomerular Filtration • Tubular Function Adequacy of Dialysis.


Structure of Function of the Kidney

The key separation functions of the kidney are:

To eliminate the water-soluble nitrogenous end-products of protein metabolism

To maintain electrolyte balance in body fluids and get rid of the excess electrolytes

To contribute to obligatory water loss and discharge excess water in the urine

To maintain acid-base balance in body fluids and tissues

To fulfill these functions, the kidney processes blood—or more accurately, plasma water—which in turn exchanges water and solutes with the extravascular water compartments: extracellular, intracellular, and transcellular. The solute concentrations in body fluids vary from site to site, yet all compartments are maintained remarkably constant in volume and composition despite internal and external stresses. The global outcome of normal renal function is a net removal of water, electrolyte, and soluble waste products from the blood stream. The kidney provides the major regulatory mechanisms for the control of volume, osmolality, and electrolyte and nonelectrolyte composition as well as pH of the body fluids and tissues.

Renal function is provided by paired, fist-sized organs, the kidneys, located behind the peritoneum against the posterior abdominal wall on both sides of the aorta. Each kidney is made up of over a million parallel mass transfer units which receive their common blood supply from the renal arteries, return the processed blood to the systemic circulation through the renal veins, and collect the waste fluids and solutes through the calyx of each kidney into the ureter and from there into the urinary bladder. These functional units are called nephrons and can be viewed as a sequential arrangement of mass transfer devices (glomerulus, proximal tubule, and distal tubule) for two fluid streams: blood and urine.

Kidney function is served by two major mechanisms: ultrafiltration, which results in the separation of large amounts of extracellular fluid through plasma filtration in the glomeruli, and a combination of passive and active tubular transport of electrolytes and other solutes, together with the water in which they are dissolved, in the complex system provided in the rest of the nephron.

Glomerular Filtration

The volume of blood flowing into the natural kidneys far exceeds the amount needed to meet their requirements for oxygen and nutrients: The primary role of the kidneys is chemical processing. As blood flows through the glomerular capillaries, about one-fifth of the plasma water is forced through permeable membranes to enter the proximal portion of the renal tubule and form the primary urine, which henceforth becomes the second fluid phase of the renal mass exchanger. The concentrated blood remain­ing in the vascular system is collected in the efferent arterioles and goes on to perfuse the tubules via the peritubular capillaries of the “vasa recta” system, where it recovers some of the lost water and eventually coalesces with the other blood drainage channels to form the renal vein. The plasma water removed from the blood in the glomerulus is termed the glomerular filtrate, and the process of removal is called glomerular filtration. Glomerular filtrate normally contains no blood cells and very little protein. Glom­erular filtration is a passive process driven by the differences in hydrostatic and oncotic pressures across the glomerular membrane. Solutes which are sufficiently small and not bound to large molecules pass quite freely through the glomerular membrane. All major ions, glucose, amino acids, urea, and creatinine appear in the glomerular filtrate at nearly the same concentrations as prevail in plasma.

The normal glomerular filtration rate (GFR) averages 120 ml/min. This value masks wide physiological fluctuations (e. g., up to 30% decrease during the night, and a marked increase in the postprandial period). Although the kidneys produce about 170 liters of glomerular filtrate per day, only 1-2 liters of urine is formed. A minimum volume of about 400 ml/day is needed to excrete the metabolic wastes produced under normal conditions (often called obligatory water loss).

Tubular Function

In the tubule, both solute and water transport take place. Some materials are transported from the lumen across the tubular epithelium into the interstitial fluid surrounding the tubule and thence into the blood of the peritubular capillaries. This process is called reabsorption and results in the return of initially filtered solutes to the blood stream. Other substances are transported from the peritubular blood to the interstitial fluid across the tubular epithelium and into the lumen. This process is called secretion and leads to elimination of those substances to a greater extent than would be possible solely through glomerular filtration. The return of filtered molecules from the kidney tubule to the blood is accompanied by the passive reabsorption of water through osmotic mechanisms.

The proximal tubule reabsorbs about two-thirds of the water and salt in the original glomerular filtrate. The epithelial cells extrude Na+ (and with it Cl-) from the glomerular filtrate into the interstitial fluid. Water follows passively and in proportionate amounts because of the osmotic pressure gradient (the proximal tubular membrane is freely permeable to water). In the loop of Henle, the glomerular filtrate, now reduced to one-third of its original volume, and still isoosmotic with blood, is processed to remove another 20% of its water content. The active element is the ascending limb of the loop of Henle, where cells pump out Na+, K+, and Cl – from the filtrate and move the Na+ and Cl – to the interstitial fluid. Because the ascending limb is not permeable to water, tubular fluid becomes increasingly more dilute along the ascending loop. The blood vessels around the loop do not carry back all the extruded salt to the general circulation, and therefore the Na+ concentration builds up down the descending limb of the loop of Henle, reaching a concentration 4-5 times higher than isoosmolar. As a result, the Na+ concen­tration in tubular fluid increases as its volume is decreased by passive transport into interstitial fluid and from there into the blood.

Countercurrent multiplication refers to the fact that the more Na+ the ascending limb extrudes the higher the concentration in the interstitial fluid, the more water removed from the descending limb by osmosis, and the higher the Na+ concentration presented to the ascending limb around the bend of the loop. Overall, the countercurrent multiplier traps salt in the medullary part of the nephron because it recirculates its locally. Countercurrent exchange refers to the interaction of the descending and ascending branches of the circulatory loops (vasa recta) with the loop of Henle which flows in the opposite direction. Substances which pass from the tubule into the blood accumulate in high concentrations in the medullary tissue fluid. Na+ and urea diffuse into the blood as it descends along the loop but then diffuse out of the ascending vessels and back into the descending vessels where the concentration is lower. Solutes are therefore recirculated and trapped (short-circuited) in the medulla, but water diffuses out of the descend­ing vessel and into the ascending vessel to be transported out.

The distal tubule of the kidney, located in the cortex, is the site of fine adjustments of renal excretion. Here again the primary motor is the Na+/K+ pump in the baso-lateral membrane, which creates a Na+ concentration gradient. The walls of the collecting duct, which traverses through a progressively hyper­tonic renal medulla tissue, are permeable to water but not to Na+ and Cl-. As a result, water is drawn out and transported by capillaries to the general circulation. The osmotic gradient created by the coun­tercurrent multiplier system provides the force for water reabsorption from the collecting duct. However, the permeability of the cell membrane in the collecting duct is modulated by the concentration of antidiuretic hormone (ADH). A decrease in ADH impairs the reabsorption of water and leads to the elimination of a larger volume of more dilute urine.

The terms reabsorption and secretion denote direction of transport rather than a difference in physi­ologic mechanism. In fact, a number of factors may impact on the net transport of any one particular solute. For example, endogenous creatinine (an end product of protein metabolism) is removed from plasma water through glomerular filtration in direct proportion to its concentration in plasma. Since it is neither synthesized nor destroyed anywhere in the kidney, and it is neither reabsorbed nor secreted in the tubule, its eventual elimination in the urine directly reflects glomerular filtration. Therefore, creatinine clearance can be used to measure glomerular filtration rate. However, glucose, which initially passes in the glomerular filtrate at the same concentration as in plasma, is completely reabsorbed from the tubular urine into peritubular capillaries as long as its plasma concentration does not exceed a threshold value somewhat above the level prevailing in normal subjects. As a result, there should be no glucose in the urine. When the threshold is exceeded, the amount of glucose excreted in the urine increases propor­tionately, producing glycosuria.

Several weak organic acids such as uric acid and oxalic acid, and some related but not naturally occurring substances such as p-aminohippuric acid (PAH), barbiturates, penicillates, and some x-ray contrast media, have the special property of being secreted in the proximal tubule. For example, PAH concentration in glomerular filtrate is the same as in plasma water. So avid is the tubular transport system for PAH that tubular cells remove essentially all the PAH from the blood perfusing them. Therefore, the removal of PAH is almost complete, and the rate of appearance of PAH in the urine mirrors the rate of presentation of PAH to the renal glomeruli, that is to say, renal plasma flow. Therefore, PAH clearance can be used, in association with the hematocrit, to estimate the rate of renal blood flow.

Urea appears in the glomerular filtrate at the same concentration as in plasma. However, one-third of urea diffuses back into the blood in the proximal tubule. In the distal nephron, urea (as an electrically neutral molecule without specific transport system) follows the fate of water (solvent drag). If large amounts of water are reabsorbed in the distal tubule and the collecting duct, then an additional third of the urea can be reabsorbed. However, if water diuresis is large, then correspondingly more urea is excreted.

Kidney Disease

The origin of kidney disease may be infectious, genetic, traumatic, vascular, immunologic, metabolic, or degenerative [Brenner & Rector, 1986]. The response of the kidneys to a pathologic agent may be rapid or slow, reversible or permanent, local or extensive. Under most circumstances, an abnormal body fluid composition is more likely to arise from the unavailability or excess of a raw material than from some intrinsic disturbance of renal function. This is why many clinical problems are corrected by fluid or electrolyte therapy and secondarily by dietary measures and pharmacologic agents which act on the kidney itself. Only as a treatment of last resort, where kidney disease progresses to renal failure, do clinicians use extracorporeal body fluid processing techniques that come under the generic concept of dialysis. These invasive procedures are intended to reestablish the body’s fluid and electrolyte homeostasis and to eliminate toxic waste products. Processing can address the blood (e. g., hemodialysis) or a proxy fluid introduced in body cavities (e. g., peritoneal dialysis).

Even in healthy subjects, the GFR falls steadily from age 40 onward. Beyond age 80, it is only half of its adult value of 120 ml/min. However this physiologic deterioration is not extensive enough to cause symptoms. Since nature has provided kidneys with an abundance of overcapacity, patients do not become identifiably sick until close to 90% of original function has been lost. When kidneys keep deteriorating and functional loss exceeds 95%, survival is no longer possible without some form of replacement therapy.

Supplementation (as distinct from replacement) of renal function by artificial means is occasionally used in case of poisoning. Toxic substances are often excreted into the urine of glomerular filtration and active tubular secretion, but the body load at times exceeds the kidneys’ clearing capacity. There are no methods known to accelerate the active transport of poisons into urine. Similarly, enhancement of passive glomerular filtration is not a practical means to facilitate elimination of toxic chemicals. Processing of blood in an extracorporeal circuit may be life-saving when the amount of poison in the blood is large compared to the total body burden and binding of the compound to plasma proteins is not extensive. In such cases (e. g., methanol, ethylene glycol, or salicylates poisoning) extracorporeal processing of blood for removing the toxic element from the body is indicated. If the poison is distributed in the entire extracellular space or tightly bound to plasma proteins, dialytic removal is unlikely to affect the clinical outcome because it can only eliminate a small fraction of the toxic solute.

Unfortunately in some situations either the glomerular or the tubular function of the kidneys, or both, fails and cannot be salvaged by drug and diet therapy. Failure can be temporary, self-limiting and potentially reversible, in which case only temporary substitution for renal function will be needed. Failure can also be the expression of progressive, intractable structural damage, in which case permanent replace­ment of renal function will eventually be needed for survival. However, the urgency of external inter­vention in end-stage renal disease (ESRD) is never as acute as is the case for the replacement of cardiac or respiratory function: The signs of renal dysfunction (water retention, electrolyte shifts, accumulation of metabolic end products normally eliminated by the kidneys) develop over days, weeks, or even months and are not immediately life threatening. Even in the end stage, renal failure can be addressed by intermittent rather than continuous treatment.

Renal Failure

There are two types of renal failure: acute (days or weeks) and chronic (months or years). Acute renal failure is typically associated with ischemia (reduction in blood flow), acute glomerulonephritis, tubular necrosis, or poisoning with “nephrotoxins” (e. g., heavy metals, some aminoglycosides, and excessive loads of free hemoglobin). Chronic renal failure is usually caused by chronic glomerulonephritis (of infectious or immune origin), pyelonephritis (ascending infection of the urinary tract), hypertension (leading to nephrosclerosis), or vascular disease (most commonly secondary to diabetes).

Renal insufficiency elicits the clinical picture of uremia. Although the word uremia means that there is too much urea in the blood, urea level in itself is not the cause of the problem. Uremia, often expressed in the United States as blood urea nitrogen concentration or BUN (which is actually half the urea concentration), serves as an indicator of the severity of renal disease. Urea is a metabolic end product in the catabolism of proteins that is hardly toxic even in high concentration. However, it mirrors the impaired renal elimination and the resulting accumulation in body fluids of other toxic substances, some of which have been identified (e. g., phenols, guanidine, diverse polypeptides); others remain unknown and are therefore referred to as uremic toxins or, for reasons to be discussed later, middle molecules. The attenuation of uremic symptoms by protein restriction in the diet and by various dialytic procedures underscores the combined roles of retention, removal, and metabolism in the constellation of signs of uremia. Toxicity may result from the synergism of an entire spectrum of accumulated molecules [Vanholder & Ringoir, 1992]. It may also reflect the imbalance that results from a specific removal through mechanisms which eliminate physiologic compounds together with potential toxins.

Not until the GFR (as estimated by its proxy, creatinine clearance) falls much below a third of normal do the first signs of renal insufficiency become manifest. At that point the plasma or extracellular concentration of substances eliminated exclusively through the glomeruli, such as creatinine or urea, increase measurably, and the possibility of progressive renal failure must be considered. In such cases, over a period of months to years, the kidneys lose their ability to excrete waste materials, to achieve osmoregulation, and to maintain water and electrolyte balance. The signs of ESRD become recognizable as creatinine clearance approaches 15 ml/min, eventually leading to uremic coma as water and solute retention depress the cognitive functions of the central nervous system. Empirically, it appears that the lowest level of creatinine clearance that is compatible with life is on the order of 8 ml/min, or 11.5 liters per day, or 80 liters per week. (These numbers have a bearing on the definition of adequate dialysis in ERSD patients, because they represent the time-averaged clearance which must be achieved by much more effective but intermittent blood processing). Human life cannot be sustained for more than 7-10 days in the total absence of kidney function. Clinical experience also shows that even a minimum of residual renal clearance (KR) below the level necessary for survival can be an important factor of well­being in dialyzed patients, perhaps because the natural kidney, however sick, remains capable of elimi­nating middle molecular weight substances, whereas the artificial kidney is mostly effective in eliminating water and small molecules.

The incidence of ESRD (incidence is defined as the number of new patients entering treatment during a given year) has increased dramatically in the past 25 years in the United States and elsewhere. Whereas in the 1960s it was estimated at 700-1000 new cases a year in the United States (nearly three-quarters of them between the ages of 25 and 54), the number of new patients reached 16,000 per year at the end of the 1970s (still with the majority of cases under age 54) and 40,000 at the end of the 1980s, with the largest contingent between 65 and 74 years old. Serious kidney disease now strikes between in 1 in 5000 and 1 in 10,000 people per year in our progressively aging population. The fastest rate of growth is in the age group over 75, and the incidence of ESRD shows no signs of abating.

