Date of Award

5-5-2014

Document Type

Capstone Project

Degree Name

Bachelor of Arts

Department

Mathematics

First Advisor

Ian Besse

Abstract

Two models (based o of the Luo-Rudy 1 guinea-pig ventricular model) were produced to analyze the e ects of caveolar sodium current on a single cardiac action potential. A separate model (based off of the Pandit et al. rat left ventricular model) was produced to observe the e ect additional caveolar sodium current had on the one-dimensional propagation of a cardiac action potential in a line of cardiomyocytes. Evidence suggests that the opening of caveolae recruits additional sodium channels on the cardiomyocyte membrane that can affect both the peak voltage overshoot and the maximum upstroke velocity of the cardiac action potential the change in maximum upstroke velocity in turn can alter the conduction velocity of an electrical signal. We examined two opening mechanisms of caveolae. The first opening mechanism simulated a 1-cm2 patch of membrane perfused with a β-adrenergic agonist that opened a certain number of caveolae on the membrane. The second opening mechanism simulated a 1-cm2 patch of membrane with stochastically opening caveolae that open according to a Poisson process. The effects of these two opening mechanisms of caveolae on a single cardiac action potential using the Luo-Rudy 1 model were compared to previous computational results using the Pandit et al. model. Our simulations (which incorporated varying membrane capacitance) revealed a 4.1% increase in peak voltage overshoot and a 19.1% increase in the maximum upstroke velocity for a 42% increase in sodium current due to β-adrenergic stimulation. Incorporating stochastically opening caveolae, we observed features such as delays in ventricular repolarization, early afterdepolarizations (characteristics of a serious heart condition called Long-QT Syndrome), and the absence of ventricular repolarization. Propagating single cardiac action potentials (modeled by the Pandit et al. model) revealed a nonlinear increase in conduction velocity as the total number of caveolae on each cell in a line of cardiomyocytes increased.

Comments

Best Paper, 2014 CommonKnowledge Senior Project Writing Award

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