Sobell Department of Neurophysiology, Institute of Neurology, Queen Square, London WC1N 3BG, United Kingdom
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Baker, S. N. and R. N. Lemon. Computer simulation of post-spike facilitation in spike-triggered averages of rectified EMG. J. Neurophysiol. 80: 1391-1406, 1998. When the spikes of a motor cortical cell are used to compile a spike-triggered average (STA) of rectified electromyographic (EMG) activity, a post-spike facilitation (PSF) is sometimes seen. This is generally thought to be indicative of direct corticomotoneuronal (CM) connections. However, it has been claimed that a PSF could be caused by synchronization between CM and non-CM cells. This study investigates the generation of PSF using a computer model. A population of cortical cells was simulated, some of which made CM connections to a pool of 103 motoneurons. Motoneurons were simulated using a biophysically realistic model. A subpopulation of the cortical cells was synchronized together. After a motoneuron discharge, a motor unit action potential was generated; these were summed to produce an EMG output. Realistic values were used for the corticospinal and peripheral nerve conduction velocity distribution, for slowing of impulse conduction in CM terminal axons, and for the amount of cortical synchrony. STA of the rectified EMG from all cortical neurons showed PSF; however, these were qualitatively different for CM versus non-CM cells. Using an epoch analysis to determine reliability in a quantitative manner, it was shown that the onset latency of PSF did not distinguish the two classes of cells after 10,000 spikes because of high noise in the averages. The time of the PSF peak and the peak width at half-maximum (PWHM) could separate CM from synchrony effects. However, only PWHM was robust against changes in motor unit action-potential shape and duration and against changes in the width of cortical synchrony. The amplitude of PSF from a CM cell could be doubled by the presence of synchrony. It is proposed that, if a PSF has PWHM <7 ms, this reliably indicates that the trigger is a CM cell projecting to the muscle whose EMG is averaged. In an analysis of experimental data where macaque motor cortical cells facilitated hand and forearm muscle EMG, 74% of PSFs fulfilled this criterion. The PWHM criterion could be applied to other STA studies in which it is important to exclude the effects of synchrony.
Experiments in which spontaneous neural activity is recorded from awake, behaving animals have added considerably to our understanding of the function of the nervous system. In such studies, it is always advantageous to identify the inputs and outputs of recorded cells so that the functional role of their firing pattern can be interpreted. Identification of the output is of particular importance because it reveals the target structure of information generated by a particular neuron. In the motor cortex, for example, neurons whose axons descend as far as the pyramidal tract can be antidromically activated from electrodes chronically implanted in the tract (e.g., Evarts 1964 A diagram of the cortical and spinal network modeled in this study is given in Fig. 1. A variety of cortical cell types had input to the simulated motoneuron pool. From the discharge pattern of the motoneuron pool, a simulated EMG was produced. This permitted study of the transform from cortical input to EMG output and provided a direct and realistic comparison with experimental data. The following describes the details of the model.
Neurons
The neurons were simulated by using two complementary models published previously. The cortical neurons (Fig. 1,
INTRODUCTION
Abstract
Introduction
Methods
Results
Discussion
References
).
). This approach reveals any facilitation or suppression of muscle activity that is exerted by the PTN. An electromyogram (EMG) is recorded from a number of muscles simultaneously with the cell discharge. The rectified EMG is then averaged with respect to the neuron spikes. A brief, short-latency post-spike facilitation (PSF) in the average is conventionally taken as indicating that the trigger cell makes monosynaptic connections to the motoneurons innervating the muscle whose EMG was averaged. STA thus allows both identification of the output neuron and its target muscles.
; Kirkwood 1994
) that a PSF in a STA does not necessarily indicate that a cell connects to motoneurons but rather could occur because the trigger cell is synchronized in firing with corticomotoneuronal (CM) cells. The presence of such synchrony is well established (Baker et al. 1997
; Smith and Fetz 1989
). This issue is addressed here using a computational model of the production of PSF. It is shown that a non-CM cell can produce a significant PSF but that this is qualitatively and quantitatively different from PSF produced from a CM cell. Means of distinguishing between synchrony PSFs and those caused by direct connections from trigger cell to motoneurons are investigated and compared.
METHODS
Abstract
Introduction
Methods
Results
Discussion
References
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FIG. 1.
