Modeling excitable cells using hybrid automata

Hybrid automata are an increasingly popular modeling formalism for systems that exhibit both continuous and discrete behavior. Intuitively, a hybrid automaton is an extended finite-state automaton, the states of which encode the various phases of continuous dynamics a system may undergo, and the transitions of which are used to express the switching logic between these dynamics. Excitable cells are a good example of biologically inspired hybrid systems: trans-membrane ion fluxes and voltages may vary continuously but the transition from the resting state to the excited state is generally considered an all-or-nothing discrete response. In this work, we first show that two existing models of excitable cells fall into the hybrid automata framework. We then design a specific kind of hybrid automata: Cycle-Linear Hybrid Automata (CLHA), to model multiple physiological properties of excitable cells including action potential, restitution and hyper-polarization. Spatial simulation demonstrates that our model is 8 times faster than the traditional models. We present how machine learning techniques are applied to automatically learn the parameters of CLHA from existing data and how reachability analysis is used to verify critical conditions for the excitement of neurons. A formal analysis of abnormal excitation (early afterdepolarization) in cardiac tissue is also included. At last, a rational CLHA with more physiological details is presented.