Monthly Archives: February 2014


The application of engineering principles and technology to medicine and biology has had an increasing influence on the practice of medicine. The most visible of these contributions is in the form of medical devices. This article, however, de­scribes the engineering introduction of quantitative methods in the field of bioelectricity. When such contributions first be­came evident, in the early 1950s many physiology researchers were already employing modern quantitative methods to de­velop and utilize governing equations and suitable models of bioelectric phenomena. Today it appears that systems physi­ology lives on as biomedical engineering, while physiology has become more concerned with cell and molecular biology. On the other hand, biomedical engineering is also currently in­volved in efforts to develop and apply quantitative approaches at cellular and molecular levels.

This article, which is concerned with the electric behavior of tissues, reviews what is known about the biophysics of ex­citable membranes and the volume conductor in which they are imbedded. Our approach emphasizes the quantitative na­ture of physical models. We formulate an engineering descrip­tion of sources associated with the propagating action poten­tial and other excitable cellular phenomena. With such sources and a mathematical description of fields generated in a volume conductor the forward problem, namely a determi-


The main mammalian tissues that are electrically excitable are nerves and muscles. Although such cells vary greatly in size, shape, and electrical properties, there are nevertheless certain fundamental similarities. In order to illustrate their different cellular structures, we introduce excitable cell histol­ogy in this section, although it is somewhat ancillary to the general goals of this article, and it is very brief; the interested reader may consult one of the references for more detailed information. Some additional material will also be found later in this article in the section on “Applications.”

Nerve. A sketch of a typical neuron is given in Fig. 1(a), and contains dendrites, the cell body, and an axon. All ele­ments are enclosed by a membrane (which separates the in­tracellular from the extracellular space) and are electrically excitable. However the axon shown is myelinated, that is, its membrane is surrounded by an insulating sheath except at periodic nodes of Ranvier (to which any possible transmem­brane current is restricted). We are particularly interested in axonal propagation and the accompanying current flow fields. The diameter of nerve fibers varies from 0.3 to 20 ^m, (the very small fibers are unmyelinated), and a propagation veloc­ity of 0.5 to 120 m/sec (higher for larger diameters) is ob­served. One of the main effects of myelination is an increase in propagation velocity for the same fiber diameter. The length of an axon can vary from micrometers (cells in the cor­tex) to meters (motoneurons from the spinal cord to extrem­ities).

Skeletal Muscle. A description of skeletal muscle structure is given in Fig. 1(b). The whole muscle is shown subdivided into fascicles, each of which contains many fibers. An individ­ual fiber contains myofibrils, which constitute the contractile machinery of the muscle. The membrane surrounding each fiber is excitable. Axial propagation of an electrical impulse can take place over this membrane, just as for the nerve axon. However the muscle fiber has a transverse structure namely the T system, which is also excitable and which conducts the electrical impulse from the surface radially inward, where it activates the sarcoplasmic reticulum (SR); this, in turn, initi­ates excitation-contraction of the muscle. Because it is unmy­elinated, propagation velocity is not as great as for nerve fi-




Figure 1. (a) A motor-neuron is shown with typical structure including dendrites, cell body, and axon. Activation of the cell body arises from the summa­tion of excitatory inputs from the dendrites. A propa­gating impulse travels out on the axon to terminal buttons (neuromuscular junctions) at which the im­pulse is conducted to a target muscle. The axon shows Schwann cells that provide the myelin sheath, which effectively insulates the axon except at the nodes of Ranvier. From W. F. Ganong Medical Physiology, Los Altos, CA: Lange Medical Pub, 1971. (b) The arrangement of fibers in a whole muscle and the myofibrils contained in each fiber. The excitable plasma membrane surrounds each fiber, and the contractile machinery is responsible for the cross – striations seen in each fibril.

When skeletal muscle is viewed under the microscope, characteristic cross-striations are seen. This arises from the arrangement of thin and thick filaments, components of the myofibrils; interaction of the filaments is the basis for the de­velopment of contractile force.

