Voltage clamping with a single microelectrode

zyxwvu zyxwvu zyxw zyx zyxw JOURNAL OF NEUROBIOLOGY VOL. 6 , NO. 4, PP. 411-422 Voltage Clamping with a Single Microelectrode w. A. WILSON and MARCIA MONAHAN GOLDNER Epilepsy Center, V.A.Hospital, Durham, N o r t h Carolina, and Department of Physiology and Pharmacology, D u k e University Medical Center, Durham, N o r t h Carolina SUMMARY A technique is described which allows neurons to be voltage clamped with a single microelectrode, and the advantages of this circuit with respect to conventional bridge techniques are discussed. In this circuit, the single microelectrode is rapidly switched from a current passing to a recording mode. The circuitry consists of: (1) an electronic switch; (2) a high impedance, ultralow input capacity amplifier; (3) a sample-and-hold module; (4) conventional voltage clamping circuitry. The closed electronic switch allows current to flow through the electrode. The switch then opens, and the electrode is in a recording mode. The low input capacity of the preamplifier allows the artifact from the current pulse to rapidly abate, after which time the circuit samples the membrane potential. This cycle is repeated a t rates up to 10 kHz. The voltage clamping amplifier senses the output of the sample-and-hold module and adjusts the current pulse amplitude to maintain the desired membrane potential. The system was evaluated in Aplysia neurons by inserting two microelectrodes into a cell. One electrode was used to clamp the cell and the other to independently monitor membrane potential a t a remote location in the soma. INTRODUCTION Voltage clamping is one of the most powerful techniques developed for the study of electrical events occurring in cell membranes. Under voltage clamp conditions, the membrane voltage is electronically controlled by the investigator. When spacial potential differences are prevented along the entire area of membrane through which current flows, and the potential is rapidly stepped to another voltage, the current which flows (following a brief capacitive transient) is the ionic current through the membrane. The voltage clamp technique has been applied most successfully to the study of ionic mechanisms in axons which approximate right circular cylinders (Hodgkin, Huxley, and Katz, 1952). The geometry of large axons makes possible rigorous space clamping of an extensive length of membrane, and since it is possible to determine accurately the area of membrane through which current flows, current densities (A/cm2) may be used to compare data from different cells. However, many electrically active cells more closely re411 zyxw zyxwvutsr 01975 by John Wiley & Sons, Inc. 412 zyxwvutsr WILSON A N D GOLDNER semble spheres or spheres with long, branching cylinders attached, and it is even more difficult to clamp such cells than axons. In large spherical cells (e.g., Aplysia cell bodies) (Alving, 1969), or in small, specialized regions of large cylindrical cells (e.g., end-plates in skeletal muscles) (Takeuchi and Takeuchi, 1959), it is possible to approach voltage clamp conditions by using two intracellular microelectrodes (one to sense voltage and the other to pass current). An additional extracellular electrode is common to both current and potential circuits. In these systems, voltage clamping is particularly applicable for three types of measurements. First, qualitatively accurate voltage clamp data of slow ionic currents may be obtained (David, Wilson, and Esceta, 1974). Second, the technique also lends itself well to studies of drugs in which, with a single cell, data can be collected before and after the application of a pharmacologic agent. Each cell then acts as its own control and data can be normalized by measuring the percentage change in a given parameter with the introduction of the drug (Deguchi and Narahashi, 1971). Third, voltage clamping also allows synaptic events to be separated (Wilson and Wachtel, 1970). Although in Aplysia neurons the clamp does not hold the postsynaptic membrane a t a constant potential during a postsynaptic potential, it is able to return the soma membrane each time to the holding potential, thus preventing summation of individual postsynaptic potentials (Wilson and Wachtel, 1970). This has proved to be valuable in the study of the amplitude and the frequency of individual postsynaptic potentials. Voltage clamping with microelectrodes is limited by the following constraints: (1) cell injury induced by penetration of two electrodes, (2) visual inaccessability of deeply imbedded cells, (3) difficulty in determining area of membrane through which current flows, (4) difficulty in obtaining uniformity of membrane potential using a point source of current, and (5) slow speed of clamping due to current-sink characteristics of cell geometry. For the three types of measurements listed in which voltage clamping can be used effectively, the first two constraints could be removed by a circuit which requires