Computer heart model

A Computer Heart Model Incorporating Anisotropicc Propagation;
I. Model Construction and Simulation of Normal Activation

Michel Lorange and Ramesh M. Gulrajani,
J. Electrocardiol. 26(4):246-261, 1993

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This paper describes the "Lorange-Gulrajani model", one of the first anisotropic propagation models of the human heart. Like the models by Miller and Geselowitz (1978) and by Mailloux and Gulrajani (1982), it was still a cellular automaton model, with fixed propagation velocities and predefined action potential waveforms. What was new about this model was the anisotropic propagation (faster along than across the fibers). This property required a mathematical description of the fiber orientation throughout the heart. Because of the spatial variation of the fiber orientation, the spatial resolution of the model had to be much higher than that of previous models: it incorporated 250,000 points at 1-mm resolution (versus 4000 points for the Miller-Geselowitz model).

The Lorange-Gulrajani model was a milestone in the development of our present heart model, which still incorporates some of its code (translated from Fortran to C). The cardiac anatomy is also still in use, although a more accurate description of the fiber orientation and heterogeneity of ventricular cell types were introduced later.

This paper was the first in a series of 4, published subsequently in the same journal. In papers 2-4 the model was used to study several pathologies.

Later developments were a reaction-diffusion model (Trudel et al, 2004) and a bidomain reaction-diffusion model (Potse et al, 2006).


Present-day computer models of the entire heart, capable of simulating the activation isochrones and subsequently the body surface potentials, focus on considerations of myocardial anisotropy. Myocardial anisotropy enters into play at two levels, first by affecting the spatial pattern of activation owing to faster propagation along cardiac fibers and second by altering the equivalent dipole sources used to calculate the surface potentials. The construction of a new and detailed model of the human heart is described, based on 132 transverse sections obtained following a computed tomography scan of a frozen human heart whose chambers were inflated with pressurized air. The entire heart anatomy was reconstructed as a three-dimensional array of approximately 250,000 points spaced 1 mm apart. Conduction in the thin-walled atria was assumed isotropic from the sinus node region to the atrioventricular node, where it was subject to a 50 ms delay. A two-tier representation of the specialized conduction system was used, with the initial segments of the left and right bundles represented by a system of cables that feeds to the second tier, which is a sheet of conduction tissue representing the distal Purkinje system. Approximately 1,120 "Purkinje-myocardium" junctions present at the terminations of the cables and sprinkled uniformly over the sheet, transmit the excitation to the ventricles. A stylized representation of myocardial fiber rotation was incorporated into the ventricles and the local fiber direction at each model point used to compute the velocity of propagation to its nearest neighbors. Accordingly, the activation times of the entire ventricular myocardium could be determined using the 1,120 or so Purkinje-myocardium junctions as start points. While myocardial anisotropy was considered in the ventricular propagation process, it was ignored in the computation of the equivalent dipole sources. Nevertheless, the computed electrocardiogram, vectorcardiogram, and body surface potential maps obtained with the new heart model properly positioned inside an inhomogeneous torso model were all within normal limits.