Cardiac Muscle. The cardiac muscle fiber looks superficially like that of the skeletal muscle fiber containing, in particular, similar contractile proteins (the T system location differs from that of skeletal muscle) and show the same striation pattern. Cardiac cells, however, do not comprise long fibers, as in skel­etal muscle. A typical cardiac cell length is only 100 ^m. How­ever cardiac cells are interconnected by gap junctions, which are sites through which ions and hence electric activity may easily pass. Consequently cardiac muscle propagation can take place throughout cardiac tissue as if, functionally, cell membranes were contiguous (syncytial).

Smooth Muscle.

Smooth muscle differs from skeletal and cardiac muscle in that it does not exhibit cross-striations. It also has a poorly developed SR. There are thick and thin con­tractile filaments, however their structure is irregular, which accounts for the absence of a banded appearance. Smooth muscle cells range in size from 2 to 10 ^m diameter and 20­600 jU, m length. Individual cells are joined together mechani­cally by attachment plaques and, often, electrically via gap junctions. This structural arrangement is similar to that found in cardiac muscle. The gap junctions are of low electric resistance and contribute intercellular coupling, which acts to synchronize electrical activity of adjoining cells.

Excitable Cells—Membrane Structure

The simplest electrophysiologic model is that of a single excit­able cell lying in an unbounded uniform conducting medium. If we imagine the cell to have been activated, then action cur­rents will be observed to flow from the activated site through­out the intracellular and extracellular space. The source of this current is associated with the membrane (since both in­tracellular and extracellular regions are passive). This section is devoted to a consideration of the structure and function of the biological membrane.

The main constituent of the biological membrane is a lipid bilayer, approximately 5 nm thick, as illustrated in Fig. 2. Because this material is oily, it has a very high electrical re­sistance and is an effective insulator to ion movement. There are, however, transmembrane proteins that contain aqueous channels; it is only the presence of these channels that en­dows membranes with ionic permeability.

Channel proteins have been studied biophysically by elec­tron microscopy, electron diffraction, and biologically at the level of molecular structure. Although a fairly consistent pic­ture emerges, we still do not have an accurate structural model. Based on what is known, Hille (1) created the cartoon of a channel protein given in Fig. 2. A typical such protein is approximately 120 A in length and 80 A in diameter. Impor­tant for ion movement is the aqueous channel. These chan­nels also have gates, the opening and closing of which control ion flow. These gates are typically sensitive to electric fields in the membrane, implying that the channel protein contains charged regions that are influenced by the electric field to cause a conformational change, which, in some way, controls the gate. Another important channel property is selectivity, Lipid



Figure 2. The figure shows the membrane that bounds an excitable cell consisting of a lipid bi­layer (two layers of lipid with their hydrophillic heads facing outward and nonpolar tails inward) and an ionic channel that penetrates this layer. The channel structure is based on electron micros­copy and electron diffraction studies. ‘‘The chan­nel is drawn as a transmembrane macromolecule with a hole through the center. The external sur­face of the molecule is glycosylated. The functional regions—selectivity filter, gate, and sensor—are deduced from voltage-clamp experiments and are only beginning to be charted by structural studies. We have yet to learn how they actually look

An important tool in the study of membranes is molecular genetics. These techniques have been used to determine the primary structure of most channels of interest. Unfortunately it has not been possible to deduce the secondary and tertiary structure. However educated guesses lead to a determination of which portions of the primary amino acid sequence is intra­membrane, cytoplasmic, and extracellular. As noted in Fig. 2 the channel protein extends into the cytoplasm as well as the extracellular space.

