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Model Mathematics

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Component: environment

Component: membrane

\frac{d}{d time} (V) = \frac{Istim - (i_Na + i_s + i_x1 + i_K1)}{C}

Component: sodium_current

i_Na = (g_Na m^{3} h j + g_Nac) (V - E_Na)

Component: sodium_current_m_gate

alpha_m = \frac{(- 1) (V + 47)}{ⅇ^{(- 0.1) (V + 47)} - 1} beta_m = 40 ⅇ^{(- 0.056) (V + 72)} \frac{d}{d time} (m) = alpha_m (1 - m) - (beta_m m)

Component: sodium_current_h_gate

alpha_h = 0.126 ⅇ^{(- 0.25) (V + 77)} beta_h = \frac{1.7}{ⅇ^{(- 0.082) (V + 22.5)} + 1} \frac{d}{d time} (h) = alpha_h (1 - h) - (beta_h h)

Component: sodium_current_j_gate

alpha_j = \frac{0.055 ⅇ^{(- 0.25) (V + 78)}}{ⅇ^{(- 0.2) (V + 78)} + 1} beta_j = \frac{0.3}{ⅇ^{(- 0.1) (V + 32)} + 1} \frac{d}{d time} (j) = alpha_j (1 - j) - (beta_j j)

Component: slow_inward_current

E_s = - 82.3 - (13.0287 \ln (Cai 0.001)) i_s = g_s d f (V - E_s) \frac{d}{d time} (Cai) = \frac{(- 0.01) i_s}{1} + 0.07 (0.0001 - Cai)

Component: slow_inward_current_d_gate

alpha_d = \frac{0.095 ⅇ^{\frac{- (V - 5)}{100}}}{1 + ⅇ^{\frac{- (V - 5)}{13.89}}} beta_d = \frac{0.07 ⅇ^{\frac{- (V + 44)}{59}}}{1 + ⅇ^{\frac{V + 44}{20}}} \frac{d}{d time} (d) = alpha_d (1 - d) - (beta_d d)

Component: slow_inward_current_f_gate

alpha_f = \frac{0.012 ⅇ^{\frac{- (V + 28)}{125}}}{1 + ⅇ^{\frac{V + 28}{6.67}}} beta_f = \frac{0.0065 ⅇ^{\frac{- (V + 30)}{50}}}{1 + ⅇ^{\frac{- (V + 30)}{5}}} \frac{d}{d time} (f) = alpha_f (1 - f) - (beta_f f)

Component: time_dependent_outward_current

x1_open ~ p.d.f. (λ x: (\frac{1}{\sqrt{2 π 1 e -6}} ⅇ^{\frac{- ({(x - 8 e -3)}^{2})}{2 1 e -6}}))

i_x1 = \frac{x1 x1_open (ⅇ^{0.04 (V + 77)} - 1)}{ⅇ^{0.04 (V + 35)}}

Component: time_dependent_outward_current_x1_gate

alpha_x1 = \frac{5 e -4 ⅇ^{\frac{V + 50}{12.1}}}{1 + ⅇ^{\frac{V + 50}{17.5}}} beta_x1 = \frac{0.0013 ⅇ^{\frac{- (V + 20)}{16.67}}}{1 + ⅇ^{\frac{- (V + 20)}{25}}} \frac{d}{d time} (x1) = alpha_x1 (1 - x1) - (beta_x1 x1)

Component: time_independent_outward_current

i_K1 = 0.0035 (\frac{4 (ⅇ^{0.04 (V + 85)} - 1)}{ⅇ^{0.08 (V + 53)} + ⅇ^{0.04 (V + 53)}} + \frac{0.2 (V + 23)}{1 - (ⅇ^{(- 0.04) (V + 23)})})

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}

Source: Derived from workspace Beeler, Reuter, 1977 uncertainty example at changeset b5412f13ad89.

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Reconstruction of the action potential of ventricular myocardial fibres, with modifications to demonstrate uncertainty.