The thalamocortical system as a neuronal machine: The interaction of ventrolateral nucleus with sensorimotor cortex in the cat

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Research Reports THE THALAMOCORTICAL SYSTEM AS A NEURONAL MACHINE: THE INTERACTION OF VENTROLATERAL NUCLEUS WITH SENSORIMOTOR CORTEX IN THE CAT

R. N. J O H N S O N AND G. R. H A N N A

Division of Biomedical Engineering, and Department of Neurology, University of Yirginia School of Medicine, Charlottesville, Va. 22901 (U.S.A.) (Accepted August 31st, 1969)

INTRODUCTION

Numerous studies have been conducted on the cerebellothalamocorticalpathway, considering both cerebellar3-5,12,13,17,23,30 and ventrolateral thalamice,ioAs,la,20, z2, 2a-ze influences on sensorimotor cortex. However, a quantitative treatment of this system from the standpoint of a computing machine, as suggested by Eccles et aLS, has not been undertaken. One of the difficulties in making such an analysis is that responses change with successive stimuli, a fact which has been known since Morison and Dempsey is first described augmentation. Schlag and associates24, 25, using paired stimuli, have studied the time relationship between ventrolateral (VL) thalamic stimulation and the responses evoked in both pyramidal tract (PT) and sensorimotor cortex (MC). Their work suggests that a functional relationship exists, in a mathematical sense, between stimulus intervals and the magnitude of these responses. In this study we considered the ventrolateral thalamic projections to sensorimotor cortex in the cat as a functioning neuronal machine. The first phase of this work involved the search for a suitable method of quantification of the cortical response evoked by VL stimulation. Once such a method was established, we explored the conditions under which mathematical relations could be obtained. Finally, the performance of the neuronal machine has been observed in both closed loop and open loop form - - i.e., before and after interruption of the contralateral brachium conjunctivum (BC) - - to observe the quantitative nature of cerebellar control on the VL-MC system. METHODS

These experiments were conducted on 28 adult, female cats, weighing from 2 to 3 kg. Nineteen were anesthetized with sodium pentobarbital (30 mg/kg) injected intravenously with subsequent doses given when necessary such that withdrawal of the forepaw to pinching was just abolished. Nine cases were operated under regional Brain Research, 18 (1970) 219-239

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analgesia and immobilization with succinylcholine and curare, respiration being maintained by a positive pressure pump. Regional analgesia was obtained by careful infiltration and topical application of lidocaine at the sites of incision and at all pressure points of the stereotaxic instrument. Body temperature was maintained between 37.0 ° and 37.5 ° C by means of an electric heating pad (direct current), automatically controlled from a rectal temperature probe. In 10 of the cases operated on under general anesthesia, the cerebellum was either completely removed by suction (2 cases) or the brachium conjunctivum (BC) contralateral to the thalamic stimulation site was destroyed by a stereotaxically placed electrical lesion (8 cases). Cortical responses from thalamic stimulation were measured with the flexible, printed-circuit recording array of 20 electrodes previously describedlL The cortical electrode was inserted through a trephine hole near the vertex, and then advanced rostrally between the skull and dura mater until the contact points lay over the right sigmoid gyri. In this manner, direct operative exposure and manipulation of the cortical areas under investigation were avoided. The cortical electrode points were coupled through 20-position rotary switches to a 6-channel, battery powered, differential amplifier. The output was then further amplified, displayed on a multi-channel cathode ray oscilloscope (Tektronix RM565), and recorded photographically. Monopolar cortical recordings were made by connecting the stereotaxic frame to amplifier ground, using as a reference the electrical contact with the animal at the two auditory meati and the two inferior orbital margins. Differential recordings were also made between two cortical electrode points, the second one usually at least 6 mm away from the electrode over the point of maximum response. The criterion for considering this second cortical electrode as a valid indifferent reference was that no evoked cortical response could be detected monopolarly from this electrode. The differential method was used to reduce stimulus artifact and 60 cycle hum. Whenever this cross cortical method of recording was employed, we also made simultaneous monopolar recordings from the cortical points of interest, as a control. The thalamic electrode (coaxial) consisted of a center stainless steel wire (diameter 0.35 mm) with the terminal 40-50 mm electropolished to a long tapering point. The outer conductor consisted of a coat of conductive paint between two layers of epoxy insulation with an exposed band approximately 0.5 mm from the tip. The exposed tip of the center conductor was 10-50 # m in diameter. The thalamic electrode was inserted diagonally from the contralateral side, at an angle of 45 ° from the horizontal, penetrating the corpus callosum at about the midline. Rectangular pulses of 1 msec duration were delivered, either singly or in closely spaced pairs (50-350 msec), to the bipolar thalamic electrode. Stimulus amplitudes were adjusted from 1.5 to a maximum of 2 times threshold and held constant throughout each experiment. The thalamic electrode was stereotaxically inserted to within several millimeters of the anticipated target zone (right ventrolateral nucleus), at which point stimulation was commenced and a careful monopolar search of all 20 electrode points was conducted. The thalamic electrode was then slowly advanced and all cortical points were again scanned. By this method, a specific area in thalamus could Brain Research, 18 (1970) 219-239

