Date of Award

Spring 5-2-2022

Degree Type


Degree Name

Doctor of Philosophy (PhD)


Mathematics and Statistics

First Advisor

Dr. Vladimir Bondarenko

Second Advisor

Dr. Igor Belykh

Third Advisor

Dr. Jun Kong

Fourth Advisor

Dr. Gennady Cymbalyuk


Atrial fibrillations and heart failure are among the leading cardiovascular diseases in the world. Understanding the development and progression of these diseases requires a thorough knowledge of the electrophysiological mechanisms in a healthy and diseased cardiac myocyte. This goal can be achieved by using mathematical modeling along with experimental investigations. Here, we developed two new comprehensive mathematical models of the mouse atrial and ventricular myocytes. The first one is a novel compartmentalized mathematical model of mouse atrial myocytes. This model combines the action potential, [Ca2+]i dynamics, and β-adrenergic signaling cascade for a subpopulation of right atrial myocytes with a developed transverse-axial tubule system. The model consists of three compartments related to β-adrenergic signaling (caveolae, extracaveolae, and cytosol) and employs local control of Ca2+-release. It also simulates the mechanisms of action potential generation and describes atrial-specific Ca2+ handling and frequency dependences of the action potential and [Ca2+]i transients. The model showed that the T-type Ca2+ current significantly affects the later stage of the action potential with little effect on [Ca2+]i transients. Blocking the small-conductance Ca2+-activated K+ current leads to the prolongation of the action potential at high intracellular Ca2+ concentrations. Simulation results obtained from the atrial cell model were compared to those from ventricular myocytes. The developed model presents a valuable tool for studying complex electrical properties in the mouse atria and could be applied to understand atrial physiology and arrhythmogenesis. The second model is a novel compartmentalized mathematical model of failing mouse ventricular myocytes after TAC procedure. The model effectively describes the cell geometry, action potentials, [Ca2+]i transients, and β1- and β2-adrenergic signaling in the failing cells. Simulation results obtained from a failing cells’ model were compared to those from the normal ventricular myocytes. Exploration of the model revealed the sarcoplasmic reticulum Ca2+ load mechanisms in failing ventricular myocytes. We also described a proarrhythmic behavior of Ca2+ dynamics upon stimulation with isoproterenol and mechanisms of the proarrhythmic behavior suppression. The developed model can be used to explain the existing experimental data on failing mouse ventricular myocytes and make experimentally testable predictions of the failing myocyte behavior.


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