# Model Mathematics

### Component: membrane

$dd time V =- i_Na + i_Ca + i_to + i_K + i_K1 + i_b_Na + i_b_Ca + i_NaCa + i_NaK + rho_x ⁢ S -1.0 ⁢ V_x2 + rho_y ⁢ S -1.0 ⁢ V_y2 Cm ∂ 2.0 ∂ x 2.0 V = V_x2 ∂ 2.0 ∂ y 2.0 V = V_y2$

### Component: sodium_current

$i_Na = g_Na ⁢ m 3.0 ⁢ v 2.0 ⁢ V - E_Na E_Na = R ⁢ T F ⁢ln⁡ Na_e Na_i$

### Component: sodium_current_m_gate

$dd time m = alpha_m ⁢ 1.0 - m - beta_m ⁢ m alpha_m = 0.32 ⁢ V + 47.13 1.0 -ⅇ -0.1 ⁢ V + 47.13 beta_m = 0.08 ⁢ⅇ- V 11.0$

### Component: sodium_current_v_gate

$dd time v = v_infinity - v tau_v v_infinity = 0.5 ⁢ 1.0 -tanh⁡ 7.74 + V ⁢ 0.12 tau_v = 0.25 + 2.24 ⁢ 1.0 -tanh⁡ 7.74 + V ⁢ 0.12 1.0 -tanh⁡ 0.07 ⁢ V + 92.4$

### Component: calcium_current

$i_Ca = g_Ca ⁢ d_infinity ⁢ f ⁢ f_Ca ⁢ V - E_Ca E_Ca = R ⁢ T 2.0 ⁢ F ⁢ln⁡ Ca_e Ca_i$

### Component: calcium_current_d_gate

$d_infinity = alpha_d alpha_d + beta_d alpha_d = 14.98 ⁢ⅇ- 0.5 ⁢ V - 22.36 16.68 2.0 16.68 ⁢ 2.0 ⁢π beta_d = 0.1471 - 5.3 ⁢ⅇ- 0.5 ⁢ V - 6.27 14.93 2.0 14.93 ⁢ 2.0 ⁢π$

### Component: calcium_current_f_gate

$dd time f = alpha_f ⁢ 1.0 - f - beta_f ⁢ f alpha_f =6.87e-3 1.0 +ⅇ- 6.1546 - V 6.12 beta_f = 0.069 ⁢ⅇ -11.0 ⁢ V + 9.825 + 0.011 1.0 +ⅇ -0.278 ⁢ V + 9.825 +5.75e-4$

### Component: calcium_current_f_Ca_gate

$f_Ca = 1.0 1.0 + Ca_i 0.0006$

### Component: transient_outward_current

$i_to = g_to ⁢ r_infinity ⁢ to ⁢ V - E_to E_to = R ⁢ T F ⁢ln⁡ 0.043 ⁢ Na_e + K_e 0.043 ⁢ Na_i + K_i$

### Component: transient_outward_current_r_gate

$r_infinity = alpha_r alpha_r + beta_r alpha_r = 0.5266 ⁢ⅇ- 0.0166 ⁢ V - 42.2912 1.0 +ⅇ- 0.0943 ⁢ V - 42.2912 beta_r =5.186e-5⁢ V + 0.5149 ⁢ⅇ- 0.1344 ⁢ V - 5.0027 1.0 +ⅇ- 0.1348 ⁢ V -5.186e-5$

### Component: transient_outward_current_to_gate

$dd time to = alpha_to ⁢ 1.0 - to - beta_to ⁢ to alpha_to =5.612e-5⁢ V + 0.0721 ⁢ⅇ -0.173 ⁢ V + 34.2531 1.0 +ⅇ -0.1732 ⁢ V + 34.2531 beta_to =1.215e-4⁢ V + 0.0767 ⁢ⅇ1.66e-9⁢ V + 34.0235 1.0 +ⅇ- 0.1604 ⁢ V + 34.0235 tau_to = 1.0 p ⁢ alpha_to ⁢ V + p ⁢ beta_to ⁢ V to_infinity = alpha_to ⁢ V - V_shift alpha_to ⁢ V - V_shift + beta_to ⁢ V - V_shift$

### Component: delayed_rectifier_potassium_current

$i_K = g_K ⁢ X 2.0 ⁢ V - E_K E_K = R ⁢ T F ⁢ln⁡ K_e K_i$

### Component: delayed_rectifier_potassium_current_X_gate

$dd time X = X_infinity - X tau_X X_infinity = 0.988 1.0 +ⅇ -0.861 - V ⁢ 0.0620 tau_X = 240.0 ⁢ⅇ- 25.5 + V 2.0 156.0 + 182.0 ⁢ 1.0 +tanh⁡ 0.154 + 0.0116 ⁢ V + tau_X_a tau_X_a = 40.0 ⁢ 1.0 -tanh⁡ 160.0 + 2.0 ⁢ V$

### Component: inward_rectifier_potassium_current

$i_K1 = g_K1 ⁢ K1_infinity ⁢ V - E_K$

### Component: inward_rectifier_potassium_current_K1_gate

$K1_infinity = alpha_K1 alpha_K1 + beta_K1 alpha_K1 = 0.1 1.0 +ⅇ 0.06 ⁢ V - E_K + 200.0 beta_K1 = 3.0 ⁢ⅇ2.0e-4⁢ V + 100.0 +- E_K +ⅇ 0.1 ⁢ V - 10.0 + E_K 1.0 +ⅇ- 0.5 ⁢ V - E_K$

### Component: calcium_background_current

$i_b_Ca = g_b_Ca ⁢ V - E_Ca$

### Component: sodium_background_current

$i_b_Na = g_b_Na ⁢ V - E_Na$

### Component: sodium_potassium_pump

$i_NaK = g_NaK ⁢ f_NaK ⁢ f_NaK_a f_NaK = 1.0 1.0 + 0.1245 ⁢ⅇ -0.0037 ⁢ V + 0.0365 ⁢ sigma ⁢ⅇ -0.037 ⁢ V f_NaK_a = 1.0 1.0 + 10.0 Na_i 1.5 ⁢ K_e K_e + 1.5 sigma = 0.1428 ⁢ⅇ Na_e 67.3 - 1.0$

### Component: sodium_calcium_pump

$i_NaCa = g_NaCa ⁢ f_NaCa f_NaCa = 87.5 3.0 + Na_e 3.0 -1.0 ⁢ 1.38 + Ca_e -1.0 ⁢ 1.0 + 0.1 ⁢ⅇ -0.024 ⁢ V -1.0 ⁢ Na_i 3.0 ⁢ Ca_e ⁢ⅇ 0.013 ⁢ V - Na_e 3.0 ⁢ Ca_i ⁢ⅇ -0.024 ⁢ V$

### Component: ionic_concentrations

Source
Derived from workspace Bernus, Wilders, Zemlin, Verschelde, Panfilov, 2002 at changeset 1503a0990dcc.
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