Overview of the model. Cortical cells ( ) are modeled after Ashby and Zilm (1982)
. A common input cell connects to a population of target cells, synchronizing them. Most of these cells are corticomotoneuronal (SCM) and make monosynaptic connections to the motoneurons (
). The S cell is synchronized with the SCM cells, but has no connections to the motoneurons. The CM cell is corticomotoneuronal but is not synchronized with the other cortical cells. Its central conduction time from cortex to spinal cord is 1.4 ms. The motoneurons innervate motor units, which generate realistic motor unit action potentials (MUAPs). These are summed to produce the simulated electromyogram (EMG). The peripheral conduction time varies linearly with motor unit recruitment number.
) were based on the description by Ashby and Zilm (1982)
. The membrane potential rose linearly at a constant rate of K for all the cells until it crossed the firing threshold (taken arbitrarily to be 0 mV). The cell was then assumed to have produced an action potential, and its potential was reset to a subthreshold value. A value for K of 82.5 µV/ms was used, chosen so that a cell which had an afterhyperpolarization (AHP) of 10 mV below threshold would fire at a frequency of 8.25 Hz. The precise value of the AHP was determined from
where I is the next interspike interval, chosen at random after each threshold crossing from a gamma distribution with a shape parameter of 4 and a mean equal to the reciprocal of the desired average firing rate. Inputs to the cells produced excitatory postsynaptic potentials (EPSPs) with a sigmoidal rising phase of variable duration and an exponentially decaying falling phase with a time constant of 4.8 ms. These summed linearly with the cell membrane potential and were therefore able on some occasions to cause a threshold crossing to occur slightly earlier than it would have done without the input. The advantage of this model neuron is that it is computationally simple so that simulation time is reduced. It is an obvious simplification of the complex behavior of a cortical neuron but suffices to produce a realistic spike train having the desired stochastic properties.
(1)
) were simulated with the use of a published model (model 9-2; see Powers 1993
). Briefly, this is a single-compartment biophysical model, having a fast and slow potassium and a low- and high-threshold calcium voltage-gated conductance, whose combined action produces a realistic AHP after cell firing. The membrane time constant was 6 ms. Action potentials were not simulated explicitly; instead, whenever the membrane potential crossed threshold, it was clamped to a depolarization of +20 mV for 1 ms and then reset to the threshold level. After this, there was a 1-ms refractory period. The threshold for spike initiation was not fixed but varied with a fast and slow time course. This is a far more realistic model of the motoneuron than that according to Ashby and Zilm (1982)
, but considerably more computationally intensive to simulate.
was extended for the current study as follows. Inputs to the cell produced activation of a synaptic conductance having a reversal potential of 0 mV with an
function-shaped time course given by
where gmax = 0.015 µS and
(2)
= 0.2 ms. These parameters produced an EPSP with a height of 70 µV and rise time of 1 ms. Synaptic noise was simulated in the motoneurons by adding Gaussian noise to the simulated membrane potential with an SD of 2 mV and time constant of 4 ms, in accordance with experimental data from Calvin and Stevens (1968)
. The cells were made to fire tonically by activating the synaptic conductance by a constant amount independent of the activity of simulated inputs. The level of this constant shunt conductance was chosen to produce the desired firing rate in preliminary, calibration runs, with no cortical inputs to the motoneurons. One advantage of this model over more simplistic treatments is that the membrane potential rise after a spike is not quite linear but has a decreasing slope as the threshold is approached. This is in accord with findings in human motoneurons by Olivier et al. (1995)
and Matthews (1996)
and may bias the cells to respond somewhat preferentially to synchronous inputs (Matthews 1996
).
Motoneuron pool
The mean firing rate for each motoneuron and the number of motoneurons simulated were determined from the model of a tonically firing motoneuron pool proposed by Wani and Guha (1975), based on the results of Milner-Brown et al. (1973a
,b
) regarding motoneuron recruitment order and firing rate. Their model was solved numerically for the first dorsal interosseus (1DI) muscle contracting at 2% of its maximum voluntary contraction (a strength typical of the activation of this muscle during many skilled tasks). This indicated that 103 of the total of 377 motoneurons would be tonically firing. The first recruited motor unit would be firing at 8.5 Hz, and the last would be firing at 8.0 Hz.