only one intracellular microelectrode for voltage clamping. The single microelectrode technique most commonly applied utilizes a bridge circuit in which the membrane serves as the unknown resistor in one arm of a bridge (however, see Muller, 1973). But these circuits become inaccurate when electrode resistance varies with current, and since voltage clamping requires the passage of large currents through microelectrodes, such systems are not adaptable to voltage clamping. This paper describes a circuit with which a cell may be voltage clamped using a single intracellular microelectrode. The clamp was designed to study small, slowly changing membrane currents which accompany subthreshold phenomena. As in all voltage clamp systems which use microelectrodes, its effectiveness is limited by the use of a point source of current. The theory of the circuit, electronic implementation, and experimental confirmation as well as the theoretical and practical advantages and limitations of the technique are discussed. zyxwv SINGLE ELECTRODE VOLTAGE CLAMPING ’1 zyx zy 413 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQP Open ~ I$ct-l. TOP TCYCLE ., zyxwvutsr zyxwv zyxw ,+ Hold Sam *I ‘e B Fig. 1. Recording and stimulating through a single microelectrode. (A) A switching system designed to eliminate V , from voltage record. When S1 is rapidly cycled from “open” to “closed,” pulses of current flow through Re The pulses are integrated in R,C,, and the measured voltage is V,. V,,, is sampled between pulses of current. (B) Timing cycle for the switching system. A schematic illustration showing the sequence of events by which rapid cycling of S1 produces a steady potential V,,, on which is super-imposed a small a-c component. VOis sampled See text for details. after S1 has been open a sufficient time for VOto equal V,. METHOD AND RESULTS T h e theory of operation The operation of the single electrode clamp (SEC) system is described in two parts. First, the previously used methods for recording voltage and injecting current through the same microelectrode are compared with the technique used in this system. The application to clamping then follows in a straight forward manner. In conventional systems, current is passed via an electrode with resistance Re across a membrane with resistance R,. In Figure l A , this condition exists when S1 is closed. Voltage source V , in series with Re, behaves as a current source. Under steady-state conditions the voltage seen at the amplifier output (Vo) is the sum of the voltage across the electrode ( V e ) ,and the voltage 414 zyxwvuts zyxwv zyxwvu WILSON A N D GOLDNER across the cell membrane (V,). In order to accurately measure V,,,, V , must be eliminated from the voltage records. With the conventional techniques used for recording and stimulating through a single electrode, an attempt is made to subtract V , from V Oby means of a Wheatstone bridge circuit. However, this technique fails if Re changes for any reason after the bridge is balanced. In this study, a switching system is used to inject pulses of current through a microelectrode and then to sample the resultant membrane potential between the pulses. The mathematical theory of such a discontinuous system has been reviewed previously (Brennecke and Hindeman, 1974a,b), and thus only a brief description is presented here. Switch (Sl) in Figure 1A is rapidly cycled to intermittently connect the voltage source V to the microelectrode. Thus, pulses of current are passed through the microelectrode and are integrated in the membrane R C circuit. During the interval when S1 is closed, a large potential develops across R, and is reflected in Vo. However, Vo is the input to a sample-and-hold amplifier which is in the hold mode during this pulse. When S1 opens, Ve is eliminated by cessation of current flow and the sample and hold circuit samples VO,which now represents only V,. This sample is held until after the next closure of S1, at which time another sample of V , is obtained. Proper operation of the switching system depends on several constraints. Referring to Figure l B , the cycling time ( T c y c l e ) of S1 must be much shorter than the time constant of the cell membrane (7, = R,C,) in order that the pulses of current may be smoothed into a d-c voltage. This voltage will be proportional to the amplitude and duration of the pulse. The cycling rate must also be much greater than the highest frequencies of interest in the recorded signal, so that the sample output will accurately represent the actual signal. In addition, the time constant of the input circuit (71 = ReCi,) must be very short compared to Tcycle. When S1 is closed ( T c l ) ,the capacitance C;, (representing the sum of the amplifier input capacitance, cable capacitance, and microelectrode capacitance) charges to V and remains a t that voltage as long as 5’1 is closed. When S1 is open (Top),Ci, discharges to V , with the time constant 71. For the recording system to accurately