Direction selectivity of simple cells in the primary visual cortex: Comparison of two alternative mathematical models. I: Response to drifting gratings

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Abstract

Two models of a single hypercolumn in the primary visual cortex are presented, and used for the analysis of direction selectivity in simple cells. The two models differ as to the arrangement of inhibitory connections: in the first (“antiphase model”) inhibition is in phase opposition with excitation, but with a similar orientation tuning; in the second (“in-phase model”), inhibition is in phase with excitation, but with broader orientation tuning. Simulation results, performed by using drifting gratings with different orientations, and different spatial and temporal frequencies, show that both models are able to explain the origin of direction preference of simple cells.

Introduction

Simple cells in the primary visual cortex respond selectively to input stimuli with particular spatial and temporal characteristics, such as elongated bars with a specific orientation, velocity and direction of motion. While the spatial characteristics of cell response (such as spatial frequency and orientation tuning) have been the subject of many theoretical studies in past years, which provided results in good agreement with experimental data [1], [2], [3], [4], [5], the physiological mechanisms that determine direction selectivity (i.e., the preference for one direction of motion compared with the opposite one) and the other temporal properties of simple cells are still less well understood.

A classical method to characterize a simple cell in V1 is to determine its spatial receptive field (RF), which is traditionally defined as the region of visual space within which a stimulus can affect the cell response. Of course, direction preference cannot be comprehended from knowledge of the spatial RF only, but requires analysis of the temporal nature of its evolution. De Angelis et al. in some influential papers (see, among others [6], [7], [8]), stressed the idea that the RF is a complex spatio-temporal entity, in which the spatial properties evolve and change dramatically with time during presentation of a stimulus. These dynamical aspects of the RF now appear essential for the genesis of direction preference in simple cells.

Experimental studies demonstrated that simple cells in V1 exhibit a variety of RF, which range from completely space–time separable to space–time inseparable [6] (see also Fig. 3 in [8]). Theoretical and psychophysical studies suggest that direction selectivity is related to the existence of an inseparable spatio-temporal RF. Accordingly, a variety of dynamic properties of simple cells (including the preferred direction for motion and the temporal frequency tuning) can be predicted fairly well from knowledge of the spatio-temporal RF profile, using linear methods (such as, analysis in the Fourier domain) [6], [7], [8], [9]. Although analysis of the spatio-temporal RF has revealed an essential instrument for the comprehension of motion selectivity, some important problems are still a matter of debate and deserve theoretical investigation.

First, what is the neural circuitry responsible for the emergency of inseparable spatio-temporal RFs? Experimental data demonstrate that the RF of cells in the lateral geniculate nucleus (LGN) that are afferents to simple cells have a center-surround organization. They are approximately space–time separable, apart from some moderate deviation from separability [8], [10]. Hence, inseparability must originate in the path from the LGN to V1 or within the striate cortex.

A frequent hypothesis is that space–time inseparability arises from temporal diversity in the LGN. Geniculate cells can have sustained, transient, lagged and non-lagged timing [11], [12], [13].

Saul and Humphrey observed that convergence of thalamic cells with lagged and non-lagged temporal properties can generate space–time inseparable RF, and that the timing differences among these thalamic inputs may be the basis of direction selectivity [13], [14]. The same mechanism can explain the reversal of direction selectivity, which is occasionally observed in the response of simple and complex cells at high temporal frequencies [14]. Recent mathematical models demonstrate that orientation and direction selectivity can actually emerge from the convergence of lagged and non-lagged ON and OFF inputs from thalamic to simple cells, via a classic Hebbian learning process in an anisotropic environment [15], [16] or via different learning rules (such as the BCM rule) in a more natural environment [17].

The previous studies emphasized the thalamic input to explain direction selectivity. However, much experimental data demonstrate that the response of simple cells is strongly determined by intracortical circuitry too. The massive interconnections in the primary visual cortex overwhelm the geniculate input: experimental data obtained by eliminating the effect of intracortical synapses suggest that thalamic input is on the order of 30–40% of the overall input to simple cells [18] or even on the order of 10% [19].

