Abstract

Cardiac electrical waves are responsible for coordinating functionality in the heart muscle. When these waves are disrupted, it is referred to as a cardiac arrhythmia, which can be life threatening. Over the last two decades, experimental techniques to study electrical waves in the heart have been improved. Nevertheless, methods for observing electrical waves in the heart still do not provide enough data to draw conclusions about wave propagation. Observations about wave propagation can be made on the surface of the heart, but to collect data on the interior, the methods currently available either do not provide high enough spatial resolution or change the conduction properties of the region to be observed. The lack of depth information leaves us uncertain as to the precise mechanisms by which waves cause arrhythmias. Numerical models have been developed for these wave dynamics, but they are only approximations for qualitative behavior. For decades, the weather-forecasting community has faced similar problems with the approximate nature of numerical models and lack of available data, and tools known as data assimilation have been developed within that community to deal with this problem. We aim to apply these methods to cardiac wave propagation. By combining observations with numerical models through data- assimilation techniques from weather forecasting, we will attempt to constrain wave dynamics in the heart muscle interior. In this thesis, we present the first approach for coupling data-assimilation techniques with a cardiac cellular model. Using the Fenton-Karma (FK) model of cardiac cellular processes to represent wave dynamics and the Ensemble Transform Kalman Filter data-assimilation technique, synthetic observations have been integrated with the FK model. By analyzing the sensitivity of state-variable values in the FK model, we have developed initial conditions for data assimilation that are able to quantitatively approximate wave behavior in a 1-D setting. This work will provide a proof of concept and give insight into challenges in the 2- and 3-D cases.

Library of Congress Subject Headings

Arrhythmia--Mathematical models; Kalman filtering

Publication Date

5-30-2014

Document Type

Thesis

Student Type

Graduate

Degree Name

Applied and Computational Mathematics (MS)

Department, Program, or Center

School of Mathematical Sciences (COS)

Advisor

Matthew J. Homan

Advisor/Committee Member

Elizabeth M. Cherry

Advisor/Committee Member

Laura M. Munoz

Comments

Physical copy available from RIT's Wallace Library at RC685.A65 S36 2014

Campus

RIT – Main Campus

Plan Codes

ACMTH-MS

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