Computer modelling of transthoracic electric field during defibrillation shocks: an efficient finite difference implementation

A 3-dimensional model of transthoracic electric field of an implantable defibrillator has been developed for an implementation on a personal computer. The shape of the thorax and relevant organs are defined in a rectangular 3.5 mm grid. This grid is used to simulate the heart and areas of possible electrode placement (e.g. subpectoral active can, right heart cavities, subcutaneous array) while the grid is gradually degraded to up to 4 cm cubes in remote areas. According to the organ, each cube of the grid has a pre-defined conductivity and the whole model is described by a set of finite-difference equations. The equation set is solved by Gauss-Jordan elimination. The model permits the placement of electrodes only in realistically pre-defined areas. The triangularisation of the part of the equation matrix related to other nodes is independent of individual experiments and can be performed once for all computations. Similarly, when defining a batch of experiments which use only a subset of electrode positions, the strategy can be repeated. In this way, the computation demands of the model were minimised. Following an initial triangularisation phase common to all experiments, each experiment batch starts with a sub-matrix triangularisation (≈3 hours on a 200 MHz Pentium based computer). Individual experiments then take 3-6 minutes each including compactations of total impedance, intracardiac current density, and simulated defibrillation thresholds. The model is set-up in 7 different configurations including normal heart, 3 stages of left ventricular dilatation and 3 stages of hypertrophy