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The real-time sorting of neuro-electric action potentials in multiple unit studies
192
ELECTROENCEPHALOGRAPHY AND CLINICAL NEUROPHYSIOLOGY
THE REAL-TIME SORTING OF NEURO-ELECTRIC ACTION
POTENTIALS
IN MULTIPLE UNIT STUDIES t WILLIAM SIMON 2
Massachusetts Institute of Technology Research Laboratory c] Electronics and Center Development Office, Cambridge, Mass. (U.S.A.) (Accepted for publication: June 24, 1964)
Within the last few years, measurements from clusters of nerve cells have begun to provide clues to the functional relationships of cells in the central nervous system. Records from a single micro-electrode will often show action potentials from a number of cells. The action potentials of individual cells are distinguished from each other by waveform. Visual examination of a record of a few hundred action potentials will usually reveal a small number of clearly defined groups (see Fig. 1). Visual sorting, however, is a slow tedious job which does not allow the experimenter to see his results while the preparation is still viable. In the past year some progress has been made in computer analysis of the micro-
Time
~
electrode data. Gerstein and Clark (1960) have reported the use of the TX2 computer at Lincoln Laboratory to classify action potentials by a waveform comparison method. The technique they used, however, requires a very i This work was supported in part by the U.S. Army, Navy, and Air Force under Contract DA 36-039-AMC03200(E); in part by the National Science Foundation (Grant GP-2495), the National Institutes of Health (Grant MH-04737-04), and the National Aeronautics and Space Administration (Grant NsG-496). Present address: Department of Physiology, Harvard Medical School, Boston, Massachusetts.
I msec
Fig. 1 At least three clearly defined groups of action potentials can be seen in the above photograph. A fourth group is discernible just under the first peak on the left.
Electroenceph. clin. Neurophysiol., 1965, 18:192-195
SORTING OF ACTION POTENTIALS
193
t1
I
~ ....~
t2
~lll~JJ
mw~¢
Time Fig. 2 T h e c o m p u t e r m a r k s the times at which samples are taken by blanking points on the trace. The two points s h o w n here were quite effective separators o f the four groups. T h e sweep rate is twice that of Fig. 1. a r g e c o m p u t e r (64000 word m e m o r y ) a n d runs at a rate considerably less t h a n real-time rate so that an intermediate tape recording of the micro-electrode signal m u s t be used. A m e a n s by which action potentials could be sorted in a m o d e r a t e size m a c h i n e in real-time, a n d online was needed. In a typical m a m m a l i a n experiment, action potentials f r o m a single neuron occur at an average interval of approximately 50 100 msec, a l t h o u g h action potentials f r o m different cells can occur simultaneously. A t this rate, any m e t h o d of sorting in real-time m u s t be operationally simple in order to r u n fast e n o u g h on m o d e r a t e size c o m p u t e r s such as a L I N C ~with a 2000 word m e m o r y . O n e of our early a t t e m p t s at sorting was based on the amplitude of the voltage at s o m e fixed time following a threshold level crossing. T h e separation that could be obtained f r o m the voltage at a single point did n o t permit sufficiently clean separation of the classes. Typically, at a p o i n t in time at which one action potential shape was separable from the others by amplitude, r e m a i n i n g ones differed only in slope. A l t h o u g h this difference is readily seen on a p h o t o g r a p h , a circuit which s a m p l e s only a single point in time would fail to separate the groups. The procedure of m e a s u r i n g voltages at two p o i n t s in time following the oscilloscope trigger (as s h o w n in Fig. 2) has been quite successful. Separation of action potential w a v e f o r m s can be seen by plotting a h i s t o g r a m Laboratory I n s t r u m e n t C o m p u t e r .
in two i n d e p e n d e n t d i m e n s i o n s which represent the voltages V (tl), V (t~) m e a s u r e d at two times. Fig. 3 and 4 are c o m p u t e r displays of such h i s t o g r a m s . Fig. 3 represents the frequency of occurrence of a particular voltage pair V (tD, V 02) by density at each point. Alternatively, in Fig. 4, a modified stereographic projection is employed. Both displays are useful in identifying clusters o f action potential waveforms. A s is easily seen from these figures, there were four g r o u p s of action potentials in these data. W a v e f o r m s falling into each of the separated g r o u p s are s h o w n in Fig. 5. T h e c o m p u t e r p r o g r a m is used as follows: Data are entered directly f r o m the micro-electrode experiment (or a tape recording played at real-time rate). A display such as Fig. 2 is p r o d u c e d o n a conventional analog oscilloscope. T h e triggering of the oscilloscope by each action potential is used to synchronize the c o m p u t e r p r o g r a m . A t two s u b s e q u e n t points in time, tl and t2, voltage readings are t a k e n a n d entered into the c o m p u t e r by an analog-to-digital converter 2. The times t~ and t2 are defined by knob-controlled p r o g r a m parameters. At intervals, the c o m p u t e r displays a h i s t o g r a m of the frequency of ~' T h e voltages s a m p l e d need n o t be the action potential amplitudes at time tl or tz. In s o m e cases it is better to use the time derivative of the amplitude (as produced by an a n a l o g differentiating circuit). This m a y provide better separation of action potential waveforms whose m o s t c o n s p i c u o u s difference is slope.
