Asaumi R, Toshimoto K, Tobe Y, Hashizume K, Nunoya KI, Imawaka H, Lee W,
Sugiyama Y. Comprehensive PBPK Model of Rifampicin for Quantitative Prediction of
Complex Drug-Drug Interactions: CYP3A/2C9 Induction and OATP Inhibition Effects.
CPT Pharmacometrics Syst Pharmacol. 2018 Mar;7(3):186-196. doi:
10.1002/psp4.12275. Epub 2018 Feb 5. PubMed PMID: 29368402; PubMed Central PMCID:
PMC5869557.
library(depot)
library(dplyr)
mod <- depot("rifampicin", end = 200, delta = 0.1)e <- ev(amt = 600, ii = 24, total = 7)
e
. Events:
. time cmt amt evid ii addl
. 1 0 1 600 1 24 6
out <- mod %>% mrgsim_e(e, add = 0.05)
plot(out, Ccentral ~ time)
[ PROB ]
1: Asaumi R, Toshimoto K, Tobe Y, Hashizume K, Nunoya KI, Imawaka H, Lee W,
Sugiyama Y. Comprehensive PBPK Model of Rifampicin for Quantitative Prediction of
Complex Drug-Drug Interactions: CYP3A/2C9 Induction and OATP Inhibition Effects.
CPT Pharmacometrics Syst Pharmacol. 2018 Mar;7(3):186-196. doi:
10.1002/psp4.12275. Epub 2018 Feb 5. PubMed PMID: 29368402; PubMed Central PMCID:
PMC5869557.
[ PARAM ]
Rdif = 0.129
beta = 0.2 // 0.2/0.5/0.8
gamma = 0.778
Km_u_uptake = 0.146 // 1.23 // ug/mL
SFKp = 6.65 // 1 // KpScaleRif
Emax_UGT_RIF = 1.34 // 1.00
EC50_u_UGT_RIF = 0.0526 // ug/mL
Emax_CYP3A4_RIF = 4.57 // 12.3
EC50_u_CYP3A4_RIF = 0.05 // ug/mL
kdeg_UGT_liver = 0.0158 // per h
kdeg_CYP3A4_liver = 0.0158 // per h
kdeg_UGT_ent = 0.0288 // per h
fm_UGT_liver = 0.759 // same
fm_UGT_ent = 0.759 // same
[ PARAM ]
fB = 0.0778
fH = 0.0814
fE = 0.115
Fa = 1.000
Fg = 0.943
[ PARAM ]
Kp_skin = 0.326
Kp_muscle = 0.0947
Kp_adipose = 0.0629
Kp_serosa = 0.200
[PARAM]
fBCLint_all_kg = 0.251 // 0.204 // L/h/kg
PSdif_E_kg = 0.161 // 0.143 // L/h/kg
CLrenal_kg = 0.011 // L/h/kg
[ PARAM ]
Qvilli_kg = 0.257 // L/hr/kg
Qh_kg = 1.24 // L/hr/kg
Qmuscle_kg = 0.642 // L/h/kg
Qskin_kg = 0.257 // L/h/kg
Qadipose_kg = 0.223 // L/h/kg
Qserosa_kg = 0.274 // L/h/kg
[ PARAM ]
VHE_kg = 0.0067 // L/kg (Vi)
VHC_kg = 0.0174 // L/kg (Vh)
Vcentral_kg = 0.0743 // L/kg (VbRif)
Vskin_kg = 0.111 // L/kg
Vadipose_kg = 0.143 // L/kg
Vmuscle_kg = 0.429 // L/kg
Vserosa_kg = 0.00893 // L/kg
Vent_kg = 0.00739 // L/kg
Vmucblood_kg = 0.00099 // L/kg
[PARAM]
ka = 37.6 // 3.26 // per hr
WT = 80
[CAPTURE] Qh VHE VHC Vmax_uptake Ccentral
[ MAIN ]
if(NEWIND <= 1) {
// -------------------------------------------
double fBCLint_all = fBCLint_all_kg*WT;
double CLint_all = fBCLint_all / fB;
double CLrenal = CLrenal_kg*WT;
double PSdif_E = PSdif_E_kg*WT;
// -------------------------------------------
double Qvilli = Qvilli_kg*WT;
double Qh = Qh_kg*WT;
