Tuesday 18 Dec 2012: A curved-space description for the dynamics of excitation waves in the heart
Hans Dierckx - Ghent University, Belgium
Harrison 203 (room TBC) 15:00-16:00
The living cells in your heart incite each other to contract by passing on electrical activity to each other. While a single, coherent wave causes effective pumping of blood, a spiral-shaped activation pattern leads to tachycardia (>100 beats per minute), and chaotic electrical activity is known to underlie lethal fibrillation events.
Mathematically, the problem boils down to a set of parabolic PDEs, in which the transmembrane voltage and local ion concentrations appear as the state variables. Importantly, the excitation waves travel about 3 times faster along the axis of the elongated cardiac cells than in transverse directions, which prevented several general results for the isotropic case to be valid for anatomically realistic heart models. Recent developments, however, show that distances may be locally rescaled to considerably simplify both calculations and results. Hereby, one ends up working in a curved space, where it is necessary to think in terms of geodesics and curvature tensors to extend the findings known from isotropic excitable media.
In this talk, I will show how we used the curved-space formalism to derive the laws of motion for wave fronts and filaments (i.e. the local rotation axis of spiral shaped patterns) in anisotropic cardiac tissue.