Surface EMG
After the discharge of each motoneuron in the model, a motor unit action potential (MUAP) was generated. The form of this potential was intended to approximate closely the potential which would be recorded by a surface EMG electrode. The potentials were based on data gathered in two human subjects specifically for this investigation.
; Yemm 1977
) provide a representation of the MUAP as it is recorded by the surface electrodes. To determine the twitch tension of the unit, averages of the force record were also produced with only those spikes where the succeeding interspike interval was >100 ms. This spike selection reduced contamination from the effects of succeeding spikes, which could artificially increase the measurement of twitch tension (see Calancie and Bawa 1986
; Nordstrom et al. 1989
). The model of Wani and Guha (1975)
gives expressions for the twitch tension of 1DI motor units as a function of unit recruitment order. It was therefore possible to determine the approximate recruitment order of each unit from its twitch tension.
Network
The three main classes of cortical cell whose firing was used to produce STAs of the simulated rectified EMG are shown in Fig. 1. One nonsynchronized CM cell made monosynaptic connections to all the motoneurons of the pool. It had a spike train that was independent of the activity of other cortical cells. The synchronized CM (SCM) cells also made monosynaptic connections to the motoneurons, but in contrast their discharges were synchronized with each other because they received synaptic input from a "common input" cell firing tonically at 40 Hz. This input produced an EPSP in the SCM cells. In initial simulations, the size and rise time of this EPSP was adjusted so that the cross-correlation peak between two of the SCM cells would have a peak duration of 15 ms and a peak strength A = 0.06, where
) and that the waveform shape should change smoothly as the motoneuron recruitment number increased. An interpolation algorithm was therefore used to produce a surface potential for each of the 103 motor units in the model.
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FIG. 2.
Examples of the MUAPs used in this study. On the left are examples of actual potentials recorded from 2 human subjects and extracted from the surface EMG by motor unit triggered averaging. Motor unit recruitment number is shown beside the traces, estimated from the unit twitch tension using the model of Wani and Guha (1975) .
, time of the intramuscular action potential used to trigger the averages. On the right are examples of interpolated MUAPs, generated by the algorithm described in the text. These traces are plotted starting at the potential onset. A: subject NA; B: subject MM. Note the smooth change in size and shape of the interpolated potentials in A not evident in B.
Here j is an index identifying a particular experimentally recorded MUAP, and i indexes the principle components. The equality of Eq. 3 is exact if the sum is taken over all n principle components pi; however, it is a feature of principle component analysis that use of only the first few terms of the summation yields a good approximation to sj. The coefficients cji then provide a representation of sj in a small number of parameters.
(3)
where the bracket notation [x] has been used to indicate the mean of the points in vector x. This constrains the average voltage level of each interpolated waveform to be zero, so ensuring that there are no small differences between the negative and positive phases, which on average would lead to a DC offset in the final simulated EMG.
(4)
. Thomas et al. (1987)
however showed a similar lack of correlation, and Lemon et al. (1990)
noted that the extent of correlation varied between subjects. Examples of the interpolated MUAPs from each subject's data are shown in Fig. 2.
, given by
where D is the peripheral conduction distance, estimated as 0.5 m for a hand muscle in the adult macaque monkey. Equation 5 allows for the small amount of peripheral dispersion that occurs and makes the simplifying assumption that conduction velocity for the 377 motoneuron axons is perfectly correlated with recruitment number n (Burke 1981
(5)
) over the range of 55-85 m/s (Lemon et al. 1986
). The range of conduction times
obtained for the pool of 103 motoneurons used here was 8.0-9.2 ms.
and where P is the area of the cross-correlation peak above baseline, nT is the number of cross-correlation trigger spikes, and nr is the number of cross-correlation response spikes.
(6)
). Subsequent simulations investigated the effect of varying the width of the cortical synchrony peak (see RESULTS). It is obviously unlikely that this observed cortical synchrony is produced by a single common input cell; rather it is the result of common input from a population of cells. This is reflected in the slow rise time of the EPSP from the model common input cell. However, for the purposes of the modeling described here, it is only important that the SCM cells in the model show synchronous firing which is quantitatively similar to that seen in experimental data; the exact means by which this is achieved is unimportant. The number of SCM cells present in the network could be varied, thereby altering the amount of synchrony in the total input to the motoneuron pool.
