The ''heart'' of Mathematics
Department of Mathematics and Statistics professor Victor LeBlanc uses techniques from Applied Mathematics to study arrhythmias in the heart.
Your normal heartbeat is caused by a wave of electricity that moves throughout the heart muscle in a precise sequence and synchrony that makes the ventricles and atria contract in clockwork fashion, and this is what pumps your blood into and out of your heart and keeps you alive. This happens roughly 2.5 billion times in a normal person’s lifetime, and most of us never even give it a second thought!
However, for many people, this mechanism sometimes breaks down and they suffer from irregular heartbeats, or arrythmias, which are at the very least inconvenient, and at the worse can be fatal.
Professor LeBlanc’s research work deals with the study of spiral waves, which are precursors to many types of arrhytmias. In heart tissue, spiral waves rotate in specific areas of the heart, and this destroys the normal electrical rhythm that makes the heart contract in the precise order it must to ensure a regular heartbeat. Using techniques from differential equations, dynamical systems and group theory, Professor LeBlanc and his research team studies how these rotating spiral waves interact with geometrical features of the heart, such as ischemic (diseased) tissue, and at the small scale, the discrete nature of the network of cardiac cells which comprises the heart. This analysis allows us to gain a better understanding of how these geometrical structures stabilize and affect the dynamics of spiral waves. The goal is that this work will eventually be helpful in the quest to develop efficient strategies to identify, control and eliminate spiral waves and the subsequent arrhythmias.
About the figure: This figure is taken from the recent paper “Lattice symmetry-breaking perturbations for spiral waves” , L. Charette and V.G. LeBlanc (2014), to appear in SIAM Journal of Applied Dynamical Systems (Download the preprint). On the left, we see a snapshot of a rotating spiral wave observed in a numerical simulation of a model for the electrical activity of cardiac tissue. On the right, we see typical epicyclic paths that are traced out in space by the “tip” of the spiral wave as it rotates around a medium which has a lattice structure, such as the gap junctions between cardiac cells.