# Model Mathematics

### Component: membrane

$dd time V =Istim- i_Na + i_s + i_x1 + i_K1 C$$IStimC=Istim$

### Component: fast_sodium_current

$i_Na = g_Na ⁢ m 3.0 ⁢ h ⁢ V - E_Na$

### Component: fast_sodium_current_m_gate

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

### Component: fast_sodium_current_h_gate

$alpha_h = 0.135 ⁢ⅇ -80.0 - V 6.8 if V < -40.0 0.0 otherwise$$beta_h = 3.56 ⁢ⅇ 0.079 ⁢ V + 3.1e5 ⁢ⅇ 0.35 ⁢ V if V < -40.0 1.0 0.13 ⁢ 1.0 +ⅇ- V + 10.66 11.1 otherwise$$dd time h = alpha_h ⁢ 1.0 - h - beta_h ⁢ h$

### Component: slow_inward_current

$E_s = -82.3 - 13.0287 ⁢ln⁡ Cai ⁢0.001 i_s = g_s ⁢ d ⁢ f ⁢ V - E_s dd time Cai = -0.01 ⁢ i_s + 0.07 ⁢ 0.0001 - Cai$

### Component: slow_inward_current_d_gate

$alpha_d = 0.095 ⁢ⅇ- V - 5.0 100.0 1.0 +ⅇ- V - 5.0 13.89 beta_d = 0.07 ⁢ⅇ- V + 44.0 59.0 1.0 +ⅇ V + 44.0 20.0 dd time d = alpha_d ⁢ 1.0 - d - beta_d ⁢ d$

### Component: slow_inward_current_f_gate

$alpha_f = 0.012 ⁢ⅇ- V + 28.0 125.0 1.0 +ⅇ V + 28.0 6.67 beta_f = 0.0065 ⁢ⅇ- V + 30.0 50.0 1.0 +ⅇ- V + 30.0 5.0 dd time f = alpha_f ⁢ 1.0 - f - beta_f ⁢ f$

### Component: time_dependent_outward_current

$i_x1 = x1 ⁢ 8.0e-3 ⁢ⅇ 0.04 ⁢ V + 77.0 - 1.0 ⅇ 0.04 ⁢ V + 35.0$

### Component: time_dependent_outward_current_x1_gate

$alpha_x1 = 0.0005 ⁢ⅇ V + 50.0 12.1 1.0 +ⅇ V + 50.0 17.5 beta_x1 = 0.0013 ⁢ⅇ- V + 20.0 16.67 1.0 +ⅇ- V + 20.0 25.0 dd time x1 = alpha_x1 ⁢ 1.0 - x1 - beta_x1 ⁢ x1$

### Component: time_independent_outward_current

$i_K1 = 0.0035 ⁢ 4.0 ⁢ⅇ 0.04 ⁢ V + 85.0 - 1.0 ⅇ 0.08 ⁢ V + 53 +ⅇ 0.04 ⁢ V + 53.0 + 0.2 ⁢ V + 23.0 1.0 -ⅇ -0.04 ⁢ V + 23.0$
Source
Derived from workspace Ebihara, Johnson, 1980 at changeset 276e14b37407.
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