Electrical Modeling of Excitable Cells

Abstract

The human brain is the most wonderful and mysterious organ of human body. This masterpiece creation of nature manages the actions in such a way that they happens in real time at right place. It also stores information so that the behavior can be modi ed according to the past experience. A single cubic centimeter of human brain contain several million nerve cells, each of which may communicate with thousands of other cells in information processing networks that make the most elaborate computer look primitive. These cells can be excited by stimulation, therefore are known as excitable cells. The excitable cells found in brain are called neurons. Neuron is the basic structural and functional unit of human brain which is specialized for the conduction of nerve impulses. Upon receiving a threshold stimulus, the membrane of neuron quickly depolarizes at the point of stimulation, and this electrical impulse propagates along the axon of neuron in the form of action potential. Hodgkin and Huxley model explains in detail the formation and propagation of action potential through nerve cell. This model contains the set of non-linear di erential equations that can be solved by numerical method techniques only. Computationally the model is very complex and almost takes 1200 ops for simulating a single neuron. Another category of excitable cells are found in heart, called cardiac myocytes. The formation of action potential of cardiac myocytes can be explained by Luo-Rudy model which is the extension of Hodgkin and Huxley model. Computationally Luo-Rudy model is almost ten times more complex than Hodgkin and Huxley model. Therefore, there is a need of simpler model for excitable cells that can implement the behavior of excitable cells down to ionic channel level. In our study we used a new concept of acti ers for the rst time to model excitable cells. Acti ers are the electrical circuits that can amplify and rectify at the same time. The model is conductance based and captures the ionic channel level characteristics of excitable cells. Computationally, the acti er model takes 12 ops for simulating neuron and 15 ops for simulating cardiac myocyte, almost a decrease of 100 times in computational cost of Hodgkin and Huxley model. We reported some common behaviors of neurons and cardiac myocytes. The results are in good agreement with the experimental data.