double Qmuscle = Qmuscle_kg*WT;
double Qskin = Qskin_kg*WT;
double Qadipose = Qadipose_kg*WT;
double Qserosa = Qserosa_kg*WT;
double Qhart = Qh - Qserosa - Qvilli;
// -------------------------------------------
double VHE = VHE_kg*WT;
double VHC = VHC_kg*WT;
double Vcentral = Vcentral_kg*WT;
double Vskin = Vskin_kg*WT;
double Vadipose = Vadipose_kg*WT;
double Vmuscle = Vmuscle_kg*WT;
double Vserosa = Vserosa_kg*WT;
double Vent = Vent_kg*WT;
double Vmucblood = Vmucblood_kg*WT;
// -------------------------------------------
double Vmax_uptake = 1.0 / (1 + Rdif) * CLint_all / beta * Km_u_uptake;
double PSdif_inf = Rdif / (1 + Rdif) * CLint_all / beta;
double PSdif_eff = Rdif / (1 + Rdif) * CLint_all / beta / gamma;
double CLint = Rdif / (1 + Rdif) * CLint_all / (1 - beta) / gamma;
double Qgut = fE * PSdif_E * Qvilli / (Qvilli + fB * PSdif_E);
double CLint_E = (Qgut * (1.0 / Fg - 1.0) - (1.0- Fa) * fE * PSdif_E * 20.0) / fE;
}
[CMT]
Xgutlumen
central Cmuscle Cskin Cadipose Cserosa Cmucblood Cent
CHE1 CHE2 CHE3 CHE4 CHE5
CHC1 CHC2 CHC3 CHC4 CHC5
[INIT]
UGT_ratio_HC1 = 1
UGT_ratio_HC2 = 1
UGT_ratio_HC3 = 1
UGT_ratio_HC4 = 1
UGT_ratio_HC5 = 1
UGT_ratio_ent = 1
// CYP3A4_ratio_HC1 = 1
// CYP3A4_ratio_HC2 = 1
// CYP3A4_ratio_HC3 = 1
// CYP3A4_ratio_HC4 = 1
// CYP3A4_ratio_HC5 = 1
[ ODE ]
double Ccentral = central/Vcentral;
// Model Equations for Rifampicin
// Central compartment
// Muscle: 63
// Skin: 64
// Adipose: 65
// Central: 51
// CHE5: 60
//Vcentral * dCcentral / dt =
// y51' = 1 / VbRif * (
// Qh * y60 +
// Qm * ( y63 / ( KpScaleRif * KpmRif ) - y51 ) +
// Qs * ( y64 / ( KpScaleRif * KpsRif ) - y51 ) +
// Qa * ( y65 / ( KpScaleRif * KpaRif ) - y51 ) -
// ( Qhart + Qser + Qvilli ) * y51 - CLrRif * y51 )
// )
dxdt_central =
Qh * CHE5 -
Qhart * Ccentral -
Qserosa * Ccentral -
Qvilli * Ccentral -
CLrenal * Ccentral +
Qmuscle * (Cmuscle / (SFKp * Kp_muscle) - Ccentral) +
Qskin * (Cskin / (SFKp * Kp_skin) - Ccentral) +
Qadipose * (Cadipose / (SFKp * Kp_adipose) - Ccentral);
// Distribution compartments (tissue; muscle_ skin_ adipose and serosa)
// Vtissue * dCmuscle / dt =
dxdt_Cmuscle =
(1.0/Vmuscle) * Qmuscle * (Ccentral - Cmuscle / (SFKp * Kp_muscle));
// Vtissue * dCskin / dt =
dxdt_Cskin =
(1.0/Vskin) * Qskin * (Ccentral - Cskin / (SFKp * Kp_skin));
// Vtissue * dCadipose / dt =
// y65' = 1 / Va * Qa * ( y51 - y65 / ( KpScaleRif * KpaRif ) )
dxdt_Cadipose =
(1.0/Vadipose) * Qadipose * (Ccentral - Cadipose / (SFKp * Kp_adipose));
// Vtissue * dCserosa / dt =
dxdt_Cserosa =
(1.0/Vserosa) * Qserosa * (Ccentral - Cserosa / (SFKp * Kp_serosa));
// Mucosal blood compartment
