V Srinivasa Chakravarthy

Grid cells are a special class of spatial cells found in the medial entorhinal cortex (MEC) characterized by their strikingly regular hexagonal firing fields. This spatially periodic firing pattern is originally considered to be independent of the geometric properties of the environment. However, this notion was contested by examining the grid cell periodicity in environments with different polarity (Krupic et al., 2015) and in connected environments (Carpenter et al., 2015). Aforementioned experimental results demonstrated the dependence of grid cell activity on environmental geometry. Analysis of grid cell periodicity on practically infinite variations of environmental geometry imposes a limitation on the experimental study. Hence we analyze the dependence of grid cell periodicity on the environmental geometry purely from a computational point of view. We use a hierarchical oscillatory network model where velocity inputs are presented to a layer of Head Direction cells, outputs of which are projected to a Path Integration layer. The Lateral Anti-Hebbian Network (LAHN) is used to perform feature extraction from the Path Integration neurons thereby producing a spectrum of spatial cell responses. We simulated the model in five types of environmental geometries such as: (1) connected environments, (2) convex shapes, (3) concave shapes, (4) regular polygons with varying number of sides, and (5) transforming environment. Simulation results point to a greater function for grid cells than what was believed hitherto. Grid cells in the model encode not just the local position but also more global information like the shape of the environment. Furthermore, the model is able to capture the invariant attributes of the physical space ingrained in its LAHN layer, thereby revealing its ability to classify an environment using this information. The proposed model is interesting not only because it is able to capture the experimental results but, more importantly, it is able to make many important predictions on the effect of the environmental geometry on the grid cell periodicity and suggesting the possibility of grid cells encoding the invariant properties of an environment.

Spatial cells in the hippocampal complex play a pivotal role in the navigation of an animal. Exact neural principles behind these spatial cell responses have not been completely unraveled yet. Here we present two models for spatial cells, namely the Velocity Driven Oscillatory Network (VDON) and Locomotor Driven Oscillatory Network. Both models have basically three stages in common such as direction encoding stage, path integration (PI) stage, and a stage of unsupervised learning of PI values. In the first model, the following three stages are implemented: head direction layer, frequency modulation by a layer of oscillatory neurons, and an unsupervised stage that extracts the principal components from the oscillator outputs. In the second model, a refined version of the first model, the stages are extraction of velocity representation from the locomotor input, frequency modulation by a layer of oscillators, and two cascaded unsupervised stages consisting of the lateral anti-hebbian network. The principal component stage of VDON exhibits grid cell-like spatially periodic responses including hexagonal firing fields. Locomotor Driven Oscillatory Network shows the emergence of spatially periodic grid cells and periodically active border-like cells in its lower layer; place cell responses are found in its higher layer. This model shows the inheritance of phase precession from grid cell to place cell in both one- and two-dimensional spaces. It also shows a novel result on the influence of locomotion rhythms on the grid cell activity. The study thus presents a comprehensive, unifying hierarchical model for hippocampal spatial cells.

Oscillatory phenomena are ubiquitous in the brain. Although there are oscillator-based models of brain dynamics, their universal computational properties have not been explored much unlike in the case of rate-coded and spiking neuron network models. Use of oscillator-based models is often limited to special phenomena like locomotor rhythms and oscillatory attractor-based memories. If neuronal ensembles are taken to be the basic functional units of brain dynamics, it is desirable to develop oscillator-based models that can explain a wide variety of neural phenomena. Autoencoders are a special type of feed forward networks that have been used for construction of large-scale deep networks. Although autoencoders based on rate-coded and spiking neuron networks have been proposed, there are no autoencoders based on oscillators. We propose here an oscillatory neural network model that performs the function of an autoencoder. The model is a hybrid of rate-coded neurons and neural oscillators. Input signals modulate the frequency of the neural encoder oscillators. These signals are then multiplexed using a network of rate-code neurons that has afferent Hebbian and lateral anti-Hebbian connectivity, termed as Lateral Anti Hebbian Network (LAHN). Finally the LAHN output is de-multiplexed using an output neural layer which is a combination of adaptive Hopf and Kuramoto oscillators for the signal reconstruction. The Kuramoto-Hopf combination performing demodulation is a novel way of describing a neural phase-locked loop. The proposed model is tested using both synthetic signals and real world EEG signals. The proposed model arises out of the general motivation to construct biologically inspired, oscillatory versions of some of the standard neural network models, and presents itself as an autoencoder network based on oscillatory neurons applicable to time series signals. As a demonstration, the model is applied to compression of EEG signals.

