Model Mathematics

Component: environment

Component: OB_p

ddtime OB_p = D_OB_u TGF_beta K_D1_TGF_beta + TGF_beta - D_OB_p OB_p 1 1 + TGF_beta K_D2_TGF_beta

Component: OB_a

ddtime OB_a = D_OB_p OB_p 1 1 + TGF_beta K_D2_TGF_beta - A_OB_a OB_a

Component: OC_a

ddtime OC_a = D_OC_p OC_p pi_RANKL_act_OC_p - A_OC_a OC_a TGF_beta K_D3_TGF_beta + TGF_beta

Component: BV

ddtime BV = k_form OB_a_tilde - k_res OC_a_tilde OC_a_tilde = OC_a - OC_a_initial OB_a_tilde = OB_a - OB_a_initial

Component: TGF_beta

TGF_beta = alpha k_res OC_a + S_TGF_beta D_TGF_beta_tilde

Component: PTH

PTH = beta_PTH + P_PTH_d D_PTH_tilde pi_PTH_act_OB_p = PTH K_D4_PTH + PTH pi_PTH_act_OB_a = PTH K_D5_PTH + PTH pi_PTH_rep_OB_p = 1 1 + PTH K_D6_PTH pi_PTH_rep_OB_a = 1 1 + PTH K_D7_PTH

Component: OPG

OPG = beta1_OPG OB_p + beta2_OPG OB_a pi_PTH_rep_OB + P_OPG_d beta1_OPG OB_p + beta2_OPG OB_a pi_PTH_rep_OB OPG_max + D_OPG_tilde P_OPG_e = beta1_OPG OB_p + beta2_OPG OB_a pi_PTH_rep_OB 1 - OPG OPG_max pi_PTH_rep_OB = pi_PTH_rep_OB_p

Component: RANKL

RANKL = RANKL_eff 1 + K_A1_RANKL OPG + K_A2_RANKL RANK beta_RANKL + P_RANKL_d beta_RANKL + D_RANKL_tilde RANKL_eff RANKL_eff = R1_RANKL OB_p + R2_RANKL OB_a pi_PTH_act_OB RANKL_tot = RANKL 1 + K_A1_RANKL OPG + K_A2_RANKL RANK pi_RANKL_act_OC_p = RANKL K_D8_RANKL + RANKL P_RANKL = P_RANKL_e + P_RANKL_d P_RANKL_e = beta_RANKL 1 - RANKL_tot RANKL_eff D_RANKL =- D_RANKL_tilde RANKL_tot pi_PTH_act_OB = pi_PTH_act_OB_p

Component: model_parameters