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be related to a single point on pericruciate cortex where maximum short latency, surface positive responses occurred. Since the cortical electrode points were 3 mm apart, occasionally the point of maximum response would occur between two electrodes. When this occurred, data were taken from both electrode points simultaneously. At the termination of each experiment, electrode locations were marked by electrolytic deposition of iron (direct current of 5 mA-sec) from both thalamic and cortical electrodes. After sacrifice with intravenous pentobarbital, iron deposits were identified by means of the potassium ferrocyanide reaction, grossly on the cortex, and in 20 /~m coronal sections through thalamus, stained for Nissl substance (cresyl violet) or myelin sheath (Weil). Basic stereotaxic references were the atlases of Snider and Niemer 27 and Jasper and Ajmone Marsan 14. Electrophysiological data were obtained directly from the film and from photographic enlargements. Area measurements were taken from the photographic enlargements using a planimeter. In order to minimize the effect of the width of the oscilloscope trace on area measurements, the tracing point of the planimeter was adjusted to follow the center of the trace at all times. The variables measured are defined in Results. RESULTS

Definition of variables In order to make a quantitative evaluation of the cortical evoked response elicited from VL stimulation, a set of variables associated with the response must be identified. In particular, some method of assessment of machine 'output' is desired. A number of investigators 7,2°,24,z5 have illustrated the relationships which exist between cortical potentials following VL stimulation and PT cell discharges. From this it can be expected that the first 10-25 msec interval of the cortical evoked response will contain or reflect information of some sort concerning the PT output. Waveform A (Fig. 1) was obtained from an experimental preparation under general anesthesia, while waveforms B through D were obtained from a single preparation under regional analgesia. In general, after the stimulus, a period of 10-25 msec exists during which oscillatory activity occurs, with the initial deflection always surface positive. For most experiments conducted under general anesthesia (Fig. 1A), this smooth oscillatory response is terminated with an obvious notch or inflection (T1 and T2) and then followed by a highly variable negative wave. Bishop et al. 2, in studies on cat visual cortex, refer to this positive-negative wave occurring before the inflection as the primary response. For the regional analgesia cases, termination of this dynamic phase is also quite obvious, with the following wave usually going negative but to a lesser extent than for the general anesthesia cases. This time interval (Tn) measured from the start of the stimulus to the termination of the oscillatory response is considered to be machine 'output time'. For these experiments the practice has been to define machine output as:

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Fig. 1. Variables associated with evoked response pulse pairs. Sn denotes the time of delivery of a stimulus with the subscript indicating association with either the first or second pulse of the pair. The pulse pair interval (t) denotes the time interval between $1 and S~. Positivity upwards in all examples. A, Typical response obtained from a preparation (Case No. 193) under general anesthesia. The initial positive-negative response (shown shaded) is terminated with an obvious notch or inflection (T1 and T~,). The shaded areas under the curve, along with the T~ and T2 intervals, are used to calculate specific output as defined in the text. B, Typical response obtained from a preparation (Case No. 187) under regional analgesia. The dynamic phase is again indicated by shading and its termination by T1 or "1"2.Specific output has a measured value of 2.8 for this example. B-D, Three responses taken sequentially from the same preparation (Case No. 187) to illustrate the attenuation of the second response of the pair when t is greater than the clock time (Cx). Clock time is measured from the stimulus to the start of the afterdischarge as shown in C and D. In B, t is approximately equal to C~ and specific output approaches a maximum of about 2.72. An estimate of the clock time associated with the second pulse of the pair is indicated as Ca in A.

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Fig. 2. Nonsequential test showing the change in specific output (solid circles) as a function of the pulse pair interval (t). An estimate of specific output (triangles) has been obtained using the clock time (Cl) measured from the single pulse just preceding each pulse pair, along with equation 1 from the text• The extreme boundaries for all 13 single pulse C1 values are shown by the dashed cone (115143 msec) with the mean value indicated by m (133 msec). Note the attenuation of specificoutput for t values greater than the maximum clock time• Case No. 187, regional analgesia, semilogarithmic plot.

where Y1 is arbitrarily selected as the standard. The time interval between the first and second pulse of the pair is denoted as t. Another important variable is that associated with the afterdischarge and denoted as C1 in Fig. 1C and referred to as clock time. Clock time is measured from the stimulus to the vicinity of the start of the afterdischarge and generally has a value of about 150 msec. In subsequent illustrations it will be shown to be the point where the specific output attains a theoretical value of 2.72. The method to identify clock time (Cx) is shown in Fig. 1 in sequence D, C, B, where in D, t is 20 msec greater than the expected C1 value and Y2 is zero. When t is only 15 msec greater than C1 some response exists (Fig. 1C) and when t = C1, maximal response occurs (Fig. IB). Specific output has a measured value of 2.8 in Fig. lB. Due to variation in gross waveforms, C1 must be tested for each experimental preparation to set up some visual standard of measurement. This C1 measure is numerically equivalent to the latency of the L response as defined by Schlag 25 and has similar extreme values (110-350 msec).

