The geometry of excitability. (English) Zbl 0856.92002

Winfree, A. T.

Nadel, Lynn (ed.) et al., 1992 lectures in complex systems. Papers from the summer school held in Santa Fe, NM, USA, 1992. Reading, MA: Addison-Wesley. St. Fe Inst. Stud. Sci. Complexity, Lect. 5, 207-298 (1993).

This chapter presents a series of lectures given at St. John’s College in Santa Fe. I am keeping the first three of these five lectures unpedantic and devoid of scholarly apparatus. There are few citations in the first three, and I am leaving out all physiological details and mathematics, to try instead to convey the context in which they may have interest. The last two lectures are deliberately redundant. They review and supplement by traversing much of the same material from a somewhat different direction. Every step is keyed to a bibliography of about 247 publications. These should suffice for whatever follow-up to choose. (From the introduction.)
First lecture (Chapter headings): Excitability; Excitable media; Heart muscle (“myocardium”); The Belousov-Zhabotinsky medium; Spiral waves radiated from rotors; The fundamental problem of electrophysiology; Other wave equations.
Second lecture: Meander; Rotors in the electrophysiologists’ myocardial membrane model; Rotors in living myocardium.
Third lecture: Chemical organizing centers; Twist; The local geometry approximation; What organizing centers are not.
Fourth lecture: Two-dimensional physiology; Two-dimensional physiology falls short of understanding fibrillation, due to ignoring the third dimension of myocardium; Past two-dimensional vortex computations and physical chemistry; Past three-dimensional vortex computations.
Fifth lecture: Three-dimensional investigations; Computer-assisted tomography for new three-dimensional laboratory experiments.
For the entire collection see [Zbl 0840.00045].

MSC:

92C30

Physiology (general)

Keywords:

heart muscle; spiral waves; meander; rotors; Belousov-Zhabotinsky medium; electrophysiology; wave equations; myocardial membrane model; myocardium; local geometry approximation; two-dimensional vortex computations; physical chemistry; three-dimensional vortex computations; computer-assisted tomography