Keck Center for Integrative Neurosciences, UCSF, San Francisco, California 94143-0732
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ABSTRACT |
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Sanger, Terence D. and Michael M. Merzenich. Computational Model of the Role of Sensory Disorganization in Focal Task-Specific Dystonia. J. Neurophysiol. 84: 2458-2464, 2000. We present a new computational model for the development of task-specific focal dystonia. The purpose of the model is to explain how altered sensory representations can lead to abnormal motor behavior. Dystonia is described as the result of excessive gain through a sensorimotor loop. The gain is determined in part by the sensory cortical area devoted to each motor function, and behaviors that lead to abnormal increases in sensory cortical area are predicted to lead to dystonia. Properties of dystonia including muscular co-contraction, overflow movements, and task specificity are predicted by properties of a linear approximation to the loop transformation. We provide simulations of several different mechanisms that can cause the gain to exceed 1 and the motor activity to become sustained and uncontrolled. The model predicts that normal plasticity mechanisms may contribute to worsening of symptoms over time.
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INTRODUCTION |
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Task-specific focal dystonia is a
frustratingly complex disease that is often refractory to medical
therapy. It includes diseases such as writer's cramp or musician's
cramp, and it is characterized by involuntary movements that occur over
seconds or minutes often involving co-contraction of antagonist muscles
and leading to abnormal and frequently painful limb postures
(Bressman 1998; Fahn et al. 1987
, for
review). Patients with dystonia may be severely impaired in their
ability to perform common tasks or indeed to use the affected limb at
all. The response to medical therapy including anticholinergic agents,
dopamine depleting agents, or GABA agonists is frequently
unsatisfactory, and patients may be left with prolonged or permanent
deficits. An understanding of the mechanisms underlying dystonia would
therefore be of potentially significant benefit.
There is evidence from studies in monkeys of disorganization of sensory
cortical representations (Byl et al. 1996a,
1997
; Merzenich and deCharms 1996
). In
particular, monkeys with focal hand dystonia were found to have neurons
in primary sensory cortex that responded to tactile stimulation over
more than one finger, or over both the palmar and dorsal surfaces of
the fingers. Clinical studies in humans have shown abnormalities of
tactile form perception (Byl et al. 1996b
) and spatial
and sensory processing (Bara-Jimenez et al. 2000
). The
central representations of individual fingers show closer spacing in
focal dystonia (Bara-Jimenez et al. 1998
; Butterworth et al. 1999
; Byrnes et al.
1998
; Elbert et al. 1998
), and there is evidence
of abnormal interactions between signals from median and ulnar nerve in
writer's cramp (Tinazzi et al. 2000
).
It is not known whether the sensory abnormalities are a cause or a result of the motor abnormalities. Prolonged abnormal postures might lead to plasticity in sensory systems that result in the observed changes in sensory maps. It is more difficult to describe how the motor abnormality might be caused by the sensory changes. We seek to provide a model to explain how the sensory abnormalities could lead to the motor manifestations of dystonia. In particular, we will demonstrate that properties of a linear model predict that sensory de-differentiation may cause not only poor fractionation of movement, but also excessive contraction of the involved muscles.
We hypothesize that task-specific dystonia such as writer's cramp or
musician's cramp is the biomechanical manifestation of an unstable
sensorimotor control loop. The control loop includes motor cortex that
produces an effect on muscles that is eventually transmitted through
sensory systems to sensory cortex, which has projections back to the
equivalent areas in motor cortex. If the gain of signals sent through
this loop is >1, then motor cortical cells will continue to increase
their firing rates until maximal muscle contraction occurs. In this
paper, we will show that the loop gain can be analyzed in terms of a
linear approximation to the motor to sensory transform. Several
features of task-specific dystonia then arise as natural consequences
of instability in this loop, including the following.
1)
Symptoms may be present only during one task, but with progression may worsen to involve multiple tasks.
2)
During a movement, muscle force may increase progressively until the task must be halted.
3)
There is spread of activity into muscles normally uninvolved in or antagonistic to desired movements.
