You are here: Home / Exposures / Miftakhov, Abdusheva, Christensen, 1999 / Numerical Simulation of Motility Patterns of the Small Bowel. I. Formulation of a Mathematical Model

Model Mathematics

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Component: environment

Component: model_constants

Component: membrane

\frac{d}{d time} (V) = (- (\frac{1.0}{Cm alpha})) (i_Ca_T + i_Ca_L + i_Ca_K + i_K + i_Cl)

Component: gate_voltage

V_tilde = \frac{127.0 V + 8265.0}{105.0}

Component: T_type_calcium_current

i_Ca_T = g_Ca_T m^{3.0} h (V - E_Ca)

Component: T_type_calcium_current_m_gate

alpha_m = \frac{0.1 (50.0 - V_tilde)}{ⅇ^{5.0 - (V_tilde 0.1)} - 1.0} beta_m = 4.0 ⅇ^{\frac{25.0 - V_tilde}{18.0}} m = \frac{alpha_m}{alpha_m + beta_m}

Component: T_type_calcium_current_h_gate

alpha_h = 0.07 ⅇ^{\frac{25.0 - V_tilde}{20.0}} beta_h = \frac{1.0}{1.0 + ⅇ^{5.5 - (V_tilde 0.1)}} \frac{d}{d time} (h) = \frac{alpha_h (1.0 - h) - (beta_h h)}{alpha lamda}

Component: L_type_calcium_current

i_Ca_L = g_Ca_L x_Ca (V - E_Ca)

Component: L_type_calcium_current_x_Ca_gate

\frac{d}{d time} (x_Ca) = \frac{\frac{1.0}{1.0 + ⅇ^{0.15 (- V_tilde - 50.0)}} - x_Ca}{alpha tau_x_Ca}

Component: potassium_current

i_K = g_K n^{4.0} (V - E_K)

Component: potassium_current_n_gate

alpha_n = \frac{0.01 (55.0 - V_tilde)}{ⅇ^{\frac{55.0 - V_tilde}{10.0}} - 1.0} beta_n = 0.125 ⅇ^{\frac{45.0 - V_tilde}{80.0}} \frac{d}{d time} (n) = \frac{alpha_n (1.0 - n) - (beta_n n)}{alpha lamda}

Component: calcium_activated_potassium_current

i_Ca_K = \frac{g_Ca_K Ca (V - E_K)}{0.5 + Ca} \frac{d}{d time} (Ca) = \frac{rho}{alpha} (K_c x_Ca (E_Ca - V) - Ca)

Component: leak_chloride_current

i_Cl = g_Cl (V - E_Cl)

Source: Derived from workspace Miftakhov, Abdusheva, Christensen, 1999 at changeset ffc28b0c98c8.

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Numerical Simulation of Motility Patterns of the Small Bowel. I. Formulation of a Mathematical Model