Biomedical subjects

M Schmick

Publications and source records attributed to M Schmick.

2 recordsLinked to original sources

PubMed2000

Intermingled basins due to finite accuracy

We investigate numerically first a chaotic map interrupted by two small neighborhoods, each containing an attracting point, and secondly a periodically tilted box within which disorderly colliding disks can reach different attracting configurations, due to dissipation. For finite, arbitrarily small accuracy, both systems have basins of attraction that are indistinguishable from intermingled basins: any neighborhood of a point in phase space leading to one attractor contains points leading to the other attractor. A bifurcation destabilizing the fixed points or the disk configurations causes on-off intermittency; the disks then alternate between a "frozen" and a gaslike state.

Journal Article↗

PubMed1999

Simulation of vessel morphogenesis using cellular automata.

We present a cellular automaton model, including lateral inhibition of an autocatalytic morphogen, as well as a genetic switch that differentiates tissue into substrate-depleting vessels. This model yields isotropic morphogenesis, including: dichotomous and lateral branching, blind vessel ends, and closed loops due to anastosmosis. The algorithm consists of a list of simple rules describing the essential biophysical features, permitting comfortable programming and fast computations. Depending on the choice of the substrate s, the model is applicable to leaf veins (s is auxin), insect trachea (s is CO2) or neovascularization (s is an angiogenesis factor). Sequential addition of rules can be correlated to evolutionary steps in leaf morphogenesis.

Algorithms↗