The Squid Axon

Hodgkin and Huxley (2) pioneered a quantitative study of ex­citable membranes in the 1950s. For their preparation, they used the giant axon of the squid. This axon was chosen be­cause of its large diameter (approximately 500 ^m), which allowed the insertion of an axial electrode. Until this time all measurements of the electric behavior of excitable cells uti­lized only external electrodes, which left much information inaccessible. In the absence of intracellular potentials the conventional wisdom was that the resting membrane was de­polarized, meaning that it was at zero transmembrane poten­tial (the term depolarization continues to be used, although it now simply implies activation of an excitable membrane). Hodgkin and Huxley measured resting potentials on the order of —70 mV (inside minus outside).

The squid axon, like any nerve, can be activated by passing an adequate (transthreshold) pulse of current between two electrodes in the external bath. A propagating action poten­tial of the shape described in Fig. 3 is initiated at the activat­ing end and travels to the opposite end. Except for end effects propagation is characterized by an unchanging waveshape and uniform velocity (assuming an axially uniform prepa­ration).

The squid axon exemplifies an unmyelinated nerve fiber. Although this is not typical of nerve fibers in the human body, it presents a very simple model for analysis. One may con­sider that the intracellular space is simply a uniform electro­lyte, whereas the extracellular space (sea water) constitutes an independent electrolyte. Both intracellular and extracellu­lar regions are electrically passive, and consequently what­ever mechanism is responsible for the action potential must involve the membrane.

From a chemical analysis of intracellular fluid and sea wa­ter (which constitutes the extracellular environment for the squid), Hodgkin and Huxley determined that the major ions available for current flow are K+, Na+, and Cl—. They also noted that the ionic composition of the extracellular fluid dif­fers markedly from the intracellular. The intracellular and extracellular concentrations of the aforementioned ions asso­ciated with the squid giant axon are shown in Table 1.

The squid axon contains a very high intracellular potas­sium concentration. If we assume the membrane to be perme­able only to potassium, then from Table 1 we would expect potassium ions to flow out of the intracellular space to the lower concentration extracellular space. This single ion move­ment can only be transient, because positive charge will accu­mulate at the outside of the membrane, leaving negative

Table 1. Intracellular and Extracellular Concentrations of Ions Associated with the Squid Giant Axon


Intracellular (mM)

Extracellular (mM)










Source. Hodgkin-Huxley (2).

Even though the resting potassium permeability exceeds that of the chloride and sodium ions, the latter are not negli­gible. However from the numerical values found previously, it is clear that there is no transmembrane potential that will equilibrate all ions. Consequently the condition that must be met at rest is that of a zero net transmembrane current that is, a steady-state condition where

IK + ICl + INa = 0 ()



charge at the inside surface of the membrane and thereby establishing an electric field that acts inward and inhibits fur­ther potassium efflux. (Note that the lipid bilayer constitutes an ideal capacitive dielectric, and a typical membrane capaci­tance for charge storage is 1 ^F/cm2). Equilibrium requires that the outward flux due to diffusion be balanced by the in­ward flux due to the resultant electric field (additional details will be presented shortly). BIOELECTRIC PHENOMENA

Unitary K currents

models have been formulated from experiments conducted with macroscopic membranes. Illustrative of this approach is the now classical work of Hodgkin and Huxley (2), who con­structed the first mathematical model of excitable membrane behavior in the early 1950s. This model was so successful that it continues to be utilized today, although we now have im­proved models for cardiac tissue and for myelinated nerve.

In the 1950s electrode sizes were much larger than today. To accommodate a larger electrode, Hodgkin and Huxley chose the giant squid axon as their preparation. This cell has a diameter of approximately 500 ^m and was large enough to accommodate an axial electrode. Their second electrode was a concentric cylinder, which was placed in the extracellular electrolyte (sea water). This configuration insured no axial variation in potential so that the entire cell membrane be­haved synchronously (i. e., like a large number of membrane patches in parallel). They described this arrangement as space clamped. From their studies Hodgkin and Huxley con­cluded that the transmembrane current was essentially car­ried by sodium and potassium ions (chloride being at or close to equilibrium). But while a patch electrode is capable of mea­suring a single ion current, the transmembrane current in the whole axon preparation would necessarily contain both so­dium and potassium contributions. To separate these they im­plemented the voltage clamp.