Internal states and past history Consider the case where the experimenter applies some stimulus routine to a neural system and obtains a resulting evoked response which he then quantifies in some way. Then the experimenter immediately repeats his stimulus routine in an identical fashion but gets different quantitative results. What causes this difference? It is pertinent to consider whether this system under study forms a 'rigid' machine or a 'self-modifying' one. I f this is a 'self-modifying' machine, our results depend not only on the construction of the machine, but also on the organization of the experiments executed with it a. In particular, we are concerned with the initial state of the machine

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at the time of stimulation and whether or not the same initial state exists at the time of the next stimulation. For if the machine does not return to the same state when our stimulation experiment is repeated the response will be different. An important step in the experimental procedure is to search for a method of establishing a constant initial state, or reference. Consider the results illustrated in Fig. 2, obtained from the following experimenter interaction with the neuronal machine. A single stimulus pulse (SP) is applied and then followed 1 sec later by a pulse pair (DP) whose interval (t) is about 50 msec. This SP-DP sequence is then repeated for varying pulse pair intervals from 50 to 150 msec. The specific output (solid circles) is then plotted (Fig. 2) as a function of the pulse pair interval (t). From Fig. 2 we assume that the following approximate relationship applies between the specific output (Y2/YI), the pulse pair interval (t) and the clock time (C1) measured by the previously defined method, over an interval of t values from about 50 msec to t = C1. Yz/Ya ~ exp (t/CD for SP-DP sequence only.

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A value for C1 cannot be obtained from the first pulse of a pair when the pulse pair interval is less than the clock time (Ca). This was demonstrated when defining C1 values (Fig. 1). It is possible to measure the C1 value associated with the stimulus pulse given 1 sec before the pulse pair since a visual standard was established when C1 was measured as previously indicated. This is useful, since it gives an indication of the amount of variation which can be expected in clock time values. The single pulse C1 values have a mean of 133 msec, with a minimum of 115 msec and a maximum of 143 msec. If these C1 values obtained from the single stimulation are assumed to be a good guess for the C~ value associated with the first pulse of the pair, using equation 1, an estimate of specific output can be calculated and plotted in Fig. 2 (triangles). The extreme boundaries for all 13 single pulse values are shown by the dashed cone in Fig. 2. All measured values of specific output do not fall within the dashed cone, with the greatest deviation occurring for t values between 110 msec and 120 msec (compare to Fig. 5, case No. 170). However, a least squares curve fit of a straight line through the 11 specific output points (obtained for t < C1 max) falls approximately on the mean of the C1 values obtained from the single pulse measurements. The clock time calculated by this method is 137 rnsec. Consider this change in technique. Suppose we use sequential double pulse stimuli, set at a basic rate of 1/sec, and then plot specific output as a function of the pulse pair interval. The results of such an experiment are shown in Fig. 3 taken from the same animal (No. 187) immediately following the experiment shown in Fig. 2. The procedure is to start with a low t value (10 msec) and increase in the steps shown in Fig. 3. Specific output cannot be calculated for t values less than about 50 msec since Y2 is obscured by the negative wave following the first evoked response of the pair. Note that in the portion of the curve marked 1 (Fig. 3) 7 out of the 8 values taken are outside the dashed cone representing C1 values. Brain Research, 18 (1970) 219-239

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Fig. 3. Sequential test (1/sec) showing the change in specific output (solid circles) as a function of the pulse pair interval (t). The break indicated between curves 1 and 2 is the result of an equipment limitation, as the stimulator used required a scale change at t values of 110 msec. The dashed cone indicates the extreme boundaries of the single pulse C1 values (117-145 msec) measured sequentially (1/sec) in the interval between taking the data for curves 1 and 2. The mean clock time is labeled m above and has a value of 132 msec. Note that 7 out of the 8 values plotted in curve 1 are outside the dotted cone. Curve 2 illustrates again that specific output values are attenuated for t values greater than the maximum clock time. Case No. 187, regional analgesia, semilogarithmic plot. I

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Fig. 4. Cyclic sequential test (l/sec) illustrating multi-valued behavior. The first data point in the cycle is indicated by the arrow head. Cycle 1 was obtained from a preparation under general anesthesia (Case No. 193) while cycle 2 was obtained from Case No. 192 under regional analgesia. The mean clock time (156 msec) labeled m above and shown by a dashed line was, by chance, the same for the 2 cases. Semilogarithmic plot. T h e s t i m u l a t o r u s e d required a scale c h a n g e at t values o f 110 m s e c , as i n d i c a t e d b y the b r e a k b e t w e e n curves 1 a n d 2. D u r i n g this scale c h a n g e , 28 sec o f single p u l s e s e q u e n t i a l testing w a s c o n d u c t e d , a l l o w i n g the single p u l s e C1 data to be o b t a i n e d as i n d i c a t e d (Fig. 3) w i t h q

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Fig. 5. Machine trajectories for constant pulse pair intervals. Case No. 170, general anesthesia, stimulus rate 1.5/sec. A, Specific output calculated for the first pulse pair following a single stimulus and plotted as a function of the pulse pair interval. The extreme boundaries for the single pulse C1 values are shown by the dashed cone (305-350 msec) with the mean value indicated by m (322 msec). The numbers refer to the machine trajectories plotted in B and in Fig. 6A. Any value for specific output estimated from a plot such as this is referred to as a reference value. Semilogarithmic plot. B, Specific output plotted in the order of occurrence of the pulse pairs for constant pulse pair intervals. The value of specific output for pulse pair number 1 is plotted as a function of t in A above• The t values for each curve are as follows: 1, 64 msec; 2, 84 msec; 3, 94 msec; 4, 105 msec. about the same when using the S P - D P method (Fig. 2) or the single pulse sequential (l/sec) method (Fig. 3). The application of a statistical technique (t test) reveals that this small difference in sample means would occur 9 times out o f 10 due to chance alone (t = 0.115, P > 0.9). F r o m this we conclude that C1 values measured by either method are about the same. It seems, though, comparing Fig. 2 to Fig. 3, that sequential paired pulse testing produces specific output values which differ considerably from values obtained by the single pulse-double pulse routine. That is, specific output values are influenced in some fashion by previous pulse pairs. Cyclic sequential paired pulse testing (1/sec) produces the hysteresis-like effects shown in Fig. 4. These data are taken f r o m two different cases, one under general anesthesia and the other under regional analgesia. Such multi-valued behavior is not unexpected from a device whose output appears to depend on previous outputs, or perhaps better stated, on its past history o f use.