Basal ganglia circuit is an important subcortical system of the brain thought to be responsible for reward-based learning. Striatum, the largest nucleus of the basal ganglia, serves as an input port that maps cortical information. Microanatomical studies show that the striatum is a mosaic of specialized input-output structures called striosomes and regions of the surrounding matrix called the matrisomes. We have developed a computational model of the striatum using layered self-organizing maps to capture the center-surround structure seen experimentally and explain its functional significance. We believe that these structural components could build representations of state and action spaces in different environments. The striatummodel is then integrated with other components of basal ganglia, making it capable of solving reinforcement learning tasks. We have proposed a biologically plausible mechanism of action-based learning where the striosome biases the matrisome activity toward a preferred action. Several studies indicate that the striatum is critical in solving context dependent problems. We build on this hypothesis and the proposed model exploits the modularity of the striatum to efficiently solve such tasks.

Head direction (HD) cells, grid cells, and place cells, often dubbed spatial cells, are neural correlates of spatial navigation. We propose a computational model to study the influence of multisensory modalities, especially vision, and proprioception on responses of these cells. A virtual animal was made to navigate within a square box along a synthetic trajectory. Visual information was obtained via a cue card placed at a specific location in the environment, while proprioceptive information was derived from curvature-modulated limb oscillations associated with the gait of the virtual animal. A self-organizing layer was used to encode HD information from both sensory streams. The sensory integration (SI) of HD from both modalities was performed using a continuous attractor network with local connectivity, followed by oscillatory path integration and lateral anti-Hebbian network, where spatial cell responses were observed. The model captured experimental findings which investigated the role of visual manipulation (cue card removal and cue card rotation) on these spatial cells. The model showed a more stable formation of spatial representations via the visual pathway compared to the proprioceptive pathway, emphasizing the role of visual input as an anchor for HD, grid, and place responses. The model suggests the need for SI at the HD level for formation of such stable representations of space essential for effective navigation.

To facilitate the selection of an optimal therapy for a stroke patient with upper extremity hemiparesis, we propose a cortico-basal ganglia model capable of performing reaching tasks under normal and stroke conditions. The model contains two hemispherical systems, each organized into an outer sensory-motor cortical loop and an inner basal ganglia (BG) loop, controlling their respective hands. The model is trained to simulate two therapeutic approaches: the constraint induced movement therapy (CIMT) in which the intact is arrested, and Bimanual Reaching in which the movements of the intact arm are found to aid the affected arm. Which of these apparently mutually conflicting approaches is right for a given patient? Based on our study on the effect of lesion size on arm performance, we hypothesize that the choice of the therapy depends on the lesion size. Whereas bimanual reaching is more suitable for smaller lesion size, CIMT is preferred in case of larger lesion sizes. By virtue of the model’s ability to capture the experimental results effectively, we believe that it can serve as a benchmark for the development and testing of various rehabilitation strategies for stroke.