To set the stage for the Hodgkin and Huxley’s experiments we first describe the basic model they chose. As we’ve already noted they assumed that the transmembrane current basi­cally consisted of sodium and potassium. Recognizing the con­tributions from both electric field and diffusion they assumed the relationships introduced earlier, namely that

ik = gK (Vm – ek ) INa gNa(Vm — ENa )

where the conductivities gK and gNa were expected to be func­tions of time and transmembrane potential. In Eq. (11) EK and ENa are the potassium and sodium equilibrium (Nernst) potentials, the difference from Vm being the net ion driving force. IK and INa are ‘‘ensemble’’ current densities per unit area of memberane. To account for a small additional leakage cur­rent they added

I1 = g1 (Vm — E1 )

where gl is an experimentally determined constant and El is chosen so that the total ionic current reduces to zero at rest.

Although Hodgkin and Huxley could only guess at the presence of separate single channels of potassium and so­dium, their model is consistent with current understanding. To fit their measurements they assumed that the potassium conductivity satisfied

— 4

gK = §Kn

We may interpret this to describe a functional potassium channel with four subunits, each of which must be open for the channel to be open (hence the probability of an open chan­nel is n4 if n is the probability of an open subunit). Because n describes a probability, then 0 < n < 1, while gK is the largestpossible value of potassium conductance (all potassium chan­nels open). The temporal behavior of the probability n was assumed to follow Eq. (10) where the rate constants a and 3 depend solely on Vm.

The Hodgkin-Huxley model has been applied successfully to tissue other than squid axons. For myelinated nerve it is applied at the Nodes of Ranvier, assuming the myelin sheath to insulate the intracellular from extracellular space else­where. It has also been used in the simulation of activation of striated muscle. However in both aforementioned applications the modification introduced by Frankenhaeuser (9) is gener­ally more satisfactory. For cardiac muscle the action potential differs from the aforementioned by a very long plateau and slow recovery (each phase lasting for roughly 100 msec). This plays an important functional role in protecting the heart by introducing a long refractory period and hence inhibiting the re-entry of excitation (since activation can be present for per­haps 60 msec). Present day electrophysiological models of the cardiac action potential (10) differ considerably from the sim­ple Hodgkin-Huxley model in that they contain as many as 11 current sources. The unique plateau arises from a delicate balance of component currents which are capable of adapting to changes in the heart rate. These models also include the calcium ion flow; this ion is important since it contributes to maintaining the plateau and also since it triggers the cou­pling from electrical to mechanical activity of the heart muscle.

Knowledge Acquisition Is Based on the Target User

Since the expertise of the user is a known factor in the suc­cessful implementation of an ES, expertise is therefore rela­tive to the design strategy. The modeling and design of the ES must be in concert with the level of expertise to be assessed. Building systems that can be flexible and adapt to such re­quirements require the ES designer to apply elective automa­tion design theories. Typically ES are limited to use by one of three classes of users. The first, the novice, finds the most system utility at a level where rote or procedural knowledge is sufficient, engages the highest use of automation when available, and seeks simplicity in the interface. Second, the journeyman finds utility in the middle range of the system, partially utilizing manual and automated functions, and will tolerate most levels of complex interfaces with some training and practice. Last, the expert is capable of self-instruction on the system since they operate the system using principles and experience-based knowledge. Experts will not tolerate limited flexibility in the system’s functional implementation.

