Interaction of Three-Dimensional Patterns with Heterogeneities in Chemical Media
It has been suggested that ventricular fibrillation, which can lead to heart failure, may result from the presence of a three-dimensional pattern ("mother rotor") of electrical activity that becomes stable in the heart. Cardiac tissue is an excitable medium because it can propagate electrical waves; these waves can form patterns and become stable if they encounter obstacles on their way. The goal of this project is to generate three-dimensional patterns (called scroll waves or rotors) in a chemical medium, observe the interaction between these patterns and small semi-inert objects, and analyze the dynamics of the pattern as it interacts with the object.
The Belousov-Zhabotinsky (BZ) reaction constitutes an analogous medium that can propagate chemical rather than electrical waves. In the BZ reaction, an organic acid is oxidized by bromate ions in the presence of a metal catalyst. The oxidation state of the metal ion and the concentration of some intermediate species oscillate during the reaction. Heart tissue and the BZ reaction medium share the property of excitability, which is the foundation for the study of three-dimensional patterns in this chemical medium with the aim of understanding arrhythmias in the heart.
Pulse-Coupled Chemical Oscillators as a Model for Neural Networks
We are studying the behavior of systems consisting of the Belousov-Zhabotinsky oscillating chemical reaction in flow reactors coupled via pulses of chemicals injected into the "postsynaptic" reactor when the electrochemical potential of the "presynaptic" reactor crosses a threshold. The system resembles a set of synaptically coupled neurons. We can control the strength of the coupling, whether it is excitatory or inhibitory, the delay between the "action potential" and the delivery of "neurotransmitter," and the topology of the coupling. Initial experiments are aimed at modeling the behavior of the pyloric network in the crustacean stomatogastric ganglion. The project involves learning about chemical oscillators; performing experiments; and, if the student has strong computational skills, carrying out numerical simulations.