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).
abstract
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.