We derive a homogenized description of the electrical communication along a single strand of myocytes in the presence of gap-junctional and electric-field coupling. In the model, cells are electrically coupled through narrow clefts that are resistively connected to extracellular space. Cells are also coupled directly through gap junctions. We perform… (More)
We present a multiscale model and an adaptive numerical scheme for simulating cardiac action potential propagation along a linear strand of heart muscle cells. This model couples macroscale partial differential equations posed over the tissue to microscale equations posed over discrete cellular geometry. The microscopic equations are used only near action… (More)
Acknowledgements I am indebted to many people who made this dissertation possible. First and foremost, I would like to thank my mother, father, and the rest of my family for the support and sacrifices they made to allow me to pursue my interests in mathematics. I would also like to thank my advisors, Charlie Peskin and Nader Masmoudi, for giving me the… (More)
We derive the values for the intracellular and extracellular conductivities needed for bidomain simulations of cardiac electrophysiology using homogenization of partial differential equations. In our model, cardiac myocytes are rectangular prisms and gap junctions appear in a distributed manner as flux boundary conditions for Laplace's equation. Using… (More)
Empirical study of an adaptive multi scale model for simulating cardiac conduction. Adaptive multiscale model for simulating cardiac conduction.
Over the last ten years, I have taught freshmen and masters students from MIT (in Multivariable Calculus , Computational Science and Engineering), engineering students from The Cooper Union (in Ordinary Differential Equations, Boundary Value Problems, Probability and Statistics), and undergraduates at New York University (in Quantitative Reasoning). For all… (More)
We modify and empirically study an adaptive multiscale model for simulating cardiac action potential propagation along a strand of cardiomyocytes. The model involves microscale partial differential equations posed over cells near the action potential upstroke and macroscale partial differential equations posed over the remainder of the tissue. An important… (More)