Orientation contrast sensitivity from 
long-range interactions in visual cortex 
Klaus R. Pawelzik Udo Ernst Fred Wolf Theo Geisel 
Institut ffir Theoretische Physik and SFB 185 Nichtlineare Dynamik, 
Universit/t Frankfurt, D-60054 Frankfurt/M., and 
MPI ffir StrSmungsforschung, D-37018 GSttingen, Germany 
email: {klaus,udo,fred,geisel} @chaos.uni-frankfurt.de 
Abstract 
Recently Sillito and coworkers (Nature 378, pp. 492, 1995) demon- 
strated that stimulation beyond the classical receptive field (cRF) 
can not only modulate, but radically change a neuron's response to 
oriented stimuli. They revealed that patch-suppressed cells when 
stimulated with contrasting orientations inside and outside their 
cRF can strongly respond to stimuli oriented orthogonal to their 
nominal preferred orientation. Here we analyze the emergence of 
such complex response patterns in a simple model of primary vi- 
sual cortex. We show that the observed sensitivity for orientation 
contrast can be explained by a delicate interplay between local 
isotropic interactions and patchy long-range connectivity between 
distant iso-orientation domains. In particular we demonstrate that 
the observed properties might arise without specific connections be- 
tween sites with cross-oriented cRFs. 
I Introduction 
Long range horizontal connections form a ubiquitous structural element of intra- 
cortical circuitry. In the primary visual cortex long range horizontal connections 
extend over distances spanning several hypercolumns and preferentially connect 
cells of similar orientation preference [1, 2, 3, 4]. Recent evidence suggests that 
Modeling Orientation Contrast Sensitivity 91 
their physiological effect depends on the level of postsynaptic depolarization; act- 
ing exitatory on weakly activated and inhibitory on strongly activated cells [5, 6]. 
This differental influence possibly underlies perceptual phenomena as 'pop out' and 
'fill in' [9]. Previous modeling studies demonstrated that such differential interac- 
tions may arise from a single set of long range excitatory connections terminating 
both on excitatory and inhibitory neurons in a given target column [7, 8]. By and 
large these results suggest that long range horizontal connections between columns 
of like stimulus preference provide a central mechanism for the context dependent 
regulation of activation in cortical networks. 
Recent experiments by Sillito et al. suggest, however, that lateral connections 
in primary visual cortex can also induce more radical changes in receptive field 
organization [10]. Most importantly this study shows that patch-suppressed cells 
can respond selectively to orientation contrast between center and surround of a sti- 
mulus even if they are centrally stimulated orthogonal to their preferred orientation. 
$illito et al. argued, that these response properties require specific connections 
between orthogonally tuned columns for which, however, presently there is only 
weak evidence. 
Here we demonstrate that such nonclassical receptive field properties might instead 
arise as an emergent property of the known intracortical circuitry. We investigate a 
simple model for intracortical activity dynamics driven by weakly orientation tuned 
afferent excitation. The cortical actitvity dynamics is based on a continous firing 
rate description and incorporates both a local center-surrond type interaction and 
long range connections between distant columns of like orientation preference. The 
connections of distant orientation columns are assumed to act either excitatory or 
inhibitory depending on the activation of their target neurons. It turns out that this 
set of interactions not only leads to the emergence of patch-suppressed cells, but 
also that a large fraction of these cells exhibits a selectivity for orientation contrast 
very similar to the one observed by Sillito et al.. 
2 Model 
Our target is the analysis of basic rate modulations emerging from local and long 
range feedback interactions in a simple model of visual cortex. It is therefore ap- 
propriate to consider a simple rate dynamics :k = -c. x + F(x), where x = {xi, i = 
1...N} are the activation levels of N neurons. F(x) = g(Imex(X) + Ilar(X) + Iext), 
where g(I) = co. (I- Ithres) if I > Ithres, and g(I) - 0 otherwise, denotes the firing 
rate or gain function in dependence of the input I. 
The neurons are arranged in a quadratic array representing a small part of the visual 
cortex. Within this layer, neuron i has a position ri and a preferred orientation 
i E [0,180]. The input to neuron i has three contributions I: I ex + 1 at + I xt. 
lmex -- Y7=  me_ is due to a mexican-hat shaped coupling structure 
i -- mex ' 1 'wij xj 
 mex E7 =  lat_ denotes input from long-range 
with weights wij , Ilar '- elat' WL(Xi)' l'Wij 3:j 
orientation-specific interactions with weights  tat and the third term models the 
'ij ' 
/?t. (1 + i), where Vi denotes the 
orientation dependent external input Iet = eet' o,i 
noise added to the external input. w (x) regulates the strength and sign of the long- 
92 K. R. Pawelzik, U. Ernst, E Wolf and T. Geisel 
o) b) ) 
Figure 1: Structure and response properties of the model network. a) Coupling 
structure from one neuron on a grid of N - 1600 elements projected on the orien- 
tation preference map which was used for stimulation (i,i = 1...N). Inhibitory 
and excitatory couplings are marked with black and white squares, respectively, 
the sizes of which represent the coupling strength. b) Activation pattern of the 
network driven by a central stimulus of radius rc- 11 and horizontal orientation. 
c) Self-consistent orientation map calculated from the activation patterns for all 
stimulus orientations. Note that this map matches the input orientation preference 
map shown in a) and b). 
range lateral interaction in dependence of the postsynaptic activation, summarizing 
the behavior of a local circuit in which the inhibitory population has a larger gain. 
