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Model Mathematics

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Component: environment

Component: membrane

i_Stim = \{\begin{matrix} stim_amplitude if time \geq stim_start \land time ≦ stim_end \land time - stim_start - (⌊ \frac{time - stim_start}{stim_period} ⌋ stim_period) ≦ stim_duration \\ 0 otherwise \end{matrix} \frac{d}{d time} (V) = - (i_ns + i_Kur + i_to + i_K1 + i_b_Na + i_NaK + i_Stim)

Component: non_specific_current

i_ns = g_ns V

Component: transient_outward_K_current

E_K = RToF \ln (\frac{K_c}{K_i}) i_to = g_to {oa}^{3} oi (V - E_K)

Component: transient_outward_K_current_oa_gate

alpha_oa = \frac{0.65}{ⅇ^{\frac{V + 10}{- 8.5}} + ⅇ^{\frac{V - 30}{- 59}}} beta_oa = \frac{0.65}{2.5 + ⅇ^{\frac{V + 82}{17}}} oa_inf = \frac{1}{1 + ⅇ^{\frac{V + 20.47}{- 17.54}}} tau_oa = \frac{15}{alpha_oa + beta_oa} \frac{d}{d time} (oa) = \frac{oa_inf - oa}{tau_oa}

Component: transient_outward_K_current_oi_gate

alpha_oi = \frac{1}{18.53 + ⅇ^{\frac{V + 113.7}{10.95}}} beta_oi = \frac{1}{35.56 + ⅇ^{\frac{V + 1.26}{- 7.44}}} oi_inf = \frac{1}{1 + ⅇ^{\frac{V + 43.1}{5.3}}} tau_oi = \frac{15}{alpha_oi + beta_oi} \frac{d}{d time} (oi) = \frac{oi_inf - oi}{tau_oi}

Component: ultra_rapid_K_current

i_Kur = (g_Kur 0.005 + \frac{0.05}{1 + ⅇ^{\frac{- (V - 15)}{13}}}) {ua}^{3} ui (V - E_K)

Component: ultra_rapid_K_current_ua_gate

alpha_ua = \frac{0.65}{ⅇ^{\frac{V + 10}{- 8.5}} + ⅇ^{\frac{V - 30}{- 59}}} beta_ua = \frac{0.65}{2.5 + ⅇ^{\frac{V + 82}{17}}} ua_inf = \frac{1}{1 + ⅇ^{\frac{V + 33.3}{- 9.6}}} tau_ua = \frac{1}{alpha_ua + beta_ua} \frac{d}{d time} (ua) = \frac{ua_inf - ua}{tau_ua}

Component: ultra_rapid_K_current_ui_gate

alpha_ui = \frac{1}{21 + ⅇ^{\frac{V - 185}{28}}} beta_ui = \frac{1}{ⅇ^{\frac{V - 158}{- 16}}} ui_inf = \frac{1}{1 + ⅇ^{\frac{V - 99.45}{27.48}}} tau_ui = \frac{5}{alpha_ui + beta_ui} \frac{d}{d time} (ui) = \frac{ui_inf - ui}{tau_ui}

Component: inward_rectifier

i_K1 = \frac{g_K1 (V + 86.75)}{1 + ⅇ^{\frac{V + 20}{20}}}

Component: background_currents

E_Na = RToF \ln (\frac{Na_c}{Na_i}) i_b_Na = g_b_Na (V - E_Na)

Component: sodium_potassium_pump

i_NaK = \frac{\frac{\frac{i_NaK_max K_c}{K_c + k_NaK_K} {Na_i}^{1.5}}{{Na_i}^{1.5} + {k_NaK_Na}^{1.5}} (V - V_rev)}{V - B}

Source: Derived from workspace Atrial fibroblast model at changeset ecea16d65843.

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Morgan atrial fibroblast 2016.cellml