The prevalence of ESRD (prevalence is defined as the total number of patients present in the population at a specific time) has grown apace: In the United States, about 1000 people were kept alive by dialysis in 1969; 58,253 in 1979; 163,017 in 1989; close to 200,000 now. This is the result of a combination of factors which include longer survival of patients on hemodialysis and absolute growth of an elderly population suffering from an increasing incidence of diseases leading to ESRD such as diabetes. World­wide, over 500,000 people are being kept alive by various modalities of “artificial kidney” treatment: about a third in the United States, a third in Europe, and a third in Japan and Pacific Rim countries. Another 500,000 or so have benefitted from dialytic treatment in the past but have since died or received transplants [Lysaght & Baurmeister, 1993]. Close to 85% of current patients are treated by maintenance hemodialysis, and 15% are on peritoneal dialysis. These numbers do not include about 100,000 people with a functional renal transplant, most of whom required hemodialysis support while waiting for a donor organ, and who may need it again, if only for a limited period, in case of graft rejection.

The mortality of ESRD patients in the United States has inched upward from 12%—16% per year in the 1970s and 1980s and has risen abruptly in recent years to levels in the order of 20%-25%. This has led to extensive controversy as to the origin of this deterioration, which has not been observed to the same extent in other regions with a similarly large population of ESRD patients, such as Western Europe and Japan, and may reflect for the United States insufficient dialysis as well as the burden of an increasingly older population.

Treatment of Renal Failure

Profound uremia, whether caused by an acute episode of renal failure or by the chronic progressive deterioration of renal function, used to be a fatal condition until the middle of the twentieth century.

The concept of clearing the blood of toxic substances while removing excess water by a membrane exchange process was first suggested by the experiments of Abel, Rowntree, and Turner at the Johns Hopkins Medical School. Back in 1913, these investigators demonstrated the feasibility of blood dialysis to balance plasma solute concentrations with those imposed by an appropriately formulated washing solution. However, their observation was not followed by clinical application, perhaps because experi­ments were limited by the difficulty of fabricating suitable exchange membranes, and blood anticoagu­lation was then extremely precarious. Collodion, a nitrocellulose film precipitated from an alcohol, ether, or acetone solution was the sole synthetic permeable membrane material available until the advent of cellophane in the 1930s. The unreliability of anticoagulants before the discovery of heparin also made continuous blood processing a hazardous process even in laboratory animals.

In 1944, Kolff in the Netherlands developed an artificial kidney of sufficient yet marginal capacity to treat acute renal failure in man. This device consisted of a long segment of cellophane sausage tubing coiled around a drum rotating in the thermostabilized bath filled with a hypertonic, buffered electrolyte solution, called the dialysate. Blood was allowed to flow from a vein into the coiled cellophane tube. Water and solute exchange occurred through the membrane with a warm dialysate pool, which had to be renewed every few hours because of the risk of bacterial growth. The cleared blood was returned to the circulatory system by means of a pump. After World War II, a somewhat similar system was developed independently by Alwall in Sweden. Because of the technical difficulty of providing repeated access to the patient’s circulation, and the overall cumbersomeness of the extracorporeal clearing process, hemo­dialysis was limited to patients suffering from acute, and hopefully reversible, renal failure, with the hope that their kidneys would eventually recover. To simplify the equipment, Inouye and Engelberg [1953] devised a coiled cellophane tube arrangement that was stationary and disposable, and shortly thereafter Kolff and Watschinger (by then at the Cleveland Clinic) reported a variant of this design, the Twin Coil, that became the standard for clinical practice for a number of years.

Repeated treatment, as needed for chronic renal failure, was not possible until late 1959, when Scribner and Quinton introduced techniques for chronic access to the blood stream which, combined with improvements in the design and use of hemodialysis equipment, allowed the advent of chronic intermit­tent hemodialysis for long-term maintenance of ESRD patients. This was also the time when Kiil first reported results with a flat plate dialyzer design in which blood was made to flow between two sheets of cellophane supported by solid mats with grooves for the circulation of dialysate. This design—which had been pioneered by Skeggs and Leonard, McNeill, and Bluemle and Leonard—not only needed less blood volume to operate then the coiled tube devices, it also had the advantage of requiring a relatively low head of pressure to circulate the blood and the dialysate. This meant that the two fluids could circulate without high pressure differences across the membrane. Therefore, in contrast to coil dialyzers, where a long blood path necessitated a high blood pressure at the entrance of the exchanger, flat plate dialyzers could transfer metabolites through the membrane by diffusion alone, without coupling it with the obligatory water flux deriving from high transmembrane pressure. When ultrafiltration was needed, it could be achieved by circulating the dialysate at subatmospheric pressures.

Device development was also encouraged by the growing number of home dialysis patients. By 1965, the first home dialysate preparation and control units were produced industrially. Home dialysis programs based on the twin coil or flat plate dialyzers were soon underway. At that time the cost of home treatment was substantially lower than hospital care, and in the United States, Social Security was not yet under­writing the cost of treatment of ESRD.

In 1965 also, Bluemle and coworkers analyzed means to pack the maximum membrane area in the minimum volume, so as to reduce the bulkiness of the exchange device and diminish the blood loss associated with large dialyzers and long tubing. They concluded that a tightly packed bundle of parallel capillaries would best fit this design goal. Indeed by 1967, Lipps and colleagues reported the initial clinical experience with hollow fiber dialyzers, which have since become the mainstay of hemodialysis technology.

In parallel developments. Henderson and coworkers [1967] proposed an alternative solution to the problem of limited mass transfer achievable by diffusion alone with hemodialysis equipment. They projected that a purely convective transport (ultrafiltration) through membranes more permeable to water than the original cellulose would increase the effective clearance of metabolites larger than urea. The lost extracellular volume was to be replaced by infusing large volumes of fresh saline into the blood at the inlet or the outlet of the dialyzer to replace the lost water and electrolytes. The process was called hemodiafiltration or, sometimes, diafiltration. (The procedure in which solutes and water are removed by convective transport alone, using large pore membranes and without substantial replacement of the fluid, is now known as hemofiltration and is used primarily in patients presenting with massive fluid retention.)

As is intuitively apparent, the effectiveness of hemodialysis with a given devices is related to the duration of the procedure. In the pioneer years, dubbed “the age of innocence” by Colton [1987], patients were treated for as many as 30 hours a week. Economics and patient convenience promoted the development of more efficient transfer devices. Nowadays, intermittent maintenance dialysis can be offered with 10 hours (or even less) of treatment dividend in 3 sessions per week. Conversely, nephrologists have developed (mostly for use in the intensive care unit) the procedure known as continuous arterio-venous hemodialysis (with its variant continuous arterio-venous hemofiltration) in which blood pressure from an artery (aided or not by a pump) drives blood through the exchange device and back into a vein. Continuous operation compensates for the relatively low blood flow and achieves stable solute concen­trations, as opposed to the seesaw pattern that prevails with periodic treatment.

The concept of using a biologic membrane and its blood capillary network to exchange water and solutes with a washing solution underlies the procedure known as peritoneal dialysis, which relies on the transfer capacity of the membranelike tissue lining the abdominal cavity and the organs it contains. In 1976, Popovich and Moncrief described continuous ambulatory peritoneal dialysis (CAPD), a procedure in which lavage of the peritoneal cavity is conducted as a continuous form of mass transfer through introduction, equilibration, and drainage of dialyzate on a repetitive basis 4-6 times a day. In CAPD, a sterile solution containing electrolytes and dextrose is fed by gravity into the peritoneal cavity through a permanently installed transcutaneous catheter. After equilibriation with capillary blood over several hours, this dialyzate is drained by gravity into the original container and the process is repeated with a fresh solution. During the dwell periods, toxins and other solutes are exchanged by diffusional processes. Water transfer is induced by the osmotic pressure difference due to the high dextrose concentration in the treatment fluid. This procedure is analyzed in detail in Chapter 131.

Plasmapheresis, i. e., the extraction of plasma from blood by separative procedures (see Chapter 132), has been used in the treatment of renal disease [Samtleben & Gurland, 1989]. However, the cost of providing fresh plasma to replace the discarded material renders plasmapheresis impractical for frequent, repeated procedures, and plasmapheresis is used mainly for other clinical indications.

Most hemodialysis is performed in free-standing treatment centers, although it may also be provided in a hospital or performed by the patient at home. The hemodialysis circuit consists of two fluid pathways. The blood circuitry is entirely disposable, though many centers reuse some or all circuit components in order to reduce costs. It comprises a 16-gauge needle for access to the circulation (usually through an arteriovenous fistula created in the patient’s forearm), lengths of plasticized polyvinyl chloride tubing (including a special segment adapted to fit into a peristaltic blood pump), the hemodialyzer itself, a bubble trap and an open mesh screen filter, various ports for sampling or pressure measurements at the blood outlet, and a return cannula. Components of the blood side circuit are supplied in sterile and nonpyrogenic conditions. The dialysate side is essentially a machine capable of (1) proportioning out glucose and electrolyte concentrates with water to provide a dialysate of appropriate composition; (2) sucking dialysate past a restrictor valve and through the hemodialyzer at subatmospheric pressure; and (3) monitoring temperature, pressures, and flow rates. During treatment the patient’s blood is anticoagulated with heparin. Typical blood flow rates are 200-350 ml/min; dialysate flow rates are usually set at 500 ml/min. Simple techniques have been developed to prime the blood side with sterile saline prior to use and to return to the patient nearly all the blood contained in the extracorporeal circuit after treatment. Whereas most mass transport occurs by diffusion, circuits are operated with a pressure on the blood side, which may be 100-500 mmHg higher than on the dialysate side. This provides an opportunity to remove 2-4 liters of fluid along with solutes. Higher rates of fluid removal are technically Possible but physiologically unacceptable. Hemodialyzers must be designed with high enough hydraulic permeabilities to provide adequate fluid removal at low transmembrane pressure but not so high that excessive water removal will occur in the upper pressure range.

Although other geometries are still employed, the current preferred format is a “hollow fiber” hemo – dialyzer about 25 cm in length and 5 cm in diameter, resembling the design of a shell and tube heat exchanger. Blood enters at the inlet manifold, is distributed to a parallel bundle of capillary tubes (potted together with polyurethane), and exits at a collection manifold. Dialysate flows countercurrent in an external chamber. The shell is typically made of an acrylate or polycarbonate resin. Devices typically contain 6000-10,000 capillaries, each with an inner diameter of 200-250 microns and a dry wall thickness as low as 10 microns. The total membrane surface area in commercial dialyzers varies from 0.5 to 1.5 m2, and units can be mass-produced at a relatively low cost (selling price around $10—$15, not including tubing and other disposable accessories). Several reference texts (see For Further Information) provide concise and comprehensive coverage of all aspects of hemodialysis.

Renal Transplantation

The uremic syndrome resembles complex forms of systemic poisoning and is characterized by multiple symptoms and side effects. Survival requires that the toxins be removed, and the resulting quality of life depends on the quantity of toxins which are actually eliminated. Ideally, one would like to clean blood and body fluids to the same extent as is achieved by normal renal function. This is only possible at the present time with an organ transplant.

The feasibility of renal transplantation as a therapeutic modality for ESRD was first demonstrated in 1954 by Murray and coworkers in Boston, and Hamburger and coworkers in Paris, in homozygous twins. Soon the discovery of the first immunosuppressive drugs led to the extension of transplantation practice to kidneys of live, related donors. Kidney donation is thought to be innocuous since removal of one kidney does not lead to renal failure. The remaining kidney is capable of hypertrophy, meaning that the glomeruli produce more filtrate, and the tubules become capable of increased reabsorption and secretion. A recent Canadian study indicates that the risk of ESRD is not higher among living kidney donors than in the general population, meaning that a single kidney has enough functional capacity for a lifetime. Nonetheless, cadaver donors now constitute the main organ source for the close to 10,000 renal trans­plants performed in the United States every year. Even though under ideal circumstances each cadaver donor allows two kidney transplants, the scarcity of donors is the major limitation to this form of treatment of ESRD. Most patients aspire to renal transplant because of the better quality of life it provides and the freedom from the time constraints of repeated procedures. However, the incidence of ESRD is such that only one patient in five can be kept alive by transplantation. Dialysis treatment remains a clinical necessity while waiting for a transplant, as a safety net in case of organ rejection, and for the many patients for whom transplantation is either contraindicated or simply not available.

Mass Transfer in Dialysis

In artificial kidneys, the removal of water and solutes from the blood stream is achieved by

Solute diffusion in response to concentration gradients

Water ultrafiltration and solute convection in response to hydrostatic and osmotic pressure gra­dients

Water migration in response to osmotic gradients

In most cases, these processes occur simultaneously and in the same exchange device, rather than sequentially as they do in the natural kidney with the cascade of glomerular filtration, tubular reabsorp­tion, and final adjustments in the collecting tubule.

Mechanistically, the removal of water and solutes from blood is achieved by passive transport across thin, leaky, synthetic polymer sheets or tubes similar to those used in the chemical process call dialysis. Functionally, an artificial kidney (also called hemodialyzer, or dialyzer or filter for short) is a device in which water and solutes are transported from one moving fluid stream to another. One fluid stream is blood; the other is dialysate: a human-made solution of electrolytes, buffers, and nutrients. The solute concentration as well as the hydrostatic and osmotic pressures of the dialysate are adjusted to achieve transport in the desired direction (e. g., to remove urea and potassium ions while adding glucose or bicarbonate to the bloodstream).

Efficiency of mass transfer is governed by two and only two independent parameters. One, which derives from mass conservation requirements, is the ratio of the flow rates of blood and dialysate. The other is the rate constant for solute transport between the two fluid streams. This rate constant depends upon the overall surface area of membrane available for exchange, its leakiness or permeability, and such design characteristics as fluid channel geometry, local flow velocities, and boundary layer control, all of which affect the thickness of stationary fluid films, or diffusion barriers, on either side of the membrane.


The overall mass transfer efficiency of a hemodialyzer is defined by the fractional depletion of a given solute in the blood as it passes through the unit. Complete removal of a solute from blood during a single pass defines the dialyzer clearance for that solute as equal to dialyzer blood flow. In other terms, dialyzer blood flow asymptotically limits the clearance of any substance in any device, however efficient.

Under conditions of steady-state dialysis, the mass conservation requirement is expressed as

N □ Qb( □ C, oD^ Qd(Do □ Cj] (130.1)

Where N is the overall solute transfer rate between blood and dialysate, Qb and Qd are blood flow and dialysate flow rates respectively, and CBi, CBo, CDi, and CDo, are the solution concentrations C in blood, B, or dialysate, D, at the inlet, i, or the outlet, o of the machine.

Equation (130.1) about mass conservation leads to the first and oldest criterion for dialyzer effective­ness, namely clearance K, modeled after the concept of renal clearance. Dialyzer clearance is defined as the mass transfer rate N divided by the concentration gradient prevailing at the inlet of the artificial kidney.


K □ (130.2)

CBi □ CDi

Since mass transfer rate also means the amount of solute removed from the blood per unit of time, which in turn is equal to the amount of solute accepted in the dialysate per unit of time, there are two expressions for dialysance

K ^ (130.3)

B C □ C

CBi □ CDi

Which afford two methods for measuring it. Any discrepancy must remain within the error of measure­ments, which under the conditions of clinical hemodialysis easily approaches □ 10%. As in the natural kidney, the clearance of any solute is defined by the flow rate of blood which is completely freed of that solute while passing through the exchange device. The dimensions of clearance are those of flow (a virtual flow, one may say), which can vary only between zero and blood flow (or dialysate flow, whichever is smaller), much in the way the renal clearance of a substance can only vary between zero and effective renal plasma flow.