The importance of intracortical circuitry is further stressed by the analysis of experimental data on orientation tuning and direction selectivity. The orientation tuning curve of simple cells is usually sharper than that predicted on the basis of the thalamic input alone and, above all, exhibits contrast invariance [20]. These aspects can be explained quite well by intracortical processing mechanisms (both inhibitory and excitatory), which sharpen the thalamic orientation curve and avoid occurrence of the “iceberg effect” (i.e., a loss of orientation tuning) at high levels of contrast. Nevertheless, different opinions can be found in the current literature as to the exact arrangement of this intracortical circuitry, especially as to intracortical inhibition [1], [2], [5], [20]. In a recent paper, using simple firing rate neurons, we demonstrated that two alternative models, which exploit either feedforward inhibition arranged in antiphase with feedback excitation, or feedforward inhibition in phase with feedback excitation but with broader orientation tuning, are able to explain the same experimental data on orientation selectivity, provided suitable parameter values are chosen for intracortical synapses [5].

Similarly, experimental results of several groups [7], [21] show that the direction index [defined as: (response to the preferred direction -response to the non-preferred direction)/response to the preferred direction] measured for simple cells is about two times or three times larger than that estimated from the RF via a linear prediction. De Angelis et al. [7] proposed that incorporation of non-linear terms, such as those that characterize the contrast–response function, may help to explain these discrepancies. However, it seems reasonable to consider that intracortical circuits, which play an important role in setting the orientation tuning curve, can also play a major role in direction selectivity enhancement. Reid et al. [21] observed the existence of a significant amount of non-linear suppression in the non-preferred direction, which might be ascribed to intracortical inhibition.

Considering the massive role of intracortical synapses, some models assume that inseparable RFs are generated by delays within cortical loops. These cause inhibition in the null direction and excitation in the preferred direction, resulting in direction selectivity [22], [23]. However, these models neglect any difference between lagged and non-lagged thalamic input.

The data described above suggest a different model. As proposed by Saul and Humphrey [13] geniculate input, coming from lagged and non-lagged cells, can set up a spatio-temporally inseparable RF, corresponding to an initial bias for one preferred direction. This initial preference is then sharpened by intracortical circuitry, in a way similar to that occurring for the orientation tuning. Nevertheless, we are not aware of any theoretical study that integrates both the role of geniculate (lagged and non-lagged) input and of intracortical circuits into a single comprehensive model of motion response. Previous models, in fact, stress the role of geniculate delays only [15], [17], or focus only on intracortical delays [22], [23].

Accordingly, in the present paper we investigate the role of thalamic input and intracortical circuitry in determining motion selectivity and direction preference with the aid of original simple mathematical models. To this end, two models developed previously (antiphase model and in-phase model, see [5], which considered only orientation selectivity, not direction selectivity) are extended and enhanced in order to include temporal properties (such as a distinction of lagged and non-lagged inputs and band-pass frequency tuning). The models are then used to simulate the response of the thalamic and cortical cells to drifting gratings with different spatial and temporal frequencies and directions of motion.

The basic hypothesis that we are going to test is that convergence of thalamic inputs, with different delays, can produce RFs with various degrees of space–time separability but moderate direction selectivity. This initial moderate bias for one direction is then enhanced and sharpened by intracortical circuitry that, depending on synaptic strength, may lead to various levels of direction preference. A property of our models is that cortical circuitry does not incorporate any delay, but just improves direction tuning of an initial biased input from LGN. This clearly distinguishes our circuital model from those by Suarez and Maex [22], [23].

In a subsequent paper [24], the model will be used to study the response to moving bars with various lengths, widths and velocities, in order to explore whether the models can explain contradictory findings (such as the effect of a reduction in bar length on the preferred direction, and the existence of axial responses to small moving dots).

