;;;; Drug administration ;;;;

;-----------------------------------------------------------------------

iv(adm=1,cmt=1) ;IV Bolus (Study A)

iv(adm=2,cmt=1) ;infusion during 4 hours; (Study A)

depot(type=3, target=Ais, p=F) ; depot compartment used for IM administration, linked to injection site (Study B)

EQUATION:

;definition of the initial time;

t_0=0

;-----------------------------------------------------------------------

;;;Physiological parameters;;;

;-----------------------------------------------------------------------

;Volumes of each compartment, as fraction of total body volume (see Table 2);

;FracVINJSITE=0.003 ;injection site compartment;

;FracVMUSCLE=0.45 ;muscle compartment

;FracVFAT=0.176 ;fat compartment

;FracVSKIN=0.0528 ;skin compartment

;FracVLIVER=0.017 ;liver compartment

;FracVKIDNEY=0.003 ;kidney compartment

;FracVGUTWALL=0.0519 ;gut wall compartment

;FracVBLOOD=0.0412 ;blood compartment

;FracVDUODENUM=0.0018 ;duodenum compartment

;FracVJEJUNUM1=0.018 ;distal jejunum compartment

;FracVJEJUNUM2=0.018 ;proximal jejunum compartment

;FracVILEUM=0.0018 ;ileum compartment

;FracVCOLON1=0.0046 ;proximal colon compartment

;FracVCOLON2=0.0077 ; distal colon compartment

;FracVBILE=0.00175 ; (2100ml/24h/50kg)

;-----------------------------------------------------------------------

;Adjusted Volumes for simulation, avoid unrealistic negative values during simulation of the popPBPK model

FracVVREST=1- (FracVMUSCLE+FracVFAT+FracVSKIN+FracVLIVER+FracVKIDNEY+FracVBLOOD+FracVDUODENUM+FracVJEJUNUM1+FracVJEJU NUM2+FracVILEUM+FracVCOLON1+FracVCOLON2+FracVBILE)

if FracVVREST <0

FracVREST=0

else
  FracVREST=1-
  (FracVMUSCLE+FracVFAT+FracVSKIN+FracVLIVER+FracVKIDNEY+FracVBLOOD+FracVDUODENUM+FracVJEJUNUM1+FracVJEJU
  NUM2+FracVILEUM+FracVCOLON1+FracVCOLON2+FracVBILE)

end
FVadjust=FracVMUSCLE+FracVFAT+FracVSKIN+FracVLIVER+FracVKIDNEY+FracVBLOOD+FracVDUODENUM+FracVJEJUNUM1+FracVJEJUNUM2+FracVILEUM+FracVCOLON1+FracVCOLON2+FracVBILE+FracVREST

;HAEMATOCRIT=0.412
; Blood flow of each compartment, as fraction of cardiac output (see Table 2);

;QTOT=8.7 ;l/h/kg, cardiac output

;FracQcInjsite=0.009

;FracQcMuscle=0.292

;FracQcFat=0.11

;FracQcSkin=0.035

;FracQcKidney=0.098

;FracQcLiver=0.225 ;(Hepatic Artery + Portal vein)

;FracQcGutWall=0.18 ;(Portal vein solely)

FracQQcRest=1-(FracQcInjsite+FracQcMuscle+FracQcFat+FracQcSkin+FracQcKidney+FracQcLiver)

;Adjusted Flows for simulation, avoid unrealistic negative values during simulation of the popPBPK model

if FracQQcRest <0

FracQcRest=0

else

FracQcRest=1-(FracQcInjsite+FracQcMuscle+FracQcFat+FracQcSkin+FracQcKidney+FracQcLiver)

end

FQadjust=FracQcInjsite+FracQcMuscle+FracQcFat+FracQcSkin+FracQcKidney+FracQcLiver+FracQcRest

;Digestive transit time, calculated according to the length of the different segments and based on Wilfart, 2007 (See Table 2)

;Kd=5.26 ;Duodenum transit constant

;Kjp=0.51 ;Proximal jejunum transit constant

;Kjd=0.51 ;Distal jejunum transit constant

;Ki=5.26 ;Ileum transit constant

;Kc1=0.06 ;initial value of Proximal colon transit constant

;Kc2=0.04 ;initial value of Distal colon transit constant

;Partition coefficients;

;PMUSCLE=1.66

;PFAT=0.33

;PSKIN=0.63

;PLIVER=1.73

;PKIDNEY=3.44

;PGUTWALL=0.83

; PREST = 1.86 ; calculated

;Absolute compartment volume values

;------------------------------------------------------------

VINJSITE=(FracVINJSITE/FVadjust)*BODYWEIGHT

VMUSCLE=(FracVMUSCLE/FVadjust)*BODYWEIGHT

VFAT=(FracVFAT/FVadjust)*BODYWEIGHT
; Blood flow of each compartment, as fraction of cardiac output (see Table 2);