Since dialyzer clearance is a function of blood flow, a natural way to express the efficiency of a particular exchange device consists of “normalizing” clearance with respect to blood flow as a dimensionless ratio

— □ Cb – Cbo (130.5)

Qb CBi – C«


C o C

□ CDo D [Extraction fraction) (130.6)

Qb CBt – CDi

K/Qb can vary only between zero and one and represents the highest attainable solute depletion in the blood which is actually achieved in a particular device for a particular solute under a particular set of circumstances.

Another generalization of the dialysance concept may be useful in the case where the direction of blood flow relative to the direction of dialysate flow is either parallel, random, or undetermined, as occurs with the majority of clinical hemodialyzers. Under such circumstances, the best performance which can be achieved is expressed by the equality of solute concentration in outgoing blood and outgoing dialysate (CBo = CDo = Ce or equilibrium concentration). This limit defines, after algebraic rearrangement of Eqs. (130.3) and (130.4), the maximal achievable clearance at any combination of blood and dialysate flow rates without reference to solute concentrations.

Max □ Qb D Qd (130.7)

Qb □ Qd

Since blood and dialysate flows can usually be measured with a reasonable degree of accuracy, the concept of —max provides a practical point of reference against which the effectiveness of an actual dialyzer can be estimated.


So far we implicitly assumed that differences in concentration across the membrane provide the sole driving force for solute transfer. In clinical hemodialysis, however, the blood phase is usually subject to a higher hydrostatic pressure than the dialysate phase. As a result, water is removed from the plasma by ultrafiltration, dragging with it some of the solutes into the dialysate. Ultrafiltration capability is a necessary consequence of the transmural pressure required to keep the blood path open with flat sheet or wide tubular membranes. It is also clinically useful to remove the water accumulated in the patient’s body in the interval of dialysis. Ultrafiltration can be enhanced by increasing the resistance to blood flow at the dialyzer outlet, and thereby raising blood compartment pressure, by subjecting the dialysate to a negative pressure or by utilizing membranes more permeable to water than the common cellophanes.

Whenever water is removed from the plasma by ultrafiltration, solutes are simultaneously removed in a concentration equal to or lower than that present in the plasma. For small, rapidly diffusible molecules such as urea, glucose, and the common electrolytes, the rate of solute removal almost keeps pace with
that of water, and ultrafiltrate concentration is the same as that in plasma. With compounds characterized by a larger molecular size, the rate of solute removal lags behind that of water. Indeed with some of the largest molecules of biological interest, ultrafiltration leads to an actual increase in plasma concentration during passage through the artificial kidney.

Defining ultrafiltration as the difference between blood flow entering the dialyzer and blood flow leaving the dialyzer

F □ Qb, □ QBo

One can rewrite the mass conservation requirement as

QBiCBi CKmountofsolutein the incoming blood]

QBoCBo Qimountofsolutein the outgoing blood]

Kb ( □ Cd, DQ mount cleared in the dialyzer]

The clearance equations can then be rewritten as

Kb □-

подпись: kb □-(130.8)

D Qd, ,

4 Ю

подпись: d qd , ,
4 ю


подпись: (130.9)Qd, □ C„,r

Kd □-

CBi □ CDi

The clearance is now defined as the amount of solute removed from the blood phase per unit of time, regardless of the nature of the driving force, divided by the concentration difference between incoming blood and incoming dialysate.

When CDi = 0


подпись: (130.10)□ Q □

Kb □ Qb, □ Qbo Qg


подпись: (130.11)

Kd □

подпись: kd □QDo CDo


When CD, = 0 and CBo = CB,

K„ □ F

подпись: k„ □ f(130.12)

The practical value of these equations is somewhat limited, since their application requires a high degree of accuracy in the measurement of flows and solute concentrations. The special case where there is no solute in the incoming dialysate (CDi = 0) is important for in vitro testing of artificial kidneys.


The definition of clearance is purely operational. Based upon considerations of conservation of mass, it is focused primarily on the blood stream from which a solute must be removed, thus, in final analysis, on the patient herself or himself. Clearance describes the artificial kidney as part of the circulatory system

And of the fluid compartments which must be cleared of a given solute. To relate the performance of a

Hemodialyzer to its design characteristics, clearance is of limited value.

To introduce into the picture the surface area of membrane and the continuously variable (but predictable) concentration difference between blood and dialysate within the artificial kidney, one must define the rate constant of solute transfer, or permeability PD.


подпись: n 130.1 130.2 130.3 130.4 130.5 130.6 130.7 130.8 Pierre M. Galletti 130.9 (deceased) 130.10 130.11 Clark K. Colton 130.12 Massachusetts Institute 130.13 Of Technology Michael J. Lysaght 130.14 Brown University 130.15 Artificial Kidney

A □□C

подпись: a □□c(130.13)

Where N is the overall solute transport rate between blood dialysate, A is the membrane area, and DC is the average solute concentration difference between the two moving fluids.

Permeability is defined by Eq. (130.13) as the amount of solute transferred per unit area and per unit of time, under the influence of a unit of concentration driving force. The proper average concentration, DC, driving force is the logarithmic mean of the concentration differences prevailing at the inlet and at the outlet

□ C □□C

□ C □


130.1 130.2 130.3 130.4 130.5 130.6 130.7 130.8 Pierre M. Galletti 130.9 (deceased) 130.10 130.11 Clark K. Colton 130.12 Massachusetts Institute 130.13 Of Technology Michael J. Lysaght 130.14 Brown University 130.15 Artificial Kidney



130.1 130.2 130.3 130.4 130.5 130.6 130.7 130.8 Pierre M. Galletti 130.9 (deceased) 130.10 130.11 Clark K. Colton 130.12 Massachusetts Institute 130.13 Of Technology Michael J. Lysaght 130.14 Brown University 130.15 Artificial Kidney

The boundary conditions on the concentration driving force (□ C, and □ Q) are uniquely determined by the geometry of the dialyzer. The three most common cases to consider are: (1) cocurrent flow of blood and dialysate; (2) laminar blood flow, with completely mixed dialysate flow; and (3) countercurrent

Blood and dialysate flow. The boundary conditions on concentration driving force follow. Cocurrent flow is

130.1 130.2 130.3 130.4 130.5 130.6 130.7 130.8 Pierre M. Galletti 130.9 (deceased) 130.10 130.11 Clark K. Colton 130.12 Massachusetts Institute 130.13 Of Technology Michael J. Lysaght 130.14 Brown University 130.15 Artificial Kidney

Mixed dialysate flow is

130.1 130.2 130.3 130.4 130.5 130.6 130.7 130.8 Pierre M. Galletti 130.9 (deceased) 130.10 130.11 Clark K. Colton 130.12 Massachusetts Institute 130.13 Of Technology Michael J. Lysaght 130.14 Brown University 130.15 Artificial Kidney

Countercurrent flow is

130.1 130.2 130.3 130.4 130.5 130.6 130.7 130.8 Pierre M. Galletti 130.9 (deceased) 130.10 130.11 Clark K. Colton 130.12 Massachusetts Institute 130.13 Of Technology Michael J. Lysaght 130.14 Brown University 130.15 Artificial Kidney

Thus permeability can be expressed as in the following equations. Cocurrent flow is

Ln( □ CDi □


Cu„ □ C,

130.1 130.2 130.3 130.4 130.5 130.6 130.7 130.8 Pierre M. Galletti 130.9 (deceased) 130.10 130.11 Clark K. Colton 130.12 Massachusetts Institute 130.13 Of Technology Michael J. Lysaght 130.14 Brown University 130.15 Artificial Kidney


A Q □ Cdo D^Q^Bo □ Cd

Countercurrent flow is

Ln Q □ Cd


PD □ n_ _ Cb^_ _ n (130.17)

A Q □ Cdo O^Q^Bo □ Cd

By simultaneous solution of Eqs. (130.3), (130.4), and (130.12), and use of the formal definition of the logarithmic mean concentration driving force (130.14), the clearance ratio (K/Qb) can be expressed as a function of two dimensionless parameters (Z and R), neither of which involves solute concentration terms [Leonard & Bluemle, 1959; Michaels, 1966]. Cocurrent flow is



подпись: (130.19)Mixed dialysate flow is

Qb 1 □ Z [1 □ exp[Q r

Countercurrent flow is

Where Z = Qb/Qd and R = PD A/Qb

Michaels has expressed graphically Eqs. (130.8-130.20) as plots of clearance ratio (K/Qb) versus flow ratio (Qb/Qd) with various solute transport ratios (Pn, A/Qb) as parameters. These plots give an appre­ciation of the relative importance of the variables affecting dialyzer efficiency and permit one to recognize readily the factors which limit mass transfer under a particular set of conditions.

And CDo from

подпись: and cdo fromFor the computation of actual permeability coefficients, from pooled data obtained at varying solute concentrations, Eqs. (130.15-130.17) can be rearranged, using definitions of N, CBo Eqs. (130.2-130.4). Cocurrent flow is




AQb □ Qd O 1 □ k/Qb □ k/Qd


130.1 130.2 130.3 130.4 130.5 130.6 130.7 130.8 Pierre M. Galletti 130.9 (deceased) 130.10 130.11 Clark K. Colton 130.12 Massachusetts Institute 130.13 Of Technology Michael J. Lysaght 130.14 Brown University 130.15 Artificial Kidney



?□□ ^Mn [8] □ K/QB (130.22)

D A 1 □ K/ QB □ K/Qd

Countercurrent flow is

PdD ^b-d ln1 – —Qd (130.23)

A(d □ Qb □ 1 □ k/Qb

As remarked by Leonard and Bluemle [1959], when, and only when, QD is much greater than QB, the above equations (130.18-130.23) reduce to Renkin’s [1956] formula

Pn □ ^Mn — (130.24)

D A 1 □ K—b


K dip A Q

—□ 1 □«pg-Bg d3».25)

Historically, Eq. (130.25) played an important role in pointing out to designers that the clearance ratio (K/QB) can be improved equally well by an increase in exchange area (A) or in permeability (P). However, caution is required in applying the equation to some of the efficient modern dialyzers. First, the assump­tion that dialysate flow is “infinitely” large with respect to blood flow is seldom verified. Furthermore, the functions relating permeability to dialysance, Eqs. (130.21-130.24), or to the individual solute con­centrations and flows, Eqs. (130.15-130.17), have an exponential form. When the overall permeability approaches that of the membrane alone, when the outgoing solute concentrations approach the equilib­rium conditions, or when clearance approaches blood flow, one deals with the steep part of that expo­nential function. Any slight error in the experimental measurements will lead to a disproportionately larger error in calculated permeability.

Overall Transport

Ignoring boundary layer effects for the moment, and assuming that diffusion within the membrane is analogous to that in free solution, Eq. (130.26) can be integrated across a homogeneous membrane of thickness d to yield

□ SDm Dc (130.27)


Where S represents the dimensionless solute partition coefficient, i. e., the ratio of solute concentration in external solution to that at the membrane surface, and Dm represents solute diffusion within the membrane and is assumed to be independent of solute concentration in the membrane. If two or more solutes are dialysing at the same time, the degree of separation or enrichment will be proportional to the ratio of their permeabilities. The closer the permeability of a membrane is to that of an equivalent thickness of free solution, the more rapid will be the resultant dialytic transport. Equation (130.27) is often further simplified to this expression for flux per unit of membrane area

□PnDC (130.28)

Where thickness is incorporated into an overall membrane mass transfer coefficient with units of cm/s, and DC is the logarithmic mean concentration.

Chemical engineers provided a firm foundation for describing the overall performance of hemodia – lyzers recognizing the importance of understanding and describing mass transfer in each of the three phases of a hemodialyzer (blood, membrane, dialysate), the individual mass transfer resistances of which sum to the overall mass transfer resistance of the device [Colton, 1987]. Solutions adjacent to the membranes are rarely well mixed, and the resistance to transport resides not just in the membrane but also in the fluid regions termed boundary layers, on both the dialysate and blood side. Moreover, some dialyzers are designed to direct flow parallel to the surface of the membrane rather than expose it to a well-mixed bath. Boundary layer effects typically account for 25-75% of the overall resistance to solute transfer [Lysaght & Baurmeister, 1993]. In many exchanger designs, boundary layer effects can be

Minimized by rapid convective flow targeted to the surface of the membrane where fluid pathways are

Thin, flow near the membrane is laminar, and boundary layer resistance decreases with increasing wall shear rates. When geometry permits higher Reynolds numbers, flow becomes turbulent, and fluid resis­tance varies with net tangential velocity. Geometric obstacles (e. g., properly spaced obstacles) or fluid mechanical modulation (e. g., superimposed pulsation) are often-used tactics to minimize boundary layer effects, but all result in higher energy utilization. Quantitatively, the membrane resistance becomes part of an overall mass transfer parameter Pn which for conceptual purposes can be broken down into three independent and reciprocally additive components for the triple laminate: blood boundary layer (sub­script B), membrane (subscript M), and dialysate boundary layer (subscript D), such that

□ — □— □— (130.29)



Or reciprocally

R □ RB □ RM □ Rd (130.30)

Where Pn is the device-averaged mass transfer coefficient (or permeability) in cm/s and Rn is the device­averaged resistance in s/cm. DB can be estimated for many relevant conditions of geometry and flow using mass transport analysis based upon wall Sherwood numbers [Colton et al., 1971]. PM is best obtained by measurements employing special test fixtures in which boundary layer resistances are negligible or known [Klein et al., 1977]. PD is more problematic and is usually obtained by extrapolations based upon Wilson plots [Leonard & Bluemle, 1960]. Boundary layer theory, as well as technique for correlation,

Estimation, and prediction of the constituent mass transfer coefficients, is reviewed in detail by Colton and coworkers [1971] and Klein and coworkers [1977]. Overall solute transport is obtained from local flux by mass balance and integration; for the most common case of countercurrent flow







□pa□ 0 D

Exp — r4 □ —B

0 —b □ —d

— DD —

R! □ rn- —B

—D 1=1


130.1 130.2 130.3 130.4 130.5 130.6 130.7 130.8 Pierre M. Galletti 130.9 (deceased) 130.10 130.11 Clark K. Colton 130.12 Massachusetts Institute 130.13 Of Technology Michael J. Lysaght 130.14 Brown University 130.15 Artificial Kidney



Where CBi and CDi represent inlet concentrations in the blood and dialysate streams in g/cm3, A represents membrane surface area in cm2, Qb and Qd are blood and dialysate flow rates in cm3/min, and □ and Pn are as defined in Eqs. (130.28) and (130.29). Derivations of this relationship and similar expressions for cocurrent or crossflow geometries can be found in reviews by Colton and Lowrie [1981] and Gotch and colleagues [1972].

As pointed out by Lysaght and Baurmeister [1993], hemodialysis is a highly constrained process. Molecular diffusion is slow, and the driving forces are set by the body itself, decreasing in the course of purification and not amenable to extrinsic augmentation. The permeant toxic species are not to be recovered, and their concentrations are necessarily more dilute in the dialysate than in the incoming blood. The flow and gentle nature of dialysis has a special appeal for biologic applications, particularly when partial purification of the feed stream, rather than recovery of a product, is intended.