measure V,, VO must equal V,,, a t the end of TOp. To meet this requirement, 7 1 must be much shorter than Top. If the system is designed so that this requirement is met along with Tcyclebeing much less than T,, then recording and stimulating can occur independent of changes in Re, in contrast to “bridge balancing” techniques. A neuron from the abdominal ganglion of Aplysia californica is used to illustrate the calculation of the necessary circuit performance specifications. A reasonable value of the membrane time constant is 50 msec, and the duration of an action potential is about 10 msec. By referring to Figure l B , it can be seen that time Tcycleshould be much shorter than 10 msec in order to have a sufficient number of samples in an action potential to properly represent it. Judging ten samples to be sufficient, Tcycle is 1.0 msec. This cycle time is of the membrane time constant and therefore the current pulses are reason~ zyxw zyx zyxwvu zyx zy zyx zyxwvu zyxwvu SINGLE ELECTRODE VOLTAGE CLAMPING 415 ably smoothed to charge the membrane capacitance to a d-c level, with a very small a-c component. Topis governed by the time constant 71, and for Ci, to charge to V,, TOp should equal 1071. If Top were 50% of Tcvcle(0.5 msec), then 7 1 could be no longer than 0.05 msec. For an electrode resistance of 10 MO, Ci, would have to be less than 5.0 pF, and for a cycle rate of 10 kHz, C;, would have to be less than 0.5 pF. Electronic implementation of the single electrode recording and stimulating system Electronic implementation of the system hinges on two crucial circuit components; (1) switch SI and (2) a high input impedance, low input capacity preamplifier. T o achieve the high switching speeds required, an electronic switch (field effect transistor) was used for Sl rather than a mechanical device. When in the open mode, it should ideally have infinite resistance and draw no current. Furthermore, it should produce no artifact at the moment of switching. Initial efforts were devoted to selecting a suitable field effect transistor switch which could be directly connected as S1 in Figure 1A. However, the insertion of such a switch into a high impedance circuit allows the junction capacitances of the transistor to couple the drive signal (switch control signal) into the input of the preamplifier, producing a large artifact a t the moment of switching, and occluding the true signal. To avoid the switching artifact, the bootstrap arrangement shown in Figure 2 is used. A summing amplifier with a gain of one is connected from the out- Fig. 2. Technique for removing SI from a high impedance point in the circuit. When S1 is open, the potential is equal on both sides of RI and no current flows through it. When S1 is closed, current proportional to voltage source V is passed through the microelectrode. R1 is made small to reduce switching artifact. put of the preamplifier to its input via resistance RI. If S1 is open, the potential across RI is zero and no current flows; i.e., RI appears to have infinite resistance. (Any error introduced by a small deviation from unity gain is minimized by making RI large.) When S1 is closed, the output of the voltage source, V , also appears at the input of the summing amplifier and current 416 zyxwvuts zyxwv WILSON AND GOLDNER flows through the microelectrode. This current is proportional to the sign and magnitude of V. With this circuit configuration, the problem of using S1 in a high impedance system is avoided since the load resistance R1 can be made small. The second critical aspect of this system is the design of a high input impedance amplifier with extremely low input capacity. Such an amplifier has been designed and described by Kootsey and Johnson (1973). In this amplifier, the power supply of the input stage is driven a t the appropriate d-c level plus the potential of the input signal, thus reducing input capacitances to approximately 0.01 pF. This technique is used for the input preamplifier, and in addition, the input cables are guarded with shields driven at the same potential as the input. To compensate for the small electrode tip capacitances which result from immersing the electrode in a conducting medium, negative capacitance feedback was incorporated into the system. A measure of average current is obtained by recording the voltage across a known resistance, RI, as is shown in Figure 3. A differential amplifier mea- zy zyxwvu -- -- Fig. 3. Measurement of average current. A differential amplifier measures the potential drop across RI. This pulsed output is filtered by a low pass filter to obtain average current. sures the potential Vl across RI. The current through RI is VIIRI. Because this current is in pulse form, it is necessary to obtain its average value. This is accomplished by the use of a low-pass filter following A3. An alternate solution would be to use a second sample-and-hold network to sample Vr and then multiply it by the appropriate constant to obtain average