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