Hemodialysis membranes vary in chemical composition, transport properties, and, as we will see later, biocompatibility. Hemodialysis membranes are fabricated from these classes of materials: regenerated cellulose, modified cellulose, and synthetics [Lysaght & Baurmeister, 1993]. Regenerated cellulose is most commonly prepared by the cuproamonium process and are macroscopically homogenous. These extremely hydrophilic structures sorb water, bind it tightly, and form a true hydrogel. Solute diffusion occurs through highly water-swollen amorphous regions in which the cellulose polymer chains are in constant random motion and would actually dissolve if they were not tied down by the presence of crystalline regions. Their principles advantage is low unit cost, complemented by the strength of the highly crystalline cellulose, which allows polymer films to be made very thin. These membranes provided effective small-solute transport in relatively small exchange devices. The drawbacks of regenerated cel­lulose are their limited capacity to transport middle molecules and the presence of labile nucleophilic groups which trigger complement activation and transient leukopenia during the first hour of exposure to blood. The advantages appear to outweigh the disadvantages, since over 70% of all hemodialyzers are still prepared from cellulosics, the most common of which is supplied by Akso Faser AG under the trade name Cuprophan.

A variety of other hydrophilic polymers account for 20% of total hemodialyzer production, including derivatized cellulose, such as cellulose acetate, diacetate, triacetate, and synthetic materials such as poly­carbonate (PC), ethylenevinylalcohol (EVAL), and polyacrylonitrile-sodium methallyl sulfonate copoly­mer (PAN-SO3), which can all be fabricated into homogeneous films.

At the opposite end of the spectrum are membranes prepared from synthetic engineered thermoplas­tics, such as polysulfones, polyamides, and polyacylonitrile-polyvinylchloride copolymers. These hydro­phobic materials, which account for about 10% of the hemodialyzer market, form asymmetric and anisotropic membranes with solid structures and open void spaces (unlike the highly mobile polymeric structure of regenerated cellulose). These membranes are characterized by a skin on one surface, typically a fraction of a micron thick, which contains very fine pores and constitutes the discriminating barrier
Determining the hydraulic permeability and solute retention properties of the membrane. The bulk of the membrane is composed of a spongy region, with interstices that cover a wide size range and with a structure ranging from open to closed cell foam. The primary purpose of the spongy region is to provide mechanical strength; the diffusive permeability of the membrane is usually determined by the properties of this matrix. As the convective and diffusive transport properties of these membranes are, to a large extent, associated independently with the properties of the skin and spongy matrix, respectively, it is possible to vary independently the convective and diffusive transport properties with these asymmetric structures. There is often a second skin on the other surface, usually much more open than the primary barrier. These materials are usually less activating to the complement cascade than are cellulosic mem­branes. The materials are also less restrictive to the transport of middle and large molecules. Drawbacks are increased cost and such high hydraulic permeability as to require special control mechanisms to avoid excess fluid loss and to raise concerns over the biologic quality of dialysate fluid because of the possibility of back filtration carrying pyrogenic substances to the blood stream.

The discovery of asymmetry membrane structures launched the modern era of membrane technology by motivating research on new membrane separation processes. Asymmetric membranes proved useful in ultrafiltration, and a variety of hydrophobic materials have been used including polysulfone (PS), polyacrylonitrile (PAN), its copolymer with polyvinylchloride (PVC), polyamide (PA), and polymethyl methacrylate (PMMA). PMMA does not form an obvious skin surface and should perhaps be placed in a class of its own.


Although low rates of ultrafiltration have been used routinely for water removal since the beginning of hemodialysis, the availability of membranes with very high hydraulic permeabilities led to radically new approaches to renal substitutive therapy. Such membranes allowed uniformly high clearance rates of solutes up to moderate molecular weights (several thousands) by the use of predominantly convective transport, thereby mimicking the separation capabilities of the natural kidney glomeruli. Progress in the development of this pressure-driven technique, which has come to be known as hemofiltration, has been reviewed by Henderson [1982], Lysaght [1986], and Ofsthum et al. ]1986].

In ultrafiltration, the solute flux Js (the rate of solute transport per unit membrane surface area) is equal to the product of the ultrafiltrate flux JF (the ultrafiltrate flow rate per unit membrane surface area) and the solute concentration in the filtrate, cF In turn cF is related to the retentate concentration CR in the bulk solution above the membrane by the observed rejection coefficient R:

JS □ JpCP □ JFQ□ R)R (130.32)

Thus, knowledge of the ultrafiltrate flux and observed rejection coefficient permits prediction of the rate of solute removal.

With increasing transmembrane pressure difference, the ultrafiltrate flux increases and then levels off to a pressure-independent value. This behavior arises from the phenomenon of concentration polarization [Colton 1987]. Macromolecules (e. g., proteins) that are too large to pass through the membrane build up in concentration in a region near the membrane surface. At steady state, the rate at which these rejected macromolecules are convected by the flow of fluid towards the membrane surface must be balanced by the rate of convective diffusion away from the surface. Estimation of the ultrafiltrate flux reduces largely to the problem of estimating the rate of back transport of macromolecules away from the membrane surface

JF □ k ln – pw (130.33)


Where k is the mass transfer coefficient for back transport of the rejected species, and cpw and cpb are the plasma concentrations of rejected species at the membrane surface and in the bulk plasma, respectively. Attainment of an asymptotic, pressure-independent flux is consistent with the concentration at the wall cpw reaching a constant value. As with diffusive membrane permeability, solute rejection coefficients must be measured experimentally, since the available theoretical models and details of membrane structure are inadequate for prediction.

In hemofiltration the magnitude of the maximum clearance is determined by the blood and ultrafiltrate flow rates and whether the substitution fluid is added before or after filtration. Solutes with molecular weights up to several thousand are cleared at essentially the same rate in hemofiltration, whereas there is a monotonic decrease with increasing molecular weight in hemodialysis. If a comparison is made with devices of equal membrane surface area, it is generally found that hemodialysis provides superior clear­ance for low-molecular-weight solutes such as urea. The superiority of hemofiltration becomes apparent at molecular weights of several hundred.

Hemodialysis and hemofiltration represent two extremes with membranes having relatively low and relatively high hydraulic permeabilities, respectively. As a variety of new membranes became available with hydraulic permeabilities greater than that of regenerated cellulose, various groups began to examine new treatment modalities in which hemodialysis was combined with controlled rates of ultrafiltration which were higher than those employed in conventional hemodialysis but smaller than those used in hemofiltration [Funck-Brenato et al., 1972; Lowrie et al., 1978; Ota et al., 1975]. The advantage of such an approach is that it retains the high clearance capabilities of hemodialysis for low-molecular-weight solutes while adding enhanced clearance rates for the high-molecular-weight solutes characteristic of hemofiltration. A variety of systems is now commercially available and in clinical use, mainly in Europe and Japan. The proliferation of mixed-mode therapies has led to a panopoly of acronyms: hemodialysis (HD), hemofiltration (HF), high-flux dialysis (HFD), hemodiafiltration (HDF), biofiltration (BF), con­tinuous arteriovenous hemofiltration (CAVH), continuous arteriovenous hemodialysis (CAVHD), slow continuous ultrafiltration (SCUF), simultaneous dialysis and ultrafiltration (SDUF), and so on.

Rigorous description of simultaneous diffusion and convection in artificial kidneys has not yet been carried out. Available analyses span a wide range of complexity and involve, to varying degrees, simplifying assumptions. Their predictions have not been systematically compared with experimental data. In view of the growing interest in various “high-flux” membranes and their application for enhanced solute removal rates and/or shortened treatment times, further refinement may be helpful.


Whereas the above analysis is founded on understanding the solute-removal capabilities of hemodialyzers, clinical application must also consider the limitations imposed by the transport of solute between body fluid compartments. The earliest physiologic models were produced by chemical engineers [Bell et al., 1965; Dedrick & Bischoff, 1968] using techniques which had been developed to describe the flow of material in complex chemical processes and were applied to the distribution of drugs and metabolites in biologic systems. This approach has progressively found its way into the management of uremia by hemodialysis [e. g., Farrell, 1983; Gotch & Sargent, 1983; Lowrie et al., 1976; Sargent et al., 1978].

Pharmacokinetics summarizes the relationships between solute generation, solute removal, and con­centration in the patient’s blood stream. It is most readily applied to urea as a surrogate for other uremic toxins in the quantitation of therapy and in attempts to define its adequacy. In the simplest case, the patient is assumed to have no residual renal function and to produce no urea during the relatively short periods of dialysis. Urea is generated in the body from the breakdown of dietary protein, which empirically has been found to approximate where G is the urea generation rate and I the protein intake (both in mg/min). If reliable measurements of I are not available, one assumes an intake of 1 gram of protein per kg of body weight per day.

Urea accumulates in a single pool equivalent to the patient’s total body water and is removed uniformly from that pool during hemodialysis. Mass balance yields the following differential equation:

DQv □

□ G □ Kc (130.35)


Where c is the blood urea concentration (equal to total body water urea concentration) in mg/ml; V is

The urea distribution volume in the patient in ml; G is the urea generation rate in mg/min; t is the time

From onset of hemodialysis in minutes; and K is the urea clearance in ml/min. V can be measured by tritiated water dilution studies but is usually 58% of body weight. Generation is calculated from actual measurement or estimate of the patient’s protein intake (each gram of protein consumed produces about 250 mg of urea). Therefore, a 70-kg patient, consuming a typical 1.0 g of protein per kilogram of body weight per day, would produce 28 g of urea distributed over a fluid volume of 40.6 L. In the absence of any clearance, urea concentration would increase by 70 mg/100 ml every 24 hours. The reduction of urea concentration during hemodialysis is readily obtained from Eq. (130.32) by neglecting intradialytic generation and changes in volume:

N Kt Q

Cf □ ci expg g (130.36)

Where ci and ct represent the urea concentrations in the blood at the beginning and during the course

Of treatment. A 3-1/2-hour treatment of a 70-kg patient (V = 40.6 L) with a urea clearance of 200 ml/min would lead to a 64% reduction in urea concentration or a value of 0.36 for the ct/c’ ratio. (This parameter almost always falls between 0.30 and 0.45.)

The increase in urea concentration between hemodialysis treatments is obtained from Eq. (130.33), again assuming a constant V:

Cf □ cf □ Gt (130.37)

Where cf is the urea concentration in the patient’s blood at the end of the hemodialysis and ct the concentration at time t during the intradialytic interval. Urea concentration typically increases by about 50-100 mg/100 ml/24 hours. Even a small residual renal clearance will prove numerically significant. Therefore in oliguric patients who still exhibit a minimum of kidney function, one should use the slightly more complex equations given by Sargent and Gotch [1989] or Farrell [1988].

The exponential decay constant in Eq. (130.33), Kt/v, expresses the net normalized quantity of hemo­dialysis therapy received by a uremic patient. It is calculated simply by multiplying the urea clearance of the dialyzer (in ml/min) by the duration of hemodialysis (in min) and dividing by the distribution volume (in ml) which in the absence of a better estimate is taken as 0.58 □ body weight. Gotch and Sargent [1983] first recognized that this parameter provides an index of the adequacy of hemodialysis. Based upon a retrospective analysis of various therapy formats, they suggested a value of 1.0 or greater as representing an adequate amount of hemodialysis for most patients. Although not immune to criticism, this approach has found widespread clinical acceptance and represents the current prescriptive norm in hemodialysis therapy.

Adverse effects of uremia can be attributed to:

Retention of solutes normally degraded or excreted by the kidneys.

Overhydration associated with inadequate balance between fluid intake and water removal.

Absence of factors normally synthesized by the kidneys.

Pathophysiologic response to the decline in renal function on the part of other organ systems.

Pathologic response of the organism to repeated exposure to damaging procedures and foreign materials.

Adequacy of Dialysis

As outlined in Table 130.1, the uremic syndrome under dialysis is more complex than observed in ESRD before the institution of treatment. The pathology observed not only is related to insufficient removal of toxic solutes but also comprises some unavoidable adverse effects of extracorporeal blood processing, including the interactions of blood with foreign materials [Colton et al., 1994]. The attenuation of uremic syndrome symptoms by protein restriction in the patient’s diet and by various dialytic procedures underscores the combined roles of retention, removal, and metabolism in the constellation of signs of the disease. Toxicity may result from the synergism of the entire spectrum of accumulated molecules, which is surprisingly large (see Table 130.2 and Vanholder and Ringoir [1992]. The uremic syndrome resembles complex forms of systemic poisoning and is characterized by multiple symptoms and side effects. Survival requires that the toxins be removed, and survival quality depends on the quantity of toxins that are actually eliminated. Ideally, one would like to clean blood and body fluids to the same extent as is achieved by normal renal function. This is possible with an organ transplant that works without interruption but is only asymptotically approached with intermittent dialysis.

There is a compelling need for objective definition of the adequacy of ESRD treatment: How much removal in how much time is necessary for each individual? The answer is indirect and approximate. Some define adequacy of dialysis by clinical assessment of patient well-being. More sophisticated proce­dures, such as electromyography, electroencephalography, and neuropsychologic tests, may refine the clinician’s perception of inadequate dialysis. Yet inadequate therapy can remain unrecognized when therapeutic decisions are based exclusively on clinical parameters. The inverse is also true, and follow – up of dialysis adequacy should never be restricted to static markers of toxicity or dynamic biochemical parameters such as clearance, kinetic modeling, and the like.

Most patients undergoing dialysis do not work or function as healthy people do, and often their physical activity and employment status does not go beyond the level of taking care of themselves. In many centers, the best patients in a hemodialysis program are selectively removed for transplantation. Hospitalization rate is an approximate index of dialysis inadequacy. About 25 percent of all hospitaliza­tions are due to vascular access problems. Comparison among centers may be difficult, however, because of differences in local conditions for hospital admission. Vanholder and Ringoir [1992] have attempted to relate the adequacy of dialysis to the relevant solute concentrations in blood and distinguish among solute-related factors, patient-related factors, and dialysis-related factors (Table 130.3). Their analysis constitutes a useful point of departure for adjusting the quantity of dialysis to the specific needs of an individual patient, which is a complex problem, since it requires not only an appreciation of what the removal process can do, but also of the generation rate of metabolic end products (related to nutrition, physical activity, fever, etc.) and the dietary load of water and electrolytes. Dialysis patients are partially rehabilitated, but their condition rarely compares to that of recipients of a successful renal transplant.


The treatment of chronic renal failure by artificial kidney dialysis represents one of the most common, and certainly the most expensive, component of substitutive medicine. From an industrial viewpoint,

Patients each “consuming” perhaps 100 hemodialysis filters per year (allowing for some reuse


Middle molecules



Trace metals (e. g., bromine) Uric acid Cyclic AMP Amino acids Myoinositol Mannitol Oxalate Glucuronate Glycols Lysozyme Hormones Parathormone Natriuretic factor Glucagon Growth hormone Gastrin Prolactin Catecholamines Xanthine Hypoxanthine Furanpropionic acid Amines Putrescine Spermine Spermidine Dimethylamine Polyamines Endorphins Pseudouridine Potassium Phosphorus Calcium Sodium Water Cyanides

подпись: middle molecules
trace metals (e.g., bromine) uric acid cyclic amp amino acids myoinositol mannitol oxalate glucuronate glycols lysozyme hormones parathormone natriuretic factor glucagon growth hormone gastrin prolactin catecholamines xanthine hypoxanthine furanpropionic acid amines putrescine spermine spermidine dimethylamine polyamines endorphins pseudouridine potassium phosphorus calcium sodium water cyanides



□-guanidinipropionic acid Guanidinosuccinic acid Gamma-guanidinobutyric acid Taurocyanine Creatinine Creatine Arginic acid Homoarginine N-a-acetylarginine Phenols O-cresol P-cresol Benzylalcohol Phenol Tyrosine Phenolic acids

P-hydroxyphenylacetic acid □-(m hydroxyphenyl)- hydracrylic acid Hippurates

P-(OH)hippuric acid o-(OH)hippuric acid Hippuric acid Benzoates Polypeptides □2-microglobulin Indoles

Indol-3-acetic acid Indoxyl sulfate 5-hydroxyindol acetic acid Indo-3-acrylic acid 5-hydroxytryptophol N-acetyltryptophan Tryptophan

From the 150 units per year that would be needed for 3 times per week treatment) means a production of 50 million filters. With each unit selling for an approximate price of 15 dollars, the world market is on the order of $750 million. From a public health viewpoint, if one is to take the U. S. figure of $30,000 for the world average annual cost of a single dialysis patient, the aggregate economic impact of the medical application of hemodialysis approaches $15 billion a year (of which less than 10 percent is spent on the purchase of technology; health care personnel costs are the most expensive component of the treatment).

