Vignesh Muralidharan

A computational model of altered gait patterns in parkinson's disease patients negotiating narrow doorways

We present a computational model of altered gait velocity patterns in Parkinsons 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.

A Model of Multisensory Integration and Its Influence on Hippocampal Spatial Cell Responses

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.

A Neurocomputational Model of the Effect of Cognitive Load on Freezing of Gait in Parkinson's Disease

Experimental data show that perceptual cues can either exacerbate or ameliorate freezing of gait (FOG) in Parkinsons 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 Parkinsons Disease.

A unified hierarchical oscillatory network model of head direction cells, spatially periodic cells, and place cells

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.

A Biologically Plausible Architecture of the Striatum to Solve Context-Dependent Reinforcement Learning Tasks

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 striatum model 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.

A Cortico-Basal Ganglia Model to Understand the Neural Dynamics of Targeted Reaching in Normal and Parkinson’s Conditions

We present a cortico-basal ganglia model to study the neural mechanisms behind reaching movements in normal and in Parkinson’s disease conditions. The model consists of the following components: a two-joint arm model (AM), a layer of motor neurons in the spinal cord (MN), the proprioceptive cortex (PC), the motor cortex (MC), the prefrontal cortex (PFC), and the basal ganglia (BG). The model thus has an outer sensory-motor cortical loop and an inner cortico-basal ganglia loop to drive learning of reaching behavior. Sensory and motor maps are formed by the PC and MC which represent the space of arm configurations. The BG sends control signals to the MC following a stochastic gradient ascent policy applied to the value function defined over the arm configuration space. The trainable connections from PFC to MC can directly activate the motor cortex, thereby producing rapid movement avoiding the slow search conducted by the BG. The model captures the two main stages of motor learning, i.e., slow movements dominated by the BG during early stages and cortically driven fast movements with smoother trajectories at later stages. The model explains PD performance in stationary and pursuit reaching tasks. The model also shows that PD symptoms like tremor and rigidity could be attributed to synchronized oscillations in STN–GPe. The model is in line with closed-loop control and with neural representations for all the nuclei which explains Parkinsonian reaching. By virtue of its ability to capture the role of cortico-basal ganglia systems in controlling a wide range of features of reaching, the proposed model can potentially serve as a benchmark to test various motor pathologies of the BG.

A Basal Ganglia Model of Freezing of Gait in Parkinson’s Disease

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.

A computational model that explores the effect of environmental geometries on grid cell representations

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 was originally considered to be invariant to 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 grid cell periodicity from a computational point of view using a model that was successful in generating a wide range of spatial cells, including grid cells, place cells, head direction cells and border cells. We simulated the model in four types of environmental geometries such as: 1) connected environments, 2) convex shapes, 3) concave shapes and 4) regular polygons with varying number of sides. Simulation results point to a greater function for grid cells than what was believed hitherto. Grid cells in the model code not just for local position but also for more global information like the shape of the environment. The proposed model is interesting not only because it was able to capture the aforementioned experimental results but, more importantly, it was able to make many important predictions on the effect of the environmental geometry on the grid cell periodicity.

AN OSCILLATORY NETWORK MODEL OF HEAD DIRECTION, SPATIALLY PERIODIC CELLS AND PLACE CELLS USING LOCOMOTOR INPUTS

We propose a computational modeling approach that explains the formation of a range of spatial cells like head direction cells, grid cells, border cells and place cells which are believed to play a pivotal role in the spatial navigation of an animal. Most existing models insert special symmetry conditions in the models in order to obtain such symmetries in the outcome; our models do not require such symmetry assumptions. Our modeling approach is embodied in two models: a simple one (Model #1) and a more detailed version (Model #2). In Model #1, velocity input is presented to a layer of Head Direction cells, with no special topology requirements, the outputs of which are presented to a layer of Path Integration neurons. A variety of spatially periodic responses resembling grid cells, are obtained using the Principal Components of Path Integration layer. In Model #2, the input consists of the locomotor rhythms from the four legs of a virtual animal. These rhythms are integrated into the phases of a layer of oscillatory neurons, whose outputs drive a layer of Head Direction cells. The Head Direction cells in turn drive a layer of Path Integration neurons, which in turn project to two successive layers of Lateral Anti Hebbian Networks (LAHN). Cells in the first LAHN resemble grid cells (with both hexagonal and square gridness), and border cells. Cells in the second LAHN exhibit place cell behaviour and a new cell type known as corner cell. Both grid cells and place cells exhibit phase precession in 1D and 2D spaces. The models outline the neural hierarchy necessary to obtain the complete range of spatial cell responses found in the hippocampal system.