IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-25, NO. 6, NOVEMBER 1978

519

A Light-Scattering System for High-Speed Cell AnalysisJ. M. CROWELL, MEMBER, IEEE, R. D. HIEBERT, SENIOR MEMBER, IEEE, G. C. SALZMAN, MEMBER, IEEE, B. J. PRICE, L. S. CRAM, AND P. F. MULLANEY

Abstract-A flow-system instrument is described in which the light scattered by a biological cell is detected simultaneously at 32 angles in the forward direction as the cell passes through a focused laser beam at 10 m/s. Cluster analysis is applied to the scatter pattern data to enable discrimination among cell types.

INTRODUCTION

OPTICAL ANALYSIS of biological cells is proving to be a valuable tool in medical and biological research. The use of flow systems to make rapid and quantitative optical measurements on single cells has found applications in differential leukocyte counting [1, 2], immunology [1, 3, 4], and cancer cell identification [1, 5]. Most optical methods used for single-cell analysis rely upon fluorescence or computer image analysis. Both of these require that the cell be stained.

This paper describes a flow-system instrument which examines the differential light-scattering characteristics of unstained cells and which classifies cells on the basis of their morphology at rates of up to 60,000 cells/min. A preliminary report on this instrument has been published elsewhere [6] . The principles of flow systems for biological cells are described in detail elsewhere [1, 7]. Cells suspended in a suitable medium are introduced into a laminar flow stream so that they pass through a focused laser beam one at a time. The laser light is scattered by each cell into a pattern indicative of cell morphology. This scattering is a combination of diffraction by the whole cell and by its organelles, refraction through the cell, and reflection from the cell surface and from surfaces of the organelles. All these processes mutually interfere to produce an optical signature for the cell. It has been shown [8] that scattering at small angles from the incident beam (0-20) is principally due to diffraction effects and is indicative of overall cell size. Intermediate angle scattering (2-700) is mostly refraction with a small contribution from diffraction by organelles. Large-angle scattering (70-1800) is dominated by reflection. Manuscript received November 2, 1977; revised June 5, 1978. This work was performed under the auspices of the U.S. Department of Energy. J. M. Crowell, G. C. Salzman, B. J. Price, L. S. Cram, and P. F. Mullaney are with the Biophysics and Instrumentation Group, Los Alamos Scientific Laboratory, University of California, Los Alamos, NM 87545. R. D. Hiebert is with the Electronics Group, Los Alamos Scientific Laboratory, University of California, Los Alamos, NM 87545.

EXPERIMENTAL APPARATUS A schematic drawing of the light-scattering system is shown in Fig. 1. A 7-mW helium-neon laser beam (Spectra Physics, Inc., Model 256) is focused by a 15-cm focal-length spherical lens onto a cell sample stream which is surrounded by a saline or distilled water sheath. The sample stream, typically 30 Mm in diameter, and sheath flow through a chamber which is filled with the same fluid as the sheath. The resulting laminar flow is such that each cell passes through the focused laser beam. Refraction at the inner and outer surfaces of the chamber exit window is taken into account. The laser beam passes out of the flow chamber and strikes the photodetector array (Recognition Systems, Inc., Model WRD-6420A). One-half of this light-scatter detector consists of 32 concentric rings, each of which is a separate photodetector. The rings span 1800 of azimuthal angle. As the cell traverses the laser beam, the current pulse from each ring is proportional to the intensity of light striking its annular area. Therefore, simultaneous pulse signals from the entire concentric array of rings give a composite measure of scattered light intensity as a function of polar angle. The signal processing electronics system block diagram is shown in Fig. 2. Each of the 32 pulse signals is logarithmically amplified and its magnitude stored by a peak sense-and-hold circuit. One of the signals is selected as a trigger to indicate the presence of a cell in the laser beam. When the trigger signal exceeds a preset threshold, the master control unit activates all peak sense-and-hold circuits which are then locked so that subsequent pulses do not enter the system until processing is complete. The 32 signals are then multiplexed to a fast analog-to-digital converter (ADC) (Datel Systems, Model ADC-G1OB-2A). The digitized output of the ADC is transferred to the computer memory (Digital Equipment Corporation, Model PDP-11/45) via the master control and a direct memory access (DMA) interface (Digital Equipment Corporation, Model DRI 1-B). When data from all 32 detectors have been transmitted to memory, the peak sense-and-hold circuits are cleared and another event can be accepted. Approximately 250 Ms are needed to acquire an event and to transfer its scatter pattern to the computer. The raw data in the computer memory are periodically transferred to magnetic disk for subsequent analysis. Conventional pulse-height analysis and mathematical pattern recognition routines are described

below.

