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. Thus, this study aimed to determine the sensitivity of the QRS complex of the ECG to the anatomical location and regional number of PMJs. The QRS complex was simulated using an image-based human torso and biventricular model, and cardiac electrophysiology was simulated using Cardioid. The PMJs were modeled as discrete current injection stimuli, and the location and number of stimuli were varied within initial activation regions based on published experiments. Results indicate that the QRS complex features were most sensitive to the presence or absence of four "seed" stimuli, and adjusting locations of nearby "regional" stimuli provided finer tuning. Decreasing number of regional stimuli by an order of magnitude resulted in virtually no change in the QRS complex. Thus, a minimal 12-stimuli configuration was identified that resulted in physiological excitation, defined by QRS complex feature metrics and ventricular excitation pattern. Overall, the sensitivity results suggest that parameterizing PMJ location, rather than number, be given significantly higher priority in future studies creating personalized ventricular models from patient-derived ECGs.

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. The asymptotic model is implemented for a prototype 3D cylindrical fiber with a passive membrane in an isotropic extracellular region. The validity of this approach is tested by comparing the numerical solution of the asymptotic model to the analytical solutions. The results show that the asymptotic model predicts steady-state transmembrane potential directly under the electrodes with the root mean square error of 0.539 mV, i.e., 1.04% of the maximum transmembrane potential. Thus, this work has created a computationally efficient algorithm that facilitates studies of the complete spatiotemporal dynamics of nerve fibers in three dimensions.

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 1.43-times larger than for line-source electrodes, which results in lower thresholds for stimulation and electroporation. Therefore, for fibers that are close to the stimulating electrodes, one would benefit from using the formula that accounts for the electrodes' geometry.