In particular, wt(x) can be derived analytically from a simple cortical microcircuit 
(Fig.2). This circuit consists of an inhibitory and excitatory cell population con- 
nected reciprocally. Each population receives lateral input and is driven by the 
external stimulus I. The effective interaction wL depends on the lateral input L 
and external input I. Assuming a piecewise linear gain function for each popu- 
lation, similar as those for the xi's, the phase-space I-L is partitioned in some 
regions. Only if both I and L are small, wL is positive; justifying the choice 
w = xsn - tanh (0.55- (x - xa)/xb) which we used for our simulations. 
The weights t mex 
-ij are given by 
wi *x = -a,x.lri-rj12+b,x for Iri-rjl_<r,x 
wi? ex = ain . I ri - rj 12 -- bin for /'ex < I ri -- rj I --< l'in (1) 
and wi? x = 0 otherwise. In this representation of the local interactions weights 
and scales are independently controllable. In particular if we define 
2 2  Cre I 2 bin = ain(rin -- rex 
__ __ )2 
aex 4 ' ain bex - aex?'ex 
71'l'ex 7r(l'in q- 'ex)(l'in -- /-ex) 3' ' 
(2) 
r,x and tin denote the range of the excitatory and inhibitory part of the mexican 
hat, respectively. Here we used rex - 2.5 and tin = 4.0. Cre! controls the balances of 
inhibition and excitation. With constant activation level x i -- XO Vi the inhibition 
is cr,t times higher than the excitation and I,,x = e,,ex  (1 - cr,t) 'x0. 
Modeling Orientation Contrast Sensitivity 93 
h e 
ILGN 
Figure 2: Local cortical circuit (left), consisting of an inhibitory and an excitatory 
population of neurons interconnected with weights wie, Wei, and stimulated with 
lateral input L and external input I. By substituting this circuit with one single 
excitatory unit, we need a differential instead of a fixed lateral coupling strength 
(w, right), which is positive only for small I and L. 
The weights  at 
wij are 
-- exp 
2grlat,q, 2 2grlat, r 2 
if lri - rj I > tin (3) 
and 0 otherwise. rrtat,O and rrtat,r provide the orientation selectivity and the range 
of the long-range lateral interaction, respectively. The additional parameter ctat 
_ tat such that y-,v=  tat 
normalizes wij 1 wij  1. 
The spatial width and the orientation selectivity of the input fields are modeled by 
a convolution with a Gaussian kernel before projected onto the cortical layer 
0,i -- 27rrrecp,r2 y exp 
j----1 
2rYrecp,r 2 ' exp - 
2(recp, 2 ' 
In our simulations, the orientation preference of a cortical neuron i was given by 
the orientation preference map displayed in Figla. 
3 Results 
We analyzed stationary states of our model depending on stimulus conditions. The 
external input, a center stimulus of radius rc = 6 at orientation c and an annulus 
1The following parameters have been used in our simulations leading to the results 
shown in Figs. l-4. rli = 0.1 (external input noise), e,e = 2.2, ela = 1.5, ee = 1.3, 
Ash = 0.0, Aa = 0.2, Ab = 0.05, t, = 0.6, s, = 0.5, c,t = 2.0 (balance between inhibition 
lt such that EjN__i wli t  1, 171at,c b -'- 20, 171at,r -- 15 
and excitation), ctt normalizes wij - 
rr,p, = 5, rr,p, = 40, r, = 2.5, and ri = 5.0. 
94 K. R. Pawelzik, U. Ernst, F. Wolf and T. Geisel 
a) b) C) 
Figure 3: Changes in patterns of activity induced by the additional presentation of 
a surround stimulus. Grey levels encode increase (darker grey) or decrease (lighter 
grey) in activation x. a) center and surround parallel, b) and c) center and surround 
orthogonal. While in b), the center is stimulated with the preferred orientation, in 
c), the center is stimulated with the non-preferred orientation. 
of inner radius rc and outer radius r8 = 18 at orientation s, was projected onto 
a grid of N = 40 x 40 elements (Fig. la). Simulations were performed for 20 ori- 
entations equally spaced in the interval [0, 180]. When an oriented stimulus was 
presented to the center we found blob-like activity patterns centered on the cor- 
responding iso-orientation domains (Fig. lb). Simulations utilizing the full set of 
orientations recovered the input-specificity and demonstrated the self-consistency 
of the parameter set chosen (Fig. lc). While in this case there were still some devi- 
ations, stimulation of the whole field yielded perfect self-consistency (not shown) in 
the sense of virtually identical afferent and response based orientation preferences. 