// Vmucosal blood * dCmucosal blood / dt =
// y68' = 1 / Vmucb * ( Qvilli * ( y51 - y68 ) +
// fgRif * PSdifentRif * y67 - fbRif * PSdifentRif * y68 ),
dxdt_Cmucblood =
Qvilli * (Ccentral - Cmucblood) +
fE * PSdif_E * Cent - fB * PSdif_E * Cmucblood;
dxdt_Cmucblood = dxdt_Cmucblood * (1/Vmucblood);
// Gut lumen compartment
// dXgut lumen / dt = -
// y66' = - KaRif / FaRif * y66 + fgRif * PSdifentRif * 20 * y67,
dxdt_Xgutlumen =
- ka / Fa * Xgutlumen + fE * PSdif_E * 20 * Cent;
// Enterocyte compartment
// Vent * dCent / dt =
//
// y67' = 1 / Vent * ( KaRif * y66 + fbRif * PSdifentRif * y68 -
// fgRif * ( PSdifentRif * 21 + CLmetgRif * ( 1 + fmUGTgRif * ( y86 - 1 ) ) ) * y67 ),
dxdt_Cent =
ka * Xgutlumen +
fB * PSdif_E * Cmucblood -
fE * (PSdif_E * 21 +
CLint_E * (1 + fm_UGT_ent * (UGT_ratio_ent - 1))) * Cent;
dxdt_Cent = dxdt_Cent * (1/Vent);
// Extent of enzyme induction in hepatocytes (enzyme; UGT, CYP3A or CYP2C9. HC_i; i = 1~5)
// UGT
// dEnzymeratio_HC_i / dt =
dxdt_UGT_ratio_HC1 =
kdeg_UGT_liver *
(1 + Emax_UGT_RIF * fH * CHC1 / (fH * CHC1 + EC50_u_UGT_RIF) - UGT_ratio_HC1);
dxdt_UGT_ratio_HC2 =
kdeg_UGT_liver *
(1 + Emax_UGT_RIF * fH * CHC2 / (fH * CHC2 + EC50_u_UGT_RIF) - UGT_ratio_HC2);
dxdt_UGT_ratio_HC3 =
kdeg_UGT_liver *
(1 + Emax_UGT_RIF * fH * CHC3 / (fH * CHC3 + EC50_u_UGT_RIF) - UGT_ratio_HC3);
dxdt_UGT_ratio_HC4 =
kdeg_UGT_liver *
(1 + Emax_UGT_RIF * fH * CHC4 / (fH * CHC4 + EC50_u_UGT_RIF) - UGT_ratio_HC4);
dxdt_UGT_ratio_HC5 =
kdeg_UGT_liver *
(1 + Emax_UGT_RIF * fH * CHC5 / (fH * CHC5 + EC50_u_UGT_RIF) - UGT_ratio_HC5);
// Extent of enzyme induction in ent (enzyme; UGT or CYP3A)
// UGT
// dEnzymeratio_ent / dt =
dxdt_UGT_ratio_ent =
kdeg_UGT_ent *
(1 + Emax_UGT_RIF * fE * Cent / (fE * Cent + EC50_u_UGT_RIF) - UGT_ratio_ent);
// CYP3A4
// dxdt_CYP3A4_ratio_HC1 =
// kdeg_CYP3A4_liver *
// (1 + Emax_CYP3A4_RIF * fH * CHC1 / (fH * CHC1 + EC50_u_CYP3A4_RIF) - CYP3A4_ratio_HC1);
// dxdt_CYP3A4_ratio_HC2 =
// kdeg_CYP3A4_liver *
// (1 + Emax_CYP3A4_RIF * fH * CHC2 / (fH * CHC2 + EC50_u_CYP3A4_RIF) - CYP3A4_ratio_HC2);
// dxdt_CYP3A4_ratio_HC3 =
// kdeg_CYP3A4_liver *
// (1 + Emax_CYP3A4_RIF * fH * CHC3 / (fH * CHC3 + EC50_u_CYP3A4_RIF) - CYP3A4_ratio_HC3);
// dxdt_CYP3A4_ratio_HC4 =
// kdeg_CYP3A4_liver *
// (1 + Emax_CYP3A4_RIF * fH * CHC4 / (fH * CHC4 + EC50_u_CYP3A4_RIF) - CYP3A4_ratio_HC4);
// dxdt_CYP3A4_ratio_HC5 =
// kdeg_CYP3A4_liver *
// (1 + Emax_CYP3A4_RIF * fH * CHC5 / (fH * CHC5 + EC50_u_CYP3A4_RIF) - CYP3A4_ratio_HC5);
// Hepatic extracellular compartments (HE_i; i = 1~5)
// (VHE / 5) * dCHE_i / dt =