In this model, motor abnormalities can arise from sensory
de-differentiation if the sensory changes lead to increased loop gain.
Gain can be increased by increasing the relative sensory cortical
representation of a limb. Sensory cortical increase could occur due to
adaptation in response to the repetitive use of a limb, coupling of
multiple sensory signals from the limb, or voluntary co-activation of
muscles leading to correlated sensory activity (Allard et al.
1991; Jenkins et al. 1990
; Kaas et al.
1983
; Merzenich et al. 1983a
,b
; Wang et
al. 1995
). Only certain mechanical modes of the sensorimotor
loop may be unstable, and as a result only focal or task-specific
dystonia may be observed. Instability will occur as the gain approaches
1, and becomes more severe and persistent as the gain increases beyond
1. We further hypothesize that plasticity mechanisms in sensory and
motor systems may contribute to the emergence or progression of
symptoms. The onset of dystonia may be delayed until after many years
of successful task performance if during those years the sensory
representation is slowly changing and the gain is gradually increasing.
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METHODS |
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Cortical representation
To use control-theoretic concepts to understand biological
systems, a model for representation of signals in cortical neural populations is needed. The probability of firing for each neuron will
be given by a Poisson process
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(1) |
If (t) is the firing rate at time t, then the
loop gain for a single neuron i is given by
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(2) |
Now, consider a sensorimotor loop as shown in Fig. 1, which depicts the transformation from the motor cortical representation m through the external world to the resulting sensory cortical representation s. C represents the map from sensory to motor cortex; W is the mapping computed by the external world, including motor neurons, muscles, physical plant, and sensory processing. In this figure, the boxes indicate the data representation in each component of the system.
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Figure 2 shows a detailed picture in more
standard control-theoretic notation, in which the boxes represent
transformations between signals. Here, motor activity m
propagates to the physical muscles through the motor mapping
M, then through the musculoskeletal and external mechanical
plant P to the sensory receptors, then through the sensory
mapping S to sensory cortex. represents the combined
delays in motor to sensory information transmission. C
represents the intracortical sensory to motor mapping that is assumed
to connect sensations to the causative motor commands. u is
an initial command issued to motor cortex to generate a desired voluntary movement, and n is an external source of sensory
"noise" (that may include important but uncontrollable components
of the environment). B is the internal mapping from motor
cortex through basal ganglia and thalamus back to motor cortex. For
simplicity, let W = S(n +
PM) represent the complete nonlinear probabilistic transformation from motor cortex m to sensory cortex
s including delays. m and s are
vectors of integers indicating the number of spikes occurring during a
short time interval
t. We define
m and
s to be the
average rates of the Poisson processes generating the spikes for
m and
s.1
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All the transformations M, B, P, S, C, and W are
probabilistic, in the sense that they describe the average firing rate
of an output neuron for each possible input firing pattern. For
example, s = Wm means that
Wm gives the vector of average firing rates for each sensory
neuron sj in s, when the motor
firing pattern is given by m. The resulting firing pattern
s is generated randomly from the firing rate
s by spike generators modeled as independent
time-varying Poisson processes. This formulation ignores information
that may be encoded in details of timing of the spike train, since we
are primarily concerned with understanding saturation of the average
firing rate.
Loop gain
To understand the loop gain, consider the case in which the
probability of a sensory spike is determined only by whether a motor
spike occurred at some particular previous time. This is a special case
of the general nonlinear mapping s = Wm, and it implies that mi and
sj are "time-locked" in the sense that
mi's effect on
sj is seen exactly at time
t later. Taking expected values, we have
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(3) |
We can describe the sensory to motor transform C in cortex
the same way, and again assuming that sensory spike firing is rare, C can be approximated linearly. In this case, we have
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(4) |
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(5) |
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(6) |
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(7) |
In the following, we are concerned with enlargement of the sensory
representation of different control modes, and without loss of
generality we can simplify the discussion by assuming that each mode is
represented directly by a discrete subpopulation of sensory cells that
are uncorrelated with other populations. In the linear approximation,
two cells firing at a rate spikes per second have the same effect
as one cell firing at a rate 2
spikes per second. We will therefore
represent the transform W as the product PGV,
where V is an orthogonal matrix indicating the
transformation of the pattern
m into the
pattern
s, P is a diagonal matrix
each of whose integer elements pi gives
the number of cells representing a single mode, and G is a
diagonal matrix that gives the attenuation of each mode as it passes
through the "world" transform W. In general, the
elements gi of G will be very
small since most of the motor command will be seen only weakly
reflected in the sensory response. If we assume that the sensory
populations are uncorrelated as above, then GV finds
uncorrelated modes, and its output
GV
m must be uncorrelated.
