Further information
Professor Darryl Holm, Department of Mathematics, Imperial College London presents this Department of Bioengineering seminar.
Abstract: The description of cardiac electrophysiology at the tissue level is found by averaging over cellular behavior. This averaging produces the bidomain model for waves of cardiac activation potential. The bidomain model is a system of coupled reaction-diffusion equations whose solution is challenging for analysis and computation because of its singular parabolic nature, its wide range of time scales and the complex cascade of nonlinear bifurcations in its solution behavior.
Upon assuming that the conductance tensors in the two domains are proportional, the bidomain model reduces to the monodomain model, a member of the Hodgkin-Huxley family of reaction-diffusion equations. A further approximation results in the eikonal model, which arises from a Fermat/Huygens variational principle. The eikonal model is a phenomenological description of cardiac waves whose solution follows the wave front by lumping its cardiac repolarization dynamics that sustains it and produces its pulse shape into a prescribed position-dependent wave front velocity (the conduction velocity).
Here we trace the steps leading first from the bidomain model to the monodomain model and next to the eikonal model. After these steps are summarized, we compare some of the shared properties of these models that are relevant to further cardio-mathematical modelling.
Biography: Darryl Holm spent thirty-four years at Los Alamos National Laboratory before moving five years ago to Imperial College London as Professor of Applied Mathematics. During his career, Darryl developed a wide range of interests that were informed by the geometric approach to dynamical systems. Reviews of most of his publications in mathematics appeared in Mathematical Reviews, available on MathSciNet. His main interest is in deriving and analyzing nonlinear evolution equations for multiscale phenomena. Applications of these equations range from climate modeling and ocean circulation, to template matching in imaging science, to directed self-assembly in nanoscience, to telecommunications. (In telecommunications, Holm holds a patent on the iterated-mapping approach for controlling the optical pulse propagation and re-amplication process.) The
solution behavior of these includes equations solitons (governed by the Camassa-Holm equation), turbulence (modelled by the LANS-alpha equation), template marching for biomedical images (modelled by the EPDiff equation) and electrocardial waves. His BioEngineering lecture will treat last is the topic, introducing a new electrocardial-wave model called the eikonal-Darcy equation.
Light refreshments served from 3.30pm in the Staff Breakout Room (RSM 3.24).
For further details please contact Dr Jennifer Siggers (j.siggers@imperial.ac.uk).
All are welcome.