Multiscale stochastic neuron modeling - with applications in deep brain stimulation (wip)

In recent years deep brain stimulation (DBS) has seen success in curing adverse effects of several illnesses e.g. Parkinson. Current DBS method uses implanted brain which stimulate neurons. The mechanism behinds its success is still being researched, and there is a need for theoretical tools. To this end a comprehensible model will aid in the development of DBS-signals (Cubo, Medvedev, and Åström 2016). Ionic channels, and synaptic channels, are simulated through Gillespie's algorithm implemented in C compiled with Mex. A neuron tree is formulated spatially and the propagation of electric potential in the neuronal membrane is calculated using a Crank Nicholson scheme. The membrane current is sent to COMSOL where the extracellular potential is calculated. We show that the stochastic model of a neuron has lower threshold current for a potential spike compared to the deterministic model, and simulate propagation through chains of neurons showing that the potential field resembles that of measured EEGs.