Therefore the expected value
E[GV
m
mTVTG]
is diagonal. This implies that V is the matrix of
eigenvectors of the covariance matrix Rm = [
m
mT].
We hypothesize that the sensory to motor mapping C forms
links between each sensory state and the motor commands that cause it,
thereby completing the motor-sensory loop. This means that the cortical
mapping C is an inverse of the external mapping
W. Since C is the linear approximation to the
mapping between the rates of sensory neuron firing
s and the rates of motor neuron firing
m, each element of C can be no
greater than the maximum number of motor cortical spikes that can
result from a single sensory cortical spike. Label this maximum number of output spikes per input spike nmax.
Similarly, because the spike rate
m is
measured over a finite period of time, there is a minimum nonzero value
of each element of
m that can be measured.
Since there is a maximum achievable spike rate for
s, there is an effective minimum value
nmin = min
(
m)/max (
s) for
nonzero elements of C. Ideally, C = VTG
1P
1,
but the limitation on nmax and
nmin means that in reality we have
C = VTN where
N is a diagonal matrix of gains
ni, with
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(8) |
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(9) |
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(10) |
If the command signal u to the motor cortex is sustained
during a prolonged movement, then the signal returning through the motor-sensory loop will add to the sustained command. In normal circumstances, this effect would be expected to be very small and not
lead to significant changes in the force output. However, in the
circumstance of pathologically increased loop gain, the feedback can
become significant and lead to instability even at loop gains that are
<1. In this case, we have
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(11) |
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(12) |
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(13) |
A further cause for instability can occur if the structure of the
control modes changes. For instance, if two fingers are consistently
co-activated, if they are sutured together, or if pressure is applied
simultaneously and repeatedly to multiple fingers, then there may be a
new combined mode representing the combined sensory stimulus to the two
fingers. The combined sensory receptors and sensory cortical cells for
the two original populations will lead to a larger total population,
and a higher gain for the combined mode. This effect would be
particularly severe if a combined mode involved a combination of
agonist and antagonist muscle activation, since co-contraction may lead
to increased correlated spindle fiber activation from both muscles, and
the proprioceptive feedback gain will therefore be much higher.
Plasticity mechanisms can worsen this effect, since the cortical
representation for the two modes will fuse and possibly enlarge
(Allard et al. 1991; Byl et al. 1996a
,
1997
; Dinse et al. 1993
; Jenkins
et al. 1990
; Wang et al. 1995
; Xerri et
al. 1996
, 1999
). This leads to much more highly
correlated distributed activity in sensory cortical areas
(Recanzone et al. 1992
; Wang et al. 1995
)
that can far more powerfully excite motor cortex neurons, given their
relatively short integrative time constant.
Simulations
The simulation in Fig. 3 shows the
effect of increased loop gain on neural firing rates. In each case, the
initial motor command u = m(0) is a randomly
chosen vector of spike counts, and C and W are
random matrices normalized to a total gain of either 0.95 or 1.05. m(t + t) is defined as a vector of
the integer number of spikes that occurred between times t
and t +
t, and this vector is generated from
Poisson statistics with rates given by CWm(t). The time-steps are in units of
t.