Yet “maintenance dialysis on the whole is non-physiological and can be justified only because of the finiteness of its alternative” [Burton, 1976]. Dialytic removal remains nonspecific, with toxic as well as useful compounds eliminated indiscriminately. A better definition of disturbed metabolic pathways will be necessary to formulate treatment hypotheses and design adapted equipment. Sensors for on-line monitoring of appropriate markers may also help to evaluate the modeling of clearance processes. The confusing interference of interactions between the patient and the foreign materials in the dialysis circuit may be reduced as more compatible materials become available. A better clinical condition of the ESRD patient remains the ultimate goal of dialysis therapy because at the moment it seems unlikely that either preventative measures or organ transplantation will reduce the number of patients whose lives depend on the artificial kidney.

Solute-related factors

Compartmental distribution Intracellular concentration Resistance of cell membrane Protein binding Electrostatic charge Steric configuration Molecular weight Dialysis-related factors Dialysis duration Interdialytic intervals Blood flow

Mean blood flow Blood flow pattern Concentration gradients Dialysate flow Dialyzer surface Dialyzer volume Dialyzer membrane resistance Dialyzer pore size

Patient-related factors Body weight Distribution volume

Intake and generation of solutes metabolic precursors

Residual renal function

Quality of vascular access

Absorption from the intestine


Blood viscosity

Absorption of solutes on the membrane, on other parts of the circuit Ultrafiltration rate Intradialytic changes in efficiacy Changes with indirect effect on solute-related factors Blood pH Heparinization Free fatty acid concentration

Defining Terms

Arteriovenous fistula: A permanent communication between an artery and an adjacent vein, created

Surgically, leading to the formation of a dilated vein segment which can be punctured transcuta – neously with large bore needles so as to allow connecting the circulatory system with an extracor – poreal blood processing unit.

Artificial kidney: A blood purification device based on the removal of toxic substances through semi­

Permeable membranes washed out by an acceptor solution which can safely be discarded.

Blood urea nitrogen (BUN): The concentration of urea in blood, expressed as the nitrogen content of

The urea (BUN is actually 0.47 times, or approximately half, the urea concentration).

Boundary layer: The region of fluid adjacent to a permeable membrane, across which virtually all

(99%) of the concentration change within the fluid occurs.

Catheter: A tube used to infuse a fluid in or out of the vascular system or a body cavity.

Clearance: A measure of the rate of mass removal expressed as the volume of blood which per unit of

Time is totally cleared of a substance through processing in a natural or artificial kidney. Clearance has the dimensions of a flow rate and can be defined only in relation to a specific solute. Clearance can also be viewed as the minimal volume flow rate of blood which would have to be presented to a processing device to provide the amount actually recovered in the urine or the dialysate if extraction of that material from blood were complete. Clearance is measured as the mass transfer rate of a substance divided by the blood concentration of that substance.

Continuous ambulatory peritoneal dialysis: A modality of peritoneal dialysis in which uninter –

Rupted—although not evenly effective—treatment is provided by 4-6 daily cycles of filling and emptying the peritoneal cavity with a prepared dialysate solution. Solute removal relies on diffusive equalization with molecular species present in capillary blood. Water removal relies on the use of hyperosmotic dialysate.

Continuous arteriovenous hemodialysis: A dialytic procedure in which blood, propelled either by

Arterial pressure or by a pump, flows continuously at a low flow rate through a dialyzer, from where it returns to a vein, providing for uninterrupted solute and fluid removal and nearly constant equilibration of body fluids with the dialysate solution.

Dialysate: A buffered electrolyte solution, usually containing glucose at or above physiologic concen­

Tration, circulated through the water compartment of a hemodialyzer to control diffusional trans­port of small molecules across the membranes and achieve the blood concentrations desired.

Dialysis: A membrane separation process in which one or more dissolved molecular species diffuse across a selective barrier in response to a difference in concentration.

Dwell time: The duration of exposure of a solution used to draw waste products and excessive water

Out of the blood during peritoneal dialysis.

ESRD: End-stage renal disease.

Glomerular filtration rate: The volume of plasma water, or primary urine, filtered in the glomerulus

Per unit of time. Measured, for instance, by creatinine clearance, it expresses the level of remaining renal function in end-stage renal disease.

Hemodiafiltration: Removal of water and solutes by a combination of diffusive and convective trans­

Port (paired filtration-dialysis) across a dialysis membrane to achieve effective transport of small and middle molecules. To compensate for the water loss, a large volume of saline or balanced electrolyte solution must be infused in the blood circuit to prevent hemoconcentration.

Hemodialysis: A modality of extracorporeal blood purification in which blood is continuously circu­

Lated in contact with a permeable membrane, while a large volume of balanced electrolyte solution circulates on the other side of the membrane. Diffusion of dissolved substances from one stream to the other removes molecules that are in excess in the blood and replaces those for which there is a deficiency. Increased removal can be achieved by increasing the duration of the procedure, the overall membrane area, or the membrane permeability.

Hemofiltration: Removal of water and solutes by convective transport, controlled by a large hydrostatic

Pressure difference between blood and a liquid compartment across a large-pore, high-water-flux membrane.

Membrane: A thin film of natural or synthetic polymer which allows the passage of dissolved molecules

And solvents in response to a concentration or pressure difference (diffusion or filtration) across the polymer.

Middle molecules: Molecules of intermediate molecular weight (roughly of 1000 to 30,000 daltons)

Which are presumed to be responsible for the toxic manifestations of end-stage renal disease and therefore should be eliminated by substitutive therapy.

Peritoneal dialysis: A process in which metabolic waste products, toxic substances, and excess body

Water are removed through a membranelike tissue that lines the internal abdominal wall and the organs in the abdominal cavity.

Permeability: The ability of a membrane to allow the passage of certain molecules while maintaining

A physical separation between two adjacent phases.

Permselectivity: The property of a membrane whereby a differential rate of molecular transport

Between two phases is achieved based on characteristics such as molecular weight, molecular size, degree of hydration, affinity for membrane material, and electric charge. The most common feature leading to permselectivity is membrane pore size.

Residual renal clearance: The small level of renal function (measured as creatinine clearance by the

Diseased kidneys) remaining in some patients in end-stage renal disease, particularly in the early years of dialytic treatment.

Ultrafiltration: The process whereby plasma water flows through a membrane in response to a hydro­

Static pressure gradient, dragging with it solute molecules at concentrations equal or lower to that prevailing in plasma.

Uremia: A condition in which the urea concentration in blood is chronically elevated, reflecting an

Inability to remove from the body the end products of protein metabolism.

Uremic toxins: Partly unidentified and presumably toxic substances appearing in the blood of patients

In end-stage renal failure, which can be eliminated to a variable extent by chemical processing of body fluids.


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Wilson EE. 1915. A basis for rational design of heat transfer apparatus. Trans Am Soc Mech Eng 37:47.

Further Information

An extensive review of renal pathophysiology is to be found in: B. M. Brenner and F. C. Rector, eds., The Kidney, 3d ed., Saunders Publishing Co., Philadelphia, 1986. Two volumes addressing the clinical aspects of dialysis are A. R. Nissanson, R. Fine, and D. Gentile, Clinical Dialysis, Appleton Lange Century Crofts, Norwalk, 1984; and H. J. Gurland, ed., Uremia Therapy, Springer Verlag, Berlin, 1987. The principles of designs and functions of dialysis therapy are outlined in P. C. Farrel, Dialysis Kinetics, ASAIO Primers in Artificial Organs, vol. 4, J. B. Lippincott, Philadelphia, 1988; and J. F. Maher, Replacement of Renal Function of Dialysis, 3d ed., Klumer, Boston, 1989. Recent reviews of specific aspects in the operation of artificial kidneys are C. K. Colton, “Analysis of Membrane Processes for Blood Purification,” Blood Purification 5:202-251, 1987; C. K. Colton and E. G. Lowrie, “Hemodialysis Physical Principles and Technical Consid­erations,” in B. M. Brenner and F. C. Rector, Jr., eds., The Kidney, 2d ed., vol 2, Saunders, Philadelphia; and C. K. Colton, R. A. Ward, and S. Shaldon, “Scientific Basis for Assessment of Biocompatibility in Extracorporeal Blood Treatment,” Nephrology Dialysis, Transplantation, 9(Suppl. 2):11, 1994.

Ongoing contributions to the field of artificial kidney therapy are often found in biomaterials journals (e. g., the Journal of Biomaterials Research) and in artificial organ publications (e. g., the Transactions of the American Society for Artificial Organs, the ASAIO Journal, the International Journal of Artificial Organs, and Artificial Organs). Clinical contributions can be found in Kidney International, Nephron, and Blood Purification.

Lysaght, M. J., Moran, J. “Peritoneal Dialysis Equipment.” The Biomedical Engineering Handbook: Second Edition. Ed. Joseph D. Bronzino Boca Raton: CRC Press LLC, 2000

129.1 Gas Exchange Systems 129.2 Cardiopulmonary Bypass 129.3 Artificial Lung Versus Natural Lung 129.4 Oxygen Transport 129.5 Co2 Transport 129.6 Coupling of O2 and CO2 Exchange 129.7 Shear-Induced Transport Augmentation and Devices for Improved Gas Transport Artificial Lungs and Blood-Gas Exchange Devices

Pierre M. Galletti (deceased) Clark K. Colton

Massachusetts Institute of Technology

The natural lung is the organ in which blood exchanges oxygen and carbon dioxide with the body environment. In turn, blood brings oxygen to all body tissues, so as to oxidize the nutrients needed to sustain life. The end products of the chemical reactions that take place in tissues (globally referred to as metabolism) include carbon dioxide, water, and heat, which must all be eliminated. In mammals, oxygen is obtained from the air we breathe through diffusion at the level of the pulmonary alveoli and then carried to the tissues by the hemoglobin in the red blood cells. The carbon dioxide produced by living cells is picked up by the circulating blood and brought to the pulmonary capillaries from where it diffuses into the alveoli and is conveyed out by ventilation through the airways. These processes can be slowed down to a fraction of resting levels by hypothermia or accelerated up to 20-fold when the demand for fuel increases, as for instance with hypothermia, fever, and muscular exercise.

Only a fraction of the oxygen in the air is actually transferred from the pulmonary alveoli to the pulmonary capillary blood, only a fraction of the oxygen carried by arterial blood is actually extracted by the tissues, and only a fraction of the oxygen present in tissues is actually replenished in a single blood pass. Similarly, only a fraction of the CO2 present in tissues is conveyed to the circulating blood, only a fraction of the mixed venous blood CO2 content is actually discharged in the alveoli, and only a fraction of the CO2 in the aveolar gas is eliminated into each breath. Delicately poised physiologic mechanisms, further balanced by chemical buffer systems, maintain the gas exchange system in equilibrium.

The challenge of replacing the function of the natural lungs by an exchange device allowing continuous blood flow and continuous blood arterialization was first outlined by physiologists at the end of the 19th century but could not be met reliably until the 1950s. The large transfer areas needed for blood-gas exchange in an artificial lung were initially obtained by continuous foaming and defoaming in a circulating blood pool or by spreading a thin film of blood in an oxygen atmosphere. Because the direct blood-gas interface was found to be damaging to blood as well as difficult to stabilize over extended periods, membrane-mediated processes were introduced and are now almost universally preferred.

Gas Exchange Systems

Artificial lungs are often called blood oxygenators because oxygen transfer has traditionally been seen as the most important function being replaced and, in most situations, has proved more limiting than CO2 transfer. The change in blood color between inlet and outlet also encourages the term oxygenator, considering that changes in blood CO2 content are not visible to the eye and are more difficult to measure than oxygen transfer.

As is the case for most artificial organs, artificial lungs may be called upon to replace entirely the pulmonary gas exchange function (when the natural organ is totally disabled or, while still sound, must be taken out of commission for a limited time to allow a surgical intervention) or to assist the deficient gas transfer capacity of the natural organ, either temporarily, with the hope that the healing process will eventually repair the diseased organ, or permanently, when irreversible lung damage leaves the patient permanently disabled.

Since most artificial lungs cannot be placed in the anatomical location of the natural lung, venous blood must be diverted from its normal path through the central veins, right heart, and pulmonary vascular bed and rerouted, via catheters and tubes, through an extracorporeal circuit which includes the artificial lung before being returned, by means of a pump, to the arterial system.

The procedure in which the pulmonary circulation is temporarily interrupted for surgical purposes and gas exchange is provided by an artificial lung is often referred to as extracorporeal circulation (ECC) because, for convenience sake in the operating room, the gas exchange device as well as the pumps which circulate the blood are located outside the body.

The vision of coupling extracorporeal blood pumping with extracorporeal gas exchange at a level of performance sufficient to permit unhurried surgical interventions in adult patients originated with Gibbon [1939] whose initial laboratory models relied on rotating cylinders to spread blood in a contin­uously renewed thin film, in the tradition of 19th-century physiologists. Gibbon’s clinical model [1954], built with technical support from IBM, was a stationary film oxygenator, a bulky device in which venous blood was evenly smeared over a stack of vertical wire screen meshes in an oxygen atmosphere, flowing gently downward to accumulate in a reservoir from where blood could be returned to a systemic artery. The main problems with that design, besides its cumbersome dimensions, were to avoid blood streaming and to maintain a constant blood-gas exchange area. Other investigators tried to increase the flexibility of the system by replacing the stationary film support with rotating screens or rotating discs partly immersed in a pool of blood. This allowed some control of gas transfer performance by changing the rational speed, but minimizing the blood content of the device dictated a tight fit between the discs and the horizontal glass cylinder surrounding them. Foaming and hemolysis were encountered at high disc spinning velocity, and these designs were eventually abandoned.

The very first strategy of physiologists for exchanging oxygen and carbon dioxide in venous blood had been to bubble pure oxygen through a stationary blood pool. To turn this batch process into a continuous operation for totally body perfusion, blood was collected through cannulae from the central veins by a syphon or a pump, driven upward in a vertical chimney, mixed with a stream of oxygen gas bubbles, and finally passed through filters and defoaming sponges so as to collect bubble-free arterialized blood, which could then be used to perfuse the arterial tree. The efficiency of bubble oxygenators is extremely high because the smaller the bubbles, the larger the blood-oxygen exchange area developed by a steady current of gas. In the limiting case, it is even possible to saturate venous blood by introducing no more oxygen into the blood than is consumed by the tissues. This process, however, doe not remove any carbon dioxide. Since the partial pressure of CO2 in the excess gas vented from the bubble oxygenator cannot exceed the CO2 partial pressure in arterialized blood (and in actuality is much lower), it follows the carbon dioxide transfer rate of bubble oxygenators is a direct function of the volume inflow rate of oxygen, which must exceed oxygen uptake severalfold to transfer both O2 and CO2. Thus, the operating conditions for a bubble oxygenator are dictated to a major extent by the requirements for adequate Co2 removal.

