Efficient Computational Modeling of Human Ventricular Activation and Its Electrocardiographic Representation: A Sensitivity Study.

Patient-specific models of the ventricular myocardium, combined with the computational power to run rapid simulations, are approaching the level where they could be used for personalized cardiovascular medicine. A major remaining challenge is determining model parameters from available patient data, especially for models of the Purkinje-myocardial junctions (PMJs): the sites of initial ventricular electrical activation. There are no non-invasive methods for localizing PMJs in patients, and the relationship between the standard clinical ECG and PMJ model parameters is underexplored.

Asymptotic model of electrical stimulation of nerve fibers.

We present a novel theory and computational algorithm for modeling electrical stimulation of nerve fibers in three dimensions. Our approach uses singular perturbation to separate the full 3D boundary value problem into a set of 2D "transverse" problems coupled with a 1D "longitudinal" problem. The resulting asymptotic model contains not one but two activating functions (AF): the longitudinal AF that drives the slow development of the mean transmembrane potential and the transverse AF that drives the rapid polarization of the fiber in the transverse direction.

Activating function of needle electrodes in anisotropic tissue.

We present an analytical solution for the electrical potential and activating function (AF) established by cylindrical needle electrodes in anisotropic tissue. We compare this activating function to (1) AF computed assuming line-source electrodes and (2) AF computed using a finite element program. The results show that when the fiber is two needle diameters away from the electrodes, the maximum of the AF for needle electrodes is 1.