Mathematically Modeling Electrical Wave Propagation in Cardiac Fibers : Kinematic Models and Restitution

ISBN-13: 9783639119817 / Angielski / Miękka / 2009 / 120 str.

John Cain

Opis

This monograph provides a mathematical analysis ofelectrical wave propagation in cardiac tissue. Models of the cardiac action potential are similar tothe Nobel Prize-winning Hogdkin-Huxley model of thenerve action potential. In Chapter 2, we carefullyconstruct a simple, two-variable model of the cardiacaction potential, modeling the cell membrane as anelectrical circuit. Unlike nerve cells, cardiactissue exhibits a feature known as electricalrestitution, which can be exploited to predict theonset of certain arrhythmias. Chapters 3 and 4illustrate how to derive restitution relationshipsfor both the duration and velocity of actionpotential, using the model from Chapter 2 as astarting point. Finally, in Chapter 5 we use theserestitution relationships to analyze how cardiacfibers respond to a sudden change in the pacing rate. Our mathematical analysis provides some rathersurprising predictions regarding how abnormal rhythmsmay originate.

O autorze

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.