Accuracy and speed considerations of a new numerical method for modeling cardiac excitation

A fast algorithm called the modified backward Euler (mBE) method, an explicit, variable timestep method, has been developed. Despite its explicit nature, the algorithm is unconditionally stable, allowing the use of timesteps several orders of magnitude larger than the timestep limit imposed by forward Euler methods. A guard cell algorithm also allows the use of timesteps larger than those imposed by the Courant Friedrich Levy (CFL) stability condition. The algorithm was applied to a two-dimensional tissue using the advanced Luo-Rudy ventricular cell model. Characteristic properties of action potential (AP) propagation including velocity, AP amplitude and duration, maximum membrane voltage and V˙_max were computed versus computational speed and compared to those obtained from a forward Euler fixed timestep (FEFT) method. Overall, for a given accuracy in velocity of 1% to 3%, the computational speed was increased by a factor of 30 to 40 over the FEFT, while the other errors were kept below 1%.