Corticospinal conduction delay
The pyramidal tract contains fibers of widely varying diameters, implying a range of conduction velocities from 5 to 85 m/s (Humphrey and Corrie 1978; Mediratta and Nicoll 1983
; Tan et al. 1979
). Because monosynaptic connections from the cortex are only present to any great extent in primates, it has been assumed that it must be only the very large corticospinal fibers (another primate feature) which make such connections. However, more recent research has shown that, although CM connections are less frequently seen from slow PTNs, they do exist (Fetz and Cheney 1980
; Lemon et al. 1986
; Porter and Lemon 1993
).
.
Implementation
Simulations were carried out with a 0.2-ms time step. In one pass, each cell was first updated; for the motoneurons this required solution of the seven differential equations given by Powers (1993) Figure 4 presents analysis of three simulation runs. In Fig. 4A, a cross-correlation histogram is presented between two SCM cells; this will be identical for all SCM-SCM pairs and for each SCM cell cross-correlated with the S cell. This shows the central peak caused by common synaptic input, with a peak width of ~15 ms. In Fig. 4, parts B and C, the interspike interval histograms are shown for a cortical and motoneuronal cell, respectively; in each case they resemble those seen in experimental data. Note that the cortical cell model was designed to produce an interval histogram with a gamma distribution. By contrast, the variability in the interspike intervals in the motoneuron model of Fig. 4C resulted from the simulated noise, in agreement with the proposal of Calvin and Stevens (1968)
Quantitative determination of the separation of causal and synchrony PSFs
To provide an objective and quantitative assessment of whether PSFs generated by pure synchrony can be distinguished from those caused by monosynaptic connections, the 47 epochs of 10,000 spikes resulting from the simulation presented in Fig. 5 were subjected to a further analysis which automatically measured various parameters from each average. It was important that this analysis should be entirely automated, so that no experimenter bias could enter the measurement process, a concern when working with noisy averages of this kind.
Effect of different surface motor unit action potentials
Measurements made of timing of effects in STAs differ from those taken from cross-correlation histograms in one crucial respect; they include a component due to the shape and duration of the MUAPs. A concern with the classification presented by Fig. 7 must therefore be that it is highly dependent on the MUAPs used in the simulations. Different sets of potentials could result in altered criteria being needed to separate synchrony from genuine PSFs such that the generality of the results would be lost. To investigate this, the EMG was recalculated from the stored motoneuron firing times of the simulation illustrated in Fig. 7 using diverse sets of MUAPs.
Sensitivity to the width of cortical synchrony
One of the most important parameters of the model presented above is the width of the cross-correlation peak between two synchronized cortical cells. The chosen value of 15 ms is the best estimate available from a small data set gathered in our laboratory (Baker 1995
Comparison with experimental data
The main result of the simulations presented above is that PWHM can be used to separate PSFs due purely to synchrony from those with a monosynaptic component. It is of immediate interest to compare these simulated PWHM distributions with those measured from experimental data, to determine what fraction of PSFs would be rejected by this method. The PWHM was therefore measured from 76 PSFs using data previously obtained in this laboratory (Baker 1995 Model assumptions
In constructing a model such as the one presented here, it is inevitably necessary to make assumptions where experimental data are incomplete. Before conclusions can be drawn from this model, it is necessary to examine these assumptions.
Possibility of PSF caused by cortical synchrony
One of the most important predictions of the simulations presented here is that a cortical cell which makes no causal connections to motoneurons but is synchronized with other cells that do could produce a significant PSF of rectified EMG. This disagrees with the reports in the literature which have addressed this question to date (Lemon et al. 1985 Differences between genuine causal and synchrony PSFs
In all simulations illustrated, there were clear qualitative differences in the PSFs produced by the CM, SCM, and S cells. The S cell peaks were broader than the CM and SCM peaks and had a later time to peak. Both S and SCM cells generated PSFs with earlier onset latencies than reasonable for a causal effect (Fig. 5). These differences are clearest in the relatively noise-free averages of Figs. 5 and 8.
Quantification of PSF
An important finding of this study is that the size of a PSF from a cell which does make connections to motoneurons can be heavily influenced by the extent to which it is synchronized with other CM cells. Thus in Fig. 4, whereas the fast SCM cell PSF is only slightly larger than that of the CM cell when 10 SCM cells are synchronized together (Fig. 4D), it is more than twice the height when 30 SCM cells are present (Fig. 4F). Measures made from the area under the peak (e.g., mean percentage increase) (Cope et al. 1987 The authors thank Dr. Peter Kirkwood for critical discussion of this work.