001 8-9294/78/1 100-0519$00.75 C 1978 IEEE

520

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-25, NO. 6, NOVEMBER 1978

Multiangle Light Scatter System

Flow cell

Focusing lens \

I

Fig. 1. Schematic diagram of light-scatter photometer and layout of photodiode array. De ector ings

Peak Sense Amplifiers rand Holds

Fig. 2. Block diagram of signal processing and data assimilation electronics.

ELECTRONICS AND DATA ASSIMILATION The system signal flow paths are indicated in Fig. 2. Functional designs were dictated by the basic requirements of having to measure with minimal processing time the pulsed lightsignal levels from many photodiode elements having a wide dynamic operating range. Dynamic range is achieved with logarithmic pulse amplifiers. The peak pulse amplitudes are sensed simultaneously when an event trigger occurs, and the analog levels are stored for subsequent sequential digitization by the fast ADC. The DMA interface allows rapid transfer of digitized data to main computer storage without significantly bothering the CPU. The entire system is interconnected through the master control. Fig. 3 shows the analog pulse processing circuitry for one detector channel. Each of the 32 detector rings is a mesadiffused silicon photodetector on a common substrate. Signals

are transported from the detector array to the

amplifying

chassis via 93-2 coaxial cables. To minimize signal crosstalk and effects from detector capacitance, virtual ground is maintained on all detectors by using transimpedance preamplifiers (U1). These amplifiers have switchable feedback networks to change the sensitivity span and to give proper compensation for the detector plus cable input capacitance. Detector capacitance varies from about 200 pF for the innermost ring to 14,000 pF for the outermost ring, and these impedances must be properly matched to obtain optimum monotonic pulse response. The preamplifier feeds one input of differential amplifier U2 which, in turn, feeds the logarithmic amplifier networks associated with U4, U5, U6, and U7. Actual logarithmic compression is achieved with integrated circuit type SN76502N. This device has four 30-dBV log stages, of which two are used in this application. Switches (not shown in Fig. 3) are ar-

CROWELL et al.: LIGHT-SCATTERING SYSTEM FOR CELL ANALYSIS

Switchable

Z f Networks

Inverter/ Differential Amp

30dB gain

521

Log Amplifier

Differential

Amplifier

Output

Amplifier

+ Sig

Detector ring

G1 (Sample) -G2 (Hold)

Gate signals from master control

Fig. 3. Abbreviated schematic diagram of logarithmic pulse amplifier and peak sense-and-hold for each detector channel.

ranged to select either one and one-half decades or three decades of input pulse amplitude span to produce a 10-V output signal range. The other input of amplifier U2 receives dc output voltage levels from amplifier U3. One input of this amplifier senses the average output voltage of the entire amplifier via the low-pass filter elements R2-C2. The other input of U3 is fed by a fixed dc reference of about -500 mV. Since U3 introduces high dc gain with negative feedback in a loop with the main logarithmic amplifier, the average output base-line voltage of the logarithmic amplifier is stabilized and referenced at the proper operating point. In this way, accurate logarithmic pulse amplification can be achieved even in the presence of a high dc "background" from ambient light or sensor leakage currents. Amplifiers U8 and U9 are in a straightforward gated peak sense-and-hold circuit. Pulse peak sensing is done via hot carrier diode CR1, and the amplitude is held on CI. Two gates are used. Field effect transistor (FET) Q1 switch closes during the sample period GI when the master control has received an event trigger. At the same time, the hold switch (FET Q2) across C1 opens for a period G2 which is long enough to allow readout through the multiplexer. In this way, only those pulses from the array which are time-correlated are sensed and held. Four of these amplifiers with peak sense-and-hold are combined in one single-width nuclear instrument module (NIM), and eight modules are combined in one NIM bin to complete the 32-channel system. The master control functions related to signal gating, signal multiplexing, and synchronization with the computer are shown in simplified block form in Fig. 4. The associated timing diagram is shown in Fig. 5. The event trigger may be a signal

