Mathematical Modeling in Computational Biology:

Focus on Excitable Media and Cardiac Electrophysiology



Java applets:


Cardiac Electrophysiology Models: 1 Cell

Ions, Diffusion, and Membrane Potential


Ions, diffusion, and Nersnt potential

Zhang et al. (rabbit, central, 2000)

Goldman-Hodgkin-Katz equation

Zhang et al. (rabbit, peripheral, 2000)

Generation of a neural action potential


Generation of cardiac action potential

Courtemanche et al. (human, 1998)

Excitable Media Models: 1 Cell

Nygren et al. (human, 1998)

Hodgkin-Huxley (nerve, 1952)


Hodgkin-Huxley with phase space

Noble (Purkinje, 1962)

FitzHugh-Nagumo (simplified nerve)

DiFrancesco-Noble (Purkinje, 1985)

FitzHugh-Nagumo with phase space


Karma (generic cardiac)

Beeler-Reuter (generic, 1977)

Single Cell Properties

Luo-Rudy I (guinea pig, 1991 )

All-or-nothing repolarization (BR model)

Luo-Rudy “dynamic” (guinea pig, 2001)

Membrane resonance (HH model)

Fox et al. (canine, 2002)

Action potential duration restitution (1D map)

Hund-Rudy (canine, 2004)

Biphasic restitution (1D map)

Priebe-Beuckelmann (human, 1998)

Propagation and Block in 1D

Bernus et al. (reduced PB, human, 2002)

FitzHugh-Nagumo, ring

ten Tusscher et al. (human epi, M, endo, 2004)

Control of APD alternans with external signal, ring

Iyer et al. (human, 2004)

Alternans suppression

Minimal (human epi, M, endo, 2005)

Liminal length and space and time constants

Cardiac Electrophysiology Models: 1D

Liminal length and stimulus parameters

3-variable, ring (discordant alternans)

Liminal length and capacitance

Noble, cable/ring

Liminal length and ionic conductances

Beeler-Reuter, cable/ring

Stimulation voltage profile

Luo-Rudy I, cable/ring

S1-S2 propagation and block

Luo-Rudy dynamic, cable/ring

3D Realistic Cardiac Anatomies

Excitable Media/Cardiac Models: 2D

3D human heart (structure and dynamics)

FitzHugh-Nagumo, square

3D rabbit ventricular structure

Karma, square

3D canine ventricular structure

FitzHugh-Nagumo, slice of rabbit ventricles

3D porcine ventricular structure


Virtual reality:


Virtual Cardiac Museum


Cardiac Anatomical Structures




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