This work was funded by the Wellcome Trust and the Medical Research Council.
Address reprint requests to S. N. Baker. Received 22 December 1997; accepted in final form 4 June 1998.
) and a utilization time of 0.1 ms (Lemon 1984
), this allowed a conduction velocity to be calculated for each cell. A cumulative distribution graph for these data is plotted in Fig. 3 (
).
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FIG. 3.
Cumulative probability curve showing the distribution of conduction velocity estimated from antidromic responses of 132 identified corticomotoneuronal (CM) cells to pyramidal tract stimulation in 3 monkeys. , observed distribution; - - -, a correction after Humphrey and Corrie (1978)
to remove the effects of electrode sampling bias. Based on unpublished data from R. N. Lemon, K.M.B. Bennett, and D. Flament.
to correct PTN conduction velocity distributions for the sampling bias toward large cells in the recordings were applied to the data of Fig. 3. The result of such a correction is shown in Fig. 3 (- - -).
n out of a total of n was determined by
The conduction time from the cortex to the spinal segment of termination for each SCM cell was derived assuming a conduction distance of 100 mm, producing a variation in conduction time from 1.6 ms to 10 ms. Discharges from the fastest and slowest conducting SCM cells were used in the STA analysis.
(7)
; Shinoda et al. 1976
, 1979)
. Shinoda et al. (1986)
estimated the terminal conduction velocity to be as low as 1 m/s. In addition, motoneurons in a single motor nucleus can extend over two to three spinal segments (Jenny and Inukai 1983
), implying a variable conduction distance along the stem axon from cortex to individual motoneurons. The delay between cortical cell firing and the production of an EPSP in a motoneuron could therefore vary considerably from one motoneuron to the next. To simulate the effect of such terminal slowing of impulse conduction, an additional delay was added to the conduction time from each CM or SCM cell to each motoneuron. The extra delay was randomly determined from a uniform distribution between 0 and 1 ms. Shinoda et al. (1986)
found
1-ms conduction time in the terminal collaterals. The use of a uniform distribution
1 ms may somewhat overestimate the variability in conduction time; however, the cross-correlation peak between a CM cell and motor unit which these assumptions produced had a similar width to those published by Lemon et al. (1990)
.
, by using an exponential integration scheme (MacGregor 1987
). If any cortical cell produced an action potential, a EPSP was set up in its target motoneurons after a preset delay. Whenever a motoneuron fired, it was followed by the production of its surface MUAP. The instantaneous value of the total surface EMG potential was determined by summing the appropriate points of all currently occurring motor unit potentials. This voltage value was then written to disk together with the times of any cell action potentials that had occurred.
25 computers, with a different initial seed for the random number generator in each case. The separate data files were then combined end to end to produce the final data for analysis. Spikes from the initial and final one second of each file so combined were deleted so that only periods when the network had reached a stable activity pattern were included in the analysis. The files so produced were analyzed using a commercially available neurophysiological data analysis package (Spike2, Cambridge Electronic Design). STAs of the simulated rectified EMG were compiled using spikes from each of the three classes of cortical cells (CM, SCM, and S).
RESULTS
Abstract
Introduction
Methods
Results
Discussion
References
.
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FIG. 4.
Analysis of 3 simulations, illustrating features of the model and the effect of changing the number of synchronized CM (SCM) cells in the network. A: cross-correlation between 2 SCM cells, showing a central peak 15-ms wide. Size of this peak agrees with experimental observations. B and C: interval histograms of cortical cells and motoneurons, respectively, compiled with 1-ms binwidth. D-F: spike-triggered averaging (STAs) of rectified EMG triggered from 4 different simulated cortical cells. Constructed using MUAPs from subject NA. SCMs and SCMf are the slowest and fastest SCM cells present in each network. Different panels result from simulations with different numbers of SCM cells in the network (10, 20, and 30 cells for D-F, respectively). Arrows, time of the triggering spike; dotted lines, earliest possible onset latency for a causal, monosynaptic effect from a fast CM cell. G: cross-correlation histograms, constructed with a cortical cell as the trigger and all 103 motoneurons in the pool as the response. Same simulation as F, with 30 SCM cells in the network. Motoneuron firing was registered at the spinal cord; hence, latency of the effects does not include the peripheral conduction delay, unlike the STAs. Dotted lines, earliest possible onset latency for a causal effect (1.4 ms). All measures compiled from 10,000 trigger spikes.