For combinations of center and surround inputs we observed patch-suppressed re- 
gions. These regions exhibited substantial responses for cross-oriented stimuli which 
often exceeded the response to an optimal center stimulus alone. Figs.3 and 4 sum- 
marize these results. Fig.3 shows responses to center-surround combinations com- 
pared to activity patterns resulting from center stimulation only. Obviously certain 
regions within the model were strongly patch-suppressed (Fig.3, light patches for 
same orientations of center and surround). Interestingly a large fraction of these 
locations exhibited enhanced activation when center and surround stimulus were 
orthogonal. Fig.4 displays tuning curves of patch-suppressed cells for variing the 
orientation of the surround stimulus. Clearly these cells exhibited an enhancement 
of most responses and a substantial selectivity for orientation contrast. Parameter 
variation indicated that qualitatively these results do not depend sensitively of the 
set of parameters chosen. 
4 Summary and Discussion 
Our model implements only elementary assumptions about intracortical interac- 
tions. A local sombrero shaped feedback is well known to induce localized blobs of 
activity with a stereotyped shape [12]. This effect lies at the basis of many models 
of visual cortex, as e.g. for the explanation of contrast independence of orientation 
Modeling Orientation Contrast Sensitivity 95 
0.8 
x 
c 0.6 
o 
.> 
--' 0.4 
 0.2 
-90 +90 
o 
Orientation 
Figure 4: Tuning curves for patch-suppressed cells preferring a horizontal stimulus 
within their cRF. The bold line shows the orientation tuning curve of the response 
to an isolated center stimulus. The dashed and dotted lines show the tuning curve 
when stimulating with a horizontal (dashed) and a vertical (dotted) center stimulus 
while rotating the surround stimulus. The curves have been averaged over 6 units. 
tuning [13, 14]. Long range connections selectively connect columns of similar orien- 
tation preference which is consistent with current anatomical knowledge [3, 4]. The 
differential effect of this set of connections onto the target population was modeled 
by a continuous sign change of their effective action depending on the level of post- 
synaptic input or activation. Orientation maps were used to determine the input 
specificity and we assumed a rather weak selectivity of the afferent connections and 
a restricted contrast which implies that every stimulus provides some input also to 
orthogonally tuned cells. This means that long-range excitatory connections, while 
not effective when only the surround is stimulated, can very well be sufficient for 
driving cells if the stimulus to the center is orthogonal to their preferred orientation 
(Contrast sensitivity). 
In our model we find a large fraction of cells that exhibit sensitivity for center- 
surround stimuli. It turns out that most of the patch-suppressed cells respond 
to orientation contrasts, i.e. they are strongly selective for orientation discontinu- 
ities between center and surround. We also find contrast enhancement, i.e. larger 
responses to the preferred orientation in the center when stimulated with an or- 
thogonal surround than if stimulated only centrally (Fig.4). The latter constitutes 
a genuinely emergent property, since no selective cross-oriented connections are 
present. 
This phenomenon can be understood as a desinhibitory effect. Since no cells having 
long-range connections to the center unit are activated, the additional sub-threshold 
input from outside the classical receptive field can evoke a larger response (Contrast 
enhancement). Contrarily, if center and surround are stimulated with the same ori- 
96 K. R. Pawelzik, U. Ernst, E Wolf and T. Geisel 
entation, all the cells with similar orientation preference become activated such that 
the long-range connections can strongly inhibit the center unit (Patch suppression). 
In other words, while the lack of inhibitory influences from the surround should 
recover the response with an amplitude similar or higher to the local stimulation, 
the orthogonal surround effectively leads to a desinhibition for some of the cells. 
Our results show a surprising agreement with previous findings on non-classical 
receptive field properties which culminated in the paper by Sillito et al. [10]. Our 
simple model clearly demonstrates that the known intracortical interactions might 
lead to surprising effects on receptive fields. While this contribution concentrated 
on analyzing the origin of selectivities for orientation discontinuities we expect that 
the pursued level of abstraction has a large potential for analyzing a wide range 
of non-classical receptive fields. Despite its simplicity we believe that our model 
captures the main features of rate interactions. More detailed models based on 
spiking neurons, however, will exhibit additional dynamical effects like correlations 
and synchrony which will be at the focus of our future research. 
Acknowledgement: We acknowledge inspiring discussions with S. LSwel and J. 
Cowan. This work was supported by the Deutsche Forschungsgemeinschaft. 
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