;QTOT=8.7 ;l/h/kg, cardiac output

;FracQcInjsite=0.009

;FracQcMuscle=0.292

;FracQcFat=0.11

;FracQcSkin=0.035

;FracQcKidney=0.098

;FracQcLiver=0.225 ;(Hepatic Artery + Portal vein)

;FracQcGutWall=0.18 ;(Portal vein solely)

FracQQcRest=1-(FracQcInjsite+FracQcMuscle+FracQcFat+FracQcSkin+FracQcKidney+FracQcLiver)

;Adjusted Flows for simulation, avoid unrealistic negative values during simulation of the popPBPK model

if FracQQcRest <0

FracQcRest=0

else

FracQcRest=1-(FracQcInjsite+FracQcMuscle+FracQcFat+FracQcSkin+FracQcKidney+FracQcLiver)

end

FQadjust=FracQcInjsite+FracQcMuscle+FracQcFat+FracQcSkin+FracQcKidney+FracQcLiver+FracQcRest

;Digestive transit time, calculated according to the length of the different segments and based on Wilfart, 2007 (See Table 2)

;Kd=5.26 ;Duodenum transit constant

;Kjp=0.51 ;Proximal jejunum transit constant

;Kjd=0.51 ;Distal jejunum transit constant

;Ki=5.26 ;Ileum transit constant

;Kc1=0.06 ;initial value of Proximal colon transit constant

;Kc2=0.04 ;initial value of Distal colon transit constant

;Partition coefficients;

;PMUSCLE=1.66

;PFAT=0.33

;PSKIN=0.63

;PLIVER=1.73

;PKIDNEY=3.44

;PGUTWALL=0.83

; PREST = 1.86 ; calculated

;Absolute compartment volume values

VINJSITE=(FracVINJSITE/FVadjust)*BODYWEIGHT
VMUSCLE=(FracVMUSCLE/FVadjust)*BODYWEIGHT
VFAT=(FracVFAT/FVadjust)*BODYWEIGHT
VSKIN=(FracVSKIN/FVadjust)*BODYWEIGHT

VLIVER=(FracVLIVER/FVadjust)*BODYWEIGHT

VKIDNEY=(FracVKIDNEY/FVadjust)*BODYWEIGHT

VREST=(FracVREST/FVadjust)*BODYWEIGHT

VPLASMA=(FracVBLOOD/FVadjust*BODYWEIGHT)*(1-HAEMATOCRIT)

VGUTWALL=(FracVGUTWALL/FVadjust)*BODYWEIGHT

VDUODENUM=(FracVDUODENUM/FVadjust)*BODYWEIGHT

VJEJUNUM1=(FracVJEJUNUM1/FVadjust)*BODYWEIGHT

VJEJUNUM2=(FracVJEJUNUM2/FVadjust)*BODYWEIGHT

VILEUM=(FracVILEUM/FVadjust)*BODYWEIGHT

VCOLON1=(FracVCOLON1/FVadjust)*BODYWEIGHT

VCOLON2=(FracVCOLON2/FVadjust)*BODYWEIGHT

VBILE=(FracVBILE/FVadjust)*BODYWEIGHT

----------------------------------------------------------------------------

Absolute compartment blood flow values

;----------------------------------------------------------------------------

QcINJSITE=(FracQcInjsite/FQadjust)*QTOT

QcMUSCLE=(FracQcMuscle/FQadjust)*QTOT

QcFAT=(FracQcFat/FQadjust)*QTOT

QcSKIN=(FracQcSkin/FQadjust)*QTOT

QcKIDNEY=(FracQcKidney/FQadjust)*QTOT

QcLIVER=(FracQcLiver/FQadjust)*QTOT

QcGUTWALL=(FracQcGutWall/FQadjust)*QTOT

QcREST=(FracQcRest/FQadjust)*QTOT

;----------------------------------------------------------------------------

;Definition of MAR concentrations in each compartment

;----------------------------------------------------------------------------

CINJSITE=Ais/VINJSITE

CtbINJSITE=CINJSITE/PMUSCLE ; MAR concentration leaving the inj. site compartment

