Toward a dynamical theory of visual cortex
via data-driven modeling

From point-to-point representation of visual images, cortex is able to extract, through various stages of processing, information such as edges, shapes, color, movement, and texture - features that enable the brain to make sense of visual scenes. This complex task is accomplished through the interactions of very large numbers of neurons, which are the basic units of our nervous system. My immediate goals in this research are to unravel the dynamical processes responsible for feature extraction. My larger goals are to connect dynamical events on the neuronal level to cortical network functions and ultimately to human perception and behavior.

Currently I am involved in a large-scale modeling project, working in collaboration with Robert Shapley, a neurophysiologist at NYU, PhD student Logan Chariker, and others. Our first target area is the primary visual cortex, or V1. Being the area of cortex closest to sensory input, V1 is a natural place to start. It is also the largest and most complex of all the visual cortical areas. In addition to its primary function of orientation selectivity, much of the processing completed downstream (e.g. velocity computation) is initiated in V1. Also, thanks to its relative accessibility, a large volume of experimental data on V1 has been amassed over the years. This makes V1 an ideal place to test the feasibility of detailed, realistic modeling.

Our methodology for building a model that can faithfully reproduce V1's temporal dynamics is as follows: First we hypothesize, based on known neurobiology, as parsimonious a model as possible that incorporates the features we deem necessary for replicating a wide range of V1 properties. Quantities that cannot be deduced directly from biology are left open as "free parameters". We then try to determine these unknowns from experimental data. From what we have seen so far, the amount of data available seems adequate for fairly tight constraints.

Mathematically, this last step is tantamount to solving a (highly nonlinear) inverse problem: imagine having some rough ideas about a dynamical system without knowing its precise rules of operation, and trying to determine how the system operates based on knowledge of its outputs.

To tackle this "inverse problem", we use a combination of numerical simulations and mathematical analysis. Analysis of dynamical mechanisms is an integral part of this research: It is used to guide parameter tuning, for even with modern computational capabilities, high dimensional parameter sweeps are not practical. More importantly, it is not a blackbox that we are after but a model that can be analyzed and understood.

Indeed, building a realistic model is but the first step in this research. The next step is to query, or interrogate, it, to get answers to questions yet unresolved; hypothesis testing on a model is infinitely less costly than on a real brain. We are working toward a model that can make testable predictions and suggest new experiments, in short, one that can shed light on cortical processes.

1. (with A. Rangan) Emergent dynamics in a model of visual cortex, J Comp. Neurosci., Vol 35, Issue 2, 155-167 (2013).
   
2. (with L. Chariker) Emergent spike patterns in neuronal populations, J Comp. Neur osci. (2015) 38:203-220.
   
3. (with L. Chariker and R. Shapley) Orientation selectivity from very sparse LGN inputs in a comprehensive model of macaque V1 cortex, J Neurosci (2016) in press