from one of the rings in the array, or it may be from a separate sensor of the light-scattering occurrence. This trigger enters the system by way of a Schmitt discriminator to reject noise pulses. The output of the Schmitt discriminator triggers the GI (sample) pulse generator which, in turn, initiates all subsequent action. The leading edge of GI triggers the G2 (hold) pulse generator, and the trailing edge triggers the deadtime gate generator (not shown on the timing diagram) to block the system from accepting another event for analysis until the computer has completed acquisition of the data from the initial trigger. However, all G1 pulses are sent to a total count register to permit a tally of events missed during the computer busy period. The trailing edge of the sample pulse also initiates a startconvert pulse for the ADC. The leading edge of the startconvert pulse clears out the previous contents of the ADC, and the trailing edge initiates digitization of the analog level being fed to the ADC from the multiplexer. Multiplexer address is derived from the DRl 1-B word count register (DRWC) which is initially set for the maximum number of detector channels to be sequentially read out for the event of interest. For example, if all 32 channels are to be read, the DRWC will be preset to 31, and the first detector to be digitized will be the one connected to that address in the multiplexer. When digitization and assimilation of data from each detector are complete, the DRWC counts down one digit for the next detector to be read out. When the DRWC underflows (i.e., counts down to zero), the entire event data recording is complete. Referring again to Figs. 4 and 5, this timing sequence can be followed. When the ADC completes its digitization, its end of conversion (EOC) level changes state, and this transition is

522

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-25, NO. 6, NOVEMBER 1978

To/ from DR11-B G I

Total

Eve n t

Sample

count out

nt

G 2 Hold

Cycle End request cycle Schmitt

Trigger

I

I -Shot

t

-

End cycle~

~

R

~

~

~

convert Start

convert

I

DRWC DRWC overflow address

Dead time

INH(16-B it)

E

En o

IEC conversion

covernTomulplexer

To/from ADC

Fig. 4. Block diagram of master control: analog signal gating, multiplexing, signal digitizing, and computer timing.

Is- %%

%%/

Event signal Total count

out

I

End

Fig.

5.

Timing diagram for master control functions

shown

in Fig. 4.

used to trigger a cycle request pulse for the DRI 1-B. This initiates storage of data through the DMA; when storage is complete, the DRI 1-B sends back an end cycle pulse at the same time that its DRWC decrements to a new address. The end cycle pulse triggers a short delay to allow the multiplexer

time to settle to its new address, and the new start-convert signal is generated to initiate the same sequence for the newly addressed detector. At the nth cycle, the DRWC underflows and triggers the reset generator, which clears the analog holds and the deadtime gate, returning the system to a ready state for another event. Fig. 6 shows how the master control forms 16-bit input words to the DR 1I-B. The 8-bit data from each digitized detector signal become one byte of the word. Data are transferred a byte at a time via nonprocessor request (NPR) transfer to the computer memory so that information from 32 detectors is packed into 16 words. As a specimen is being processed, the total number of trigger events is being tallied in the 5-decade total count register. At a FNCT2 command from the computer, the 16 bits from the four most significant decades of the register are transferred through the 16-bit selector to the computer. Several features affecting performance of the electronic system should be noted. The fast ADC is a successive approximation type which has a conversion time of 1 Ms. To minimize error from differential nonlinearity of the conversion process, a 10-bit converter is used, with the output truncated to 8 bits. With this fast ADC and the DMA for data transfer, the total processing time for each incoming detector channel is 6 Mus or less. The intrinsic risetime of the logarithmic amplifier depends on the selected sensitivity and logarithmic compression spans. For example, with 100 k2 transimpedance on U1, the risetime is 0.5 ,s with three decades of compression and 1 Mis with one and one-half decades, and with 1 ME2 transimpedance the risetime is about 3 ,us for both compression spans. Since geometrical factors and flow velocities limit the actual system bandwidth needs to minimum risetimes of about 3 Ms, a lowpass filter with 100 kHz corner frequency is incorporated in each amplifier to minimize noise transmission.

523

CROWELL et al.: LIGHT-SCATTERING SYSTEM FOR CELL ANALYSIS

16-Bit Selector Assembly 2-line-to-l -line

8-Bit

data from ADC

16 Bit word

to DRI1-B

4

4

4

4

Total count

Decode counter I

I

FNCT 2 from DRIl-B

Fig. 6. Block diagram of master control: data word formation and selection for transmission to memory.

