Statistical Mechanics: Entropy, Order Parameters, and Complexity,
now available at
Oxford University Press
(USA,
Europe).
Your heartbeat is a wave that passes across your heart muscle. The heart tissue
is an excitable medium: a small triggering impulse can lead to a large response
(an electrical discharge across the cell membranes, together with a
contraction of the heart muscle). A piece of heart tissue can be triggered by
the excitation of a neighboring piece of tissue, which is the basis for
the wave action.
In the normal heart, a pulse propagates outward from the sinoatrial node
(your natural pacemaker, which excites itself). The animation at right
shows the heart undergoing spiral waves, which occur when your heart
is malfunctioning (ventricular tachycardia).
This exercise first studies a simple model for an excitable medium,
the FitzHugh-Nagumo equations, using nullcline analysis to develop
insight into the phase portrait of the action potential. We then couple
these equations into a simple partial differential equation representing
the heart tissue. We learn techniques for solving dynamical partial
differential equations. We develop an interactive graphical model for the
heart allowing the student to apply localized electrical "shocks" to create and
break up spiral waves.
Last modified: August 24, 2006
Statistical Mechanics: Entropy, Order Parameters, and Complexity,
now available at
Oxford University Press
(USA,
Europe).