Characterization of multiple spiral waves

This project aims at characterizing a multiple spiral wave system from a large-scale perspective. Our goal was to develop improved intuition into the complex behavior of these systems for possible applications to the study and diagnosis of cardiac tissue during fibrillation [1]. Accordingly, we focused our study on two quantities that are defined from the state of the entire system. The quantities correspond to the classical predator and prey quantities. In our model, the collection of all excited cells play the role of a predator, while excitable cells play the role of the prey (Fig. 1A). The use of “predator” and “prey” dynamical variables has provided diagnostic tools that we can use to characterize the behavior of systems containing many interacting spiral waves. Study of these quantities has allowed us to identify two characteristic types of behavior we call type 1 and type 2. The behavior of all the simulations and optical mapping experiments we studied fell into one of these categories, or in transitions between these two categories. Both types of behavior possessed a number of different distinguishing characteristics, including the degree of repetitiveness of wave propagation patterns in time, the distribution of spectral power, and inferred dynamical organization. Type-2 behavior also exhibited a strong correlation between the time intervals between consecutive extrema in the predator time history and the change in the value of the predator quantity that occurs within these time intervals. These characterizations led to the development of a theory based on the summation of behavior of the dynamics within the “domains of influence” of the individual waves present in the system as shown in Fig. 1B. We find that this theory yields behavior consistent with all the characteristics observed, and thus is a starting point towards additional understanding of this complex spatio-temporal dynamics in the heart [1].

Figure 1

(A) Definitions of the predator and prey states as applied to the time record of a single pixel taken from typical filtered optical mapping data.

(B) An example of how the domains of influence might be drawn for a particular pattern of action potential propagation in numerical simulation. Red=predator (action potential) regions; green=prey regions; blue=neither predator nor prey. Black and white dots mark spiral wave tips rotating in the clockwise and counterclockwise directions, respectively. The black lines mark the boundaries of the domains of influence (from [1]; see also “Phys. Rev. E Kaleidoscope Images 2008”).


  1. N.F. Otani et al., Phys. Rev. E 78, 021913 (2008).