CMUSCLE=Am/VMUSCLE

CtbMUSCLE=CMUSCLE/PMUSCLE ; MAR concentration leaving the muscle compartment

CFAT=Af/VFAT

CtbFAT=CFAT/PFAT ; MAR concentration leaving the fat compartment

CSKIN=As/VSKIN

CtbSKIN=CSKIN/PSKIN ; MAR concentration leaving the skin compartment

CLIVER=AI/VLIVER

CtbLIVER=CLIVER/PLIVER ; MAR concentration leaving the liver compartment

CKIDNEY=Ak/VKIDNEY

CtbKIDNEY=CKIDNEY/PKIDNEY ; MAR concentration leaving the kidney compartment
VSKIN=(FracVSKIN/FVadjust)*BODYWEIGHT

VLIVER=(FracVLIVER/FVadjust)*BODYWEIGHT

VKIDNEY=(FracVKIDNEY/FVadjust)*BODYWEIGHT

VREST=(FracVREST/FVadjust)*BODYWEIGHT

VPLASMA=(FracVBLOOD/FVadjust*BODYWEIGHT)*(1-HAEMATOCRIT)

VGUTWALL=(FracVGUTWALL/FVadjust)*BODYWEIGHT

VDUODENUM=(FracVDUODENUM/FVadjust)*BODYWEIGHT

VJEJUNUM1=(FracVJEJUNUM1/FVadjust)*BODYWEIGHT

VJEJUNUM2=(FracVJEJUNUM2/FVadjust)*BODYWEIGHT

VILEUM=(FracVILEUM/FVadjust)*BODYWEIGHT

VCOLON1=(FracVCOLON1/FVadjust)*BODYWEIGHT

VCOLON2=(FracVCOLON2/FVadjust)*BODYWEIGHT

VBILE=(FracVBILE/FVadjust)*BODYWEIGHT

Absolute compartment blood flow values

QcINJSITE=(FracQcInjsite/FQadjust)*QTOT

QcMUSCLE=(FracQcMuscle/FQadjust)*QTOT

QcFAT=(FracQcFat/FQadjust)*QTOT

QcSKIN=(FracQcSkin/FQadjust)*QTOT

QcKIDNEY=(FracQcKidney/FQadjust)*QTOT

QcLIVER=(FracQcLiver/FQadjust)*QTOT

QcGUTWALL=(FracQcGutWall/FQadjust)*QTOT

QcREST=(FracQcRest/FQadjust)*QTOT

;Definition of MAR concentrations in each compartment

CINJSITE=Ais/VINJSITE

CtbINJSITE=CINJSITE/PMUSCLE ; MAR concentration leaving the inj. site compartment

CMUSCLE=Am/VMUSCLE

CtbMUSCLE=CMUSCLE/PMUSCLE ; MAR concentration leaving the muscle compartment

CFAT=Af/VFAT

CtbFAT=CFAT/PFAT ; MAR concentration leaving the fat compartment

CSKIN=As/VSKIN

CtbSKIN=CSKIN/PSKIN ; MAR concentration leaving the skin compartment

CLIVER=AI/VLIVER

CtbLIVER=CLIVER/PLIVER ; MAR concentration leaving the liver compartment

CKIDNEY=Ak/VKIDNEY

CtbKIDNEY=CKIDNEY/PKIDNEY ; MAR concentration leaving the kidney compartment
CREST=Ar/VREST

CtbREST=CREST/PREST ; MAR concentration leaving the rest compartment

CGUTWALL=Agw/VGUTWALL

CtbGUTWALL=CGUTWALL/PGUTWALL ; MAR concentration leaving the gutwall compartment

CPLASMA=Ap/VPLASMA ; plasma MAR concentration

CBILE=Ab/VBILE ; biliary MAR concentration

CDUODENUM=Ad/VDUODENUM ; duodenal MAR concentration

CJEJUNUM1=Ajp/VJEJUNUM1 ; proximal jejunum MAR concentration

CJEJUNUM2=Ajd/VJEJUNUM2 ; distal jejunum MAR concentration

CILEUM=Ai/VILEUM ; ileum MAR concentration

CCOLON1=Ac1/VCOLON1 ; proximal colon MAR concentration

CCOLON2=Ac2/VCOLON2 ; distal colon MAR concentration

---

;Total clearance and fraction linked to different route of elimination (see Table 2)

---

CLTOT=WCLTOT*BODYWEIGHT ; total body clearance of MAR

FEadjust=FEKIDNEY+FEGUTWALL+FEBILE+FEMETABOLIC ; Sum of all clearance fraction

FracEKIDNEY=(FEKIDNEY/FEadjust) ; Fraction of clearance linked to renal excretion

FracEBile=(FEBILE/FEadjust) ; Fraction of clearance linked to biliary excretion

FracEGUTWALL=(FEGUTWALL/FEadjust) ; Fraction of clearance linked to intestinal excretion