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There are at least three mechanisms by which plasticity can lead to pathological increases in loop gain. Each mechanism corresponds to an increased gain through one element of the sensorimotor loop shown in Fig. 2. The first mechanism is caused by an increase in the size of the sensory representation of a particular movement mode. This is equivalent to increased gain through a component of the sensory transform S, and it can occur as the consequence of plasticity that increases the cortical representation of sensory signals that occur frequently or have high power. The second mechanism is caused by cross-coupling through the external world so that two normally independent modes are mutually reinforced. This is equivalent to increased gain through P and can occur as the consequence of an altered mechanical environment such as would happen if two fingers were sutured together, or were otherwise systematically co-stimulated. The third mechanism occurs when two normally independently controlled modes are activated together by the command signals u and m. This is equivalent to increased gain through the motor transformation M and can occur with repeated co-contraction of antagonist or normally uncorrelated muscles.
To illustrate the effects of plasticity on the loop gain, we simulate three different ways in which the sensory representation and the loop gain may increase. In the first, the sensory representation increases without any other change in behavior. In the second, there is external mechanical coupling between two modes of the system, as if two fingers had been sutured together. In the third, there is voluntary coactivation of two different modes, corresponding to a repeated task. The second and third intervention lead to the creation of a new combined mode of the system and therefore de-differentiation of the sensory representation.
In the simulations, W is a random block-diagonal matrix of
dimension m1 + m2 by
s1 + s2 where
m1,
m2,
s1, and
s2 are the number of neurons allocated
within motor and sensory cortex, respectively, to each of two different
muscles. The total number of neurons used in the simulations is 40 (20 each in sensory and motor cortex). The linear sensorimotor mapping
C adapts according to a Hebbian cross-correlational learning
algorithm with C =
m(t)sT(t)
(Hebb 1949
) (in the simulations, the learning rate
= 0.01). To impose a threshold on motor neuron firing or gain
nmax and nmin of the mapping C, the
system is trained with a small learning rate for only a finite number
of steps. Therefore after 200 learning steps the mapping C
is fixed and the system is tested by injecting a random motor cortical
activation onto only the m1 neurons at time 0, and then iterating the motor-sensory loop for 200 time steps of length
t. The time
Td required for spontaneous neural activity to stop is then measured. The learning and testing process is
repeated 10 times for each degree of abnormality, and results are
averaged to produce the plots shown in Fig. 5. An important feature of
the results is that there is a very rapid increase in sustained neural
activity as the loop gain becomes 1.
Enlarging sensory area (shown schematically in Fig.
4A) is described by changing
the ratio
s1/s2
of the larger to the smaller (normal) digit representation in sensory
cortex, for different values of this ratio from 0.2 to 2.0 (the total
number of neurons is fixed, so that s2 = 20 s1). The number of motor
cortical neurons are equal (m1 = m2 = 10). The elements of W
connecting m1 to
s1 and
m2 to
s2 are chosen randomly with small
values between 0 and 0.1. In this case there is no cross-coupling, so
all elements in W that connect neurons in
m1 to neurons in
s2 (and from
m2 to
s1) are set to zero. During learning,
the motor command m randomly activates neurons in either
group m1 or
m2, but never both simultaneously.
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External cross-coupling (Fig. 4B) is described by a correlation value that varies from 0 to 0.35. In this case, the number of neurons m1 = m2 and s1 = s2. Elements of W connecting m1 to s1 and m2 to s2 are again chosen randomly, but elements connecting m1 to s2 and m2 to s1 are nonzero and chosen randomly with normalization so that the column sums are all equal, and vary from 0 to 0.35. This means that the total additional input to any sensory neuron is 0.35. Again, during learning the motor command randomly activates either m1 or m2, but not both.
Voluntary co-contraction (Fig. 4C) is described by random
simultaneous activation of both populations
m1 and
m2 of motor cortical neurons. The
activation is the combination of the alternating pattern used above,
added to a pattern with random elements whose magnitude is less than
, where
varies from 0 to 0.5. In this case,
m1 = m2 and
s1 = s2, and the weights in W
connecting m1 to
s2 and
m2 to
s1 are zero.