Quantifying Performance

Quantifying performance can be aiding by using ES to stan­dardize measurement and classification of pilot performance. An ES used in quantification of pilots in training uses a rules – based approach and an optimal model to infer a score on a pilot’s ability to maneuver the aircraft, given a standard. This standard is used to define the baseline (quantify the optimal performance) and a simple network of all outcome collected in the past performances is used to define the pilots expected performance. Using a deductive process, the data collected in the pilot’s maneuvering of the aircraft is then reduced to a set of rules where the antecedent is compared with the optimal performance antecedent and the analysis is performed based on quantitative data. This greatly improves the ability of the ES to acquire new data and weight the data according to the best known performance of the pilot prior to the event under study. The resulting analysis can drive a rules-based model that will then narrow the set of variables, and identify the rules that fired, leading to a refined set of maneuvers that need attention in future training.

Another ES used to quantify performance is an induction engine developed for studying accident data. It can be said that most accidents involve pilot error. These accidents, when reduced to data, which has been processed using a qualitative approach, can lead to key rules derived through induction. While this method does not result in immediate ES utility, the rules are necessary for the construction of the network of events that preceded the accident. In applying these rules to the performance of the pilot in a simulated environment, the ES is able to rank the pilot’s performance by quantifying the rues which, in the past, had a high probability of firing if certain pre-accident events were present.

Predicting Performance

In a complex system such as an aircraft, the need exists to select the best possible match of pilot and vehicle. To do this, ES are used in ground-based test environments to provide a dynamic environment that adapts to the behavior of the pilot and challenge the pilot based on the correctness of the prior action. These systems utilize psychological principles of hu­man attention and motor skill to create a multiprocessing re­quirement in the human mind. ES capable of resolving these challenging environments then operate in the background of the test apparatus to provide a predictive model to the ex­pected behavior of the pilot, who is often behind the ES in resolving the problem. The predictive nature of these systems is implemented using both rules-based and neural network structures. The ES controls the timing and the difficulty of the task based on a Bayesian process that involves the users input and changing heuristic models that form the initial foundation of the models. The ES also uses a series of time – related rules that are derived as the system is exercised to control the tempo of the primary task—flying the aircraft. Secondary tasks are driven by the ES control algorithms and the pilots input. Results are compared to the past historical results of others who have been used to establish the baseline for comparison.

Evaluation of Pilot Performance

ESs most often emerge as the result of capturing knowledge of one or more experts in a format that facilitates computa­tional analysis. Typically the analysis is focused on directing the system to carry out certain rules and implement routines that have been programmed into the system. Often the goal of the ES designer is to achieve a human-like behavior from the system. One of the more difficult tasks of the ES designer is to implement a system that, in real-time or immediately following use, can assess the performance of the human com­ponent of the system. This is different from simply developing an ES that can influence the operator during its use. The ES needed to critique human behavior is required to have a set of analysis capabilities that not only relate to the rules and networks used in the system, but a set of principles that have their roots in the psychology of human actions.

A number of systems exist that provide such an ability to assess pilot performance. These systems are developed to aid in predicting human performance, critique performance, and quantify performance for use in a variety of future activities such as curriculum design, monitoring and controlling qual­ity, or systems engineering. Conducting knowledge acquisi­tion for assessment requires the classification of the ‘‘expert’’ relative to the system user.

Pilots operate in a dynamic environment and the variables that comprise the reasoning and observable behavior of pilots is often very abstract or difficult to define. One of the best examples of an ES used in assessing pilot performance is the U. S. Navy effort to design and implement a model of the pilot in flight-test maneuvers. The pilot model is a combination of skill-based models and rules-based models (multiple model in­tegration) whereby the skill-based portion provides a feed­back path and the rule-based portion provides the inference and feed-forward path (20). This ES employs the use of the Rasmussen’s commonly recognized model of human error comprised of the hierarchical categories of knowledge-based, rule-based, and skill-based behaviors thought to lead to hu­man error. Using a quasi-linear model, the system is capable of quantifying skill-based pilot behavior. To resolve discrete decision tasks, the use of a fuzzy-logic scheme is employed, which supports rule-based behavioral assessments and, when combined with the skill-based models, results in inference rules that can be used to derive large classes of pilot tasks.