; Fetz and Cheney 1980
; Lemon et al. 1986
).
). Thus the slowly rising initial phase of the synchrony peaks could be easily distinguished in the cross-correlation histograms but was lost in the noise of the STAs. The earliest discernable component therefore appeared to have a latency consistent with a wholly causal effect.
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FIG. 5.
A: STAs from the same simulations shown in Fig. 4F (30 SCM cells present), triggered from many more spikes (n = 470,000). ···, earliest possible onset latency for a monosynaptic effect; - - -, peak latency, measured from these relatively noise-free averages; , time of the triggering spike. B: averages compiled from epochs of 10,000 spikes with the same data as in A. A considerable variability is present in the apparent onset latency of the post-spike facilitations (PSFs). Peak latency is somewhat more constant for the CM and SCMf cells than for the S cells.
; Perkel et al. 1967
). To account for this, a regression line can be fitted to a background region of the average and then subtracted (Bennett and Lemon 1994
) (cf. Fig. 6B). The SD of the average around the regression fit is then determined, and the point at which the PSF exceeds the fit +2 SD is taken as the onset latency (Fetz and Cheney 1980
).
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FIG. 6.
A: data used to define a significance level for a PSF; 60-ms-long averages of rectified EMG with respect to 10,000 spikes were compiled, with the triggers shifted in time by 1-2 s, thereby destroying any causal link between spike train and EMG. A regression line was fitted to the first 30 ms of the average and subtracted; SD of the 1st 30 ms was then found, together with the maximum voltage in the period from 30-60 ms. This maximum was divided by the SD, forming the measure plotted on the abscissa. Ordinate lists the proportion of averages where it was smaller than the value plotted. In 95% of trials, the 30-ms test period did not exceed 5.70 times SD, providing an appropriate test level to determine the 1st point of a PSF, which is significantly different from the background. Results are illustrated from simulations by using motor unit data from subject NA; similar results were obtained with data from subject MM, with a similar significance level (5.77). B: example of the automatic latency detection method. The trace is an STA of EMG produced with MUAPs from subject NA, triggered by 10,000 spikes of the CM cell ( ).
, 30-ms control region used to fit a regression line (lower - - -); above this is shown regression line +2, and +5.7 times SD of the background region.
, region which was searched for a crossing of the detection threshold.
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FIG. 7.
Distribution of various measures made from STAs of 10,000 spikes for 4 different cortical cells. A and B: PSF onset latency, determined by a 5.7 or 2 times SD threshold, respectively. CM and SCM cell distributions overlap with the S cell, preventing reliable separation of the effects by onset latency. C: peak width at half-maximum (PWHM). D: PSF peak latency. Bimodal distributions for the CM cell in A and slowest SCM (SCMs) in C result from the bifid shape of the monosynaptic component of the PSF in these simulations.
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FIG. 8.
Effect of different MUAPs on PSFs from CM and S cells. Averages in A were constructed from potentials from subject NA, and those in B were constructed from potentials from subject MM. Numbers on the left give the extent of the temporal scaling of the interpolated MUAPs of Fig. 2, with 100% representing no scaling. The briefer potentials lead to monophasic CM cell PSFs, whereas with longer potentials 2 or 3 phases are evident, reflecting the complexity of the waveforms of the underlying motor unit potentials. In all cases, the CM and S effects are clearly different. , time of triggering spike. Compiled from 300,000 spikes.
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FIG. 9.
Histograms of the distribution of measures made from PSFs for 4 different cortical cells. Thirty epochs of 10,000 spikes were measured for simulations by using each of 16 different sets of MUAPs, and all the measures were combined for this figure. Hence, differences seen between cells here will be robust across MUAPs. A and B: PSF onset latency, measured with criteria of 5.7 and 2 times SD. C: PSF peak width. D: PSF peak time.