current. zyxwvuts zy Expansion of t h e circuit t o voltage clamping In voltage clamping systems using two electrodes, one electrode measures membrane potential and this voltage is compared to a reference voltage at the summing junction of an operational amplifier. The difference between the two voltages is amplified and current is injected or withdrawn from the cell by a second, current passing (intracellular) microelectrode until the membrane voltage matches the command voltage. As shown in Figure 4,the SEC S I N G L E ELECTRODE V O L T A G E C L A M P I N G zyx zy 417 zyxwvuts zyxwvu Fig. 4. The complete voltage clamping system. A1 is an Analog Devices 40 J. A2 is National Semiconductor LM 318H. A3 is a Transidyne General MPA 6. A4 is a high-gain, differential amplifier. S1 is an analog gate, DG 200BA by Siliconix. Resistors RI and R1 are 2 MQ and 10 KQ,respectively. zyxw employs nearly the same voltage clamp circuit as is used for dual electrode clamping. A high gain differential amplifier, Ad, subtracts the output of the sample-and-hold circuit from the reference potential and amplifies the difference. The output of A4 is connected to 5’1. Thus, under clamped conditions, the clamp replaces the simple voltage source, V, indicated in Figure 3. In two-electrode clamping systems, both the recording and the current injection microelectrodes are connected to the circuit a t all times and when a deviation from the reference potential occurs, the clamp amplifier immediately senses and corrects the error. In the SEC system, there is a time delay which must be considered. The sample-and-hold circuit updates its measure of membrane potential at the cycle frequency. Thus changes in membrane potential that begin while the circuit is in the hold mode are not noted until the next sample period and the clamp amplifier cannot correct for such changes until it receives the new voltage measurement and switch S1 closes. Thus the cycle frequency of the system must be much faster than the membrane potential changes to be controlled. The gain of the clamp amplifier A4 should be as high as possible, but, as in all such feedback circuits, there is a tendency for the system to ring or oscillate at high gains. Thus, the frequency response and gain of A4 must be adjusted for the particular physiological system under study. Once a cell is clamped, the gain of A4 can be increased to the point just below ringing. Experimental confirmation The performance of this system was evaluated by the use of neurons in the abdominal ganglion of Aplysia californica. The ganglion was removed, pinned to a paraffin surface, and perfused with artificial seawater (Instant 418 zyxwvutsrq zyxw zyxw WILSON AND GOLDNER Ocean). KC1-filled microelectrodes (5-10 MQ) were used. Before the clamping electrode was inserted into a cell, the system was tested to ascertain the maximum sampling rate and current injection that an electrode would allow. The electrode was placed in the grounded bath solution and increasingly large currents were passed through it. Good electrodes could carry average currents of more than 200 nA at a switching rate of 5000 Hz without showing signs of polarization or other artifacts. Thus, it was possible to predict the maximum current (at a given switching rate) that an electrode could carry. Preliminary experiments have shown that electrodes with beveled tips have markedly improved characteristics, but they were not used in the experiments reported here. When a satisfactory clamping microelectrode was found, both it and a second monitoring microelectrode were inserted into a single neuron soma. The second microelectrode was connected to a separate recording amplifier and was used to independently measure the membrane potential of the neuron, and to evaluate the performance of the clamp. ?he monitoring microelectrode was placed as far from the clamp electrode as possible, usually 200 to 300 p. Figure 5 shows the effective operation of the single electrode system in the current clamp mode. In both parts of the figure, the output of the sampleand-hold amplifier and the output of the monitoring electrode amplifier are compared. In this case the clamp amplifier was in the configuration shown in Figure 3, with a manually adjustable voltage source replacing the clamping amplifier. In Figure 5A, hyperpolarizing current pulses were given, and the resultant changes of membrane potential recorded a t both electrodes. There is good agreement between the two recordings (less than 2% difference). Figure 5B shows an oscilloscope tracing of an action potential recorded in the same manner. Because of the high sweep speed, it is possible to resolve the discontinuities in the output of the sample-and-hold circuit. In this case the cycle rate was 2000 Hz. To test the efficacy of the circuit in the voltage clamp configuration, similar experiments were performed under voltage clamp conditions. Figure 6A shows an oscilloscope tracing of the sample-and-hold output compared to