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RESULTS |
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Figure 3 gives simulated examples of stable and unstable loops for
neural populations that are described by the linear loop approximation
m(t +
t) = CW
m(t). The figure illustrates the increase or decrease in activity over a population of
identical neurons in the loop. If
t
50 ms
(Deuschl et al. 1989
), then at a gain of 1.05, the
simulation shows that saturation of firing will occur within 100 steps,
or 5 s.
Figure 4 illustrates three causes of instability due to enlarged sensory representation (A), external cross coupling (B), or voluntary co-activation (C). Figure 5 shows simulations of the structures from Fig. 4, demonstrating the increase in activity decay time following a single motor command.
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Figure 6 shows the time course of
gain increase during Hebbian adaptation immediately following a change
in the system. As before, time is indicated in units of
t. For this simulation, at time 0 two
previously uncorrelated modes start to be voluntarily activated
entirely synchronously as illustrated in Fig. 4C. Parameters are the same as those described for Fig. 5C, with
= 0.5 in the range that leads to instability. As the cortical map from
sensory to motor cortices C adapts to the resulting
increased sensory correlation, the loop gain to each of the motor
neurons increases. As the gain approaches 1, the time for decay of
firing rates Td
1/log (
)
becomes infinite, indicating sustained neural activity. This graph
illustrates the rapid increase in sustained activity Td that occurs as the gain
nears
1.
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DISCUSSION |
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The simulations show that changes in the sensory representation can lead to instability in the sensory-motor loop that may manifest as symptoms of dystonia. Task specificity is due to instability of only a single eigenvector. Worsening with prolonged activity occurs if continuing motor commands add to a nearly unstable loop gain. Co-contraction and spread of activity are the consequences of disordered or de-differentiated sensory-motor control modes. These properties arise as direct consequences of the linear approximation to the loop transformation CW.
To see this in more detail, if CW is initially stable with
maximum eigenvalue magnitude <1 and if the total gain increases slowly
due to change in the motor-sensory gain gi
or the sensory population size pi, then
one would expect that at first only one eigenvalue will become >1.
Only this mode will be unstable, and unless triggered by a particular
voluntary movement, ongoing motor command, or sensory input that
matches its eigenvector, no instability will be seen. Since the motor
system presumably has many different modes that are activated in a
context-dependent way, dystonia will initially be very situation
dependent. It may be possible to inhibit the dystonia by changing the
context using a "sensory trick" (Hallett 1995) that
changes the sensory pattern to be only slightly different from the
unstable eigenvector. As the loop gain increases further, more modes
will become unstable and it will become progressively easier to trigger
dystonic postures and increasingly difficult to find sensory contexts
in which these postures are inhibited.
Three regimes of behavior can be distinguished. If the largest
eigenvalue max2 of
WTCTCW is
<1, then the spontaneous neural activity will decrease toward zero
unless a new motor command is issued to motor cortex. This is the
desired behavior of the system: movement occurs only in response to
motor commands. However, if the gain is increased and the command is
continued for the duration of an ongoing movement, then the combination
of the command and the sensory feedback may lead to instability. If
max2
1, there may be prolonged
activity that may or may not saturate depending on random fluctuations
in the Poisson statistics. Again, this sustained behavior will only
occur if the pattern of activity matches the corresponding eigenvector.
If
max2 > 1, there will be
sustained motor activity even in the absence of a triggering command,
leading to dystonia at rest. The time to decay of neural activity
(Td) is proportional to
1/log
. Figure 6 shows that Td may increase
much more rapidly than
, as
approaches 1. If
> 1, then
clinical intervention will appear to be frustratingly ineffective
because even large changes in the gain may lead to no clinical
improvement until
decreases to <1.