Machine trajectories Consider the following change in experimental routine. First deliver a single pulse, and then a sequential set of double stimuli at a constant t interval. I f this is done for a n u m b e r o f t values and the specific output is plotted for the first double pulse value, the plot shown in Fig. 5A can be obtained, a plot similar to that o f Fig. 2. Now, what trajectory does the machine follow with respect to time? The plots in Fig. 5B and Fig. 6A show the values o f specific output (t held constant) obtained for the first 4 sequential double pulse pairs delivered after the single pulse stimulus.

Brain Research, 18 (1970) 219-239

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Fig. 6. The effects of a single t shift on machine trajectories. Case No. 170, general anesthesia, stimulus rate 1.5/sec. A, Specific output plotted in sequential fashion for 4 pulse pairs, with the t interval held constant. The numbers on the curve refer to the first specific output value plotted in Fig. 5A. The t value for trajectory 5 is 150 msec while trajectory 6 has a t value of 210 msec. The modifying factors (MF), as defined in the text, are indicated on the 2 curves for the change between the third and fourth pulse pairs. B, Repetition of the 2 trajectories plotted in A for 3 pulse pairs, after which the t value has been shifted. The 5' trajectory was started with a t value.of 150 msec and was then shifted to a t value of 178 msec. The 6' trajectory has an initial value of 210 msec with t shifted to 241 msec. Note the significant departure of the 5' and 6' trajectories from the 5 and 6 trajectories when t is shifted. According to A s h b y 1, ' T h e most fundamental concept o f cybernetics is that o f "difference", either that two things are recognizably different or that one thing has changed with time.' The lines o f behavior or trajectories of the machine for constant values o f t are illustrated in Fig. 5B and Fig. 6A. The change in specific output which occurs between any two successive values is defined as a modifying factor (MF) and is calculated for any pair by taking the second specific output and dividing by the first. The value o f the modifying factor for trajectory n u m b e r 5 (Fig. 6A) calculated from the third and fourth sequential pulses is 1.22 (t : 150 msec). Shown in Fig. 6B is a plot of a second test o f trajectory n u m b e r 5 (called 5') also for a t interval o f 150 msec. After 3 sequential pulse pairs delivered at 150 msec, the pulse interval is changed to 178 msec so that the 5' trajectory (Fig. 6B) shows a significant departure f r o m the 5 trajectory (Fig. 6A) at sequential pulse n u m b e r 4. F r o m the past history o f this machine, the change that should have occurred is k n o w n to be about 1.22. It is also k n o w n f r o m Fig. 5A that the reference value o f specific output for a t value o f 178 msec should be 1.74 (using the measured mean C1 value o f 322 msec). We would expect that the actual specific output would reflect both the change put in by the experimenter and the change dictated by the machine trajectory 16. The estimate o f Brain Research, 18 (1970) 219-239

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R. N. JOHNSON AND G. R. HANNA

specific output, for a t change from 150 msec to 178 msec, after 4 sequential pulses is then given as: Yz/Y1 = 1.74 (1.22) = 2.12 The measured value of specific output (Fig. 6B) was 2.13, so for this example the estimated and measured values are essentially the same. Consider trajectory 6 in Fig. 6A, which has a t value of 210 msec. The modifying factor here is 0.82. Fig. 6B shows the 6' trajectory, with a shift from a t value of 210 msec to one of 241 msec after the third pulse. The reference value, for a t interval of 241 msec, is 2.11 (based on a C1 value of 322 msec). Therefore, Y2/Y1 = 2.11 (0.82) = 1.73 The measured value of specific output is 1.65 (Fig. 6B) which is within 5 % of the estimated value. The last two examples illustrate the type of experimenter-neuronal machine interaction which appears to be taking place, at least as far as our present data indicate. Specific output can now be approximated for a shift in t by Y2/Y1 ~ (MF1) (exp (tz/C1))

(2)

where MF1 is the modifying factor obtained from a previous test at the initial pulse pair interval (h), and t2 denotes the second pulse pair interval.

