52 Grajski and Merzenich 
Neural Network Simulation 
of 
Somatosensory Representational Plasticity 
Kamil A. Grajski 
Ford Aerospace 
San Jose, CA 95161-9041 
kamil@ wdl 1.fac.ford.com 
Michael M. Merzenlch 
Coleman Laboratories 
UC San Francisco 
San Francisco, CA 94143 
ABSTRACT 
The brain represents the skin surface as a topographic map in the 
somatosensory cortex. This map has been shown experimentally to 
be modifiable in a use-dependent fashion throughout life. We 
present a neural network simulation of the competitive dynamics 
underlying this cortical plasticity by detailed analysis of receptive 
field properties of model neurons during simulations of skin co- 
activation, cortical lesion, digit amputation and nerve section. 
1 INTRODUCTION 
Plasticity of adult somatosensory cortical maps has been demonstrated experimentally 
in a variety of maps and species (Kass, et al., 1983; Wall, 1988). This report focuses 
on modelling primary somatosensory cortical plasticity in the adult monkey. 
We model the long-term consequences of four specific experiments, taken in pairs. 
With the first pair, behaviorally controlled stimulation of restricted skin surfaces (Jen- 
kins, et al., 1990) and induced cortical lesions (Jenkins and Merzenich, 1987), we 
demonstrate that Hebbian-type dynamics is sufficient to account for the inverse rela- 
tionship between cortical magnification (area of conical map representing a unit area 
of skin) and receptive field size (skin surface which when stimulated excites a cortical 
unit) (Sur, et al., 1980; Grajski and Merzenich, 1990). These results are obtained with 
several variations of the basic model. We conclude that relying solely on cortical 
magnification and receptive field size will not disambiguate the contributions of each 
of the myriad circuits known to occur in the brain. With the second pair, digit ampu- 
tation (Merzenich, et al., 1984) and peripheral nerve cut (without regeneration) (Mer- 
zenich, t al., 1983), we explore the role of local excitatory connections in the model 
Neural Network Simulation of Somatosensory Representational Plasticity $3 
cortex (Grajski, submitted ). 
Previous models have focused on the self-organization of topographic maps in general 
(Willshaw and von der Malsburg, 1976; Takeuchi and Amari, 1979; Kohonen, 1982; 
among others). Ritter and Schulten (1986) specifically addressed somatosensory plas- 
ticity using a variant of Kohonen's self-organizing mapping. Recently, Pearson, et al., 
(1987), using the framework of the Group Selection Hypothesis, have also modelled 
aspects of normal and reorganized somatosensory plasticity. 
Elements of the present study have been published elsewhere (Grajski and Merzenich, 
1990). 
2 THE MODEL 
2.1 ARCHITECTURE 
The network consists of three heirarchically organized two-dimensional layers shown 
in Figure 1A. 
,..-.,,-.....-.,.,......,,..,,.,...,,.,,,..,.,,,.., 
Skin Layer 
Cortical Layer 
Subcortical Layer 
b.) 
Figure 1: Network architecture. 
The divergence of projections from a single skin site to subcortex (SC) and its subse- 
quent projection to cortex (C) is shown at left: Skin (S) to SC, 5 x 5; SC to C, 7 x 7. 
S is "partitioned" into three 15 x 5 "digits" Left, Center and Right. The standard S 
stimulus used in all simulations is shown lying on digit Left. The projection from C 
to SC E and I cells is shown at right. Each node in the SC and C layers contains an 
excitatory (E) and inhibitory cell (I) as shown in Figure lB. In C, each E cell forms 
excitatory connections with a 5 x 5 patch of I cells; each I cell forms inhibitory con- 
54 Grajski and Merzenich 
nextions with a 7 x 7 path of E cells. In SC, these connections are 3 x 3 and 5 x 5, 
respectively. In addition, in C only, E cells form excitatory connections with a 5 by 5 
patch of E cells. The spatial relationship of E and I cell projections for the central 
node is shown at left (C E to E shown in light gray, C I to E shown in black). 