There is evidence of increased motor and supplementary motor cortical
excitability and decreased inhibition in dystonia from transcranial
magnetic stimulation studies (Chen et al. 1997;
Hallett 1998
; Ikoma et al. 1997
), as well
as from functional imaging (Brooks 1998
; Ibanez
et al. 1999
). Similarly, evidence of increased sensory cortical
excitability has been found using somatosensory evoked potential
studies (Hallett 1995
). This may reflect increased map sizes or decreased thresholds contributing to loop gain, and might be
expected to become prominent prior to the development of dystonia. In a
task or muscle-specific dystonia, note that the overall map sizes might
decrease while the populations engaged by specific movements could
increase due to progressive learning-induced changes that
de-differentiate the cortical representations. Documentation of the
progressive loss of representational topography may be an index of
increase in the loop gain.
Direct measurement of the loop gain is possible in cortical myoclonus
by correlating the somatosensory evoked potential and subsequent reflex
electromyographic (EMG) response (Rothwell et al. 1984,
1986
). However, this is not likely to provide a simple measurement for task-specific dystonia, since in dystonia the gain may
only be increased during performance of the specific chosen task, and
only particular sensory patterns may be able to excite the abnormal
modes. In fact, the sensory response to a nonspecific vibration
stimulus is reduced in dystonia on positron-emission tomography (PET)
scanning (Tempel and Perlmutter 1990
). Long-loop reflexes have been measured, and there are measurable increases in
these reflexes in dystonia (Bressman 1998
; Eisen
1987
; Marsden and Rothwell 1987
). There are also
changes in the H-reflex recovery curve (Deuschl et al.
1989
; Panizza et al. 1990
), and prolonged EMG
"tails" would be expected to follow rapid voluntary or reflex movements (Marsden and Rothwell 1987
). Simultaneous
activation of agonist and antagonist muscles is detectable as EMG
"overflow" (Bressman 1998
; Nakashima et al.
1989
). Many of these effects might only be evident in certain
postures or during performance of the affected task.
Conclusions
We have proposed a new model to explain the possibility of sensory disorganization as an etiology of focal task-specific dystonia. In our model, dystonic symptoms are related to increased gain through a sensorimotor loop. The increased gain leads to instability, which saturates the firing rate of motor cortical cells and causes a "high-ouput paralysis" of the affected muscles. Although we have proposed this model as a possible mechanism by which changes in the sensory representation could lead to dystonia, it is important to realize that dystonia might also be caused through a similar mechanism due to enlargement or de-differentiation of motor representations. Further, we have chosen to use a very simple model of the sensory representation that does not include lateral interactions within sensory or other cortices. This was done to demonstrate minimal requirements for the development of dystonia. In fact, a linear approximation to the sensory-motor loop is sufficient to predict an increase in tone resulting from sensory changes. The simulations show that, in addition, plasticity mechanisms can contribute to worsening symptoms. In this model, dystonia arises as a natural consequence of the normal behavior of the sensorimotor system in the face of abnormal sensory input. Much work remains to be done to validate the predictions and clinical relevance of this model, but it provides an initial structure to explain a possible etiologic role of sensory representations in the motor disorder of task-specific dystonia.
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ACKNOWLEDGMENTS |
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We thank E. Bizzi, M. Kilgard, N. Byl, J. Houde, E. Thiele, A. Terrien-Queen, and S. Giszter for comments and discussions.
T. D. Sanger was supported in part by a McDonnell-Pew Postdoctoral Fellowship. M. M. Merzenich was supported by National Institute of Neurological Disorders and Stroke Grants P01 NS-34835 and R01 NS-10414.
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FOOTNOTES |
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1
Note that since the Poisson rates will be
modulated by the output of other spike trains, we can distinguish the
"instantaneous" rate from the "average" rate over longer
periods of time. m and
s refer to the
average rates, which are well-defined since a Poisson process modulated
by another stationary Poisson process continues to satisfy the
independent increment property and therefore remains Poisson. See
Sanger (1998)
for further discussion.
Present address and address for reprint requests: T. D. Sanger, Stanford University, Dept. of Neurology, 300 Pasteur Dr., MS:5235, Stanford, CA 94305.
Received 20 September 1999; accepted in final form 19 July 2000.
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REFERENCES |
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