the potential measured by the remote monitoring electrode. In this case, the neuron was held at a potential below firing threshold and then a hyperpolarizing command was given. The system clamped the cell to the new potential within about 3 msec at the current electrode. A t the monitoring electrode, about 20 msec were required for the potential to reach the same final value. This additional time can be attributed to the resistance of the intracellular medium linking the two membrane areas through which current must flow to charge the membrane capacitance. Figure 6B is a similar record a t slower speeds which shows several hyperpolarizing commands, as well as the clamp current. The prolonged currents that occur just after the command represent charging of the large axon connected to the soma. Some of this current can be eliminated by ligation of the axon, as has been shown by Alving (1968). Note however, that after the axon zyxwvu z SINGLE ELECTRODE VOLTAGE CLAMPING 419 zyxwv zyxwvu 5 zyx Sec A zyxwv zyxwvutsrq B 2Omsec Fig. 5. Recording and stimulating in an Aplysia neuron with the single microelectrode system. (A) A current clamp experiment in which a hyperpolarizing pulse of current was injected. V S His the output of the sample-and-hold amplifier, while VMONis the potential recorded from an independent monitoring microelectrode located about 200 fi away. VMONis in very close agreement with VSH,indicating proper operation of the system. Data recorded on a Brush Model 260 chart recorder. Cycling rate was 2000 Hz. (B) Oscilloscope tracing of the sampleand-hold output compared to the monitoring electrode. At the high sweep speed, during an action potential, the discontinuities in sample-and-hold output can be seen. Cycling rate was 2000 Hz. charging has occurred, the clamp accurately controls the neuron a t the monitoring electrode site. As discussed earlier, the discontinuous nature of this clamping system means that it is not useful for controlling very fast events. In the present configuration, the system was not capable of totally controlling action potentials in these cells. When the command voltage was above firing threshold, action potentials were generated in remote (unclamped) regions of the axons and they partially invaded the soma. The clamp markedly reduced their amplitudes, but did not totally control them. This situation might be corrected by much higher rates of switching, and a higher current injection capability. Both would be possible using the low resistance electrodes that beveling techniques produce. DISCUSSION In this series of experiments, the operation of the single electrode voltage clamp was confirmed by monitoring the membrane voltage with a second, in- 420 zyxwvutsr zyxwv zyx WILSON AND GOLDNER zy zyxw zyxwvutsrq _ 1 "S H "MON I I VSH VMON I i 1- 4OnA zyxwv zy Fig. 6. Voltage clamping an Aplysia neuron. (A) An oscilloscope tracing comparing the output of the sample-and-hold circuit to the voltage measured by the remote monitoring electrode. In response to a hyperpolarizing command, the cell is clamped a t the site of the clamping electrode within 3 msec. At the monitoring electrode, 200 p away, about 20 msec are required for the potential to reach the same final value. This delay can be ascribed to internal resistance of the cell through which current flows to remote regions of the cell axon. Cycling rate was 7500 Hz. (B) A slower tracing of several hyperpolarizing commands. There is excellent agreement between the potential a t the clamping electrode and the monitoring electrode. The current record includes the transient current required to charge the axonal membrane capacitance through the intracellular resistance. After 150 msec the current is steady. Cycling rate is 7500 Hz. dependent microelectrode in a remote part of a large cell soma. For preparations in which this option is available, preliminary voltage clamp experiments with a second monitoring microelectrode can define the limits of the system, and within these limits, single microelectrode clamping can replace the two microelectrode techniques. A more interesting application of this system is to those preparations which have not been studied with the voltage clamp technique because they can seldom if ever be penetrated by two microelectrodes. Many neurons of the central nervous system are in this category. In such preparations it is impossible to confirm the effectiveness of the clamp by a monitoring electrode, and one must resort to mathematical models of the cell to be clamped in order to evaluate the effectiveness of the system. As with all microelectrode clamping, the most serious limitation concerns the use of a point source of current to control a large area of membrane. This subject has been extensively reviewed by Peskoff and Eisenberg (1972), with references to a paper by Engle, Barcelon, and Eisenberg (1972). They show that a step of current through a microelectrode produces three potentials. The first is a very rapid (nanosecond) drop within the microelectrode solution. The second is a "local SINGLE ELECTRODE VOLTAGE CLAMPING zyx zy 421 potential” which occurs near the electrode and is a result of the high current density in this region. This “local potential” is shown to be independent of membrane potential and to depend only on internal and external resistivity, the electrode location, and cell size. The third component, the slow “farfield potential” is established according to the membrane time constant and is dependent on the membrane parameters. In their analysis, Peskoff and Eisenberg showed that the three components are independent of one another, and that the total potential measured across a current carrying microelectrode is the algebraic sum of these three potentials. To measure cell membrane parameters, however, one would ideally wish to measure only the “far-field potential.” When the same microelectrode is used for current injection and recording, conventional systems rely on the bridge balancing technique described in the methods section. Peskoff and Eisenberg noted that while bridge balancing may compensate for the voltage drop across the microelectrode, it does not remove the “local” potential from the record. They point out several cases in which the differences between data gathered by two-microelectrode studies differ from that obtained by single microelectrode bridge balancing experiments, and they attribute these differences to unrecognized local potentials. These local potentials become even more important when microelectrodes are used to voltage clamp a region of membrane. Peskoff and Eisenberg conclude that “the potential across a region of cell membrane cannot be controlled if that region contains a microelectrode source of current.” This would certainly seem to preclude any clamping using single microelectrodes, or even double barreled units. However, the system used in the present paper is discontinuous. A current pulse is followed by a waiting period before the potential is measured. During this period, the local potential around the microelectrode dissipates. This was obviously the case in the experiments reported here, because the measured potential from the remote monitoring electrode matched that from the current passing electrode. However, the problem of local potentials must be considered before applying this technique to cells where no confirming studies are possible. zy zyxwvutsrq zyxwvuts The authors gratefully acknowledge helpful discussions and comments by Dr. John W. Moore. They also thank Mrs. Frances Bateman for secretarial assistance and the Medical Illustrations Department of the VA Hospital for preparing the figures. This work was supported by Project # 9459-01, V. A. Hospital, Durham, N. C. and National Institutes-of Health Research Grant NS09272. M. M. G. was supported by the National Institute of Mental Health Research Training Grant MH-08394. REFERENCES ALVING,B. 0. (1968). Spontaneous activity in isolated somata of Aplysia pacemaker neurons. J . Gen. Physiol. 51: 29-45. ALVING,B. 0. (1969). Differences between pacemaker and nonpacemaker neurons of Aplysia on voltage clamping. J. Gen. Physiol. 54: 512-531. BRENNECKE,R. and LINDEMAN,B. (1974a). Theory of a membrane voltage clamp with discontinuous feedback through a pulsed current clamp, Reu. Sci. Instrum. 45: 184-188. BRENNECKE,R. and LINDEMAN,B. (197413). Design of a fast voltage clamp for biological membranes using discontinuous feedback. Reu. Sci. Instrum. 45: 656-661. 422 zyxwv zyxw WILSON AND GOLDNER DAVID,R. J., WILSON,W. A. and ESCUETA,A. V. (1974). Voltage clamp analysis of pentylenetetrazol effects on Aplysia neurons. Brain Res. 67: 549-554. DEGUCHI,T. and NARAHASHI,T. (1971). Effects of procaine on ionic conductances of endplate membranes. J . Pharmac. Exptl. Therap. 176: 423-433. ENGLE,E., BARCILON,V. and EISENBERG,R. S. (1972). The interpretation of current-voltage relations recorded from a spherical cell with a single microelectrode. Biophys. J . 12: 384-403. HODGKIN,A. L., HUXLEY,A: F. and KATZ, B. (1952). Measurement of current-voltage relations in the membrane of the giant axon of Loligo. J. Physiol. 116: 424-448. KOOTSEY,J. M. and JOHNSON, E. A. (1973). Buffer amplifier with femtofarad input capacity using operational amplifiers. I E E E Trans. Biomed. Engr. BMEQO:389-391. MULLER,KENNETHJ. (1973). Photoreceptors in the crayfish compound eye: Electrical interactions between cells as related to polarized light sensitivity. J . Physiol. (London) 232: 573595. PESKOFF, A. and EISENBERG,R. S. (1973). Interpretations of some microelectrode measurements of electrical properties of cells. Annu. Reu. Biophys. 2: 65-79. TAKEUCHI,A. and TAKEUCHI,N. (1959). Active phase of frog’s end-plate potential. J . Neurophysiol. 22: 395-411. WILSON,W. A. and WACHTEL,H. (1970). A feasibility study of voltage clamping remote synapses. In: Proc. of23rd Ann. Conf. Engr. i n Med. and Biol. p. 217. zyxwvu Accepted for publication January 14,1975