2.2 DYNAMICS 
The model neuron is the same for all E and I cells: an RC-time constant membrane 
which is alepolarized and (additively) hyperpolarized by linearly weighted connections: 
ti c r = --Xr U c r + vfC rwi r :sc r + v f rwi? r :c r - v f aw r :c a 
ti c d = ---Xrn U c d + v woC. d:c  
--q:rn Ui sc'E + Wi C'E :s + V'EWi C'E :c'E 
_ vfC wC :sc j 
ti c d = -Xrn U c d + v? wfj c d :sc  + v w c J :c  - vfC w c  :sc d 
u/x,r - membrane potential for unit i of type Y on layer X; v/x'r - firing rate for unit i 
of type Y on layer X;  - skin units are OFF (=0) or ON (=1); x,,, - membrane time 
constant (with respect to unit time); w,7 st(xe):p"*0rr) - connection to unit i of post- 
synaptic type y on postsynaptic layer x from units of presynaptic type Y on presynap- 
tic layer X. Each summation term is normalized by the number of incoming connec- 
tions (corrected for planar boundary conditions) contributing to the term. Each unit 
converts membrane potential to a continuous-valued output value v via a sigmoidal 
function representing an average firing rate (13 = 4.0): 
vi = g (ui ) = 
1 1 
' ( 1 +tanh((ui--))) 
0 
ui->O.02, 
ui<0.02 
2.3 SYNAPTIC PLASTICITY 
Synaptic strength is modified in three ways: a.) activity-dependent change; b.) passive 
decay; and c.) normalization. Activity-dependent and passive decay terms are as fol- 
lows: 
Aw O = '-'syn wij + otvi vj 
w O - connection from cell j to cell i; xo,,---0.01x,=0.005 - time constant for passive 
synaptic decay; cw-0.05, the maximum activity-dependent step change; vj,vi - pre- and 
post-synaptic output values, respectively. Further modification occurs by a multiplica- 
tive normalization performed over the incoming connections for each cell. The nor- 
malization is such that the summed total strength of incoming connections is R: 
Neural Network Simulation of Somatosensory Representationai Plasticity 55 
1 
N i - number of incoming connections for cell i; w 0 - connection from cell j to cell i; 
R = 2.0 - the total resource available to cell i for redistribution over its incoming con- 
nections. 
2.4 
MEASURING CORTICAL MAGNIFICATION, RECEPTIVE FIELD 
AREA 
Cortical magnification is measured by "mapping" the network, e.g., noting which 3x3 
skin patch most strongly drives each cortical E cell. The number of cortical nodes 
driven maximally by the same skin site is the cortical magnification for that skin site. 
Receptive field size for a C (SC) layer E cell is estimated by stimulating all possible 
3x3 skin patches (169) and noting the peak response. Receptive field size is defined as 
the number of 3x3 skin patches which drive the unit at >50% of its peak response. 
3 SIMULATIONS 
3.1 FORMATION OF THE TOPOGRAPHIC MAP ENTAILS REFINEMENT 
OF SYNAPTIC PATTERNING 
The location of individual connections is fixed by topographic projection; initial 
strengths are drawn from a Gaussian distribution (Ix = 2.0, 2 = 0.2). Stand_ard-sized 
skin patches are stimulated in random sequence with no double-digit stimulation. 
(Mapping includes tests for double-digit receptive fields.) For each patch, the network 
is allowed to reach steady-state while the plasticity rule is ON. Synaptic strengths are 
then renormalized. Refinement continues until two conditions are met: a.) fewer than 
5% of all E cells change their receptive field location; and b.) receptive field areas (us- 
ing the 50% criterion) change by no more than +1 unit area for 95% of E cells. (See 
Figures 2 and 3 in Merzenich and Grajski, 1990; Grajski, submitted ). 
3.2 RESTRICTED SKIN STIMULATION GIVES INCREASED MAGNIFICA- 
TION, DECREASED RECEPTIVE FIELD SIZE 
Jenkins, et al., (1990) describe a behavioral experiment which leads to cortical soma- 
totopic reorganization. Monkeys are trained to maintain contact with a rotating disk 
situated such that only the tips of one or two of their longest digits are stimulated. 
Monkeys are required to maintain this contact for a specified period of time in order 
to receive food reward. Comparison of pre- and post-stimulation maps (or the latter 
with maps obtained after varying periods without disk stimulation) reveal up to nearly 
3-fold differences in cortical magnification and reduction in receptive field size for 
stimulated skin. 
We simulate the above experiment by extending the refinement process described 
above, but with the probability of stimulating a restricted skin region increased 5:1. 
(See Grajski and Merzenich (1990), Figure 4.) Figure 2 illustrates the change in size 
(left) and synaptic patterning (right) for a single representative cortical receptive field. 
56 Grajski and Merzenich 
Figure 2: Representative co-activation induced receptive field changes. 
Cortical RF 
Cortical RF 
a.) 
Post Co- 
Activation 
Pre Co- 
Activation 
Incoming Synaptic Strengths 
Skin to Subcortex 
Subcortex to Cortex 
low high 
3.3 AN INDUCED, FOCAL CORTICAL LESIONS GIVES DECREASED 
MAGNIFICATION, INCREASED RECEPTIVE FIELD SIZE 
The inverse magnification rule predicts that a decrease in cortical magnification is ac- 
companied by an increase in receptive field areas. Jenkins, et al., (1987) confirmed 
this hypothesis by inducing focal cortical lesions in the representation of restricted 
hand surfaces, e.g. a single digit. Changes included: a.) a re-emergence of a represen- 
tation of the skin formerly represented in the now lesioned zone in the intact surround- 
ing cortex; b.) the new representation is at the expense of cortical magnification of 
skin originally represented in those regions; so that c.) large regions of the map con- 
tain neurons with abnormally large receptive fields. 