Section snippets

Method

Two different mathematical models have been used in this work. Each model includes the thalamic input to a simple cell, feedforward inhibition coming from cortical inhibitory interneurons, and intracortical excitation. The two models differ as to the disposition of feedforward inhibition.

In the models the output of the neurons is represented as a continuous quantity describing the firing rate. Both models consider the architecture of a single hypercolumn, composed of 360 excitatory neurons and

Results

First, we performed some simulations to analyze the behavior of the thalamic input to simple cells (i.e., quantity ΔVct in Eq. (13)). These simulations are aimed at studying the role of the RF organization in the genesis of direction selectivity, by excluding the contribution of the intracortical circuitry.

The fundamental aspect of the model that we wish to demonstrate is that direction selectivity, in response to a drifting grating, originates from the superimposition of the activities in the

Discussion

In the present study we developed a simple model of motion detection, based on firing rate neurons arranged within a hypercolumn. The model incorporates two fundamental aspects, which deserve a critical analysis: the formation of thalamic input (Eqs. (13)–(15)) based on the convergence of cells with different time delays, and the intracortical disposition of synapses.

The first crucial aspect of the model is that the origin of direction preference lies in the convergence of activities from

Summary

The models embody a feedforward mechanism, based on the convergence of lagged and non-lagged responses from cells in the lateral geniculate nucleus (LGN), and an intracortical circuit. A basic assumption is that the time lag of the thalamic cells increases regularly in moving from one region to the next of the cortical receptive field. This results in an inseparable spatio-temporal RF for the cortical cell, and in moderate direction preference. This initial preference for one direction is then

Mauro Ursino was Associate Researcher from February 1992 to October 1998, and Associate Professor from November 1998 to October 2001. From November 2001 he is a Full Professor in Biomedical Engineering at the University of Bologna where he is teaching the courses “Biomedical Data and Signal Processing” and “Natural and Artificial Intelligent Systems”. In March 1990, he received the “Marotta Award” from the Italian Academy of Science.

His research activity is focused on the application of

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  • Cited by (3)

    Mauro Ursino was Associate Researcher from February 1992 to October 1998, and Associate Professor from November 1998 to October 2001. From November 2001 he is a Full Professor in Biomedical Engineering at the University of Bologna where he is teaching the courses “Biomedical Data and Signal Processing” and “Natural and Artificial Intelligent Systems”. In March 1990, he received the “Marotta Award” from the Italian Academy of Science.

    His research activity is focused on the application of Automatic Control Theory for the study of the cardiovascular system and its regulation. He performed several research studies on the mechanisms controlling local blood flow to tissue, on the intracranial pressure dynamics, on the baroreflex control, on self-sustained oscillations in microvessels (vasomotion) on the integration between the cardiovascular and respiratory control mechanisms, and on cardiovascular dynamics during hemodialysis. Recently, he started working on simulation of brain functions by neural networks. His scientific work presently includes more than 230 publications (among them, 97 papers accepted or in press on international journals and 17 on international books).

    Giuseppe-Emiliano La Cara was a Ph.D. student from October 2001 to October 2004, and a research assistant at the Department of Electronics, Computer Science and Systems, University of Bologna, from November 2004 to December of 2005. He performed original researches on brain functions and neural networks, with special emphasis on the primary visual cortex. Presently, is working as an electronic and software engineer in an Industry in Bologna (Italy), in the field of High Speed railway transportations.

    Matteo Ritrovato was a senior student at the Department of Electronics, Computer Science and Systems, University of Bologna (Italy), from July 2002 to March 2003, and scientific collaborator until November 2003. He was focused on BioImaging and Image Processing while working at Research Hospital “Istituti Ortopedici Rizzoli” (Bologna, Italy) and presently his research activities, performed at Research Hospital “Ospedale Pediatrico Bambino Gesù” (Rome, Italy), deal with functional NeuroImaging.

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