Three major advances propelled bubble oxygenators ahead of film oxygenators in the pioneer decades of cardiac surgery. The first was the identification of silicone-based defoaming compounds which could be smeared on top of the bubble chimney and proved much more effective in coalescing the blood foam than previously used chemicals. The second was the quantitative process analysis by Clark [1950] and Gollan [1956] which showed that, since small bubbles favor oxygen transfer and large bubbles are need for CO2 removal, an optimum size could be found in between, or alternatively a mix of small and large bubbles should be used. The third and practically decisive advance was made simultaneously by Rygg [1956] and DeWall [1957], who replaced the assembly of glass, steel, and ceramic parts of early bubble oxygenators with inexpensive plastic components and thereby paved the way for the industrial manu­facturing of disposable bubble oxygenators. As a result, reusable stationary film and disc oxygenators, which require careful cleaning and sterilization, slowly disappeared, and disposable bubble oxygenators dominated the field of extracorporeal gas exchange from 1960 to the early 1980s. The oxygenator and pumps designed during the pioneer phase of extracorporeal circulation are described in a book by Galletti and Brecher [1962].

In the 1970s, the bubble oxygenator was integrated with a heat exchanger (usually a stainless steel coil) and placed within a clean plastic container that also served as a venous reservoir with a capacity of several liters of blood. The level of blood-air interface allowed direct observation of changes of blood volume in the extracorporeal circuit. This simple design feature gave the equipment operator (who eventually became known as the perfusionist) plenty of time in which to react to a sudden blood loss and make compensating changes in operation.

Yet a number of problems occurred with bubble oxygenators because of their large blood-gas interface. If the blood foam did not coalesce completely, a gaseous microemboli could be carried into the arterialized bloodstream. Plasma proteins were denatured at the gas interface, leading to blood trauma associated with platelet activation and aggregation, complement activation, and hemolysis. These problems could be ameliorated by placement of a gas-permeable membrane between the blood and gas phases. The idea of using membranes permeable to respiratory gases in order to separate the blood phase from the gas phase in an artificial lung, and consequently avoid the risk of foaming or the formulation of thick blood rivulets inherent in bubble or film oxygenators, was stimulated after World War II by the growing availability of commercially produced thin plastic films for the packaging industry. The two major challenges for membrane oxygenators were, and indeed remain, that no synthetic membrane could be fabricated as thin as the pulmonary alveolar wall, and manifolding and blood distribution system could match the fluid dynamic efficiency of the pulmonary circulation, where a single feed vessel—the pulmo­nary artery—branches over a short distance and with minimal resistance to flow into millions of tiny gas exchange capillaries the size of an erythrocyte. Membrane oxygenators have progressively captured the largest share of the market for clinical gas exchange devices not only because their operation is less traumatic for blood but also because the blood content of the gas exchange unit is fixed, thereby limiting volume fluctuations to calibrated reservoirs and minimizing the risk of major shifts in intracorporeal blood volume during total body perfusion.

The interposition of a membrane between flowing gas and flowing blood reduces the gas transfer efficiency of the system as a consequence of the additional mass transfer resistances associated with the membrane itself and the geometry of the blood layer. The permeability of various polymeric materials to oxygen and carbon dioxide is summarized in Table 129.1. The very first plastic films used, such as thin sheets of polyethylene and polytetrafluoroethylene (PTFE), showed such a low diffusional perme­ability that 5-10 m2 were needed to meet even the minimal oxygen needs of an anesthetized hypothermic adult [Clowes et al., 1956]. The advent of silicone elastomer films (either as solid sheets or cast over a textile support mesh) in the 1960s established the technical feasibility of membrane oxygenators [Bramson et al., 1965; Galletti et al., 1966; Peirce et al., 1967]. Silicone rubber is about 140 times more permeable to oxygen and 230 times more permeable to CO2 than is PTFE for equivalent thickness. Even though silicone rubber and related elastomers cannot be cast as thin as PTFE, their permeability is so high that they became the standard material for early membrane oxygenator prototypes.

Extensive research was carried out in the 1960s and 1970s to develop improved membrane oxygenator designs with more efficient oxygen transport across the blood boundary layer. These designs are discussed later in this chapter. The clinical motivation was to provide continuous full or partial replacement of

Chemical Composition

Common Name

O2 Permeability cm3 (STP>mil min^m2^atm

CO2 Permeability O2 Permeability


5 □ 107



Silicone rubber










Natural rubber






Regenerated cellulose















Polyvinylidene chloride




Permeability is the product of the diffusion coefficient D and the Bunsen solubility coefficient □. The gas flux J [cm3(STP)/min^m2] across a membrane of thickness h with a partial pressure difference Dr is given by J = PDr/h.

Pulmonary gas exchanges for periods of weeks to patients with advanced respiratory failure, with the hope that in the interval the natural lung would recover. Since extensive blood trauma limited the use of blood oxygenators beyond 12-24 hours, membrane oxygenators became the key to this application. In the mid-1970s, an NIH-sponsored clinical study [Zapol, 1975] demonstrated that with the protocols used lung function was not regained after 1-3 weeks of extracorporeal circulatory with a membrane oxygenator. The major intended application of membrane oxygenators having vanished, and the high cost of silicone rubber making these devices much more expensive than bubble oxygenators, research and development almost came to a halt, leaving bubble oxygenators in control of the remaining field of use, namely cardiopulmonary bypass.

Two technical advances have over the following two decades reversed this trend: (1) the discovery that hydrophobic microporous membranes, through which gas can freely diffuse, have a high enough surface tension to prevent plasma filtration at the moderate pressures prevailing in the blood phase of an artificial lung; (2) the large-scale fabrication of defect-free hollow fibers of microporous polypropylene, which can be assembled in bundles, potted and manifolded at each extremity to form an artificial capillary bed of parallel blood pathways immersed in a cylindrical hard shell through which oxygen circulates.

Microporous hollow fiber membrane oxygenators now dominate the market. The most common embodiment of the hollow fiber membrane oxygenator features gas flow through the lumen of the fibers and blood flow in the interstices between fibers. This arrangement not only utilizes the larger outer surface area of the capillary tubes as gas transfer interface, instead of the luminal surface, it also promotes blood mixing in a manner which enhances oxygen transport, as will become apparent below.

Cardiopulmonary Bypass

Cardiopulmonary bypass (CPB), also called heart-lung bypass, allows the temporary replacement of the gas exchange function of the lungs and the blood-pumping function of the heart. As a result blood no longer flows through the heart and lungs, which then presents the surgeon with a bloodless operative field.

The terms pump-oxygenator and heart-lung machine graphically describe the equipment used. Car­diopulmonary bypass is the procedure. Open-heart surgery strictly speaking refers to interventions inside the heart cavities, which once provided the most frequent demand for cardiopulmonary bypass technol­ogy. By extension, the term is also applies to surgical procedures which take place primarily on the external aspects of the heart, such as creating new routes for blood to reach the distal coronary arteries from the aorta, e. g., coronary artery bypass grafting (CABG) or, popularly, bypass surgery. In these

129.1 Gas Exchange Systems 129.2 Cardiopulmonary Bypass 129.3 Artificial Lung Versus Natural Lung 129.4 Oxygen Transport 129.5 Co2 Transport 129.6 Coupling of O2 and CO2 Exchange 129.7 Shear-Induced Transport Augmentation and Devices for Improved Gas Transport Artificial Lungs and Blood-Gas Exchange Devices

FIGURE 129.1 Scheme of standard operating conditions during cardiopulmonary bypass.

Operations the cardiac cavities are temporarily vented (i. e., open to atmospheric pressure) to avoid the build-up of pressure which could damage the cardiac muscle.

As usually employed for cardiac surgery, the heart-lung machine is part of a total, venoarterial cardio­pulmonary bypass circuit, meaning that all the venous blood returning to the right heart cavities is collected in the extracorporeal circuit and circulated through the gas exchange device, from where it is pumped back into the arterial tree, thereby “bypassing” the heart cavities and the pulmonary circulation. On the blood side, this procedure usually involves hemodilution, some degree of hypothermia, nonpulsatile arterial perfusion at a flow rate near the resting cardiac output, and continuous recirculation of blood in an extracorporeal circuit in series with the systemic circulation of the patient. On the gas side, oxygen or an oxygen-enriched gas mixture (with or without a low concentration of CO2) flows from a moderately pressurized source in a continuous, nonrecycling manner and is vented to the room atmosphere.

CPB hinges on twin postulates: that blood circulation can be sustained by mechanical pumps while the heart is arrested and that venous blood can be artificially arterialized in an extracorporeal gas exchange device while blood flow is excluded from the lungs. Each of these claims was established separately through animal experimentation over the course of over 100 years (see Galletti and Brecher [1962]). Then surgeons and engineers combined the advances made by physiologists and pharmacologists and turned them, in the 1950s, into the basic tool of cardiac surgery. A recent update on the evolution of artificial membrane lungs for CPB surgery has been provided by Galletti [1993]. It is estimated that each year about 650,000 disposable membrane lungs are used in the operating room worldwide, with each gas exchange unit selling for a price in the range of $250-400, i. e., a market close to $2 billion.

Typical operating conditions for total cardiopulmonary bypass in an adult are summarized in Fig. 129.1 and Table 129.2. Most notable are the large differences in driving forces for 02 and CO2. An approximate comparison can be made using the inlet conditions. Thus, under normothermia and with pure oxygen fed to the gas phase, initial driving force is approximately 45 – 0 = 45 mmHg for CO2 and 760 – 47 = 713 mmHg for O2 yielding a ratio of CO2 to O2 driving forces of about 0.06. The ratio of CO2 to O2 permeability for silicone rubber is roughly 5 (Table 129.2), and the corresponding flux ration is 0.35, less than half of the metabolically determined respiratory quotient. Under these conditions, CO2 is the limiting

TABLE 129.2 Typical Operating Parameters for Cardiopulmonary Bypass in an Adult

Oxygen transfer requirement 250 mL/min

CO2 elimination requirement 200 mL/min

Respiratory gas exchange ratio (respiratory quotient) 0.8

Blood flow rate 5 L/min

Gas flow rate 5 -10 L/min

Gas partial pressures (in mmHg)

Blood in


= 40


= 45

Blood out


= 100 –

– 300


= 30

– 40

Gas in (humidified)


= 250 –

– 713


= 0 –


Gas out


= 150 –

– 675


= 10

– 30

Gas, and the device should be sized on the basis of CO2 transport rather than O2 transport requirements. This is why silicone rubber membranes have been replaced by microporous polypropylene membrane, where the solubility of CO2 in the membrane material, and consequently its permeability, is no longer the limiting factor. Indeed, with some modern membrane oxygenators, gas flow through the device may have to be controlled to avoid an excessive loss of CO2.

Artificial Lung Versus Natural Lung

Natural Lung


Must meet demand at rest and during exercise, fever, etc. Constant temperature process around 37°C

O2 and CO2 transfer are matched to achieve the respiratory quotient imposed by foodstuff metabolism (around 0.8) Continuous over a lifetime

Exchange surface area Wide transfer area (~ 70 m[7])

Highly permeable alveolar-capillary membrane

Short diffusion distances (1 -2 Dm)

Hydrophilic membrane No hemocompatibility problems Self-cleaning membrane

Gas side

To-and-fro ventilation Operates with air

Membrane structure sensitive to high oxygen partial pressure Pressure below that in blood phase to avoid capillary collapse Operates under water vapor saturation conditions Ventilation linked to perfusion by built-in control mechanisms

Can be used for gaseous anesthesia Blood side

Short capillaries (0.5 – 1 mm)

Narrow diameter (3 – 7 Dm)

Short exposure time (0.7s)

Low resistance to blood flow Sophisticated branching Minimal priming volume Capillary recruitment capability No recirculation Limited venous admixture No on-site blood mixing

Operates with normal hemoglobin concentration

Must meet demand at rest and under anesthesia Can be coupled with heat exchanger to lower body temperature.

O2 and CO2 transfer are largely independent of each other and must be controlled by the operator Usually limited to few hours

Limited transfer area (1 -3 m2)

Diffusion barriers in synthetic membrane and blood oxygenation boundary layer Relatively thick membranes (50 -100 Dm)

Hydrophobic polymers Hemocompatibility problems Protein build-up on membrane

Steady cross flow gas supply Operates with oxygen-rich mixture Membrane insensitive to high oxygen partial pressure Pressure below that on blood side to avoid bubble formation Can be clogged by water vapor condensation Ventilation dissociated from perfusion, with risks of hyper – or hypoventilation Can be used for gaseous anesthesia

Long blood path (10 -15 cm)

Thick blood film (150 -250 Dm)

Long exposure time (5 -15s)

Moderate to high resistance to blood flow Crude manifolding of entry and exit ports Moderate to large priming volume Fixed geometry of blood path Possibility of recirculation Risk of uneven perfusion of parallel beds Possibility of blood stirring and mixing Hemodilution is common

Does not require anticoagulation Requires anticoagulation How there requirements can be met in the light of the gas transport properties of blood and the characteristics of diffusional and convective transport in membrane lung devices.

Oxygen Transport

The starting point for analysis of O2 transport is the conservation of mass relation, which is derived from a material balance in a differential element within the flowing blood. By way of example, the relation commonly employed for oxygen transport of blood flowing in a tube is

^2□ d[bO2] ! □□ cR

V^Ј^+^ ^ = do2± (129.1)

^ dk □% 0 r dr ^ Dx ^

Where x is the axial coordinate, r is the radial coordinate, V is the velocity in the axial direction, DO2 is the effective diffusion coefficient of O2 in flowing blood, [O2] is the concentration of physically dissolved

O2, and [HbO2] is the concentration of O2 bound to hemoglobin. The terms on the left side of Eq. (129.1) represent convection in the axial direction of O2 in its two forms, dissolved in aqueous solution and bound to hemoglobin. The right-side term represents the diffusion of dissolved O2 in the radial direction.

By making the usual assumption that the concentration of dissolved O2 is linearly proportional to the O2 partial pressure p, [O2] = Dp, where □ is the Bunsen solubility coefficient, and by using the definition of oxyhemoglobin saturation: [HbO2] = CjS where CT is the oxygen-carrying capacity of hemoglobin (per unit volume of blood) and S is its fractional saturation, Eq. (129. 1) can be rewritten in a modified form

Dp Q C„ DS Q 1 □ □ dp Q

R4 □ —□ □ DO, □r (129.2)

Ck □ a Dp □ r Dr □ dk □

Which shows that the convective contribution is proportional to the slope of the saturation curve. Equation (129.2) must be solved subject to the appropriate initial and boundary conditions, which for a tube are

X □ 0, p □ p{ (129.3)

R □ 0, dp □ 0 (129.4)


R □ R, DDO2 dp □ PmKo □ p) (129.5)


Where pj and po are the oxygen partial pressures in the inlet blood and in the gas, respectively, and Pm is the membrane permeability for O2 diffusion, defined so as to include the membrane thickness. These conditions represent, in order, a uniform inlet concentration, symmetry about the tube axis, and the requirement that the O2 diffuison flux at the blood-membrane interface be equal to the O2 diffusion flux through the membrane.