Electroeneeph. elin. Ne irophysiol., 1965, 18:192-195
194
w . S~MOY
c~ V
Fig. 3 Histogram of the frequency of occurrence of voltage pairs V1 (t~), V2 (t2) displayed as density.
\ f . o-
. , e | e ~ ,
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
e~ 7
~
V1 (tl)
Fig. 4 The same data as in Fig. 3, displayed in a stereographic projection.
Electroenceph. clin. Neurophysiol., 1965, 18:192 195
195
SORTING OF ACTIO'., ~',If~?i l'~'x'.3
ii
i
ttt!ltltl !:,Iti!11!tllf C1
C2
{
i: --~------ t
-'~------- t
lI Ca
C4
Fig. 5 The four groups of action potentials separated. Each trace above is the superposition of many action potentials of one group.
occurrence of voltages at co-ordinates V (tl) and V (tz) and the operator watches for the build-up of distinct clusters. If at the particular settings of times tl and t2 clearly defined and separated clusters do not occur, the times at which samples are taken can be varied. With practice, only a few minutes are required to find settings which will produce good isolated clusters in the histogram of V (tD, V (t2). When the operator has arrived at a set of sampling points which produce well-separated groupings, he interrupts the program and defines the groups by means of a light pen. A particular cluster is defined as group A, another as group B, and so on. Once the operator has defined the groups, the computer will identify each subsequent action potential as belonging in one of the groups. Since different action potentials can arrive in rapid succession it is necessary that the computer be able to accept a new action potential quickly. It has been possible t~ program so that a new pulse can be accepted within 200 #sec of time t2. Therefore, as long as action potentials do not overlap, the computer will accept them.
Reference: SIMON, W. The real-time sorting of n e u r o ~ t r i c clin. Neurophysiol., 1965, 18: 192-195.
The speed requirement means that the computer cannot be used simultaneously to do any other computing besides the identification. In some of our experiments, we have used a second 1000word memory (LINC) computer to display the action potentials grouped by the first computer (Fig. 5). The second computer could also be used to compile various conditional firing probabilities or other measurements useful in the study of relations between neurons. SUMMARY Description of a method by which action potentials recorded simultaneously can be sorted in a moderate size machine in real-time and on-line. REFERENCES GERSTEIN, G. L. and CLARK, W. A. Simultaneous studies of firing patterns in several neurons. Science, 1960, 143: 1325-1327.
action potentials in multiple unit studies. Electroenceph.
ELECTROENCEPHALOGRAPHY AND CLINICAL NEUROPHYSIOLOGY
THE REAL-TIME SORTING OF NEURO-ELECTRIC ACTION
POTENTIALS
IN MULTIPLE UNIT STUDIES t WILLIAM SIMON 2
Massachusetts Institute of Technology Research Laboratory c] Electronics and Center Development Office, Cambridge, Mass. (U.S.A.) (Accepted for publication: June 24, 1964)
Within the last few years, measurements from clusters of nerve cells have begun to provide clues to the functional relationships of cells in the central nervous system. Records from a single micro-electrode will often show action potentials from a number of cells. The action potentials of individual cells are distinguished from each other by waveform. Visual examination of a record of a few hundred action potentials will usually reveal a small number of clearly defined groups (see Fig. 1). Visual sorting, however, is a slow tedious job which does not allow the experimenter to see his results while the preparation is still viable. In the past year some progress has been made in computer analysis of the micro-
Time
~
electrode data. Gerstein and Clark (1960) have reported the use of the TX2 computer at Lincoln Laboratory to classify action potentials by a waveform comparison method. The technique they used, however, requires a very i This work was supported in part by the U.S. Army, Navy, and Air Force under Contract DA 36-039-AMC03200(E); in part by the National Science Foundation (Grant GP-2495), the National Institutes of Health (Grant MH-04737-04), and the National Aeronautics and Space Administration (Grant NsG-496). Present address: Department of Physiology, Harvard Medical School, Boston, Massachusetts.
I msec
Fig. 1 At least three clearly defined groups of action potentials can be seen in the above photograph. A fourth group is discernible just under the first peak on the left.