). Smith and Fetz (1989)
found a somewhat larger mean width of 23 ms. These values are means; the width of correlation peaks between any two cells can vary widely, from as short as a few milliseconds to >30 ms. Additionally, the magnitude of synchronous activity in motor cortex can vary in a task-dependent manner (Baker et al. 1997
). Because experimental data on this point are currently so sparse and because the findings may be expected to depend importantly on it, it was decided to investigate a range of different cortical synchrony widths and to determine whether the PWHM remains capable of distinguishing genuine from synchrony PSFs.
), we simulated oscillatory synchrony between the cortical cells by adding a 25-Hz, 300-µV sine wave to the membrane potentials of the S and SCM cell. A cross-correlation produced after this manipulation is shown in the final column of Fig. 10.
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FIG. 10.
Effect of changing width and type of synchrony between cortical cells. A: cross-correlation histograms between 2 SCM cells, triggered by 300,000 spikes. Each column shows results from a different simulation, where the width and type of synchrony was changed. Note that the ordinate scale does not begin at 0. B: STA of rectified EMG triggered by CM (thin lines) and S cells (thick lines). Constructed with unscaled MUAPs from subject NA. Arrows, time of the trigger. n = 300,000, except for the simulation with 15-ms width, where n = 470,000. Calibration bars, 1 µV, 20 ms. C: distribution of the PWHM measure. Distributions are summed over all sets of MUAPs used in this study. For the S cell, the distributions are shown as histograms. For the other 3 cell classes, the distributions are given by bars, representing the region containing 95% of the measurements. CM, solid bars; fastest SCM, shaded bars; slowest SCM, open bars. Two bars are shown for the PWHM of the CM cell in the 5-ms simulation, reflecting the bimodal distribution for this cell.
). In experimental recordings, the subpeaks become smaller the further away they are from the main, central peak. This presumably reflects the fact that in vivo the oscillations cover a broadband of frequencies, such that averages of distant cycles accumulate phase errors and lead to cancellation. This was not seen in the simulated STA of Fig. 10B because the oscillations were at a fixed frequency of 25 Hz.
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FIG. 11.
A: performance of attempts to classify cell types on the basis of PWHM with different criteria. Data are derived from simulations with a cortical synchrony width of 15 ms, combining across all MUAPs as in Fig. 9. Error rates for CM, fastest SCM (SCMf), and slowest SCM (SCMs) are false-negatives, the proportion of PSFs that was incorrectly rejected as resulting from synchrony effects. Error rates for S cells are false-positives, the proportion of PSFs incorrectly accepted as caused by CM connections. B and C: dependence of classification errors on the parameters of cortical synchrony assumed in the model, with the use of a fixed criterion of PWHM <9 ms (B) or <7 ms (C). D: distribution of PWHM in 76 PSFs measured experimentally from STAs of hand and forearm muscle EMG, triggered by 43 motor cortical cells. Bins shaded black are those excepted to have a monosynaptic component because their PWHM is <7 ms. Those shaded gray would be accepted on the more relaxed criterion of PWHM <9 ms.
; Bennett and Lemon 1994
). These PSFs were seen in STAs of hand and forearm EMG triggered by 43 neurons recorded from the primary motor cortex in 4 M. nemestrina monkeys performing the precision grip task of Lemon et al. (1986)
. Figure 11D shows a distribution histogram for these PWHM values. Bins shaded in black (56/76, 74%) are those which would be accepted on the criterion developed above of PWHM <7 ms; those shaded in gray (8/76, 10%) are those which would also be accepted if a more relaxed criterion (PWHM <9 ms) were adopted. The unshaded bins (12/76, 16%) would be rejected as possibly caused by synchrony effects.
DISCUSSION
Abstract
Introduction
Methods
Results
Discussion
References
). However, there is considerable variability in strength and duration of cross-correlation peaks between pairs of cortical cells. There are often multiple peaks, with a narrow component superimposed on the broad central peak. Nevertheless, the general conclusions of the current work appear unaltered by different widths of cortical synchrony (Figs. 10 and 11), and a good separation of CM from S cell PSFs can still be achieved. The result is therefore likely to be robust in the face of synchrony consisting of a mixture of different cross-correlation widths among different cell pairs in the population.
), and it is possible that cortical synchronisation could be considerably greater in certain highly specific circumstances.
