Qualitative Modeling of Biological Neural Network: Implementation on Basal Ganglia

Abstract

Biological Neural Networks (BNN’s) are complex systems represented as directed graphs where nodes represent neurons and edges represents interaction (activation or inhibition) between neurons. In order to analyze such system, we opt for hybrid modeling which incorporates the discrete as well as continuous behaviors of BNN. For discrete modeling, we use the well-known René Thomas’ qualitative modeling approach which takes a set of logical parameters to predict the behavior of the Biological Regulatory Networks (BRNs). Basal Ganglia is a biological neural network consisting of Striatum (D1 and D2), Thalamus, Globus Pallidus internal (GPi), Globus Pallidus external (GPe), Sub Thalamic Nucleus (STN), Substantia Nigra and is strongly connected with cortex. In this thesis, we construct a qualitative model of the BNN by using GENOTECH tool in which we observe various behaviors in the form of cycles and stable states. Due to the total abstraction of time in qualitative modeling, we incorporate two types of delays in this model: activation delay (du) and inhibition delay (dl). This results in a hybrid model of Basal Ganglia for which the state of the art, Hybrid model checking tool, HyTech is used to analyze the model. We incorporate the above approach on basal ganglia to characterize its behavior associated with thalamus and hence cortex; a key area in brain involved in actions related to motor neurons. For validation of our work, we identified different pathways and corresponding delay constraints which may lead to the development of tremors which is a disease state. Hytech synthesizes delay constraints characterizing different cyclic and diverging trajectories towards stable states. The stable state shows that the system converges towards tremors. As delays are used as parameters in our model, we conclude that if a set of values of parameters satisfies the constraints that follow a particular path, it will remain in that cycle else will follow another path or a deadlock state.