Electroenceph. clin. Neurophysiol., 1965, 18:192-195
SORTING OF ACTION POTENTIALS
193
t1
I
~ ....~
t2
~lll~JJ
mw~¢
Time Fig. 2 T h e c o m p u t e r m a r k s the times at which samples are taken by blanking points on the trace. The two points s h o w n here were quite effective separators o f the four groups. T h e sweep rate is twice that of Fig. 1. a r g e c o m p u t e r (64000 word m e m o r y ) a n d runs at a rate considerably less t h a n real-time rate so that an intermediate tape recording of the micro-electrode signal m u s t be used. A m e a n s by which action potentials could be sorted in a m o d e r a t e size m a c h i n e in real-time, a n d online was needed. In a typical m a m m a l i a n experiment, action potentials f r o m a single neuron occur at an average interval of approximately 50 100 msec, a l t h o u g h action potentials f r o m different cells can occur simultaneously. A t this rate, any m e t h o d of sorting in real-time m u s t be operationally simple in order to r u n fast e n o u g h on m o d e r a t e size c o m p u t e r s such as a L I N C ~with a 2000 word m e m o r y . O n e of our early a t t e m p t s at sorting was based on the amplitude of the voltage at s o m e fixed time following a threshold level crossing. T h e separation that could be obtained f r o m the voltage at a single point did n o t permit sufficiently clean separation of the classes. Typically, at a p o i n t in time at which one action potential shape was separable from the others by amplitude, r e m a i n i n g ones differed only in slope. A l t h o u g h this difference is readily seen on a p h o t o g r a p h , a circuit which s a m p l e s only a single point in time would fail to separate the groups. The procedure of m e a s u r i n g voltages at two p o i n t s in time following the oscilloscope trigger (as s h o w n in Fig. 2) has been quite successful. Separation of action potential w a v e f o r m s can be seen by plotting a h i s t o g r a m Laboratory I n s t r u m e n t C o m p u t e r .
in two i n d e p e n d e n t d i m e n s i o n s which represent the voltages V (tl), V (t~) m e a s u r e d at two times. Fig. 3 and 4 are c o m p u t e r displays of such h i s t o g r a m s . Fig. 3 represents the frequency of occurrence of a particular voltage pair V (tD, V 02) by density at each point. Alternatively, in Fig. 4, a modified stereographic projection is employed. Both displays are useful in identifying clusters o f action potential waveforms. A s is easily seen from these figures, there were four g r o u p s of action potentials in these data. W a v e f o r m s falling into each of the separated g r o u p s are s h o w n in Fig. 5. T h e c o m p u t e r p r o g r a m is used as follows: Data are entered directly f r o m the micro-electrode experiment (or a tape recording played at real-time rate). A display such as Fig. 2 is p r o d u c e d o n a conventional analog oscilloscope. T h e triggering of the oscilloscope by each action potential is used to synchronize the c o m p u t e r p r o g r a m . A t two s u b s e q u e n t points in time, tl and t2, voltage readings are t a k e n a n d entered into the c o m p u t e r by an analog-to-digital converter 2. The times t~ and t2 are defined by knob-controlled p r o g r a m parameters. At intervals, the c o m p u t e r displays a h i s t o g r a m of the frequency of ~' T h e voltages s a m p l e d need n o t be the action potential amplitudes at time tl or tz. In s o m e cases it is better to use the time derivative of the amplitude (as produced by an a n a l o g differentiating circuit). This m a y provide better separation of action potential waveforms whose m o s t c o n s p i c u o u s difference is slope.
Electroeneeph. elin. Ne irophysiol., 1965, 18:192-195
194
w . S~MOY
c~ V
Fig. 3 Histogram of the frequency of occurrence of voltage pairs V1 (t~), V2 (t2) displayed as density.
\ f . o-
. , e | e ~ ,
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
e~ 7
~
V1 (tl)
Fig. 4 The same data as in Fig. 3, displayed in a stereographic projection.
Electroenceph. clin. Neurophysiol., 1965, 18:192 195
195
SORTING OF ACTIO'., ~',If~?i l'~'x'.3
ii
i
ttt!ltltl !:,Iti!11!tllf C1
C2
{
i: --~------ t
-'~------- t
lI Ca
C4
Fig. 5 The four groups of action potentials separated. Each trace above is the superposition of many action potentials of one group.
occurrence of voltages at co-ordinates V (tl) and V (tz) and the operator watches for the build-up of distinct clusters. If at the particular settings of times tl and t2 clearly defined and separated clusters do not occur, the times at which samples are taken can be varied. With practice, only a few minutes are required to find settings which will produce good isolated clusters in the histogram of V (tD, V (t2). When the operator has arrived at a set of sampling points which produce well-separated groupings, he interrupts the program and defines the groups by means of a light pen. A particular cluster is defined as group A, another as group B, and so on. Once the operator has defined the groups, the computer will identify each subsequent action potential as belonging in one of the groups. Since different action potentials can arrive in rapid succession it is necessary that the computer be able to accept a new action potential quickly. It has been possible t~ program so that a new pulse can be accepted within 200 #sec of time t2. Therefore, as long as action potentials do not overlap, the computer will accept them.
Reference: SIMON, W. The real-time sorting of n e u r o ~ t r i c clin. Neurophysiol., 1965, 18: 192-195.
The speed requirement means that the computer cannot be used simultaneously to do any other computing besides the identification. In some of our experiments, we have used a second 1000word memory (LINC) computer to display the action potentials grouped by the first computer (Fig. 5). The second computer could also be used to compile various conditional firing probabilities or other measurements useful in the study of relations between neurons. SUMMARY Description of a method by which action potentials recorded simultaneously can be sorted in a moderate size machine in real-time and on-line. REFERENCES GERSTEIN, G. L. and CLARK, W. A. Simultaneous studies of firing patterns in several neurons. Science, 1960, 143: 1325-1327.
action potentials in multiple unit studies. Electroenceph.