The controlled trajectory The lines of behavior or trajectories illustrated in the previous section (Fig. 5B and Fig. 6A), once established, are out of control of the experimenter unless t changes are introduced, and even then control is shared by both the experimenter (t changes) and the machine (MF value at time of t change). The following method is an attempt to force a given trajectory (on an average) on the neuronal machine by a specific sequence of stimuli. Perhaps it is appropriate to sound a note of caution at this point. The previous tests which we have illustrated are little more than straightforward observations of the facts with few assumptions being required. However, this is not true of the following test, and interpretations of the results should be made with care. This test we have come to call a 'linear exam' and the results of such a test are indicated in Fig. 7. The method involves delivering in sequential fashion at a rate of 1/sec, 3 pulse pairs at a t interval of 70 msec, 3 pulse pairs at a t interval of 85 msec, 2 at 100 msec, and 2 at 110 msec. For clock times of 125 msec, or greater, specific output values calculated from equation 1 (i.e., reference values) will produce the approximately linear test:line shown in Fig. 7. The mean C1 value for this case (No. 151, Fig. 7) was found to be 128 msec, based on a set of S P - D P tests and a plot such as Fig. 2 and Fig. 5A. To start the problem, at least 3 pulse pairs, delivered at a t value of about 40

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Fig. 7. The method of the linear exam. Case No. 151, general anesthesia, stimulus rate 1/sec. The actual pulse pair intervals for the 5 cycles shown are as follows: Cycle 1, 71 msec; 2, 87 msec; 3, 100 msec; 4 and 5, 110 msec. The linear test line (open circles) was obtained from equation 1 in the text using a measured mean clock time of 128 msec. Note that the linear test values (open circles) are only indicated at the beginning of each cycle; that is, when a t shift or 'new information' is supplied by the experimenter. The measured specific output values (solid circles) are shown grouped in cycles of similar t values, with the average of all values of a given cycle (squares) plotted at the end of each cycle. Note that the average response line is linear and approximately parallel to the linear test line. msec are applied, then a shift to a t of 70 msec and the above indicated sequence is followed. This keeps the initial measured specific output value below the reference value. The purpose of this is to show that if we start with 'depressed' responses, all following responses in the linear exam will be similarly influenced. I f only single stimuli are delivered and then the test sequence is started, the measured specific output values cluster about the linear test line. This effect was illustrated before in Fig. 3. For purposes of analysis, this test is thought of as being divided into 5 cycles. Cycle number 1 consists of the 3 pulse pairs delivered at a t value of 70 msec. The average of the specific output values is plotted at the end of the cycle (squares in Fig. 7). Cylce 2 is then started by shifting the t value on the fourth sequential pulse to 85 msec and the 3 specific output values are again measured, averaged and plotted at the end of the cycle. Cycle 3 consists of only 2 pulse pairs at a t value of 100 msec. Again, the specific output is averaged at the end of the cycle. Cycle 4 consists of 2 specific output values with t equal to 110 msec. Cycle 5 consists of the next 2 or 3 pulse pairs; however, the t value remains unchanged from that of cycle 4. A line drawn through the average of each cycle (squares) is termed the average response line. Fig. 7 shows the results of a linear exam conducted on Case No. 151. The average response line is linear and approximately parallel to the linear test line as expected. The relationship between the reference value, the measured value of specific output and the modifying factor was illustrated in equation 2. I f the average value of specific output (squares) for each cycle of Fig. 7 is used, along with the reference value (open circles) taken from the linear test line, an average modifying factor can be calculated for each cycle. The average modifying factor is essentially the same for cycles 1

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Fig. 8. The linear exam and the constant t machine trajectory conducted before electrocoagulation of BC. Case No. 223, general anesthesia, stimulus rate 1/sec. A, The linear test line (open circles) was obtained from equation 1 in the text using a measured mean clock time of 145 msec. The measured specific output values (solid circles) are shown grouped in cycles of similar t values, with the average of all values of a given cycle (squares) plotted at the end of each cycle. The actual pulse pair intervals for the 5 cycles shown are as follows: Cycle 1, 70 msec; 2, 85 msec; 3, 103 msec; 4 and 5, 111 msec. Note the differences in the linear exam shown above as compared to Fig. 9A. B, Constant t (110 msec) machine trajectory preceded by only a single pulse. The data are grouped in cycles 4' and 5' to allow comparison with cycles 4 and 5 in A above. Note the differences in the constant t trajectory when preceded by a single pulse rather than by the first 3 cycles of the linear exam routine as in A above. Also compare the modifying factor values listed here to those shown in Fig. 9B, obtained after BC ablation.

through 4 and has a mean value of 0.84. Simply stated, the average response values all are about 84 ~ of the reference values. It does appear then to be possible to impose a controlled trajectory, on an average, on the neuronal machine at least over a duration of 13 sec. The first 3 cycles of the linear exam establish this trajectory which is then maintained over the last 2 cycles even when no corresponding change is made in the pulse pair interval (t). Cerebellar influences In order to investigate cerebellar influences, 2 cases were undertaken where the cerebellum was completely removed by suction. One case seemed to indicate that as Brain Research, 18 (1970) 219-239

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Fig. 9. The linear exam and the constant t machine trajectory conducted after electrocoagulation of BC. Case No. 223, general anesthesia, stimulus rate 1/sac. A, The linear test line (open circles) was obtained from equation 1 in the text using a measured mean clock time of 130 msec. The measured specific output values (solid circles) are shown grouped in cycles of similar t values, with the average of all values of a given cycle (squares) plotted at the end of each cycle. The actual pulse pair intervals for the 5 cycles shown are as follows: Cycle 1, 71 msec; 2, 86 msec; 3, 102 msec; 4, 5 and 6, 111 msec. Note the differences between this plot and Fig. 8A, in particular, the magnitude of the change between comparable specific output values. B, Constant t (110 msec) machine trajectory preceded by only a single pulse. The data are grouped in cycles 4' and 5' to allow comparison with cycles 4 and 5 in A above. Note that the constant t trajectory seems to be controlled and follows the same slope as the linear test line (cycles 4 and 5 in A). However, when preceded only by a single pulse, the trajectory increases in much more rapid fashion, as shown in B. Compare the modifying factors listed here to those shown in Fig. 8B.

