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Cardiac electrical activity can be mapped today through the response of voltage-sensitive dyes; but poor transparency of muscle tissue has enforced shallow-depth imaging. We present a three-dimensional (3D) reconstruction method for electrical activity deep inside the myocardial wall. Our approach is nonlinear and differs substantially from standard diffusive optical tomography. It does not require matrix inversion, data regularization or a priori information concerning the original object. Opposite sides of a slab-shaped preparation are scanned in parallel by detection and illumination points with a constant vector offset between illumination and detection axes (biaxial scanning). Scanning is performed in two perpendicular directions. In each direction, a pair of 2D images is obtained under offsets of opposite signs. These two pairs are the input for a multiplicative reconstruction algorithm, whose output is a 3D image. The overall procedure was successfully tested on computer-generated sources that include points, lines and hemispheres, patterned after actual electrophysiological excitations. The algorithm is computationally efficient and stable with respect to varying noise levels in the raw data.

Recirculation of excitation, or re-entry, is one of the most important mechanisms of life-threatening cardiac arrhythmias and fibrillation. Modelling these phenomena requires large scale computations in two and three-dimensional slabs of cardiac tissue. Because of computational constraints, most of the studies use simplified (non-ionic) models of cardiac tissue, which are electrophysiologically less accurate than the detailed ionic models. In this paper, we propose a method to modify ionic models of cardiac tissue into an intermediate class of models, which are almost as efficient for computations as simplified models, and retain most of the properties of the original ionic models, such as the shape of the action potential, the restitution of action potential duration and of the conduction velocity, as well as unchanged description of most of the ionic currents.