Robustness of Action Potentials in Cardiac Myocytes

(1.1) Cm ∂V ∂t = 1 Ra ∂2V ∂x2 − Iion(V, t)− Istim(t), where Ra and Cm are the axial resistance and membrane capacitance, Iion represents the total ionic current, and Istim(t) is an applied stimulus current which instigates an action potential. The source term Iion is usually specified by some Hodgkin-Huxley type ionic model. In our simulations, we use the Luo-Rudy phase I (1991) model, one of the most widely used models for cardiac myocytes. It consists of six ionic currents generated by sodium (Na+), potassium (K+), and calcium (Ca2+) ions, [7], (while the original Hudgkin-Huxley model has only three, [2]): (1.2) Iion(V ) = INa(V ) + ISI(V ) + IK(V ) + IK1(V ) + IKp(V ) + Ib(V ), where INa is a fast sodium current, inducing fast upstroke and slow recovery after inactivation; ISI is a slow inward current; IK is a potassium current; IK1 is a potassium current that includes a negative-slope phase; IKp is a plateau potassium current; and Ib is a timeindependent background current. These currents depend on seven activation and inactivation “gates”, traditional denoted as m ,h , j, d, f , X, Cai, each of which is governed by an ODE of the form