unspecified p o r t i o n s o f c e r e b e l l u m are r e m o v e d , the m o d i f y i n g factors o b t a i n e d f r o m sequential testing change a n d specific o u t p u t a m p l i t u d e s increase. Eight cases were then c o n d u c t e d where the c o n t r a l a t e r a l b r a c h i u m c o n j u n c t i v u m (BC) was d e s t r o y e d b y e l e c t r o c o a g u l a t i o n , with sequential testing a n d the linear e x a m c o n d u c t e d b o t h before a n d after BC destruction. T h e linear e x a m c o n d u c t e d before e l e c t r o c o a g u l a t i o n o f BC for Case N o . 223 is shown in Fig. 8A. This is c o m p a r a b l e to the linear e x a m shown in Fig. 7 for Case N o . 151. T h e C1 value for this case (Fig. 8A) was f o u n d to be 145 msec. T h e responses are g r o u p e d as before a n d averaged. T h e average r e s p o n s e line is a g a i n linear a n d a p p r o x i m a t e l y p a r a l l e l to the test line. I f the average value o f specific o u t p u t (squares in Fig. 8A), a l o n g with the reference value (open circles in Fig. 8A) is used in e q u a t i o n 2 a n average m o d i f y i n g f a c t o r can be calculated for each cycle. T h e m e a n value o f the Brain Research, 18 (1970) 219-239

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R. N. JOHNSON AND G. R. HANNA

average modifying factor calculated for the 4 cycles has a value of 0.84, which is equal to the value obtained for Fig. 7. Again, this simply illustrates that the average response line is below the linear test line and this was achieved by stimulating first at t intervals of about 40 msec or less before shifting to a t value of 70 msec and commencing the test. After contralateral BC ablation, the linear exam was again conducted (Fig. 9A). Consider some of the details of Fig. 9A. First, before the linear exam was conducted, C1 was measured and found to be 130 msec, a shift from the value of 145 msec measured before BC ablation. However, this is probably not related to BC ablation, since a 1 0 ~ shift in C1 is not unusual as was illustrated in Figs. 2 and 3. The average specific output value in cycle 1 (Fig. 9A) after BC ablation is about 50 ~o greater than in cycle 1 before BC ablation. However, in cycles 2 and 3 the average specific output values are about the same for both cases. In cycle 4 it is about 25 ~ greater after BC ablation. In general, all responses are either equal or greater after BC ablation than before. The average response line is not very linear except for cycles 4 and 5. The two additional data points in cycle 6 were simply included to further illustrate this trend. The one point that is most obvious when comparing Fig. 8 with Fig. 9 is that after BC ablation, the change in specific output between adjacent pulse pairs is greater for every comparable set of sequential pulses in each cycle. If this were a continuous system it would be described as 'less damped' or more 'oscillatory' after BC ablation. A single pulse-double pulse sequential set for constant t values is shown in Fig. 8B before BC ablation and in Fig. 9B after BC ablation. The change in specific output can be characterized by using the method of modifying factors as illustrated in Fig. 6. Note that before BC ablation (Fig. 8B), the modifying factors for t = 110 msec start out at 0.67 and 1.5 and cbange in 5 pulses to 1.3 and 0.8, the expected values. The upper and lower bounds on the modifying factor are 0.67 <_ M F ~ 1.5. If the responses at t = 110 msec (Fig. 8B) are grouped in cycles comparable to cycles 4 and 5 of the linear exam (Fig. 8A), it can be seen that the average values of the 4' and 5' cycles are equal and that the general trend over 6 sequential pulses is one of decreasing specific output values. When looking at machine trajectories for constant t values after BC ablation (Fig. 9B), we observe modifying factors of 0.57 and 2.53 and a trend to 1.28 in 5 pulse pairs. The upper and lower bounds on the modifying factor have changed to 0.53 M F _<_2.53. When grouped again in cycles comparable to cycles 4 and 5 of the linear exam we note that the average value of the 5' cycle is considerably greater than for the 4' cycle, the trend being toward increasing specific output values. The line of behavior or trajectory for all cases tested was one of increasing specific output values with respect to time with BC ablated and toward decreasing specific output values with BC intact. When constant t values of 110 msec are preceded by the linear exam routine (Fig. 9A), the machine trajectory seems to be controlled and follows about the same slope as the linear test line even after BC is ablated. However, when preceded only by a single pulse, the trajectory for constant t values of 110 msec moves offin the increasing fashion as shown in Fig. 9B. It would appear then that the linear test sequence does seem to be able to control the machine trajectory even after BC is ablated. Brain Research, 18 (1970) 219-239

