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conference proceedings paper

abstract

As a measure of local repolarization time (T_R), the instant of maximum slope (T_up) of the T wave in the local unipolar electrogram is commonly used. Measurement of T_up can be difficult, especially in positive T waves. These difficulties have led some researchers to propose the instant of maximum downslope (T_down) as a marker of T_R 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 T_R 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 T_R. 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, T_up was a much better estimate for T_R than T_down. Regional fibrosis could attenuate local electrogram components and reduce accuracy of T_up as a marker for T_R. In fibrotic tissue, T_down was not related to T_R 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.

lay abstract

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.

no surprise?

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.

funding

Computational resources for this work were provided by the Réseau québécois de calcul de haute performance (RQCHP). M. Potse was supported by a postdoctoral research award from the Groupe de recherche en sciences et technologie biomédicale (GRSTB), École Polytechnique and Université de Montréal; and by the Research Center of Sacré-Coeur Hospital, Montréal, Québec, Canada.