Method for quantifiying conduction velocity during ventricular fibrillation

Velocity of propagation of electrical excitation in the heart is important for the understanding of complex arrhythmias such as ventricular fibrillation (VF). In this paper, we present a method to estimate the conduction velocity of electrical activation wavefronts that are defined to be a particular isovalue of any scalar field, such as electrical activation times, electrical phase, or indeed any other quantity that can be used to determine excitation wavefronts. This general method is based on tracking trajectories of material points that are assumed to be embedded within the wavefronts, whilst the direction of propagation is assumed to be perpendicular to the wavefront. We have derived an explicit expression for the conduction velocity in terms of the spatiotemporal gradients of the scalar field used to define wavefronts. Moreover, although it is often difficult to use activation times to compute conduction velocities during complex VF, we show that other scalar fields such as detrended voltage or electrical phase, which can faithfully represent the electrical activity during fibrillatory conduction, can be used to determine conduction velocities. We demonstrate the application of our method to determine conduction velocities from contact mapping recordings over the entire epicardial surface of the fibrillating pig heart.