Spiral-wave prediction in a lattice of FitzHugh-Nagumo oscillators
In many biological systems, variability of the components can be expected to outrank statistical fluctuations in the shaping of self-organized patterns. The distribution of single-element properties should thus allow the prediction of features of such patterns.
In a series of previous studies on established computational models of Dictyostelium discoideum pattern formation we demonstrated that the initial properties of potentially very few cells have a driving influence on the resulting asymptotic collective state of the colony [1,2].
One plausible biological mechanism for the generation of variability in cell properties and of spiral wave patterns is the concept of a ‘developmental path’, where cells gradually move on a trajectory through parameter space.
Here we review the current state of knowledge of spiral-wave prediction in excitable systems and present a new one-dimensional developmental path based on the FitzHugh-Nagumo model, incorporating parameter drift and concomitant variability in the distribution of cells embarking on this path, which gives rise to stable spiral waves. Such a generic model of spiral wave predictability allows new insights into the relationship between biological variability and features of the resulting spatiotemporal pattern.
 Geberth, D. and Hütt, M.-Th. (2008) Predicting spiral wave patterns from cell properties in a model of biological self-organization. Phys. Rev. E 78, 031917.  Geberth, D. and Hütt, M.-Th. (2009) Predicting the distribution of spiral waves from cell properties in a developmental-path model of Dictyostelium pattern formation. PLoS Comput. Biol 5, e1000422.