Simulating T-wave parameters of local extracellular electrograms
with a whole-heart bidomain reaction-diffusion model:
Proceedings of the 29th Int Conf IEEE-EMBS, Lyon, August 2007, pp 6644-6647.
As a measure of local repolarization time (TR), the instant of maximum slope (Tup) of the T wave in the local unipolar electrogram is commonly used. Measurement of Tup can be difficult, especially in positive T waves. These difficulties have led some researchers to propose the instant of maximum downslope (Tdown) as a marker of TR when the T wave is positive. To improve understanding of T-wave parameters, we simulated electrograms with a bidomain model of the human heart. To test T-wave parameters, we compared them to TR determined from the local membrane potential. We propose a simple model of the electrogram, which we validated by comparison to the bidomain model. With the simple model, it is straightforward to show that the sign of the T wave is almost uniquely determined by TR. We then used the bidomain model to simulate the effects of a variety of pathologies and technical difficulties, which the simple model could not account for. Generally, Tup was a much better estimate for TR than Tdown. Regional fibrosis could attenuate local electrogram components and reduce accuracy of Tup as a marker for TR. In fibrotic tissue, Tdown was not related to TR at all. This investigation of electrogram slopes required the simulation of extracellular potentials with about 100 times more precision than needed for simulation of visually acceptable waveforms alone. This requirement is more difficult to meet in larger models, but it was actually possible for a human-heart model with 60 million nodes. By sacrificing some spatial resolution, we kept the computational requirements within acceptable limits for multiple simulations.
The ability to determine what a theory predicts is essential to science. In complex systems, such as the heart, prediction can require extensive use of mathematics. We then use a "mathematical model" of the heart. In this paper, such a model is used to better understand a measurement method that cardiologists sometimes use in the human heart.
The somewhat provocative title of this paper is a joke, relating to the fact that extremely large computer models are required for this work, and that the size of these models makes the computations more difficult. The simulations described here can only be done on supercomputers with at least 32 processors, and a lot of care must be taken to make them work at all.
The results of this study were somewhat predictable for many researchers, but not for all. There has been quite some controversy over this subject in the literature, and still not all authors do agree that the instant of steepest upstroke of the T-wave in the unipolar electrogram always corresponds with the local repolarization time. We hope that this first mathematical study in a complete human heart is for some readers more convincing than previous mathematical studies in simpler models.
This paper also describes a preliminary version of a simple model for the local electrogram, a rule-of-thumb model intended to help understanding this relation intuitively. An improved version of the simple model was published later in Am. J. Physiol. H.
Computational resources for this work were provided by the
Réseau québécois de calcul de haute performance
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