Mathematically Modeling Electrical Wave Propagation in Cardiac Fibers

This monograph provides a mathematical analysis of
electrical wave propagation in cardiac tissue.
Models of the cardiac action potential are similar to
the Nobel Prize-winning Hogdkin-Huxley model of the
nerve action potential. In Chapter 2, we carefully
construct a simple, two-variable model of the cardiac
action potential, modeling the cell membrane as an
electrical circuit. Unlike nerve cells, cardiac
tissue exhibits a feature known as electrical
restitution, which can be exploited to predict the
onset of certain arrhythmias. Chapters 3 and 4
illustrate how to derive restitution relationships
for both the duration and velocity of action
potential, using the model from Chapter 2 as a
starting point. Finally, in Chapter 5 we use these
restitution relationships to analyze how cardiac
fibers respond to a sudden change in the pacing rate.
Our mathematical analysis provides some rather
surprising predictions regarding how abnormal rhythms
may originate.

Autorentext
John Wesley Cain received his Ph.D. in Mathematics from Duke University in 2005. Presently, he serves on the mathematics faculty at Virginia Commonwealth University, and is a Fellow of the Center for the Study of Biological Complexity. Dr. Cain's research involves applications of mathematics to problems in cardiac electrophysiology.

Klappentext
This monograph provides a mathematical analysis of electrical wave propagation in cardiac tissue. Models of the cardiac action potential are similar to the Nobel Prize-winning Hogdkin-Huxley model of the nerve action potential. In Chapter 2, we carefully construct a simple, two-variable model of the cardiac action potential, modeling the cell membrane as an electrical circuit. Unlike nerve cells, cardiac tissue exhibits a feature known as electrical restitution, which can be exploited to predict the onset of certain arrhythmias. Chapters 3 and 4 illustrate how to derive restitution relationships for both the duration and velocity of action potential, using the model from Chapter 2 as a starting point. Finally, in Chapter 5 we use these restitution relationships to analyze how cardiac fibers respond to a sudden change in the pacing rate. Our mathematical analysis provides some rather surprising predictions regarding how abnormal rhythms may originate.