Experimental data show that perceptual cues can either exacerbate or ameliorate freezing of gait (FOG) in Parkinson’s Disease (PD). For example, simple visual stimuli like stripes on the floor can alleviate freezing whereas complex stimuli like narrow doorways can trigger it. We present a computational model of the cognitive and motor cortico-basal ganglia loops that explains the effects of sensory and cognitive processes on FOG. The model simulates strong causative factors of FOG including decision conflict (a disagreement of various sensory stimuli in their association with a response) and cognitive load (complexity of coupling a stimulus with downstream mechanisms that control gait execution). Specifically, the model simulates gait of PD patients (freezers and non-freezers) as they navigate a series of doorways while simultaneously responding to several Stroop word cues in a virtual reality setup. The model is based on an actor-critic architecture of Reinforcement Learning involving Utility-based decision making, where Utility is a weighted sum of Value and Risk functions. The model accounts for the following experimental data: (a) the increased foot-step latency seen in relation to high conflict cues, (b) the high number of motor arrests seen in PD freezers when faced with a complex cue compared to the simple cue, and (c) the effect of dopamine medication on these motor arrests. The freezing behavior arises as a result of addition of task parameters (doorways and cues) and not due to inherent differences in the subject group. The model predicts a differential role of risk sensitivity in PD freezers and non-freezers in the cognitive and motor loops. Additionally this first-of-its-kind model provides a plausible framework for understanding the influence of cognition on automatic motor actions in controls and Parkinson’s Disease.

We present a computational model of altered gait velocity patterns in Parkinson's Disease (PD) patients. PD gait is characterized by short shuffling steps, reduced walking speed, increased double support time and sometimes increased cadence. The most debilitating symptom of PD gait is the context dependent cessation in gait known as freezing of gait (FOG). Cowie et al. (2010) and Almeida and Lebold (2010) investigated FOG as the changes in velocity profiles of PD gait, as patients walked through a doorway with variable width. The former reported a sharp dip in velocity, a short distance from the doorway that was greater for narrower doorways. They compared the gait performance in PD freezers at ON and OFF dopaminergic medication. In keeping with this finding, the latter also reported the same for ON medicated PD freezers and non-freezers. In the current study, we sought to simulate these gait changes using a computational model of Basal Ganglia based on Reinforcement Learning, coupled with a spinal rhythm mimicking central pattern generator (CPG) model. In the model, a simulated agent was trained to learn a value profile over a corridor leading to the doorway by repeatedly attempting to pass through the doorway. Temporal difference error in value, associated with dopamine signal, was appropriately constrained in order to reflect the dopamine-deficient conditions of PD. Simulated gait under PD conditions exhibited a sharp dip in velocity close to the doorway, with PD OFF freezers showing the largest decrease in velocity compared to PD ON freezers and controls. PD ON and PD OFF freezers both showed sensitivity to the doorway width, with narrow door producing the least velocity/ stride length. Step length variations were also captured with PD freezers producing smaller steps and larger step-variability than PD non-freezers and controls. In addition this model is the first to explain the non-dopamine dependence for FOG giving rise to several other possibilities for its etiology. © 2014 Muralidharan, Balasubramani, Chakravarthy, Lewisand Moustafa.

Freezing of gait (FOG) is a mysterious clinical phenomenon seen in Parkinson’s disease (PD) patients, a neurodegenerative disorder of the basal ganglia (BG), where there is cessation of locomotion under specific contexts. These contexts could include motor initiation, i.e., when starting movement, passing through narrow passages and corridors, while making a turn and as they are about to reach a destination. We have developed computational models of the BG which explains the freezing behavior seen in PD. The model uses reinforcement learning framework, incorporating Actor–Critic architecture, to aid learning of a virtual subject to navigate through these specific contexts. The model captures the velocity changes (slowing down) seen in PD freezers upon encountering a doorway, turns, and under the influence of cognitive load compared to PD non-freezers and healthy controls. The model throws interesting predictions about the pathology of freezing suggesting that dopamine, a key neurochemical deficient in PD, might not be the only reason for the occurrences of such freeze episodes. Other neuromodulators which are involved in action exploration and risk sensitivity influence these motor arrests. Finally, we have incorporated a network model of the BG to understand the network level parameters which influence contextual motor freezing.