Benjamin Liu


A cardiac arrhythmia is a potentially-lethal event in which the normally orderly electrical activity in the heart is disrupted -- it becomes disorganized and compromises effective contraction. To better understand arrhythmia dynamics to develop potential therapies and treatments, experimental, computational, and mathematical tools are required. Simulations of cardiac tissue provide valuable insight into the dynamics of life-threatening cardiac arrhythmias, and though much work has been done in this area, the role of the Purkinje network during ventricular arrhythmias has largely been ignored. The function of the Purkinje network is crucial to normal heart rhythm, so its inclusion into cardiac structural models is a necessary step to furthering our understanding of arrhythmias. Current technological limitations prevent the direct imaging of the intact three-dimensional Purkinje structure, making the incorporation of a Purkinje network into such simulations difficult. At this time most efforts involve generating artificial Purkinje networks either through manual drawing of Purkinje-like structures or through algorithms that generate the structures procedurally based on rules gleaned from physiological studies. Very little work has focused on the incorporation of a Purkinje network based directly on experimental data. Through dissection, photographs of the Purkinje network can be taken, but these two-dimensional photographs do not capture the three-dimensional structure of the network. Here we present a novel method for reconstructing the three-dimensional Purkinje structure based on projecting two-dimensional Purkinje structures recovered from experimental photographs onto realistic ventricular geometries. The resulting three-dimensional Purkinje structures make possible the modeling of the coupled ventricle-Purkinje system. The second major component of our work is the development of two methods by which these systems can be modeled. We implement these models using real anatomical data and find good agreement between the two models and with previous experimental studies. Our work provides a basis for the further study of ventricular arrhythmias, and in particular the role the Purkinje network plays in initiating and maintaining such events.

Library of Congress Subject Headings

Arrhythmia--Mathematical models; Purkinje cells--Mathematical models; Ventricular fibrillation--mathematical models

Publication Date


Document Type


Student Type


Degree Name

Applied and Computational Mathematics (MS)

Department, Program, or Center

School of Mathematical Sciences (COS)


Elizabeth Cherry

Advisor/Committee Member

Matthew Homan

Advisor/Committee Member

David Ross


Physical copy available from RIT's Wallace Library at RC685.A65 L48 2014


RIT – Main Campus

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