Model Mathematics

\frac{d}{d time} (Q_Ca_p) = J_bp_Ca + J_ip_Ca - (J_pb_Ca + J_pu_Ca)

\frac{d}{d time} (Q_P_p) = J_bp_P + J_ip_P + J_cp_P - (J_pb_P + J_pu_P + J_pc_P)

\frac{d}{d time} (Q_P_c) = J_pc_P - J_cp_P

\frac{d}{d time} (Q_PTH_p) = S_PTH - (k_PTH 1.0 C_PTH_p)

\frac{d}{d time} (Q_Ca_b) = J_pb_Ca - J_bp_Ca

\frac{d}{d time} (Q_P_b) = J_pb_P - J_bp_P

\frac{d}{d time} (Q_E_k) = S_E - (k_E Q_E_k)

\frac{d}{d time} (Q_D_p) = 1.0 Q_E_k - (k_D Q_D_p)

\frac{d}{d time} (Q_TCa_i) = (1.0 - Q_TCa_i) k1_D - (Q_TCa_i k2_D)

\frac{d}{d time} (Q_C_PT) = (1.0 - Q_C_PT) k3_D - (Q_C_PT k4_D)

\frac{d}{d time} (Q_TP_k) = (1.0 - Q_TP_k) k1_P - (Q_TP_k k2_P)

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

Ca_thr = 1.95 + Y_PTH_p_2plus

Ca_T = \frac{Ca_thr}{C_Ca_p}

P_thr = Y_PTH_p_2minus Q_TP_k

P_T = \frac{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 \frac{C_Ca_i}{C_Ca_i + X_R_i_Ca}

Y_PTH_p_2plus = Y_PTH_p_2plus_Max \frac{C_PTH_p}{C_PTH_p + 1.0 X_R_P_k_PTH}

Y_PTH_p_2minus = Y_PTH_p_2minus_Max \frac{X_R_P_k_PTH}{1.0 C_PTH_p + X_R_P_k_PTH}