Electronic noise referred to the input of a given channel depends upon the ring to which it is connected. With the innermost rings having small areas and low shunt capacitance, the equivalent input noise current is only 0.8 nA rms, whereas the outermost large area rings have input noise currents of about 150 nA rms. The system noise with the laser on and with sheath flow is somewhat higher. Signal pulse current amplitudes will vary with the nature of the particle traversing the laser beam and the area of the ring receiving scattered light. The area of outermost ring 32 is 2000 times that of innermost ring 2; this variation combined with the sharply decreasing light-scatter intensity with scatter angle yields typical pulse signal levels which do not vary greatly over the detector field of view. For example, 10-Mm plastic spheres yield 0.4-1.2 MA pulses for the inner rings, as well as for the outer rings. DATA PROCESSING

The digitized 8-bit intensity measured at each of the 32 detectors is copied to the computer memory by the DMA interface via a high priority NPR transfer. After each lightscatter event has been transferred, the DRI 1-B sends an interrupt signal to the processor (CPU), which then checks

for overflow in a 8192-word memory buffer. When this buffer is full, it is written to a 1,200,000-word disk cartridge capable of holding approximately 75,000 32-angle light-scatter events. Once the scatter pattern data have been stored on a disk in this raw event mode, numerous techniques may be used to process and reprocess the data with different sets of conditions placed on one or more of the 32 parameters. Ungated singleparameter pulse-height frequency distributions for each detector element are generated by unpacking each lightscatter event and adding one count to the appropriate channel (0-255 for the 8-bit data) in the distribution for each detector element, as shown for rings 8 and 21 in Fig. 7A and B. Pulse-height (intensity) windows may be set on one or more of the parameters. This has been done for the higher intensity peak on ungated ring 8 in Fig. 7. When the data in the raw event file on the disk are reprocessed with the condition that an event is acceptable only if the intensity on ring 8 falls within the specified window, the pulse-height distributions shown in Fig. 7C and D are obtained. Light-scatter patterns may be displayed directly from the raw event file, as shown in Fig. 8A for a mixture of 8- and 10-Mim diameter plastic spheres. Each trace across the graph represents one light-scatter event. These patterns are analyzed

524

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-25, NO. 6, NOVEMBER 1978

A

B

FILE - (ElI SPWf:, PT, SPECTRJ NO. s A *Z 15I- MULE'. G

-j

IX F ILE - OEl S1FH1 I')l SPECTRUM N0 21 8 1e CEGPEE:-. FULL SCALE - I1

W 2W FULL SC

w

Z _ z I _ L

Fz

-3 U U--

_

50

CHANNEL NMER

C

C250

ED

FILE - Dl SPWRI'O 1.,

SPEC TWD Hu ;J1zI r s'50 EG.EF-. FULL SCALE - 2W0IO

-j

z

z

F ILE - W.lI SPH48;i 1 s . 1 SPEC TR 8 2 eOCGF LE FULL SCALE - Iee

ArGUE -

A z z

r

r

\

1\ U) 'N

(I) i-

z

Li

U

I

I 50

I

I

la

I

1

I

2

a

I

a

I

I

I

I

I

i

20

250

50

lI

2

CHANNEL NUMBER CHANNEL NUMBER Fig. 7. Ungated (A and B) and gated (C and D) pulse-height distributions for light scattered from mixture of 8- and 10-Mum spheres at 1.50 and 8.10.

using a mathematical clustering algorithm [9] which finds the "hills" in a 32-dimensional space. In Fig. 8B, each cluster is enclosed by a pair of lines which span two standard deviations around the center of a cluster. The cluster analysis and displays in the full 32-dimensional space are shown here mainly for illustration. When the parameters are suitably orthogonalized, pattern recognition can be accomplished in a feature space of three or four dimensions.

APPLICATION TO WHITE BLOOD CELL ANALYSIS The multiangle light-scattering flow system described above has been used successfully to discriminate between lymphocytes and monocytes in human peripheral blood. The lymphocyte populations from three female and three male donors were separated by a modified Ficoll-diatrizeate (hypaque) gradient technique [101. The specific gravity of the Ficoll-hypaque solution was adjusted to 1.080 for each sample. Heparinized blood was mixed with an equal volume of physiologic saline. Approximately 4 ml of diluted blood were carefully layered over a 3-ml Ficoll-hypaque gradient in 16 X 125-mm sterile plastic tubes. Samples were centrifuged at room temperature for 45 min at 432 gm. Lymphocytes were removed and washed with Hanks' balanced salt solution. The cultures contained approximately 70-80% lymphocytes, and the remaining 20-30o were primarily monocytes. The cells were