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Response variations Typical electrical recordings (Case No. 223) are shown in Fig. 10, for pulse pairs delivered during constant t sequential tests, both before and after BC ablation. The waveforms of Fig. 10A through D are the result of 4 double pulse sequential tests, with A being the first response pair measured in the sequence at t -- 83 msec. The upper trace, in all cases, was measured before BC ablation and the lower trace after. Fig. 10B shows the responses obtained from the second pulse pair in a sequence having a constant t interval of 102 msec. Fig. 10C is the result from the third pulse pair of the sequence with a t interval of 110 msec and D illustrates the results of the fourth sequential pulse pair having a t value of 132 msec. Note that for all cases, the first response of the pair is of lower amplitude after BC ablation (lower trace) than before. Also, the second response of the pair is greater in amplitude after BC ablation (lower trace) than before. These are the two general variations which result in the changes in specific output illustrated in the previous section. The initial positive deflection for the second pulse of the pair is about the same in amplitude both before and after BC ablation. The change occurs in the latter portions of the I"2 interval, previously defined as machine 'output time'. The value for "1"2 is about 19 msec, as illustrated in Fig. 10D. The dynamic activity during the 1"2 interval damps out rapidly with BC intact; however, with BC influences removed, the Brain Research, 18 (1970) 219-239

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response continues to increase in an oscillatory fashion. This results in larger calculated Yz values over the T2 interval with BC ablated. DISCUSSION

The nature o f the measurements

In this study we have assumed that the initial 10-25 msec of the cortical response following VL stimulation will contain or reflect informatioo of some sort concerning the PT output. However, to decide what measurable aspect of the cortical evoked response closely reflects this output is a difficult problem. Some of the most obvious measures would be peak deflections, peak to peak deflections, slopes, areas and/or average deflections over the region of interest. All of these possibilities were investigated in this study and all show, to some extent, the relationships illustrated in the Results. The difficulty in developing an unambiguous definition for a particular measure over a wide range of experiments, under both regional and general anesthesia, has resulted in the measure defined in this paper and termed machine output (Y). However, machine output, even though an average value, is still some potential in microvolts measured on the cortical surface. Electrode locations, number of cells firing and many other factors must surely affect its value. Therefore, the dimensionless ratio called specific output and defined as Y2/Y1 for response pairs has been used here to overcome these difficulties. Specific output is probably only one of many methods of viewing this thalamocortical machine and its use is based on the fact that orderly relationships within a single preparation and between preparations can be obtained by using this measure. The nature of the system

The picture presented in the Results is one of a 'self-modifying' system; one whose output depends on previous outputs and on the way in which the system is tested. In order to reduce influences from past responses and establish what has been termed a reference state, the single pulse-double pulse nonsequential routine was developed. This test illustrated the exponential relationship between specific output and the pulse pair interval which exists over the interval defined as the clock time (Equation 1). What seems to be important here is that a single stimulus be presented before the pulse pair and that the interval between the single pulse and the pulse pair be greater than the clock time. The delivery of a single pulse can be viewed as a method which establishes a constant set of initial conditions within the machine. Two examples of the use of this procedure were illustrated (Figs. 2 and 5). When sequential paired pulse testing is undertaken, hysteresis-like phenomena can be observed when plotting specific output as a function of the pulse pair interval. In order to better understand the nature of the hysteresis effects, a series of machine trajectories were conducted for constant pulse pair intervals. Each trajectory was always preceded by a single pulse which establishes a proper reference point such that Brain Research, 18 (1970) 219-239

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any trajectory can be reliably repeated. After the occurrence of 3 sequential pulse pairs, a shift in the t interval was made. This led to the concept of the modifying factor used in conjunction with calculated reference values. We have found that it is best to allow at least 3 pulse pairs to occur before the t shift is made since the second specific output in any sequence shows considerable variation and results in poor estimates of the modifying factor. Klinke et al. 18 have shown that evoked responses are dependent, in part, on information concerning stimulus parameters stored by the central nervous system and the actual incoming event. This is compatible with the results shown here; namely, that the evoked response is dependent on the new information put in by the experimenter in the form of a t change and on the established trajectory existing in the machine at the time of the t change. The precise time interval between sequential pulse pairs is unimportant with the only exception being a restriction on the minimum interval. There appears to be little difference between machine trajectories conducted at basic rates of either 1/sec or 1.5/sec. When testing machine trajectories as we have done here, the interval between pairs of pulses must be great enough such that the first pulse of any following pair does not occur in the afterdischarge interval (C2) following the second pulse of the previous pair (see Fig. 1A). This would put the stimulus rate in the augmentation range (6-10/ sec), a test used by many investigatorsl°,ls,21,22,26, ~8 but one which has the disadvantage of driving the system into saturation within 4 or 5 stimuli. Adaptive control

The concept of this thalamocortical machine as being 'self-modifying' has been clearly shown by the development of modifying factors from constant t machine trajectories. However, the constant t test itself is too simple. Stark ~9 states that adaptive control is a term applied to control systems which change their characteristics when the operating conditions of the system are altered such that the system, in some sense, improves its performance. The influence of the modifying factors on specific output cannot be understood as any purposeful change which is an improvement or gives the thalamocortical machine any additional advantage. Therefore, the method of the linear exam was developed, which is a significantly more complex sequence of stimuli andrepresents an attempt to force a given trajectory on the neuronal machine. The stimulus pattern used in the linear exam was developed after considering thalamocortical system characteristics, the stimulator scales available and the ability of the experimenter to make the appropriate t settings in 1 sec intervals. The linear exam is based on the concepts of cycling of information in automata and the notion of improvement of the quality of the 'answers' on the average 9. A particular cycle consists of all responses of identical t intervals, with the responses averaged at the end of the cycle. From this we have constructed an average response line which has been shown to be approximately linear and parallel to the reference line (Figs. 7 and 8). We have concluded from this that it is possible to impose a controlled trajectory on the neuronal machine. Further, in cycle 5 of the linear exam, the Brain Research, 18 (1970)219-239