Implicit in the derivation of Eq. (129.2) are two important assumptions. The first is that, on a macroscopic scale, blood can be treated as a homogenous continuum, even though as a suspension of red blood cells in plasma, blood is microscopically heterogeneous. This simplification is acceptable as long as the volume element in which oxygen transport occurs is large compared to the size of a single

Red cell but small compared to the size of the overall diffusion path. This seems reasonable when applied to transport in membrane lungs, where the blood diffusion path thickness is usually equivalent to 20-30 red cell diameters or more.

The second important assumption is that the rate of reaction between O2 and hemoglobin is sufficiently fast, when compared to the rate of diffusion of O2 within the red cell, that the reaction can be considered at equilibrium, with the concentration of hemoglobin-bound O2 in the red blood cells directly related to the concentration of dissolved O2 in plasma via the oxyhemoglobin dissociation curve (ODC). Implicit in the use of this relationship is the assumption that the O2 diffusion resistance of the red cell membrane is insignificant.

The human ODC for normal physiologic conditions is shifted to the right by increased temperature or decreased pH because of decreased hemoglobin affinity for O2. The ODC is shifted to the right by an increase in the concentration of various organic phosphates, especially 2,3-diphosphoglycerate (DPG).

Under typical venous physiologic conditions (37°C, boundary O2 partial pressures of 40 and 95 mmHg), the reaction between hemoglobin and oxygen reaches equilibrium during the time of contact between the blood and the gas phase. The ratio of the effective permeability of blood to that of plasma in a model system is 0.87 at the hematocrit of 45%; without any facilitation within the red cell, the ratio would be 0.75. Using the most reliable data for the O2 solubility and diffusion coefficient in plasma leads to an estimate of 1.7 □ 10-5 cm2/s for the effective diffusion coefficient of O2 in normal whole blood.

We can now return to the analysis of convective transport of oxygen in a membrane lung, specifically the solution of Eq. (129.2) or its equivalent for other geometrics, on the assumption of equilibrium for the hemoglobin oxygenation reaction in such devices. The various theoretical analyses that have been carried out differ primarily in the means by which the saturation curve is handled. The most common approach is to retain its intrinsic nonlinearity and to approximate it by a suitable analytical expression. The resulting nonlinear partial differential equation does not permit analytical solution, and it is therefore necessary to resort to numerical solution with a finite difference scheme on a digital computer. This approach yields numerical values for p and S as a function of x and r. To relate theoretical prediction with experimental measurement, one must calculate the velocity-weighted bulk average values of p and S [Colton, 1976]. The average O2 partial pressure, p, and oxyhemoglobin saturation, S, that would be measured if the blood issuing from the tube were physically mixed are then calculated from

I □ R R □

^ |~~|Vpr dr □ CTVSr drnnnp □ CTS (129.6)


Vr dr

Numerical solutions provide accurate predictions. However, they apply only to specific operating conditions and cannot be generalized for design purposes. Two methods have been used to simplify the ODC and provide approximate yet useful analytical solutions.

The first is known as the advancing front theory [Marx et al., 1960; Thews, 1957]. The oxyhemoglobin saturation curve is approximated as a step function between the saturation values corresponding to the O2 partial pressure and that of the gas phase or the blood-membrane interface. The blood is treated as two regions of uniform oxyhemoglobin saturation separated by a front that moves rapidly inward. Outside the front, blood is saturated at a value corresponding to the blood-gas or blood-membrane interface, and the rest of the blood is relatively unsaturated. Oxygen diffuses through the saturated blood to the interface, where it reacts with unsaturated hemoglobin. The advancing front approximation reasonably represents the calculated saturation profiles and has proved useful in developing analytical design expres­sions for membrane lungs in terms of saturation changes effected. However, it can be in error by a very wide margin for the prediction of O2 partial pressure changes. A modification of advancing front theory, involving approximation of the partial pressure changes. A modification of advancing front theory, involving approximation of the ODC by several straight line segments, retains the ability to provide an analytical solution and gives better accuracy than the conventional step function approximation of the ODC.

The second type of simplification is to approximate the ODC by a straight line drawn between the inlet and boundary O2 partial pressures, which make QS/dp, the slope of the saturation curve constant and renders Eq. (129.2) linear. Use can then be made of existing solutions for analogous convective heat and mass transfer problems without chemical reaction.

For typical operating conditions in the clinic, the initial and boundary O2 partial pressures lie on the upper portion of the ODC, and the advancing front solution provides an overestimation of the rate of O2 transport, whereas the constant slope solution provides an underestimate. Conversely, on the lower portion of the ODC at very low O2 partial pressures, the advancing front estimate of O2 transport rate is too low and constant slope too high. The constant slope approximation is most accurate over the steep portion of the saturation cure, where it is nearly linear. Since the O2 transport rate per unit membrane surface area is much more sensitive to blood inlet O2 partial pressure than would be expected solely from the change in the overall driving force, comparative testing of membrane lungs must be carried out with identical inlet blood O2 partial pressure and oxyhemoglobin saturation.

Theoretical prediction of membrane lung performance is useful for design purposes and for providing a guide to the effect of permissive design variables. However, theoretical prediction cannot substitute for experimental data under closely controlled conditions where control of pH, temperature, and CO2 partial pressure in fresh blood allow the definition of the appropriate ODC.

CO2 Transport

The CO2 dissociation curve for normal human blood is far more linear in its normal operating range than the ODC. The fractional volume of CO2 that is removed in the process of arterialization of venous blood is also considerably less than the corresponding fractional loss of oxygen (about 10 percent of blood Co2 content, versus 25 percent for oxygen). As is the case for oxygen, the total CO2 concentration is far larger than that of gas physically dissolved in the aqueous component of blood. Plasma accounts for about two-thirds of all the CO2 carried in blood, whereas typically about 98% of O2 is carried in the red cells.

The main vehicles for CO2 transport in blood are bicarbonate, the primary carrier in both plasma and red cells, and carbamino hemoglobin, where CO2 is combined with the amino groups of hemoglobin (Fig. 129.2a). Arrows on Fig. 129.2b inDicate the direction and relative rate of each reaction whereby CO2 is removed in a membrane lung. Carbonate and hydrogen ions form bicarbonate, which decomposes to CO2 or combines with another hydrogen ion to form carbonic acid; the latter is dehydrated to liberate CO2. Since the reactions that form CO2 in plasma are very slow, biocarbonate is the predominant species. Biocarbonate can diffuse into the red cell, albeit slowly, in exchange for chloride, leading to the same chain of reactions. In the red cell, however, dehydration of carbonic acids is catalyzed by the enzyme carbonic anhydrase. This reaction liberates CO2, which, in turn, diffuses out of the red cell into the plasma and then across the blood-membrane interface. Decomposition of carbamino hemoglobin is a significant additional source of CO2. Carbamate compounds that arise from combination of CO2 with plasma proteins have a much smaller effect because of the relatively unfavorable equilibria for their formation. Finally, various ionic species, such as organic and inorganic phosphates, amino acids, and proteins, behave as weak acids at pH 7.4. The buffering power of hemoglobin is particularly strong and has a marked effect in influencing the shape of the CO2 dissociation curve.

Under clinical conditions of O2 and CO2 countertransport, two reciprocal phenomena occur which affect CO2 and O2 exchange. A decrease of CO2 partial pressure causes a shift to the left of the oxyhe­moglobin dissociation curve, leading to an increased affinity of hemoglobin when CO2 is removed (Bohr effect). Meanwhile, because oxyhemoglobin is a stronger acid than hemoglobin, uptake of O2 decreases the affinity of hemoglobin for CO2, thereby releasing additional CO2 from carbamino hemoglobin (Haldane effect). At the same time, increased acidity favors the conversion of more biocarbonate into carbonic acid, which then dissociates, releasing CO2. The simultaneous occurrence of these two effects enhances transport rates of both gases.

129.1 Gas Exchange Systems 129.2 Cardiopulmonary Bypass 129.3 Artificial Lung Versus Natural Lung 129.4 Oxygen Transport 129.5 Co2 Transport 129.6 Coupling of O2 and CO2 Exchange 129.7 Shear-Induced Transport Augmentation and Devices for Improved Gas Transport Artificial Lungs and Blood-Gas Exchange Devices

FIGURE 129.2a Schematic representation of CO2 transfer from the red blood cell to plasma and into alveolar gas, emphasizing the various buffer systems involved.

CO2 transport form

Mixed venous blood mM/L %

Arterial blood mM/L «

Veno-arterial difference mM/L «

Bicarbonate plasma














Dissolved CO2 plasma














Caibamino CO? plasma













Total in whole blood







FIGURE 129.2b Blood CO2 content. CO2 transport forms in mixed venous and arterial blood, and as components of the veno-arterial CO2 difference. Observe that the red blood cells (RBC) bicarbonate content, although it represents a large fraction of CO2 transport, does not contribute significantly to the arteriovenous difference in CO2 content. Conversely hemoglobin-bound CO2, though less abundant than bicarbonate in red blood cells, constitutes a larger fraction of the veno-arterial difference.

If the entire reaction scheme in Fig. 129.2 is assumed to be at equilibrium, the CO2 dissociation curve can be used to relate the total blood concentration of CO2 (in all forms) to the CO2 partial pressure. The CO2 dissociation curve can be linearized in the same manner as the constant slope approximation for O2 transport described above. A relation similar to Eq. (129.2) results, except that p refers to the CO2 partial pressure, and the term (CT/a) (QS/Qp) is replaced by the derivative of the total CO2 concentration with respect to the concentration of dissolved CO2. The equation is now linear, and the same simplifi­cations hold as for the O2 problem with a constant slope approximation. The membrane-limited case becomes particularly simple, and the membrane lung can be treated as simple mass or heat exchanger with a constant transport coefficient. This approach has been successfully used to correlate experimental data.

Coupling of O2 and CO2 Exchange

In the conceptual representation oF Fig. 129.3 [C Olton, 1976], the ratio of the CO2 transport rates is plotted against an index of the blood-side mass transfer efficiency divided by the membrane permeability on a logarithmic scale. With a constant slope approximation for both O2 and CO2 transport, a unique curve is obtained for a specific membrane lung design if the abscissa is taken to be the ratio of the blood-side log – mean average CO2 mass transfer coefficient divided by the CO2 membrane permeability, and the curve is parameterized by unique values of three dimensionless quantities: (1) the ratio of the membrane perme­abilities for O2 and CO2, (2) the ratio of the average blood-side transfer coefficients for O2 and CO2, and (3) the ratio of the log-mean average O2 and CO2 partial pressure driving force. The asymptotic limits plotted are very approximate characteristic values of a capillary or flat plate (sandwich) gas exchange device in which the limiting factor is either the blood mass transfer boundary layer or the membrane itself.

When transport of both O2 and CO2 is blood phase-limited—that is a relatively low blood-side mass transfer coefficient or high membrane permeability—the CO2 transport rate is higher than the O2 rate, and it is necessary to add CO2 to the inlet gas or to decrease gas flow rate to prevent excessive CO2 removal. At the other extreme, if gas transport in membrane limited, the ratio of CO2 to O2 transport is always lower than the physiological value (0.8), because no existing gas-permeable membrane has a sufficiently high CO2/O2 permeability ratio to overcome the unfavorable driving force ratio of the O2 and CO2 partial pressures (14:1) under the actual operating conditions of a membrane lung. Under either limiting condition, it is necessary to design the membrane lung on the basis of the gas that limits transport,

O2, for blood-limited conditions and CO2 for membrane-limited conditions.

Blood Limited

129.1 Gas Exchange Systems 129.2 Cardiopulmonary Bypass 129.3 Artificial Lung Versus Natural Lung 129.4 Oxygen Transport 129.5 Co2 Transport 129.6 Coupling of O2 and CO2 Exchange 129.7 Shear-Induced Transport Augmentation and Devices for Improved Gas Transport Artificial Lungs and Blood-Gas Exchange Devices

Desired Ratio


Membrane Limited


129.1 Gas Exchange Systems 129.2 Cardiopulmonary Bypass 129.3 Artificial Lung Versus Natural Lung 129.4 Oxygen Transport 129.5 Co2 Transport 129.6 Coupling of O2 and CO2 Exchange 129.7 Shear-Induced Transport Augmentation and Devices for Improved Gas Transport Artificial Lungs and Blood-Gas Exchange Devices


подпись: 0


подпись: 0Blood-Side Mass Transfer Efficiency

Membrane Permeability

FIGURE 129.3 Relative CO2 and O2 transport in a membrane lung.

A priori, it seems undesirable to operate under blood-limited conditions because full advantage is not taken of the membrane permeability. Therefore, an increase in the blood-side mass transfer efficiency is valuable, but only to the point where the ratio of CO2 to O2 transport rates is equal to the respiratory quotient. Beyond that point, further improvements in design will not reduce the size of the device required unless membrane permeability to CO2 is increased, thereby moving the operating point on the curve to the left and justifying the use of a more efficient exchange device. For example, conventional solid silicone rubber membranes cannot take advantage of high-efficiency designs because gas transport is membrane limited and has to be designed on the basis of CO2 transport rate. To make effective use of the most effective devices, it is necessary to employ microporous membranes or ultrathin membranes on microporous substrates where the CO2 permeability is no longer a limiting factor.

Shear-Induced Transport Augmentation and Devices for Improved Gas Transport

There is evidence that flow-dependent properties of blood can substantially influence the transport of O2 and CO2. The presence of velocity gradient in a stream can enhance mass transfer through blood either by shear-induced collision diffusion wherein interactions between red blood cells produce net lateral displacements and associated motions in the surrounding phase or by rotation of individual cells, which gives rise to local mechanical stirring of the adjacent fluid. Both mechanisms can lead to transport augmentation of species present in the dispersed or continuous phases. Only the first mechanism can cause dispersive migration of the particles themselves, and available evidence suggests that it is the dominant factor [Cha & Bessinger, 1994]. The shear-induced diffusion coefficient of particles in suspen­sion increases linearly with the shear rate and can be orders-of-magnitude larger than the Brownian motion diffusivity. The effect of lateral cell movement in oxygen transport in capillary tubes depends on both the shear rate and the slope of the ODC, with a maximum at the steepest portion of the curve, i. e., below the operating range of a clinical oxygenator. The extent to which such phenomena occur in blood under the clinical operating conditions of membrane lungs in cardiopulmonary bypass has not been investigated, but the effect on oxygen transport is thought to be significant.

The earliest oxygenator configurations featuring rubber membranes made the blood flow in simple enclosed geometries, such as a flat plate or hollow fiber, that were inherently inefficient from a mass transfer standpoint. It was soon recognized that the gas transport rate was limited almost entirely by transport within the blood oxygenation boundary layer. There followed extensive efforts in the 1960s and early 1970s to investigate new approaches for improving gas transfer in membrane oxygenators, as summarized in Table 129.4. These approaches relied on one or more mechanisms: (1) increasing shear rate or producing turbulence; (2) keeping the oxygenation boundary layer very thin by using an appro­priate contacting geometry or pulsatile blood flow; and (3) making use of secondary flow, which incor­porates significant velocity components normal to the membrane surface. All these approaches are demonstrably effective under laboratory conditions, but few have achieved successful commercialization because of the constraints imposed by the geometry of available membrane materials (flat sheets and capillary tubes) and the clinical demand for simple, reliable, and inexpensive devices.

