Doctoral Dissertation Defense: Zana Coulibaly
Advisor: Dr. Peercy
Location
Mathematics/Psychology : 103
Date & Time
August 4, 2015, 1:00 pm – 3:00 pm
Description
Title: Calcium Dynamics From Randomly Releasing Sparks in Cardiac Myocytes: Analyzing and Simulating a Probabilistic 3-Dimensional Mathematical Model with Point Release Sources
Abstract:
Organized calcium releases are the means through which the heart regulates the uniform contraction of individual cardiac cells during each heartbeat. At a cardiac cell level, the process involved in the regulation of calcium levels can be modeled using non-linear time-dependent reaction-diffusion equations.
This thesis uses various mathematical and analytical tools to study the dynamics of calcium that results from the study of a three-dimensional stochastic fire-diffuse-fire model in long time simulations. To ease the computational complexity that comes with the exploration of sensitive model parameters in long time simulations, we consider one-dimensional model reductions; these reductions lead to the discovery of a parameter region that supports biophysical calcium waves in the three-dimensional model. These biophysical calcium waves are achieved in our model by using large calcium currents.
A further exploration of the biophysical boundary in the parameter space reveals a range of parameter values that have a high probability of initiating spiral patterns. By treating the calcium dynamics as one emerging from a network of inhomogeneous point processes, we show that the intrinsic appearance of such patterns in our model is the result of an interplay between the spatial regularity of release sites and the amplitude of calcium release. Neither forced temporal heterogeneity nor spatial irregularity is required.
Abstract:
Organized calcium releases are the means through which the heart regulates the uniform contraction of individual cardiac cells during each heartbeat. At a cardiac cell level, the process involved in the regulation of calcium levels can be modeled using non-linear time-dependent reaction-diffusion equations.
This thesis uses various mathematical and analytical tools to study the dynamics of calcium that results from the study of a three-dimensional stochastic fire-diffuse-fire model in long time simulations. To ease the computational complexity that comes with the exploration of sensitive model parameters in long time simulations, we consider one-dimensional model reductions; these reductions lead to the discovery of a parameter region that supports biophysical calcium waves in the three-dimensional model. These biophysical calcium waves are achieved in our model by using large calcium currents.
A further exploration of the biophysical boundary in the parameter space reveals a range of parameter values that have a high probability of initiating spiral patterns. By treating the calcium dynamics as one emerging from a network of inhomogeneous point processes, we show that the intrinsic appearance of such patterns in our model is the result of an interplay between the spatial regularity of release sites and the amplitude of calcium release. Neither forced temporal heterogeneity nor spatial irregularity is required.
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