Research

Keywords:  migraine,  epilepsy,  visual perception,  decision-making,  mean-field,  dynamical systems,  neurogeometry

My research is in the domain of mathematical and computational neuroscience. I work on neuronal models for healthy and pathological brain states in terms of migraine, epilepsy, visual perception and decision-making by using three different, yet related approaches: multiscale dynamical systems/neural field approach, neurogeometric approach and biophysical approach. My research goal is towards a unification of those approaches to provide comprehensive models for different biological phenomena. 

Neurogeometric models for visual perception

Visual cortex is one of the main parts of the human brain which is responsible for first step processing of the visual scenes to which we are exposed in the nature, so that we perform proper visual perception. It detects visual features of the objects in the visual scene, such as orientation, scale, spatial frequency; and provides a selective representation of those features such that we reach to a meaningful perception of those objects from our exposure to the chaotic visual stimulus.  I use differential geometric machinery, in particular sub-Riemannian geometry, to model the columnar architecture and feature selective nature of the visual cortex, as well as its neural connectivity. I apply those models to different visual phenomena, such as cortical feature maps, migraine/epilepsy related hallucinations, and also to image processing.   

Neuronal population models via mean-field and network frameworks

Classical models describe neuronal populations by using two settings: networks and mean-field frameworks. The former refers to a framework in which each neuron is represented as a system of ordinary or stochastic differential systems. Those are high dimensional systems with complex dynamics. The latter refers to a coarse-grained continuum limit of the network. Mean-field framework describes the average behavior of the whole neuronal population as an ordinary or stochastic differential system. Those are low dimensional and simpler in comparison to networks, yet, they approximate closely the dynamics of the corresponding network. I develop and mathematically analysis mean-field, as well as network, neuronal population models by using multiscale dynamical systems and neural field equations to study neuronal activity regimes, excitability threshold patterns, migraine/epilepsy related phenomena and visual illusions.

Biophysical models for decision-making

Decision-making is a cognitive process which results in a choice among several alternatives. I employ biophysically realistic neural population models which are known as Adaptive Exponential (AdEx) mean-field models to study the decision-making paradigms. I apply my models to behavioral data obtained from humans and monkeys. This modeling approach can be applied also to neurophysiological data obtained from monkeys.