**********************************************************************
Title: Understanding pulmonary and systemic pharmacokinetics of inhaled fluticasone propionate in healthy subjects using population PK analysis 

Journal Name :European journal of drug metabolism and pharmacokinetics  

Author Name and Affliations : Juliet Rebello1, Sharvari Shukla2, K Raghu Naidu3, Jyoti Patil3, Nazma Morde1, Murray P. Ducharme4

1Clinical Research Division, Cipla Ltd, Mumbai, India, email: celestinejulietrebello@gmail.com, nazma.morde@cipla.com
2Symbiosis Statistical Institute (SSI), Symbiosis International University, Pune, India, email: sharvareeshukla@gmail.com*
3Sitec Labs, Mahape, Navi Mumbai, India email: dr_naidu@siteclabs.com, jyoti.patil@siteclabs.com
4Learn and Confirm Inc, Canada and Faculté de Pharmacie, Université de Montréal, Canada, email: murray.ducharme@learnandconfirm.ca

Corresponding author email: *Correspondence: sharvareeshukla@gmail.com
ORCID ID: 0000-0002-7029-5532

C**********************************************************************
C                                                                     *
C     		 Supplementary 1:  MODEL7  3CPT 3ABS tlag in order                               *
C                                                                     *
C    This file contains Fortran subroutines into which the user       *
C    must enter the relevant model equations and constants.           *
C    Consult the User's Guide for details concerning the format for   *
C    entered equations and definition of symbols.                     *
C                                                                     *
C       1. Symbol-  Parameter symbols and model constants             *
C       2. DiffEq-  System differential equations                     *
C       3. Output-  System output equations                           *
C       4. Varmod-  Error variance model equations                    *
C       5. Covmod-  Covariate model equations (ITS,MLEM)              *
C       6. Popinit- Population parameter initial values (ITS,MLEM)    *
C       7. Prior -  Parameter mean and covariance values (ID,NPD,STS) *
C       8. Sparam-  Secondary parameters                              *
C       9. Amat  -  System state matrix                               *
C                                                                     *
C**********************************************************************

C######################################################################C

        Subroutine SYMBOL
        Implicit None

        Include 'globals.inc'
        Include 'model.inc'


CC
C----------------------------------------------------------------------C
C   Enter as Indicated                                                 C
C----c-----------------------------------------------------------------C

      NDEqs   =  9   ! Enter # of Diff. Eqs.
      NSParam =  23   ! Enter # of System Parameters.
      NVparam =  2   ! Enter # of Variance Parameters.
      NSecPar =  0   ! Enter # of Secondary Parameters.
      NSecOut =  0  ! Enter # of Secondary Outputs (not used).
      Ieqsol  =  1  ! Model type: 1 - DIFFEQ, 2 - AMAT, 3 - OUTPUT only.
      Descr   = ' MODEL7  3CPT 3ABS tlag in order '

CC
C----------------------------------------------------------------------C
C   Enter Symbol for Each System Parameter (eg. Psym(1)='Kel')         C
C----c-----------------------------------------------------------------C

	  Psym(1)='TLagTc'
	  Psym(2)='KAinhTc'
	  Psym(3)='Vc/F'
	  Psym(4)='CL/F'
	  Psym(5)='CLd/F'              
	  Psym(6)='Vp/F'                
        Psym(7)='alphaR'
        Psym(8)='KAinhRc'
        Psym(9)='Frel'
        Psym(10)='KAinhTp'
        Psym(11)='KAinhRp'
        Psym(12)='TLagTp'
        Psym(13)='TLagRc'
        Psym(14)='TLagRp'
        Psym(15)='alphaT'
        Psym(16)='bettaR'
        Psym(17)='bettaT'
        Psym(18)='KAinhGR'
        Psym(19)='KAinhGT'
        Psym(20)='TLagGR'
        Psym(21)='TLagGT'
        Psym(22)='Cld2/F'
        Psym(23)='Vp2/F'
	
	
CC
C----------------------------------------------------------------------C
C   Enter Symbol for Each Variance Parameter {eg: PVsym(1)='Sigma'}    C
C----c-----------------------------------------------------------------C


	 PVsym(1)='ADD'
	 PVsym(2)='PROP'

CC
C----------------------------------------------------------------------C
C   Enter Symbol for Each Secondary Parameter {eg: PSsym(1)='CLt'}     C
C----c-----------------------------------------------------------------C


C----------------------------------------------------------------------C
C----------------------------------------------------------------------C
C
        Return
        End

C######################################################################C

        Subroutine DIFFEQ(T,X,XP)
        Implicit None

        Include 'globals.inc'
        Include 'model.inc'

        