then resuspended at a concentration of 106 cells/ml in Hanks' balanced salt solution. The light-scatter patterns obtained from the cells in one such culture were analyzed by the clustering algorithm, and the results of this analysis are shown in Fig. 9. Clusters marked A and B are thought to be the lymphocyte and monocyte populations, respectively. The percentages of cells in the lymphocyte and monocyte populations (indicated in Fig. 9) are what is expected in a Ficoll-hypaque preparation. The percentage of lymphocytes remained about the same in all six samples, ranging from 81-86%. The angular dependence of light-scatter intensity was identical from sample to sample for both the lymphocyte and monocyte clusters. Moreover, the monocytes, which are physically larger than the lymphocytes, scatter more light in that angular region (rings 3-9) where diffraction effects dominate. Isolated lymphocyte-monocyte cultures were resuspended in Roswell Park Memorial Institute medium 1640 and incubated for 30 min in a tissue culture flask. The lymphocytes in suspension were then washed off, leaving the monocytes attached to the flask. When the same sample as shown in Fig. 9 was treated in this manner and analyzed by the light-scatter photometer, the results shown in Fig. 10 were obtained. The "monocyte" cluster is not present, but a third cluster, type C, has appeared which up to ring 12 has a scattered light intensity

CROWELL et al.: LIGHT-SCATTERING SYSTEM FOR CELL ANALYSIS

525

A

n

z

w

z

C00

H

I -J 0

w

LU-

H H '5

B 6

i

16

21

26

31

RING NUMBER

Fig. 9. Clusters found in analysis of human peripheral blood preparation. Probable identification: (A) lymphocytes and (B) monocytes. 0' 0

--

-

.

- -.

-

-I

z w

9

14

19

24

Ring Number Fig. 8. (A) Light-scatter distributions from mixtures of 8- and 10-,Mm spheres and (B) clusters found in 32-dimensional space.

significantly lower than the lymphocyte cluster. This cluster appears in most of the samples and is probably due to monocyte nuclei. It should be emphasized, however, that completely unambiguous assignments of clusters to cell types must await further development of the light-scattering system to permit sorting of individual cell populations based upon their light-scatter properties alone. REFERENCES [1] Wolbarscht, M. L., ed. Laser Applications in Medicine and Biology, Chapter 5. New York: Plenum Press. 1974. [21 Adams, L. R. and L. A. Kamentsky. "Machine Characterization of Human Leukocytes by Acridine Orange Fluorescence." Acta Cytol., Vol. 15, 289-29 1. 1971. [31 Cram, L. S. and J. C. Forslund. "A Quantitative Method for Evaluating Fluorescent Antibodies and the Conjugation Process." Immunochemistry, Vol. 11, 667-672. 1974. [4] Bankjurst, A. D., L. S. Cram, and N. L. Warner. "Transfer of Mouse IgG2 Production by IgM Bearing Spleen Cells Separated by a Fluorescence Activated Cell Sorter." J. Immun., submitted. [5] Horan, P. K., A. Romero, J. A. Steinkamp, and D. F. Petersen. "Detection of Heteroploid Tumor Cells." J. Natl. Cancer Inst., Vol. 52, 843-848. 1974. [6] G. C. Salzman, J. M. Crowell, C. A. Goad, K. M. Hansen, R. D. Hiebert, P. M. LaBauve, J. C. Martin, M. L. Ingram, and P. F. Mullaney. "A Flow-System Multiangle Light-Scattering Instru-

z I -J

L.L

0

w

en

0

6

11

16

21

26

31

RING NUMBER

Fig. 10. Clusters found after removal of monocytes. Cluster C is probably monocyte nuclei.

ment for Cell Characterization." Clin. Chem., Vol. 21, 12971304. 1975. [7] Steinkamp, J. A., M. J. Fulwyler, J. R. Coulter, R. D. Hiebert, J. L. Horney, and P. F. Mullaney. "A New Multiparameter Separator for Microscopic Particles and Biological Cells." Rev. Sci. Instrum., Vol. 44, 1301-1310. 1973. [81 Mullaney, P. F. and P. N. Dean. "The Small Angle Light Scatter-

ing of Biological Cells." Biophys. J., Vol. 10, 764-772. 1970. [9] Goad, C. A. "A Clustering Algorithm for Mixtures of Monotone Densities." Los Alamos Scientific Laboratory report LA-7120MS. January 1978. [101 B~yum, A. "Separation of White Blood Cells." Nature, Vol. 204, 793-794. 1964.

