## Noble model

The Noble model (1962) was the first mathematical model of cardiac action potentials V dynamics [1,2]. It was a development from the Hodgkin-Huxley model
dV/dt = -(iK + iNa + iAn )/Cm ,
iK = (1.2 n4 + 1.2 exp[(-V - 90)/50] + 0.015 exp[(V+90)/60])(V + 100),
iNa = 120 (400 m3h + 0.14)(V - 40),
iAn = 0 (V + 60),
dy/dt = αy - (αy + βy )y = (y - y)/τy ,     τy = 1/(αy + βy ),     y = αy /(αy + βy ),

where y is m, h or n gate, iAn is anions (chloride) current, Cm = 12 μF/cm2.
 αn = 0.0001 (-V - 50) / (exp[(-V - 50)/10] - 1), βn = 0.002 exp[(-V - 90)/80], αm = 0.1 (-V - 48) / (exp[(-V - 48)/15] - 1), βm = 0.12 (V + 8) / (exp[(V + 8)/5] - 1), αh = 0.17 exp[(-V - 90)/20)], βh = 1 / (exp[(-V - 42)/10] + 1).
m(V), h(V), n(V) and 4 τm(V), τh(V)/10, τn(V)/600 ms are ploted below

here -100 ≤ V ≤ 50 (mV), 0 ≤ y ≤ 1. So the minimal times are τm (-85) ~ 0.1,   τh ~ 1,   τn ~ 100 and the maximum one is τn ~ 530 (ms).

You see below V(t) dynamics.
V(mV) Vmin Vmax dt(ms)   it iNa iK

m h n
The script makes 1000 it time steps dt. It is stable for dt ≤ 2 τmin = 0.2 ms (see Integration schemes for the fastest m gate).

[1] D. Noble   A modification of the Hodgkin-Huxley equations applicable to purkinje fibre action and pace-maker potentials   J. Physiol. 160 317 (1962)
[2] Noble model in Scholarpedia
[3] R. Suckley and V. Biktashev   Comparison of asymptotics of heart and nerve excitability   Phys. Rev. E 68 011902 (2003)

Heart rhythms     updated 28 May 2012