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Model Mathematics

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Component: environment

Component: membrane

J_stim = \{\begin{matrix} - 1 if time \geq 100 \land time ≦ 101 \\ 0 otherwise \end{matrix} \frac{d}{d time} (u) = - (J_fi + J_so + J_si + J_stim) Vm = V_0 + u (V_fi - V_0)

Component: m

m = \{\begin{matrix} 0 if u < u_m \\ 1 otherwise \end{matrix}

Component: p

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

Component: q

u_q = \{\begin{matrix} 0.006 if epi = 1 \\ 0.024 if endo = 1 \\ 0.1 otherwise \end{matrix} q = \{\begin{matrix} 0 if u < u_q \\ 1 otherwise \end{matrix}

Component: r

u_r = \{\begin{matrix} 0.006 if epi = 1 \\ 0.006 if endo = 1 \\ 0.005 otherwise \end{matrix} r = \{\begin{matrix} 0 if u < u_r \\ 1 otherwise \end{matrix}

Component: fast_inward_current

u_u = \{\begin{matrix} 1.55 if epi = 1 \\ 1.56 if endo = 1 \\ 1.61 otherwise \end{matrix} tau_fi = \{\begin{matrix} 0.11 if epi = 1 \\ 0.104 if endo = 1 \\ 0.078 otherwise \end{matrix} J_fi = \frac{(- m) v (u - u_m) (u_u - u)}{tau_fi}

Component: fast_inward_current_v_gate

tau_v2_minus = \{\begin{matrix} 1150 if epi = 1 \\ 10 if endo = 1 \\ 1.45 otherwise \end{matrix} tau_v1_minus = \{\begin{matrix} 60 if epi = 1 \\ 75 if endo = 1 \\ 80 otherwise \end{matrix} v_inf = \{\begin{matrix} 1 if u < u_q \\ 0 otherwise \end{matrix} tau_v_minus = q tau_v2_minus + (1 - q) tau_v1_minus \frac{d}{d time} (v) = \frac{(1 - m) (v_inf - v)}{tau_v_minus} - (\frac{m v}{tau_v_plus})

Component: slow_outward_current

tau_o1 = \{\begin{matrix} 400 if epi = 1 \\ 470 if endo = 1 \\ 410 otherwise \end{matrix} tau_o2 = \{\begin{matrix} 6 if epi = 1 \\ 6 if endo = 1 \\ 7 otherwise \end{matrix} tau_so1 = \{\begin{matrix} 30.02 if epi = 1 \\ 40 if endo = 1 \\ 91 otherwise \end{matrix} tau_so2 = \{\begin{matrix} 0.996 if epi = 1 \\ 1.2 if endo = 1 \\ 0.8 otherwise \end{matrix} k_so = \{\begin{matrix} 2.046 if epi = 1 \\ 2 if endo = 1 \\ 2.1 otherwise \end{matrix} u_so = \{\begin{matrix} 0.65 if epi = 1 \\ 0.65 if endo = 1 \\ 0.6 otherwise \end{matrix} tau_o = (1 - r) tau_o1 + r tau_o2 tau_so = tau_so1 + \frac{(tau_so2 - tau_so1) (1 + \tanh (k_so (u - u_so)))}{2} J_so = \frac{u (1 - p)}{tau_o} + \frac{p}{tau_so}

Component: slow_inward_current

tau_si = \{\begin{matrix} 1.8875 if epi = 1 \\ 2.9013 if endo = 1 \\ 3.3849 otherwise \end{matrix} J_si = \frac{(- p) w s}{tau_si}

Component: slow_inward_current_w_gate

tau_winf = \{\begin{matrix} 0.07 if epi = 1 \\ 0.0273 if endo = 1 \\ 0.01 otherwise \end{matrix} wstar_inf = \{\begin{matrix} 0.94 if epi = 1 \\ 0.78 if endo = 1 \\ 0.5 otherwise \end{matrix} tau_w1_minus = \{\begin{matrix} 60 if epi = 1 \\ 6 if endo = 1 \\ 70 otherwise \end{matrix} tau_w2_minus = \{\begin{matrix} 15 if epi = 1 \\ 140 if endo = 1 \\ 8 otherwise \end{matrix} k_w_minus = \{\begin{matrix} 65 if epi = 1 \\ 200 if endo = 1 \\ 200 otherwise \end{matrix} u_w_minus = \{\begin{matrix} 0.03 if epi = 1 \\ 0.016 if endo = 1 \\ 0.016 otherwise \end{matrix} tau_w_plus = \{\begin{matrix} 200 if epi = 1 \\ 280 if endo = 1 \\ 280 otherwise \end{matrix} w_inf = (1 - r) (1 - (\frac{u 1}{tau_winf})) + r wstar_inf tau_w_minus = tau_w1_minus + \frac{(tau_w2_minus - tau_w1_minus) (1 + \tanh (k_w_minus (u - u_w_minus)))}{2} \frac{d}{d time} (w) = \frac{(1 - r) (w_inf - w)}{tau_w_minus} - (\frac{r w}{tau_w_plus})

Component: slow_inward_current_s_gate

tau_s2 = \{\begin{matrix} 16 if epi = 1 \\ 2 if endo = 1 \\ 4 otherwise \end{matrix} tau_s = (1 - p) tau_s1 + p tau_s2 \frac{d}{d time} (s) = \frac{\frac{1 + \tanh (k_s (u - u_s))}{2} - s}{tau_s}

Source: Derived from workspace Bueno, 2007 at changeset b1ca358bc87d.; This exposure was expired. A more up-to-date exposure is available, or view related resources.

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Mathematical modeling and spectral simulation of genetic diseases in the human heart