C----------------------------------------------------------------------C
C   Lung:Tlg1,Z1&Z2,CENT1,CENT2,Tlg2,Z3&Z4,PERI1,PERI2                 C
C   Gut:Tlg3,Z5&Z6,GUT1,GUT2                                           C
C----c-----------------------------------------------------------------C
	 Real*8 T,X(MaxNDE),XP(MaxNDE),Z1,Z2,Z3,Z4,Z5,Z6,Tlg1,Tlg2,
     &   Tlg3,CENT1,CENT2,PERI1,PERI2,GUT1,GUT2,Vc,Vp,CL,CLD,Vp2,CLD2
CC
C----------------------------------------------------------------------C
C   Enter Differential Equations Below  {e.g.  XP(1) = -P(1)*X(1) }    C
C----c-----------------------------------------------------------------C
	
	  Vc=P(3)*(R(5)/62)**1 
	  Vp=P(6)*(R(5)/62)**1
	  CL=P(4)*(R(5)/62)**0.75
	  CLD=P(5)*(R(5)/62)**0.75
	  Vp2=P(23)*(R(5)/62)**1
	  CLD2=P(22)*(R(5)/62)**0.75 

	  
	  IF(R(3).EQ.1) THEN
            Tlg1=P(1)
            Tlg2=P(1)+P(12)
            Tlg3=P(1)+P(12)+P(21)
          ELSE
            Tlg1=P(13)
            Tlg2=P(13)+P(14)
            Tlg3=P(13)+P(14)+P(20)
        ENDIF

	  IF(T.GT.Tlg1) THEN 
            Z1=1
          ELSE
            Z1=0
        ENDIF

        IF(T.GT.(Tlg2)) THEN 
            Z3=1
          ELSE
            Z3=0
        ENDIF
        
	  IF(T.GT.(336+Tlg1)) THEN 
            Z2=1
          ELSE
            Z2=0
        ENDIF

        IF(T.GT.(336+Tlg2)) THEN 
           Z4=1
          ELSE
           Z4=0
        ENDIF

        IF(T.GT.(Tlg3)) THEN 
            Z5=1
           ELSE
            Z5=0
        ENDIF

        IF(T.GT.(336+Tlg3)) THEN 
            Z6=1
           ELSE
            Z6=0
        ENDIF
      
	 	
    	IF ((P(7)+P(16)).GT.1) THEN
               CENT1=P(7)
               PERI1=1-P(7)
               GUT1=0
		ELSE
               CENT1=P(7)
               PERI1=P(16)
               GUT1=1-P(7)-P(16)
		ENDIF

	  IF ((P(15)+P(17)).GT.1) THEN
               CENT2=P(15)
               PERI2=1-P(15)
               GUT2=0
		ELSE
               CENT2=P(15)
               PERI2=P(17)
               GUT2=1-P(15)-P(17)
		ENDIF

        XP(1) = +R(1)*CENT1-(Z1*(1-R(4))+Z2*R(4))*P(8)*X(1)
        XP(2) = +(Z1*(1-R(4))+Z2*R(4))*P(8)*X(1)-CL/Vc*X(2)
     &          +(Z3*(1-R(4))+Z4*R(4))*P(11)*X(3) 
     &          +(Z5*(1-R(4))+Z6*R(4))*P(18)*X(4)
     &          +(Z1*(1-R(4))+Z2*R(4))*P(2)*X(5)
     &          -(CLD/Vc*X(2)+CLD/Vp*X(6))                                
     &          +(Z3*(1-R(4))+Z4*R(4))*P(10)*X(7)
     &          +(Z5*(1-R(4))+Z6*R(4))*P(19)*X(8)
     &	           -CLD2/Vc*X(2)+CLD2/Vp2*X(9)
        XP(3) = +R(1)*PERI1-(Z3*(1-R(4))+Z4*R(4))*P(11)*X(3)
        XP(4) = +R(1)*GUT1-(Z5*(1-R(4))+Z6*R(4))*P(18)*X(4)
        XP(5) = +R(2)*P(9)*CENT2-(Z1*(1-R(4))+Z2*R(4))*P(2)*X(5)
        XP(6) = CLD/Vc*X(2)-CLD/Vp*X(6)                            
        XP(7) = +R(2)*P(9)*PERI2-(Z3*(1-R(4))+Z4*R(4))*P(10)*X(7)
        XP(8) = +R(2)*P(9)*GUT2-(Z5*(1-R(4))+Z6*R(4))*P(19)*X(8)
        XP(9) =  CLD2/Vc*X(2)-CLD2/Vp2*X(9)



















C----------------------------------------------------------------------C
C----------------------------------------------------------------------C
C
        Return
        End

C######################################################################C

        Subroutine OUTPUT(Y,T,X)
        Implicit None

        Include 'globals.inc'
        Include 'model.inc'

        Real*8 Y(MaxNOE),T,X(MaxNDE),Vc

CC
C----------------------------------------------------------------------C
C   Enter Output Equations Below   {e.g.  Y(1) = X(1)/P(2) }           C
C----c-----------------------------------------------------------------C