In Table 129.4, pAssive designs for inducing secondary flows are those for which no energy source is needed except that required for steady blood flow. A common technique has been to place obstacles, for

TABLE 129.4 Approaches for Improving Mass Transport in Membrane Oxygenators

Passive designs

Active designs

Obstacles in blood path

Oscillating toroidal chamber

Membrane undulations from external supports

Enclosed rotating disc

Membrane texturing or embossing

Pulsed flow vortex shedding

Helical flow systems

Couette flow

External blood flow over hollow fibers

Annulus, inner cylinder rotating axial flow, tangential flow.

Example screens, in the blood path to induce secondary fluid movements and/or flow separation on a small scale and thereby increase blood mixing in flat plate devices. A similar result has been obtained by creating undulations in a flat membrane with grooved or multiple point supports or by using textured membranes to direct blood flow through the exchanger.

Active signs are those in which there is energy input to achieve high shear rates or create secondary flows. Highly efficient oxygenator prototypes have been described, and at least two, the enclosed rotating disc and a pulsed-flow vortex shedding device, have been commercialized, but neither has achieved widespread clinical acceptance, in part because of the complexity or cumbersomeness of their operating mechanisms in an operating room setting.

Another widely investigated approach has been to use flow geometries that naturally induce secondary flow, for example helical coils, where, superimposed on the primary flow, is a swirling motion in each half of the tube. The secondary flow trajectory which results from centrifugal effects takes particles from the periphery and carries them into the core, back to the periphery, back to the core in a continuously repeated fashion. Such secondary motion, by continuously sweeping oxygenated blood away from the membrane and replacing it with venous blood from the central core of the channel, can be extremely effective in increasing gas transport rates to the point where the dominant resistance to diffusion lies in the membrane. However, the practical difficulty of constructing such complex devices which are also disposable has thus far prevented industrial development.

When the potential market for continuous extracorporeal membrane oxygenation collapsed, so did the intensive research and development effort in developing new devices. However, three developments, two technical and one marketing-related, over the next decade eventually led to dominance of membrane oxygenators for cardiopulmonary bypass.

The first major technical advance was the fabrication of hydrophobic microporous capillary hollow fiber membranes at prices considerably lower than for silicon rubber membranes. The driving force for the initial development of these materials was their potential in another technology, membrane plasma­pheresis for the separation of plasma from the cellular components of blood. Hollow fibers for the application had nominal pore sizes, around 0.5 Dm, which were too large for membrane oxygenation because plasma could seep through the fiber wall under pressure leading to a catastrophic decrease in membrane permeability (129.1). In the early 1980s, microporous polypropylene hollow fibers with a nominal pore size around 0.1 Dm became available and proved satisfactory for membrane oxygenation. In addition to reduced trauma and competitive pricing with bubble oxygenators, membrane lungs could be employed with a reduced, fixed blood-priming volume, thereby minimizing transfusion and hemodi – lution problems. Surprisingly, this advantage was initially viewed as a drawback by perfusionists who were used to having a large venous blood reservoir with a visible gas-blood interface.

The key marketing development of the mid-1980s was to make a membrane oxygenator by attaching it, along with a heat exchanger, to a clear plastic venous reservoir with a visible gas-blood interface. The astute move was breakthrough which put membrane oxygenators into the operating room. Their clear advantage in minimizing blood trauma and postoperative complications was so overwhelming that within a year membrane oxygenators captured the dominant market share. Shortly thereafter, bubble oxygen­ators were virtually eliminated from the U. S. marketplace.

The most recent technical development has been the inversion of the usual internal flow arrangement so that, now, gas flows through the lumen of the hollow fibers while blood is pumped over the external surface of the capillary membrane. This arrangement is most effective when the blood flow is at right angles to the hollow fiber. In that configuration the flowing blood successively encounters different fibers, and a new oxygenation boundary layer forms on each fiber. Because the boundary layer is thinnest where it begins (in this case, at the front of each fiber), and the mass transfer rate is correspondingly highest, the transport of oxygen averaged over the periphery of each fiber is much higher than with the conven­tional internal (luminal) flow of blood. Thus the transport of oxygen averaged over the periphery of each fiber is much higher than with the conventional internal (luminal) flow of blood. The performance of various membrane oxygenators is compared in Table 129.5. The data clearly demonstrate the superior performance attainable with microporous hollow fibers operated with external crossflow of blood.

TABLE 129.5 Comparison of Membrane Oxygenator Performance (Blood flow rate = gas flow rate = 51/min; AAMI conditions)


Membrane Form

Blood Path Configuration

O2, Flux cm3(STP)/min-m3

CO2/O2 Flux Ratio

Silicone Rubber Sci Med SM35


Spiral coil embedded failure



Microporous polypropylene Cobe CMI


Flat plate



Shiley M-2000


Blood screens



Bentley Bos CM-40

Hollow fiber

Internal flow



Terumo Capiox II 43

Hollow fiber

Internal flow



Bard William Harvey 4000

Hollow fiber

External cross flow



Johnson & Johnson Maxima

Hollow fiber

External cross flow




Hollow fiber

External cross flow



Bentely Univox

Hollow fiber

External cross flow



The state of the art is now fairly advanced for membrane blood oxygenators, but there is still room for improvement. Further increases in flux would further reduce cost and minimize priming volume and blood consumption. Now that membrane oxygenators are fully entrenched, it is more likely that the reduced priming volume and improved control of a closed system can be realized. Lastly, the residual gas-blood interface that still exists at the microporous membrane surface could be eliminated by coating with a very thin skin in a n asymmetric or composite structure.

Defining Terms

Advancing front theory: A type of exchanger theory addressing the limitation of oxygen transport in

A blood film through a fully saturated boundary layer leading to a front where the hemoglobin in flowing blood reacts with the dissolved oxygen.

Arterialization: A gas exchange process whereby oxygen and carbon dioxide concentrations in venous

Blood are changed to levels characteristic of arterial blood.

Artificial lung: A device which allows for continuous exchange for oxygen and carbon dioxide between

Circulating blood and a controlled gas atmosphere.

Blood oxygenator: Synonymous with artificial lung, with the accent placed on oxygen transport, which

Is the most critical aspect of natural lung replacement, since the body oxygen reserves are very limited. Depending upon the physical process used for blood-gas transfer, artificial lungs are clas­sified as bubble oxygenators, stationary or rotating film oxygenators, and membrane oxygenators. Boundary layer: The film of blood adjacent to a permeable membrane, which, by reason of local fluid

Dynamics, is not renewed at the same rate as blood in the core of the flow path, thereby creating an additional diffusion barrier between the blood and the gas phase.

Bubble oxygenator: Blood-gas transfer device in which a large exchange surface is obtained by the

Dispersion of oxygen bubbles in a venous blood stream, followed by coalescence of the foam and venting of excess gas (cocurrent blood and gas flow) or by spreading of venous blood over a continuously renewed column of foam generated by bubbling oxygen at the bottom of a reservoir (countercurrent blood and gas flow).

Bypass: Derivation or rerouting of blood around an organ or body part, to diminish its blood supply,

To abolish local circulation for the duration of a surgical intervention, or to increase blood flow permanently beyond an obstruction. The qualifier used with the word bypass designates the organ so isolated (e. g., left ventricular bypass, coronary artery bypass).

Cardiopulmonary bypass (CPB): A procedure whereby blood is prevented from circulating through

The heart cavities and the lungs. Cardiopulmonary bypass (also known as heart-lung bypass) can be partial if no obstacle is placed on venous return to the right heart cavities and consequently some of the blood continues to flow through the pulmonary circulation. In that case the arterial system is fed in part by left ventricular output and in part by the arterialized blood perfusion from the hear-lung machine. The balance between the internal and extracorporeal blood circuits depends on the setting of the pumps and the relative resistance to flow in the two venous drainage pathways. During total cardiopulmonary bypass, the cardiac muscle must receive arterial blood from the extracorporeal circuit (intermittently or continuously) to prevent hypoxic myocardial damage. Since coronary venous blood drains into the cardiac cavities, this blood must be drained to the outside to prevent an intracavitary pressure increase which could be damaging to the heart.

Catheter: A long hollow cylinder designed to be introduced in a body canal to infuse or withdraw

Materials into or out of the body.

Coronary artery bypass graft (CABG): The construction of new blood conduits between the aorta (or

Other major arteries) and segments of coronary arteries beyond lesions which partially or totally obstruct the lumen of those vessels, for the purpose of providing an increased blood supply to regions of the myocardium made ischemic by those lesions.

Extracorporeal circulation: Artificial maintenance of blood circulation by means of pumps located

Outside of the body, with blood fed through catheters advanced in an appropriate blood vessel and returning the blood to another blood vessel.

Film oxygenator: Blood-gas transfer device in which a large exchange surface is obtained by spreading

Venous blood in a thin film over a stationary or moving physical support in an oxygen-rich atmosphere.

Heart-lung bypass: Synonymous with cardiopulmonary bypass.

Heart-lung machine: A mechanical system capable of pumping venous blood around the heart and

The lungs and arterializing it in an appropriate gas exchange unit.

Hemodilution: Temporary reduction in blood erythrocyte concentration (and consequently hemoglo­

Bin content, hematocrit, oxygen-carrying capacity, and viscosity) resulting from mixing with the erythrocyte-free or erythrocyte-poor content of the liquid used to prime an extracorporeal circuit.

Hemolysis: The destruction of red blood cells with liberation of hemoglobin in surrounding plasma,

Caused by mechanical damage of the erythrocyte membrane, osmotic imbalance between intra- corpuscular and extracorpuscular ion concentration, or uncontrolled freezing-thawing cycles.

Hollow fiber: A capillary tube of polymeric material produced by spinning a melted or dissolved

Polymer through an annular orifice.

Membrane: A solid or liquid phase which acts as a barrier to prevent coalescence of neighboring

Compartments while allowing restricted or regulated passage of one or more molecular species.

Membrane lung or Membrane oxygenator: Blood-gas transfer device in which the blood compartment

Is shielded from the gas phase by a porous or solid, hydrophobic polymer membrane permeable to gases but not to liquids (in particular, blood plasma).

Metabolism: The sum of the chemical reactions occurring within a living body including build up

(anabolism) and break down (catabolism) of chemical substances.

Open heart surgery: Interventions taking place inside the cardiac cavities, such as for the replacement

Or reconstruction of cardiac valves, or the closure of abnormal communications between cardiac chambers, and which for reasons of convenience and safety, require the interruption of blood flow through the heart. By extension this stem is often used for cardiac interventions under total cardiopulmonary bypass, which address structures on the outside surface of the heart (such as coronary arteries) when drainage of the cardiac cavities through a vent is needed to avoid accu­mulation of coronary venous blood.

Oxygenation boundary layer: Stationary or slowly moving blood layer adjacent to a gas-permeable

Membrane, which progressively develops along the blood path and, once enriched with oxygen diffusion through the membrane, effectively becomes a barrier to oxygen transport perpendicular to the direction of flow.

Perfusion: A technique for keeping an organ or body part alive, though severed from its normal blood

Circulation, by introducing blood under pressure into the appropriate feeder artery.

Perfusionist: The operator of the heart-lung machine during cardiac surgery or respiratory assist


Priming volume: The volume of liquid (blood, plasma, synthetic plasma expanders, or electrolyte

Solutions) needed to fill all components of an extracoporeal circuit (oxygenator, heat exchanger, blood pumps, filter, tubing, and catheters) so as to avoid exsanguination once the intracorporeal and extracorporeal circulation systems are joined.

Pump-oxygenator: Equipment used to circulate blood through an extracorporeal circuit by means of

Mechanical blood pumps and to arterialize mixed venous blood by means of a gas exchange device. In most embodiments, the pump-oxygenator also serves to control blood temperature by means of a heat exchanger, typically incorporated in the gas exchange device. Synonymous with heart – lung machine.

Respiratory quotient: The ratio of carbon dioxide produced by tissues or eliminated by the lungs to

Oxygen consumed by tissues or taken in through the lungs.

Secondary flow: Any type of fluid motion, steady or periodic, in which the fluid is moving in a direction

Different from that of the primary flow. Secondary flow systems may be continuous in distribution, occupying the entire flow path, or comprise local elements that produce periodic remixing of the fluid.

Total body perfusion: Maintenance of blood circulation through the arterial and venous system by

Means of a positive displacement pump introducing blood into an artery under pressure and collecting it from a vein for continuous recirculation.


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DeWall RA, Lillelei CW, Vareo RL, et al. 1957. The helix reservoir pump-oxygenator. Surg Gyn Obstet 104:699.

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Further Information

Over the years, a number of books and monographs have reviewed the scientific and technical literature on gas exchange devices and their application. These include J. G. Allen, ed., Extracorporeal Circulation, Thomas, Springfield, 1958; P. M. Galletti and G. A. Brecher, Heart-Lung Bypass, Principles and Techniques of Extracorporeal Circulation, Grune and Stratton, New York, 1962; D. Hershey, ed., Blood Oxygenation, Plenum, New York, 1970; R. H. Bartlett, P. A. Drinker and P. M. Galletti, eds., Mechanical Devices for Cardiopulmonary Assistance, Karger, Basel, 1971; W. M. Zapol and J. Qvist, eds., Artificial Lungs for Acute Respiratory Failure. Theory and Practice. Academic Press, New York, 1976; G. G. Dawids and H. G. Engell, Physiological and Clinical Aspects of Oxygenator Design, Elsevier, Amsterdam, 1967; S. Hagl, W. P. Klцvekorn, N. Mayr, and F. Sebening, Thirty Years of Extracorporeal Circulation, Deutsches Herzzentrum,

Munich, 1984; P. A. Casthely and D. Bregman, Cardiopulmonary Bypass: Physiology, Related Complications and Pharmacology, Futura, Mount Kisco, N. Y., 1991.

Topical advances in artificial lungs are typically published in the Transactions of the American Society for Artificial Internal Organs or in journals such s the ASAIO Journal, the International Journal of Artificial Organs, the Japanese of Artificial Organs, and the Journal of Thoracic and Cardiovascular Surgery, as well as the Proceedings of the American Institute for Chemical Engineering and, occasionally, Chemically Engi­neering Symposium Series.

Galletti, P. M., Colton, C. K., Lysaght, M. J. “Artificial Kidney.” The Biomedical Engineering Handbook: Second Edition.

Ed. Joseph D. Bronzino

Boca Raton: CRC Press LLC, 2000

Algorithmic analysis

It is frequently important to know how much of a particular resource (such as time or storage) is required for a given algorithm. Methods have been developed for the analysis of algorithms to obtain such quantitative answers; for example, the algorithm above has a time requirement of O(n), using the big O notation with n as the length of the list. At all times the algorithm only needs to remember two values: the largest number found so far, and its current position in the input list. Therefore it is said to have a space requirement of O(1), if the space required to store the input numbers is not counted, or O(n) if it is counted.

Different algorithms may complete the same task with a different set of instructions in less or more time, space, or ‘effort’ than others. For example, a binary search algorithm will usually outperform a brute force sequential search when used for table lookups on sorted lists.

Abstract versus empirical

The analysis and study of algorithms is a discipline of computer science, and is often practiced abstractly without the use of a specific programming language or implementation. In this sense, algorithm analysis resembles other mathematical disciplines in that it focuses on the underlying properties of the algorithm and not on the specifics of any particular implementation. Usually pseudocode is used for analysis as it is the simplest and most general representation. However, ultimately, most algorithms are usually implemented on particular hardware / software platforms and their algorithmic efficiency is eventually put to the test using real code.

Empirical testing is useful because it may uncover unexpected interactions that affect performance. For instance an algorithm that has no locality of reference may have much poorer performance than predicted because it thrashes the cache.