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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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

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