Model Mathematics

\frac{d}{d time} (OB_p) = (D_OB_u pi_TGF_beta_act - (D_OB_p pi_TGF_beta_rep OB_p)) + pd_OB_p

\frac{d}{d time} (OB_a) = (D_OB_p pi_TGF_beta_rep OB_p - (A_OB_a OB_a)) + pd_OB_a

\frac{d}{d time} (OC_a) = (D_OC_p pi_RANKL_act - (A_OC_a pi_TGF_beta_act OC_a)) + pd_OC_a D_OC_p = \{\begin{matrix} 2.100 e -2 if time > 0.0 \land time ≦ 100.0 \\ 2.100 e -3 otherwise \end{matrix}

\frac{d}{d time} (BV) = k_form (OB_a - OB_a_initial) - (k_res (OC_a - OC_a_initial))

TGF_beta = \frac{alpha k_res OC_a + S_TGF_beta}{Deg_TGF_beta} pi_TGF_beta_act = \frac{TGF_beta}{KD_TGF_activate + TGF_beta} pi_TGF_beta_rep = \frac{1}{1 + \frac{TGF_beta}{KD_TGF_repress}}

PTH_tot = \frac{beta_PTH + P_PTH_d}{Deg_PTH} pi_PTH_act = \frac{PTH_tot}{PTH_tot + KD_PTH_activate} pi_PTH_rep = \frac{1}{1 + \frac{PTH_tot}{KD_PTH_repress}}

OPG_eff = (beta1_OB_p_OPG beta_OPG OB_p + beta2_OB_a_OPG beta_OPG OB_a) pi_PTH_rep OPG = \frac{OPG_eff + P_OPG_d}{\frac{OPG_eff}{OPG_max} + Deg_OPG} prod_OPG = OPG_eff (1 - (\frac{OPG}{OPG_max})) + P_OPG_d Degr_OPG = Deg_OPG OPG

RANKL_eff = (K_RANKL_OB_p OB_p + K_RANKL_OB_a OB_a) pi_PTH_act RANKL_tot = RANKL (1 + K_A1_RANKL OPG + K_A2_RANKL RANK) RANKL = \frac{\frac{RANKL_eff}{1 + K_A1_RANKL OPG + K_A2_RANKL RANK} (beta_RANKL + P_RANKL_d)}{beta_RANKL + Deg_RANKL RANKL_eff} K_RANKL_OB_p = R1_OB_p_RANKL R_RANKL K_RANKL_OB_a = R2_OB_a_RANKL R_RANKL pd_RANKL = (beta_RANKL (1 - (\frac{RANKL_tot}{RANKL_eff})) - (Deg_RANKL RANKL_tot)) + P_RANKL_d pi_RANKL_act = \frac{RANKL}{KD_RANKL_activate + RANKL} OPG_RANKL = K_A1_RANKL OPG RANKL RANKL_RANK = K_A2_RANKL RANKL RANK