// y52' = 5 / Vi * (
// Qhart * y51 +
// Qvilli * y68 +
// Qser * y62 / ( KpScaleRif * KpserRif ) -
// Qh * y52 +
// ( fhRif * PSdifeffRif * y53 - fbRif *
// ( VmaxOATPRif / ( freeKmOATPRif + fbRif * y52 ) + PSdifinfRif ) * y52 ) / 5 ),
dxdt_CHE1 =
Qhart * Ccentral +
Qvilli * Cmucblood +
Qserosa * Cserosa / (SFKp * Kp_serosa) -
Qh * CHE1 +
(fH * PSdif_eff * CHC1 -
fB * (Vmax_uptake / (Km_u_uptake + fB * CHE1) + PSdif_inf) * CHE1) / 5.0;
dxdt_CHE1 = dxdt_CHE1 * (5.0/VHE);
// (VHE / 5) * dCHE_i / dt =
dxdt_CHE2 =
Qh * (CHE1 - CHE2) +
(fH * PSdif_eff * CHC2 -
fB * (Vmax_uptake / (Km_u_uptake + fB * CHE2) + PSdif_inf) * CHE2) / 5.0;// (i = 2~5)
dxdt_CHE2 = dxdt_CHE2 * (5.0/VHE);
dxdt_CHE3 =
Qh * (CHE2 - CHE3) +
(fH * PSdif_eff * CHC3 -
fB * (Vmax_uptake / (Km_u_uptake + fB * CHE3) + PSdif_inf) * CHE3) / 5.0;// (i = 2~5)
dxdt_CHE3 = dxdt_CHE3 * (5.0/VHE);
dxdt_CHE4 =
Qh * (CHE3 - CHE4) +
(fH * PSdif_eff * CHC4 -
fB * (Vmax_uptake / (Km_u_uptake + fB * CHE4) + PSdif_inf) * CHE4) / 5.0;// (i = 2~5)
dxdt_CHE4 = dxdt_CHE4 * (5.0/VHE);
// y60' = 5 / Vi * ( Qh * ( y58 - y60 ) +
// ( fhRif * PSdifeffRif * y61 - fbRif *
// ( VmaxOATPRif / ( freeKmOATPRif + fbRif * y60 ) + PSdifinfRif ) * y60 ) / 5 ),
dxdt_CHE5 =
Qh * (CHE4 - CHE5) +
(fH * PSdif_eff * CHC5 -
fB * (Vmax_uptake / (Km_u_uptake + fB * CHE5) + PSdif_inf) * CHE5) / 5.0;// (i = 2~5)
dxdt_CHE5 = dxdt_CHE5 * (5.0/VHE);
// Hepatocytes compartments (HC_i; i = 1~5)
// (VHC / 5) * dCHC_i / dt =
// y53' = 5 / Vh * (
// fbRif * ( VmaxOATPRif / ( freeKmOATPRif + fbRif * y52 ) +
// PSdifinfRif ) * y52 - fhRif * PSdifeffRif * y53 -
// fhRif * CLintRif * ( 1 + fmUGThRif * ( y81 - 1 ) ) * y53 ) / 5,
dxdt_CHC1 =
(5.0/VHC) *
(fB * (Vmax_uptake / (Km_u_uptake + fB * CHE1) + PSdif_inf) * CHE1 -
fH * PSdif_eff * CHC1 -
fH * CLint * (1 + fm_UGT_liver * (UGT_ratio_HC1 - 1)) * CHC1) / 5.0;
dxdt_CHC2 =
(5.0/VHC) *
(fB * (Vmax_uptake / (Km_u_uptake + fB * CHE2) + PSdif_inf) * CHE2 -
fH * PSdif_eff * CHC2 -
fH * CLint * (1 + fm_UGT_liver * (UGT_ratio_HC2 - 1)) * CHC2) / 5.0;
dxdt_CHC3 =
(5.0/VHC) *
(fB * (Vmax_uptake / (Km_u_uptake + fB * CHE3) + PSdif_inf) * CHE3 -
fH * PSdif_eff * CHC3 -
fH * CLint * (1 + fm_UGT_liver * (UGT_ratio_HC3 - 1)) * CHC3) / 5.0;
dxdt_CHC4 =
(5.0/VHC) *
(fB * (Vmax_uptake / (Km_u_uptake + fB * CHE4) + PSdif_inf) * CHE4 -
fH * PSdif_eff * CHC4 -
fH * CLint * (1 + fm_UGT_liver * (UGT_ratio_HC4 - 1)) * CHC4) / 5.0;
dxdt_CHC5 =
(5.0/VHC) *
(fB * (Vmax_uptake / (Km_u_uptake + fB * CHE5) + PSdif_inf) * CHE5 -
fH * PSdif_eff * CHC5 -
fH * CLint * (1 + fm_UGT_liver * (UGT_ratio_HC5 - 1)) * CHC5) / 5.0;