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pulse pair interval remains unchanged from that of cycle 4, and yet the average response for cycle 5 still falls on or near the previously generated average response line (Figs. 7, 8A, 9A). The first 3 cycles of the linear exam establish a trajectory which is then maintained over cycles 4 and 5, even though no corresponding change is made in the t interval. As illustrated in the results, with intact cerebellum, constant t machine trajectories tend toward decreasing specific output values (Figs. 5B, 6A, 8B) when preceded by only a single pulse. When cerebellar influences are removed, constant t trajectories (Fig. 9B) tend toward increasing specific output values when preceded by only a single pulse. When preceded by the linear exam, the trajectory established in the first 3 cycles is maintained in the last 2 (Fig. 7, 8A, 9A) with or without cerebellar influences. This adoption of a specific trajectory in response to the first 3 cycles of the linear exam routine leads us to conclude that the thalamocortical projection system, when we use specific output as a measure, is properly considered as an adaptive control system. Cerebellar contributions to system performance

A number of interesting performance changes can be observed in the thalamocortical system when the system is tested both before and after contralateral BC destruction. The most noticeable variation following electrocoagulation of BC is the change which occurs in the modifying factors. This was illustrated in the Results by showing that the upper bound on the modifying factor increases from 1.5 (Fig. 8B) before BC ablation to 2.53 (Fig. 9B) after BC ablation. Cerebellum places bounds on the change in specific output (modifying factors) which occur over time. This quantitative increase in the upper bound of the modifying factor has been observed in every case where BC has been ablated. In one case (No. 226) where it appeared histologically that only about 25-50 Y/ooof BC was destroyed, this increase in bound on the modifying factor was readily apparent even when visible differences in the evoked response were not observed. Eccles et al. 8 state that cerebellum functions in some way as a form of computer which is concerned with the smooth control of movement. As far as the V L - M C system is concerned, cerebellar influences mediated through BC act to reduce response changes during sequential testing and would appear to be not in opposition to the concept of the cerebellum as a smoothing device. In addition to providing bounds on response changes, cerebellum also has been shown to influence machine trajectories. With cerebellum intact, constant t machine trajectories tend toward decreasing specific output values (Figs. 5B, 6A, 8B) and when BC is ablated, constant t trajectories (Fig. 9B) tend toward increasing specific output values. In the one case a form of negative feedback exists where responses decrease with repetition and in the second case, with BC ablated, a form of positive feedback exists where responses increase with repetition. Again cerebellum is imposing a bound on system states, which in this case is a tendency to keep subsequent specific output values below the initial values. It is interesting in this respect to note that Casey and Towe a have shown that electrical stimulation of cerebellum reduces the positive component of the evoked primary response measured from the pericruciate cortex, while the negative component is not systematically altered. Brain Research, 18 (1970) 219-239

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One other interesting effect of BC ablation, namely the oscillatory response to the second stimulus of the pair, was shown in Fig. 10A-D. In this case (No. 223), the dynamic response damps out rapidly (19 msec) with BC intact, but with BC ablated the response continues to increase in an oscillatory fashion. This tendency was seen to a variable extent in all BC ablation cases. In general, using the methods illustrated here, cerebellum can impose bounds on the modifying factors, on specific output amplitudes over sequential pulse pairs and on the dynamic activity occurring during the first 10-25 msec after a stimulus has been delivered. It is probably not improper to say, from a systems point of view, that the relationship of cerebellum to cerebrum is, at least in part, to act as a stabilizing device; since according to Ashby 1 instability constitutes an inability to put a bound on a system's states along some trajectory. This view appears to be in agreement with both clinical and experimental observations, since cerebellar lesions or interruptions of the superior cerebellar peduncle can produce ataxia. SUMMARY The concept that the ventrolateral (VL) thalamic projections to sensorimotor cortex form a 'self-modifying' machine - - i.e., a machine whose response is due to both incoming information and information from its past history of use - - has been substantiated by: (1) Developing a quantitative measure (specific output) of the cortical response evoked from pulse pairs delivered to VL. (2) Utilizing this measure to illustrate the differences which occur when nonsequential versus sequential testing is used. The dependence of specific output on both parameter changes put in by the experimenter and the existing conditions within the neuronal machine at the time of testing - - i.e., conditions set by past history - - are illustrated. The adoption of a specific trajectory due to a selected sequence of stimuli further illustrates the adaptive nature of this system. Cerebellar influences have been investigated, in part, by ablating contralateral brachium conjunctivum and observing the changes which occur in machine performance. The principal influence of the cerebellum appears to be to impose stricter bounds on the modifying factors, on specific output amplitudes over sequential trajectories and on the dynamic cortical activity occurring during the first 10-25 msec after the delivery of a stimulus to VL. ACKNOWLEDGEMENTS This research was supported in part by grants from the U.S. Public Health Service (No. F3-GM-35,680 and NB 05120) and Social and Rehabilitation Service, Department of Health, Education and Welfare (No. RD 1870-M). We are indebted to Mrs. Sharon Trader and Miss Sally Phillips for their technical assistance.

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