FracEMETABOLIC=(FEMETABOLIC/FEadjust) ; Fraction of clearance linked to metabolism

---

;Sub-division of FracEGUTWALL in the different digestive sub-compartments;

;DistDuo= 0.15 ; fraction linked to the duodenum

;DistPJ= 0.25 ; fraction linked to the proximal jejunum

;DistDJ= 0.30 ; fraction linked to the distal jejunum

;DistI= 0.30 ; fraction linked to the ileum

Distadjust=DistDuo+DistPJ+DistDJ+DistI

; Bile flow from the gallbladder to the duodenum in l/h ;

KBILE=WKBILE*BODYWEIGHT

---

; DIFFERENTIAL EQUATIONS

---

;Injection site compartment, receiving the IM injection;

ddt_Ais=(QcINJSITE*(CPLASMA-CtbINJSITE))-(ka*F*Ais)

;Muscle compartment;
CREST=Ar/VREST

CtbREST=CREST/PREST ; MAR concentration leaving the rest compartment

CGUTWALL=Agw/VGUTWALL

CtbGUTWALL=CGUTWALL/PGUTWALL ; MAR concentration leaving the gutwall compartment

CPLASMA=Ap/VPLASMA ; plasma MAR concentration

CBILE=Ab/VBILE ; biliary MAR concentration

CDUODENUM=Ad/VDUODENUM ; duodenal MAR concentration

CJEJUNUM1=Ajp/VJEJUNUM1 ; proximal jejunum MAR concentration

CJEJUNUM2=Ajd/VJEJUNUM2 ; distal jejunum MAR concentration

CILEUM=Ai/VILEUM ; ileum MAR concentration

CCOLON1=Ac1/VCOLON1 ; proximal colon MAR concentration

CCOLON2=Ac2/VCOLON2 ; distal colon MAR concentration

-----------------------------------------------------------------------

;Total clearance and fraction linked to different route of elimination (see Table 2)

;-----------------------------------------------------------------------

CLTOT=WCLTOT*BODYWEIGHT ; total body clearance of MAR

FEadjust=FEKIDNEY+FEGUTWALL+FEBILE+FEMETABOLIC ; Sum of all clearance fraction

FracEKIDNEY=(FEKIDNEY/FEadjust) ; Fraction of clearance linked to renal excretion

FracEBile=(FEBILE/FEadjust) ; Fraction of clearance linked to biliary excretion

FracEGUTWALL=(FEGUTWALL/FEadjust) ; Fraction of clearance linked to intestinal excretion

FracEMETABOLIC=(FEMETABOLIC/FEadjust) ; Fraction of clearance linked to metabolism

-----------------------------------------------------------------------

;Sub-division of FracEGUTWALL in the different digestive sub-compartments;;

;DistDuo= 0.15 ; fraction linked to the duodenum

;DistPJ= 0.25 ; fraction linked to the proximal jejunum

;DistDJ= 0.30 ; fraction linked to the distal jejunum

;Distl= 0.30 ; fraction linked to the ileum

Distadjust=DistDuo+DistPJ+DistDJ+Distl

; Bile flow from the gallbladder to the duodenum in l/h ;;

KBILE=WKBILE*BODYWEIGHT

;-----------------------------------------------------------------------

; DIFFERENTIAL EQUATIONS

;-----------------------------------------------------------------------

;Injection site compartment, receiving the IM injection;

ddt_Ais=(QcINJSITE*(CPLASMA-CtbINJSITE))-(ka*F*Ais)

;Muscle compartment;
ddt_Am=QcMUSCLE*(CPLASMA-CtbMUSCLE)

;Fat compartment;

ddt_Af=QcFAT*(CPLASMA-CtbFAT)

;Skin compartment;

ddt_As=QcSKIN*(CPLASMA-CtbSKIN)

;Liver compartment;

ddt_Ai=((QcLIVER-QcGUTWALL)*CPLASMA)+(QcGUTWALL*CtbGUTWALL)-(CtbLIVER*QcLIVER)-(FracEBile * CLTOT*CPLASMA)-(FracEMETABOLIC*CLTOT*CPLASMA)

;Kidney compartment;

ddt_Ak=QcKIDNEY*(CPLASMA-CtbKIDNEY)-(FracEKIDNEY * CLTOT * CPLASMA)

;Plasma compartment;

ddt_Ap=ka*F*Ais+(QcINJSITE*CtbINJSITE)+(QcMUSCLE*CtbMUSCLE)+(QcFAT*CtbFAT)+(QcSKIN*CtbSKIN)+(QcREST*CtbREST)+(QcKIDNEY*CtbKIDNEY)+(QcLIVER*CtbLIVER)-(QTOT*CPLASMA)

