Multiarmed Spirals in Excitable Media

Multiarm spirals in a two-dimensional cardiac substrate

“…For validation of the interpolation method, a meandering spiral wave was simulated on a 20-mm circular substrate by using the Karma action potential model (25). For plots of the APD and CV restitutions, FitzHugh-Nagumo-type models (12,13) were simulated on a 0.5-ϫ 20-mm tissue strip. The strip was stimulated at one end at progressively higher rates (2 Hz up to break frequency, in 1-Hz steps), APDs and CV were recorded between two points at the other end of the strip, and normalized restitution curves were plotted and fitted as described Table 1 (which are published as supporting information on the PNAS web site) and were the same as in the respective references.…”

“…This result is in agreement with the analytical and numerical studies of Hakim and Karma (27), who showed that rotation of multiple spirals around a common excitable, but unexcited, core (an equivalent of persistent TS) is linearly unstable in weakly excitable media (including ref. 12) and that spirals eventually invade the excitable core, collapse, and yield AS. In cardiac cultures where AS and TS occurred, each TS was followed by at least one AS, such that the firing rate in the central zone was between 50% and 100% of the rate in the periphery (Fig.…”

“…The modes of induction of these multiarmed spirals [i.e., use of an unexcitable central obstacle that is subsequently removed (2, 10) and spontaneous formation from dense multiple wavebreaks (12) or from preset spatial distributions of excited and recovered medium (13,14)] are not applicable to cardiac tissue. Moreover, healthy cardiac tissue exhibits normal excitability, in contrast to two-variable FitzHugh-Nagumo models, which require weak excitability to support stable multiarm spirals (12)(13)(14)(15). In a normally excitable medium, the existence of a stable multiarm spiral as an entity distinct from negligibly interacting adjacent single spirals was questioned by Winfree (16,17), who considered that in this case distinct rates of rotation are necessary to regard multi-and single-arm spirals as two qualitatively different phenomena.…”

“…So far, stable rotating structures with a higher degree of organization, such as multiarmed spirals, have been demonstrated experimentally in chemically (2) or light-controlled (10) Belousov-Zhabotinsky reactions, in starving social amoebae Dictyostelium discoideum (11), and in FitzHugh-Nagumo-type computer models of homogenous weakly excitable media (12)(13)(14). The modes of induction of these multiarmed spirals [i.e., use of an unexcitable central obstacle that is subsequently removed (2, 10) and spontaneous formation from dense multiple wavebreaks (12) or from preset spatial distributions of excited and recovered medium (13,14)] are not applicable to cardiac tissue. Moreover, healthy cardiac tissue exhibits normal excitability, in contrast to two-variable FitzHugh-Nagumo models, which require weak excitability to support stable multiarm spirals (12)(13)(14)(15).…”

“…In the heart, stable single-arm spirals can underlie periodic activity such as monomorphic tachycardia, whereas unstable spirals that continuously form and break up are shown to underlie aperiodic and lethal heart activity, namely fibrillation (9). So far, stable rotating structures with a higher degree of organization, such as multiarmed spirals, have been demonstrated experimentally in chemically (2) or light-controlled (10) Belousov-Zhabotinsky reactions, in starving social amoebae Dictyostelium discoideum (11), and in FitzHugh-Nagumo-type computer models of homogenous weakly excitable media (12)(13)(14). The modes of induction of these multiarmed spirals [i.e., use of an unexcitable central obstacle that is subsequently removed (2, 10) and spontaneous formation from dense multiple wavebreaks (12) or from preset spatial distributions of excited and recovered medium (13, 14)] are not applicable to cardiac tissue.…”