Implementation of a Whole-Brain system based on Chen and Campbell’s model

Abstract

The brain is one of humanity’s greatest mysteries. Despite living all our lives with it and studying it for decades or centuries, we are still far from completely understanding how it works. In response to this, a specific modelling approach emerged to simulate neuronal behaviour: neuronal models. These models are classified into three categories: those rooted in mathematics, those inspired by the biology of the human body, and those derived from observed neuronal behaviour. Mathematically inspired models are driven purely by mathematical principles to replicate the general behaviour of neurons, aiming to do so without much reliance on biological details. Examples include the Hopf model. In contrast, biologically-based models seek to faithfully mimic the structure and function of human neurons, incorporating intricate anatomical and physiological characteristics. The Hodgkin-Huxley and Izhikevich models exemplify this approach. The last type is derived from empirical observations of neuronal behaviour, often presenting simple yet effective models. While these models focus on replicating the behaviour of single groups of neurons, they can be extended to population models incorporating excitatory and inhibitory interactions or even to the Whole Brain level. Montbrio's [1] and Chen and Campbell's [2] works are examples of this, with the former creating a population version of the Firing Rate Equations (FRE) based on the Quadratic Integrate and Fire Neuron, and the latter developing a population version of the Izhikevich [3] model. However, to date and to the best of our knowledge, no Whole Brain version of the Izhikevich Single Neuron model exists. Hence, this project aims to fill this gap by sequentially progressing through the necessary steps. This involves generalising Chen and Campbell's population version to an excitatory-inhibitory type population and further extending it to a whole-brain version.

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