). In addition, there is evidence that the intracortical connections of fast and slow PTNs differ (Kang et al. 1991
; Tsukahara et al. 1968
).
that a CM cell which produces a PSF in a muscle has a cross-correlation peak with most single motor units which could be recorded in that muscle. It is possible that there are consistent changes in EPSP size with motoneuron recruitment order, as discussed by Heckman and Binder (1993)
. However, these would be expected to have less effect on the situation modeled here, where only the lower 27% of the entire motoneuron pool is active (103/377 cells).
; Lemon et al. 1993). However, without data from single unit cross-correlations, no precise values for this effect can be included in the model.
), it is not known if they are intercalated in the corticospinal pathway. However, in the anaesthetized monkey, there is a conspicuous lack of nonmonosynaptic EPSPs in motoneurons following pyramidal tract stimulation (Maier et al. 1996
), suggesting that such connections may be weak.
; Porter and Lemon 1993
; Smith and Fetz 1989
), which concluded that cortical synchrony played little role in the production of PSF.
). Second, the yield of PTNs showing PSF in an experiment is relatively small (55% from a highly selected population of PTNs) (Fetz and Cheney 1980
; Lemon et al. 1993). Finally, the peak amplitude of most experimental PSFs relative to background (percentage modulation) is <15% (Lemon et al. 1986
). In the simulation presented in Fig. 5, the fast SCM cell PSF had a percentage modulation of 15.2%. If >30 CM cells were synchronized together, the size of the PSF would be larger than that seen experimentally. This would be true independent of how many sources of common input projected to the SCM cell pool. The current model predicts that no CM cell can have a cross-correlation peak of the same amplitude as assumed here with >30 other CM cells projecting to the same muscle without producing a PSF larger than that encountered experimentally. We chose to vary the strength of cortical synchrony by keeping the strength of correlation between individual cells fixed and altering the size of the synchronized colony. This is equivalent to changing the magnitude of the correlation peak with a fixed colony; both effect the number of action potentials in the corticospinal input synchronized with the trigger.
); the data of Fig. 8 with compressed MUAPs then most accurately reflects the experimental situation, with corresponding monophasic PSFs. A second factor contributing to the production of monophasic PSFs in experimental data may be the presence of a superimposed synchrony PSF; for example, the SCMf effects for the two higher levels of synchrony investigated in Fig. 4 show no inflections on their PSFs larger than the noise level. Finally, it is possible that MUAPs show more variation in their shape and duration than accounted for by the present method of interpolating from a limited sample of recorded potentials; this increased variability could then act to smooth out the bifid cusp of the CM cell PSFs.
). With this number of triggering spikes, onset latency cannot be used reliably to discriminate synchrony from genuine PSFs (Figs. 7, A and B, and 9, A and B). Errors can be made in both directions. Hence an onset latency which is too early to be produced by monosynaptic effects must indicate a synchrony component to the peak; however, it does not preclude the presence of a superimposed genuine PSF. Conversely, a PSF onset at appropriate latency could be produced by purely synchronous effects. Given the very shallow initial part of the S cell PSF and the tendency of averages of rectified EMG to underestimate small effects (Baker and Lemon 1995
), an enormous number of spikes need to be averaged to measure these latency differences accurately. Recording in the order of 300,000 spikes is impractical, given the limitations on the length of experimental sessions when working with chronic animals and the difficulties in holding cells in the record for long periods. Any other measure that depends on accurate knowledge of the onset or offset of the PSF, such as rise time or total duration, will suffer from the same problems.
). As noted above, the dispersion in corticospinal conduction time is one of the main assumptions of this model. However, it may safely be assumed that the model would be robust to changes in this dispersion so long as the cortical synchrony width was not also allowed to become too narrow.
) will be even more susceptible, given the broad time course of the synchrony contribution. Little can be done to correct for this synchrony contribution in an experimental PSF where the size of the synchronized CM cell pool is unknown, and the only solution would seem to be the exercise of great caution in the use of STA to quantify the strength of the connection from a CM cell to the motoneuron pool innervating a particular muscle (see Bennett and Lemon 1994
).
ACKNOWLEDGEMENTS
FOOTNOTES
REFERENCES
Abstract
Introduction
Methods
Results
Discussion
References
A Primer. London: Chapman and Hall, 1986.
0022-3077/98 $5.00 Copyright ©1998 The American Physiological Society