;duodenum compartment;

ddt_Ad=(KBILE*Ab)-(Kd*Ad)+((FracEGUTWALL*CLTOT*CPLASMA)*(DistDuo/Distadjust))

;jejunum proximal compartment;

ddt_Ajp=(Kd*Ad)-(Kjp*Ajp)+((FracEGUTWALL*CLTOT*CPLASMA)*(DistPJ/Distadjust))

;jejunum distal compartment;

ddt_Ajd=(Kjp*Ajp)-(Kjd*Ajd)+((FracEGUTWALL*CLTOT*CPLASMA)*(DistDJ/Distadjust))

;ileum compartment;

ddt_Ai=(Kjd*Ajd)-(Ki*Ai)+((FracEGUTWALL*CLTOT*CPLASMA)*(DistI/Distadjust))

; proximal colon compartment;

ddt_Ac1=(Ki*Ai)-(Kc1*Ac1)

;distal colon compartment;

ddt_Ac2=(Kc1*Ac1)-(Kc2*Ac2)

;Rest compartment;

ddt_Ar=QcREST*(CPLASMA-CtbREST)

;Gut Wall compartment;

ddt_Agw=QcGUTWALL*(CPLASMA-CtbGUTWALL)-(FracEGUTWALL*CLTOT*CPLASMA)

;Bile compartment;

ddt_Ab=(FracEBile * CLTOT*CPLASMA)-(KBILE*Ab)

OUTPUT:

output={CPLASMA,CMUSCLE,CSKIN,CFAT,CKIDNEY,CLIVER,CDUODENUM,CJEJUNUM1,CJEJUNUM2,CILEUM,CCOLON1,CCOLON2,CBILE}
ddt_Am=QcMUSCLE*(CPLASMA-CtbMUSCLE)

;Fat compartment;

ddt_Af=QcFAT*(CPLASMA-CtbFAT)

;Skin compartment;

ddt_As=QcSKIN*(CPLASMA-CtbSKIN)

;Liver compartment;

ddt_Ai=((QcLIVER-QcGUTWALL)*CPLASMA)+(QcGUTWALL*CtbGUTWALL)-(CtbLIVER*QcLIVER)-(FracEBile * CLTOT*CPLASMA)-(FracEMETABOLIC*CLTOT*CPLASMA)

;Kidney compartment;

ddt_Ak=QcKIDNEY*(CPLASMA-CtbKIDNEY)-(FracEKIDNEY * CLTOT * CPLASMA)

;Plasma compartment;

ddt_Ap=ka*F*Ais+(QcINJSITE*CtbINJSITE)+(QcMUSCLE*CtbMUSCLE)+(QcFAT*CtbFAT)+(QcSKIN*CtbSKIN)+(QcREST*CtbREST)+(QcKIDNEY*CtbKIDNEY)+(QcLIVER*CtbLIVER)-(QTOT*CPLASMA)

;duodenum compartment;

ddt_Ad=(KBILE*Ab)-(Kd*Ad)+((FracEGUTWALL*CLTOT*CPLASMA)*(DistDuo/Distadjust))

;jejunum proximal compartment;

ddt_Ajp=(Kd*Ad)-(Kjp*Ajp)+((FracEGUTWALL*CLTOT*CPLASMA)*(DistPJ/Distadjust))

;jejunum distal compartment;

ddt_Ajd=(Kjp*Ajp)-(Kjd*Ajd)+((FracEGUTWALL*CLTOT*CPLASMA)*(DistDJ/Distadjust))

;ileum compartment;

ddt_Ai=(Kjd*Ajd)-(Ki*Ai)+((FracEGUTWALL*CLTOT*CPLASMA)*(DistI/Distadjust))

; proximal colon compartment;

ddt_Ac1=(Ki*Ai)-(Kc1*Ac1)

;distal colon compartment;

ddt_Ac2=(Kc1*Ac1)-(Kc2*Ac2)

;Rest compartment;

ddt_Ar=QcREST*(CPLASMA-CtbREST)

;Gut Wall compartment;

ddt_Agw=QcGUTWALL*(CPLASMA-CtbGUTWALL)-(FracEGUTWALL*CLTOT*CPLASMA)

;Bile compartment;

ddt_Ab=(FracEBile * CLTOT*CPLASMA)-(KBILE*Ab)

OUTPUT:

output={CPLASMA,CMUSCLE,CSKIN,CFAT,CKIDNEY,CLIVER,CDUODENUM,CJEJUNUM1,CJEJUNUM2,CILEUM,CCOLON1,CCOLON2,CBILE}