We simulate this experiment by eliminating the incoming and outgoing connections of 
the cortical layer region representing the middle digit. The refinement process 
described above is continued under these new conditions until topographic map and 
receptive field size measures converge. The re-emergence of representation and 
changes in distributions of receptive field areas are shown in Grajski and Merzenich, 
(1990) Figure 5. Figure 3 below illustrates the change in size and location of a 
representative (sub) cortical receptive field. 
3.4 
SEVERAL MODEL VARIANTS REPRODUCE THE INVERSE MAGNIFI- 
CATION RULE 
Repeating the above simulations using networks with no descending projections or us- 
ing networks with no descending and no cortical mutual exciatation, yields largely 
normal topography and co-activation results. Restricting plasticity to excitatory path- 
ways alone also yields qualitatively similar results. (Studies with a two-layer network 
Neural Network Simulation of Somatosensory Representationai Plasticity 
yield qualitatively similar results.) Thus, the refinement and co-acan experiments 
alone are insufficient to discriminate fundamental differences between network vari- 
Figure 3: 
Representative cortical lesion induced receptive field changes. 
Pre-Cortical Lesion Post-Cortical Lesion 
Cortical- 
Receptive 
Field 
I I 
I I 
Sub-cortical 
Receptive 
Field 
I I 
I I 
I I 
I I 
3.5 MUTUALLY EXCITATORY LOCAL CORTICAL CONNECTIONS MAY 
BE CRITICAL FOR SIMULATING EFFECTS OF DIGIT AMPUTATION 
AND NERVE SECTION 
The role of lateral excitation in the cortical layer is made clearer through simulations 
of nerve section and digit amputation experiments (Merzenich, et al., 1983; Merzen- 
ich, et al., 1984; see also Wall, 1988). The feature of interest here is the cortical dis- 
tance over which reorganization is observed. Following cessation of peripheral input 
from digit 3, for example, the surrounding representations (digits 2 and 4) expand into 
the now silenced zone. Not only expansion is observed. Neurons in the surrounding 
representations up to several 100's of microns distant from the silenced zone shift 
their receptive fields. The shift is such that the receptive field covers skin sites closer 
to the silenced skin. 
The deafferentation experiment is simulated by eliminating the connection between the 
skin layer CENTER digit (central 1/3) and SC layers and then proceeding with 
refinement with the usual convergence checks. Simulations are run for three network 
architectures. The "full" model is that described above. Two other models strip the 
descending and both descending and lateral excitatory connections, respectively. 
Figure 4 shows features of reorganization: the conversion of initially silenced zones, or 
refinement of initially large, low amplitude fields to normal-like fields (a-c). Impor- 
tanfly, the receptive field farthest away from the initially silenced representation (d) 
undergoes a shift towards the deafferented skin. The shift is comprised of a transla- 
tion in the receptive field peak location as well as an increase (below the 50% ampli- 
tude threshold, but increases range 25 - 200%) in the regions surrounding the peak and 
facing the silenced cortical zone (shown in light shading). Only the "full" model 
evolves expanded and shifted representations. These results are preliminary in that no 
parameter adjustments are made in the other networks to coax a result. It may simply 
be a matter of not enough excitation in the other cases. Nevertheless, these results 
show that local cortical excitation can contribute critical activity for reorganization. 
58 Grajski and Merzenich 
a.) 
Figure 4: 
Summary of immediate and long-term post-amputation effects. 
Post-amputation Post-amputation 
Normal Immediate Long-term Normal Immodiato Long4orm 
4 CONCLUSION 
We have shown that a.) Hebbian-type dynamics is sufficient to account for the quanti- 
tative inverse relationship between cortical magnification and receptive field size; and 
b.) cortical magnification and receptive field size alone are insufficient to distinguish 
between model variants. 
Are these results just "so much biological detail?" No. The inverse magnification- 
receptive field rule applies nearly universally in (sub)cortical topographic maps; it 
reflects a fundamental principle of brain organization. For instance, experiments re- 
vealing the operation of mechanisms possibly similar to those modelled above have 
been observed in the visual system. Wurtz, et al., (1990) have observed that following 
chemically induced focal lesions in visual area MT, surviving neurons' visual recep- 
tive field area increased. For a review of use-dependent receptive field plasticity in 
the auditory system see Weinberger, et al., (1990). 
Research in computational neuroscience has long drawn on principles of topographic 
organization. Recent advances include those by Linsker (1989), providing a theoreti- 
cal (optimization) framework for map formation and those studies linking concepts re- 
lated to localized receptive fields with adaptive nets (Moody and Darken, 1989; see 
Barron, this volume). The experimental and modelling issues discussed here offer an 
opportunity to sustain and further enhance the synergy inherent in this area of compu- 
tational neuroscience. 
4.0.1 Acknowldegements 
This research supported by NIH grants (to MMM) NS10414 and GM07449, Heating 
Research Inc., the Coleman Fund and the San Diego Supercomputer Center. KAG 
gratefully acknowledges helpful discussions with Terry Allard, Bill Jenkins, John Pear- 
son, Gregg Recanzone and especially Ken Miller. 
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