526

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-25, NO. 6, NOVEMBER 1978

J. M. Crowell (M'75), photograph and biography not available at the time of publication.

B. J. Price, photograph and biography not available at the time of publication.

R. D. Hiebert (S'48-A'50-M'55-SM'58), photograph and biography not available at the time of publication.

L. S. Cram, photograph and biography not available at the time of publication.

G. C. Salzman (M'74), photograph and biography not available at the time of publication.

P. F. Mullaney, photograph and biography not available at the time of

publication.

Electrocutaneous Nerve Stimulation-I: Model and Experiment RUDOLF BUTIKOFER AND PETER D. LAWRENCE, MEMBER, IEEE Abstract-The behavior of nerve fibers in the skin during electrocutaneous stimulation has been studied in this investigation for the purpose of understanding the influence of various current pulse parameters. One part of the investigation assessed the amount of stimulus charge, for various pulse parameters, required to depolarize the nodal membrane of myelinated nerve, using the Frankenhaeuser-Huxley model for Xenopus Laevis (toad). The second part of the investigation involved the experimental application of biphasic current pulses via a concentric electrode to the skin of a number of human subjects. The subjects were asked to match the intensity of sensation as stimulus parameters were varied. The experimental results were compared to the predictions of the model by the process of normalization for temperature differences and the loss of electrode current in adjacent passive tissues. It was found that the threshold charge increased approximately linearly with pulse width as the pulse width of each half of the symmetrical biphasic pulse increased (at constant interpulse interval). Beyond a certain value of pulse width however, the threshold charge increased more steeply. It was also found that the threshold charge decreased with increasing separation of constant duration positive and negative pulse components. The experimental results were found to closely agree with the predictions from the model.

INTRODUCTION S TUDIES of electrically induced dermal sensation have been made over many decades. This work was reviewed by Pfeiffer in 1968 [1]. A matter of some interest is the influence of the intensity and temporal parameters of a chosen stimulus waveform upon the sensation induced. The effect of Manuscript received September 26, 1977; revised June 12, 1978. This work was supported by the National Research Council of Canada under Grant A9341 and the Canada Council (Award 75 9368 and 76 9238). R. Biftikofer was with the Department of Electrical Engineering, University of British Columbia, Vancouver, B.C., Canada. He is now with the "Eidgenossische Materialprufungsanstalt," Dubendorf, Switzer-

land. P. D. Lawrence is with the Department of Electrical Engineering, University of British Columbia, Vancouver, B.C., Canada.

these parameters has been studied experimentally by observing waveform parameters which produce a threshold of sensation in a human subject. Parameters investigated by various researchers are; the number of pulses per train, duration of monophasic pulses, amplitude of monophasic pulses, duration of biphasic pulses and pulse repetition rate [2-7]. An evaluation of the effect of electrical stimuli acting directly upon nerve fibers in the skin would seem to offer some advantages to the selection of effective stimuli for such investigations and to the clinical usage of cutaneous electrical stimulation. In order to evaluate the effects of parameter variations on threshold, a modeling approach was taken here. There is evidence to suggest that the sensory effects of electrical stimuli applied to the skin are predominantly due to the direct excitation of peripheral nerve fibers [4, 8-10] . Thus a model for the passive and active properties of nerve was selected. It is well known that the fibers with the lowest threshold to electrical stimulation are the large, rapidly-conducting myelinated A-3 fibers [11, 12]. As the level of stimulation is increased, progressively more distant A-3 fibers and smaller myelinated A-6 and unmyelinated C fibers are recruited. Also, the gate theory of pain proposed by Melzack and Wall [13] and the experimental evidence for it [14, 151 indicate that when A-: fiber activity is in excess of AZ- and C fiber activity, the sensation will be pain-free. For the above reasons a model of myelinated nerve was chosen. A number of nerve models based on experimental observations has been proposed. Most of these are modifications of the work of Hodgkin and Huxley [161. These models have been reviewed by Cole [17]. Since myelinated axons were considered here, the closest model that could be found in the literature was that of Frankenhaeuser and Huxley [18] on the toad (Xenopus Laevis). This model was based on a complete set of voltage clamp experiments.

0018-9294/78/1100-0526$00.75

© 1978 IEEE

A light-scattering system for high-speed cell analysis.

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-25, NO. 6, NOVEMBER 1978 519 A Light-Scattering System for High-Speed Cell AnalysisJ. M. CROWE...
2MB Sizes 0 Downloads 0 Views