Research Interests

Wave propagation in the heart: theory and calculation. In the heart muscle, the cell membrane acts as an electric capacitor that exhibits sudden depolarization and more gradual repolarization. This behavior (the action potential) propagates as a wave from cell to cell and governs the mechanical heartbeat. Very often, the propagation is well represented macroscopically, without reference to individual cells.

Spiral-shaped waves have been observed, which are the surface manifestations of scroll waves inside the tissue. These reentrant excitations cause lethal arrhythmias; predictability is highly desirable. The mathematics is nonlinear and full of surprises. Even macroscopically, the local direction of the muscle fibers is important, as it gives rise to a nonuniform and anisotropic medium of propagation.

My work aims at finding out how mathematical analysis can help understand numerical and real experiments in that context. Currently I am seeking to adapt diffuse optical tomography towards displaying an actual excitation wave in 3D.

Selected References

Wellner, M. and Berenfeld, O. Theory of reentry. Chapter 35 in Cardiac Electrophysiology from Cell to Bedside (D.P. Zipes and J. Jalife, eds.) Saunders, 2004.

Wellner, M., Berenfeld, O., Jalife, J., and Pertsov, A.M. Minimal principle for rotor filaments. Proc. Natl. Acad. Sci., vol. 99, p. 8015, 2002.

Wellner, M., Jalife, J., and Pertsov, A.M. Waves in excitable media: effects of wave geometry. Int. Jl. Bifur. and Chaos, vol. 12, p. 1939, 2002

Berenfeld, O., Wellner, M., Jalife, J., and Pertsov, A.M. Shaping of a scroll wave filament by cardiac fibers. Phys. Rev. E, vol. 63, p. 061901, 2001.

Pertsov, A.M., Wellner, M., Vinson, M., and Jalife, J. Topological constraint on scroll wave pinning. Phys. Rev. Lett., vol. 84, p. 2738, 2000.

Wellner, M., Berenfeld, O., and Pertsov, A.M. Predicting filament drift in twisted anisotropy. Phys. Rev. E, vol. 61, p.1845, 2000.

Wellner, M., Pertsov, A.M., and Jalife, J. Spiral drift and core properties. Phys. Rev. E, vol. 59, p. 5192, 1999.

Wellner, M. and Pertsov, A.M. Generalized eikonal equation in excitable media. Phys. Rev. E, vol. 55, p. 7656, 1997.

Pertsov, A.M., Wellner, M., and Jalife, J. Eikonal relation in highly dispersive excitable media. Phys. Rev. Lett., vol. 78, p. 2656, 1997.