| Abstract: |
| Early afterdepolarizations (EADs) are abnormal behaviors that can lead to heart
failure and even cardiac death. In this presentation, we review
recent results and we mathematically investigate the occurrence and development of
these phenomena in two realistic ventricular myocyte models: the rabbit model of Sato
(2009) and the human model of O'Hara (2011). These models are of high dimension,
27 and 41 respectively, so a mix of techniques must be used in their study.
We connect the results with a reduced low-dimensional model, the Luo-Rudy
cardiomyocyte model (1991). The combined use of analytical and numerical techniques allows us
to propose a global conjecture of a mathematical mechanism of EAD creation in low- and high-dimensional
models. By examining the bifurcation structure of the model, we elucidate the dynamical elements
associated with these patterns and their transitions. Using a fast-slow analysis, we explore the emergence
and evolution of EAD in the low-dimensional model and develop new methodologies
for fast-slow decomposition for the realistic high-dimensional O`Hara model. This
decomposition has allowed us to propose some new theoretical techniques for the control
of prearrhythmia situations. |
|