# Model Mathematics

### Component: Q_Ca_p

$ddtime Q_Ca_p = J_bp_Ca + J_ip_Ca - J_pb_Ca + J_pu_Ca$

### Component: Q_P_p

$ddtime Q_P_p = J_bp_P + J_ip_P + J_cp_P - J_pb_P + J_pu_P + J_pc_P$

### Component: Q_P_c

$ddtime Q_P_c = J_pc_P - J_cp_P$

### Component: Q_PTH_p

$ddtime Q_PTH_p = S_PTH - k_PTH ⁢ 1.0 ⁢ C_PTH_p$

### Component: Q_Ca_b

$ddtime Q_Ca_b = J_pb_Ca - J_bp_Ca$

### Component: Q_P_b

$ddtime Q_P_b = J_pb_P - J_bp_P$

### Component: Q_E_k

$ddtime Q_E_k = S_E - k_E ⁢ Q_E_k$

### Component: Q_D_p

$ddtime Q_D_p = 1.0 ⁢ Q_E_k - k_D ⁢ Q_D_p$

### Component: Q_TCa_i

$ddtime Q_TCa_i = 1.0 - Q_TCa_i ⁢ k1_D - Q_TCa_i ⁢ k2_D$

### Component: Q_C_PT

$ddtime Q_C_PT = 1.0 - Q_C_PT ⁢ k3_D - Q_C_PT ⁢ k4_D$

### Component: Q_TP_k

$ddtime Q_TP_k = 1.0 - Q_TP_k ⁢ k1_P - Q_TP_k ⁢ k2_P$

### Component: model_fluxes

$J_pb_Ca = k_Ca_b ⁢ Q_Ca_b$$J_bp_P = Stoic_Ca_P ⁢ J_bp_Ca$$J_pb_P = Stoic_Ca_P ⁢ J_pb_Ca$$J_ip_Ca = Y_Ca_i_2plus ⁢ 1.0 - Q_TCa_i ⁢ 1.0 ⁢ k1_D + k_Ca_i ⁢ 1.0 ⁢ C_Ca_i - C_Ca_p - Q_TCa_i ⁢ k2_D$$J_ip_P = J_P_ing$$S_PTH = 1.0 ⁢ Y_Ca_p_1minus ⁢ k3_D ⁢ 1.0 - Q_C_PT - k4_D ⁢ Q_C_PT$$J_pc_P = k4_P ⁢ 1.0 ⁢ C_P_p$$J_cp_P = k3_P ⁢ Q_P_c$

### Component: model_parameters

$Ca_thr = 1.95 + Y_PTH_p_2plus$$Ca_T = Ca_thr C_Ca_p$$P_thr = Y_PTH_p_2minus ⁢ Q_TP_k$$P_T = P_thr C_P_p$$k1_D = Y_i_D_p_1plus$$k2_D = Y_i_D_p_1minus$$k3_D = Y_PT_D_p_1plus$$k4_D = Y_PT_D_p_1minus$$k1_P = Y_k_Jext_1plus$$Y_i_D_p_1plus = Y_i_D_p_1plus_minus_Max ⁢ a ⁢ 1.0 +tanh⁡ b_i_D ⁢ C_D_p - X_R_i_D + d$$Y_PT_D_p_1plus = Y_PT_D_p_1plus_minus_Max ⁢ a ⁢ 1.0 +tanh⁡ b_PTH_D ⁢ C_D_p - X_R_PTH_D + d$$Y_k_Jext_1plus = Y_k_Jext_1plus_minus_Max ⁢ a ⁢ 1.0 +tanh⁡ b_E_PTH ⁢ 1.0 ⁢ C_P_p - X_R_E_PTH + d$$Y_Ca_p_1minus = Y_Ca_p_1plus_minus_Max ⁢ a ⁢ 1.0 -tanh⁡ b_PTH_Ca ⁢ C_Ca_p - X_R_PTH_Ca + d$$Y_i_D_p_1minus = Y_i_D_p_1plus_minus_Max ⁢ a ⁢ 1.0 -tanh⁡ b_i_D ⁢ C_D_p - X_R_i_D + d$$Y_PT_D_p_1minus = Y_PT_D_p_1plus_minus_Max ⁢ a ⁢ 1.0 -tanh⁡ b_PTH_D ⁢ C_D_p - X_R_PTH_D + d$$Y_Ca_i_2plus = Y_Ca_i_2plus_Max ⁢ C_Ca_i C_Ca_i + X_R_i_Ca$$Y_PTH_p_2plus = Y_PTH_p_2plus_Max ⁢ C_PTH_p C_PTH_p + 1.0 ⁢ X_R_P_k_PTH$$Y_PTH_p_2minus = Y_PTH_p_2minus_Max ⁢ X_R_P_k_PTH 1.0 ⁢ C_PTH_p + X_R_P_k_PTH$
Source
Derived from workspace Raposo, Sobrinho and Ferreira, 2002 at changeset 3dcc0383f024.
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