Modeling spiral Ca2+ waves in single cardiac cells: role of the spatial heterogeneity created by the nucleus.

Excitation-contraction coupling in cardiomyocytes is known to rely on the Ca(2+)-induced Ca2+ release mechanism. This autoamplification process is also very apparent when voltage-clamped or Ca(2+)-overloaded myocytes exhibit fast-propagating Ca2+ waves. Although most of the fronts are planar, some adopt a spiral shape, revealing additional characteristics about the excitability and structure of the cardiac cell (P. Lipp and E. Niggli, Biophys. J. 65: 2272-2276, 1993: J. Engel, M. Fechner, A. Sowerby, S. Finch, and A. Stier, Biophys. J. 66: 1756-1762, 1994). Using a previously developed model for Ca2+ oscillations and waves (A. Goldbeter, G. Dupont, and M.J. Berridge, Proc. Natl. Acad. Sci. USA 87: 1461-1465, 1990; G. Dupont and A. Goldbeter, Biophys. J. 67: 2191-2204, 1994), we study by numerical simulations different conditions in which spiral Ca2+ waves can occur as a result of the spatial heterogeneity created by the nucleus in a system with geometry resembling that of a myocyte. A region of the cell lacking Ca2+ pools, acting as an obstacle able to break the propagation of planar waves, suffices to initiate a spiral wave; however, this region must be properly placed with respect to the pacemaker. An obstacle behaving as a barrier to diffusion is also able to create the initial bending that can lead to the spiral wave. We study how the occurrence of spiral Ca2+ waves in single cardiomyocytes is influenced by factors such as the stimulus location and the position, shape, and dimensions of the obstacle to planar wave propagation.