You are here: Home / Exposures / Fenton, Karma, 1998 / Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: Filament instability and fibrillation (MLR_1 Model)

Model Mathematics

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Component: environment

Component: stimulus_protocol

Istim = \{\begin{matrix} IstimAmplitude if time \geq IstimStart \land time ≦ IstimEnd \land time - IstimStart - (⌊ \frac{time - IstimStart}{IstimPeriod} ⌋ IstimPeriod) ≦ IstimPulseDuration \\ 0 otherwise \end{matrix}

Component: membrane

\frac{d}{d time} (u) = - (J_fi + J_so + J_si + J_stim) Vm = V_0 + u (V_fi - V_0)

Component: p

p = \{\begin{matrix} 0 if u < u_c \\ 1 otherwise \end{matrix}

Component: q

q = \{\begin{matrix} 0 if u < u_v \\ 1 otherwise \end{matrix}

Component: fast_inward_current

tau_d = \frac{Cm}{g_fi_max} J_fi = \frac{(- v) p (1 - u) (u - u_c)}{tau_d}

Component: fast_inward_current_v_gate

tau_v_minus = q tau_v1_minus + (1 - q) tau_v2_minus \frac{d}{d time} (v) = \frac{(1 - p) (1 - v)}{tau_v_minus} - (\frac{p v}{tau_v_plus})

Component: slow_outward_current

J_so = \frac{u (1 - p)}{tau_0} + \frac{p}{tau_r}

Component: slow_inward_current

J_si = \frac{(- w) (1 + \tanh (k (u - u_csi)))}{2 tau_si}

Component: slow_inward_current_w_gate

\frac{d}{d time} (w) = \frac{(1 - p) (1 - w)}{tau_w_minus} - (\frac{p w}{tau_w_plus})

Source: Derived from workspace Fenton, Karma, 1998 at changeset 129998a1e151.

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