Simulating the Magnetization Spin-flip of Catecholamine-type Neurotransmitters via the Ising Model

Student Classification


Faculty Mentor

Dr. Ronald Gamble



Document Type


Publication Date

Fall 2019


The Ising Model is a mathematical model that represents a lattice of atoms, each having a dipole moment or spin. The model is used to predict the second order phase transition of spins in ferromagnetic or antiferromagnetic materials, as dictated by properties such as spin-spin interaction and applied magnetic field. The hypothesis of this experiment is to apply the Ising Model to pacemaker cells of the Sinoatrial Node (SAN). This node contains distinctive ion channels that initiate and propagate the action potentials responsible for the rhythmic impulses of the heart. The modified Ising Model will target Calcium-43 nuclei because they are the dominant ions for voltage dependent calcium channels which directly affect the electric rhythm of the heart. A Hamiltonian total energy function was derived from the computational Ising Model of simulated ferromagnetism. According to this modified model, the spin of the Calcium-43 nuclei are proposed to be flipped stochastically under an associated time-constant. The influx of these spin-flipped Calcium-43 nuclei should impede ionic transport with respect to catecholamine neurotransmitters such as dopamine, which directly affects heart rate. This reduction in neurotransmission activity is theorized to cause a decrease in the excitation of cardiac action potential generated from the L-type calcium channel. The modified Ising Model is being written in a combination of FORTRAN source code and MATLAB scripting language. If the modified Ising Model is proven correct, then introducing spin-flipped Calcium-43 nuclei to L-type calcium channels in the SAN could be used as an alternative to antiarrythmic agents.

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