HPC Tier Module
Cardiac Monodomain Wave Propagation
Propagate a cardiac excitation wave and verify its speed against the exact Nagumo front - in the browser.
This tool runs inside GDBS HPC. What it computes and the authorities it applies are below.
The problem
Excitable-media and reaction-diffusion teaching needs a propagation solver whose measured conduction velocity can be checked against an exact law, rather than a simulation that merely looks like a moving wave.
The local-first solution
This plugin solves the cited monodomain equation with a finite-difference Laplacian in exact f64, measures the front conduction velocity by tracking the level set, and compares it to the closed-form Nagumo front speed - all deterministic and in your browser with nothing uploaded.
What it does
5-point (2D) / 3-point (1D) Laplacian with forward-Euler diffusion updates
Nagumo bistable cubic with its exact front speed c = sqrt(DA/2)(1-2a)
FitzHugh-Nagumo two-variable excitable kinetics for pulse and refractory demos
Measures conduction velocity from the V = 1/2 level set vs the closed form
Demonstrates counter-propagating-front annihilation and refractory non-re-excitation
Charts the wavefront profile and CV-vs-D against c ~ sqrt(D)
Honest scope
Exact: the Laplacian stencil, the forward-Euler update, the stability number, the Nagumo cubic and its closed-form front speed, and the FitzHugh-Nagumo right-hand side. It assumes a scalar isotropic monodomain with phenomenological 1-2 variable kinetics standing in for full ionic membrane channels, dimensionless units, and zero-flux boundaries; it does not model true ionic currents, anisotropy, the bidomain field, mechano-electric feedback, or 3D geometry, and reported velocity is in model units, not tissue ms^-1. Research and education only - not a medical device and not for clinical, diagnostic, or treatment decisions.
Authorities cited
- FitzHugh, R. (1961). Impulses and Physiological States in Theoretical Models of Nerve Membrane. Biophysical Journal 1(6), 445-466. DOI 10.1016/S0006-3495(61)86902-6. - the FitzHugh-Nagumo two-variable excitable model f = V - V^3/3 - w + I, g = eps(V + b - c w).
- Nagumo, J., Arimoto, S., Yoshizawa, S. (1962). An Active Pulse Transmission Line Simulating Nerve Axon. Proc. IRE 50(10), 2061-2070. DOI 10.1109/JRPROC.1962.288235. - the bistable Nagumo cubic and the propagating active pulse.
- Keener, J., & Sneyd, J. (2009). Mathematical Physiology, 2nd ed. Springer. - the cable / monodomain equation and conduction (Ch. 12); the bistable front and its closed-form speed c = sqrt(D A/2)(1-2a) (sec 9.1, eqn 9.30); counter-propagating-wave annihilation (sec 12.2). DOI 10.1007/978-0-387-75847-3.
- Murray, J. D. (2003). Mathematical Biology II: Spatial Models and Biomedical Applications, 3rd ed. Springer. sec 13.2 - the traveling-wave (tanh/logistic) ansatz for the bistable reaction-diffusion front and its wave speed.
- Clayton, R. H., et al. (2011). Models of cardiac tissue electrophysiology: Progress, challenges and open questions. Progress in Biophysics and Molecular Biology 104(1-3), 22-48. DOI 10.1016/j.pbiomolbio.2010.05.008. - the monodomain reaction-diffusion formulation D = sigma/(beta Cm) and its scope vs the bidomain / full ionic models.
- Strikwerda, J. C. (1989/2004). Finite Difference Schemes and Partial Differential Equations, 2nd ed. SIAM. - von Neumann stability of the explicit (FTCS) diffusion step; the limit r = D dt/h^2 <= 1/2 (1D) / 1/4 (2D) (Thm 6.3.1). DOI 10.1137/1.9780898717938.
- Winfree, A. T. (1987). When Time Breaks Down: The Three-Dimensional Dynamics of Electrochemical Waves and Cardiac Arrhythmias. Princeton Univ. Press. - annihilation of colliding excitation waves and the refractory wake in excitable media.
- LeVeque, R. J. (2007). Finite Difference Methods for ODEs and PDEs. SIAM. - the 5-point Laplacian (sec 3.2) and 2nd-order ghost-node Neumann (zero-flux) boundaries (sec 2.12). DOI 10.1137/1.9780898717839.
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Run the propagation solve
Compute the wave and its conduction-velocity error in your browser, with nothing uploaded to anyone's cloud. Save the run to Sandbox, attach it to a Worklog case, or share parameters through a Gate portal.