	    
	    Vc=P(3)*(R(5)/62)**1 
        
		Y(1) = X(2)/Vc
		
C----------------------------------------------------------------------C
C----------------------------------------------------------------------C
C
        Return
        End

C######################################################################C

        Subroutine VARMOD(V,T,X,Y)
        Implicit None

        Include 'globals.inc'
        Include 'model.inc'

        Real*8 V(MaxNOE),T,X(MaxNDE),Y(MaxNOE)

CC
C----------------------------------------------------------------------C
C   Enter Variance Model Equations Below                               C
C         {e.g. V(1) = (PV(1) + PV(2)*Y(1))**2 }                       C
C----c-----------------------------------------------------------------C

	  V(1) = (PV(1) + PV(2)*Y(1))**2

C----------------------------------------------------------------------C
C----------------------------------------------------------------------C
C
        Return
        End

C######################################################################C

        Subroutine COVMOD(Pmean, ICmean, PC)
C  Defines any covariate model equations (MLEM, ITS)
        Implicit None

        Include 'globals.inc'
        Include 'model.inc'

        Real*8 PC(MaxNCP)
        Real*8 Pmean(MaxNSP+MaxNDE), ICmean(MaxNDE)

CC
C----------------------------------------------------------------------C
C     Enter # of Covariate Parameters                                  C
C----c-----------------------------------------------------------------C

       

CC
C----------------------------------------------------------------------C
C   Enter Symbol for Covariate Params {eg: PCsym(1)='CLRenal'}         C
C----c-----------------------------------------------------------------C
     	
CC 		
C----------------------------------------------------------------------C
C   For the Model Params. that Depend on Covariates Enter the Equation C
C         {e.g. Pmean(1) =  PC(1)*R(2) }                               C
C----c-----------------------------------------------------------------C
		
C----------------------------------------------------------------------C
C----------------------------------------------------------------------C
C
        Return
        End

C######################################################################C

        Subroutine POPINIT(PmeanI,ICmeanI,PcovI,ICcovI, PCI)
C  Initial parameter values for population program parameters (ITS, MLEM)

        Implicit None

        Include 'globals.inc'
        Include 'model.inc'

        Integer I,J
        Real*8 PmeanI(MaxNSP+MaxNDE), ICmeanI(MaxNDE)
        Real*8 PcovI(MaxNSP+MaxNDE,MaxNSP+MaxNDE), ICcovI(MaxNDE,MaxNDE)
        Real*8 PCI(MaxNCP)

CC
C----------------------------------------------------------------------C
C  Enter Initial Values for Population Means                           C
C          {  e.g. PmeanI(1) = 10.0    }                               C
C----c-----------------------------------------------------------------C
	  
	  PmeanI(1)=0.02
	  PmeanI(2)=1
	  PmeanI(3)=313
	  PmeanI(4)=258
	  PmeanI(5)=166
	  PmeanI(6)=334
	  PmeanI(7)=0.25
	  PmeanI(8)=1
	  PmeanI(9)=1
	  PmeanI(10)=0.62
	  PmeanI(11)=0.62
	  PmeanI(12)=0.1
	  PmeanI(13)=0.02
	  PmeanI(14)=0.1
	  PmeanI(15)=0.25
	  PmeanI(16)=0.2
	  PmeanI(17)=0.2
	  PmeanI(18)=0.08
	  PmeanI(19)=0.08
	  PmeanI(20)=0.3
	  PmeanI(21)=0.3
	  PmeanI(22)=1133
	  PmeanI(23)=1400
	  

 	
        
CC
C----------------------------------------------------------------------C
C   Enter Initial Values for Pop. Covariance Matrix (Lower Triang.)    C
C         {  e.g. PcovI(2,1) = 0.25    }                               C
C----c-----------------------------------------------------------------C

	  PcovI(1,1)=(PmeanI(1)*0.5)**2
	  PcovI(2,2)=(PmeanI(2)*0.5)**2
	  PcovI(3,3)=(PmeanI(3)*0.5)**2
	  PcovI(4,4)=(PmeanI(4)*0.5)**2
        PcovI(5,5)=(PmeanI(5)*0.5)**2  
        PcovI(6,6)=(PmeanI(6)*0.5)**2
        PcovI(7,7)=(PmeanI(7)*0.5)**2  
        PcovI(8,8)=(PmeanI(8)*0.5)**2  
        PcovI(9,9)=(PmeanI(9)*0.5)**2
        PcovI(10,10)=(PmeanI(10)*0.5)**2
        PcovI(11,11)=(PmeanI(11)*0.5)**2
        PcovI(12,12)=(PmeanI(12)*0.5)**2
        PcovI(13,13)=(PmeanI(13)*0.5)**2
        PcovI(14,14)=(PmeanI(14)*0.5)**2
        PcovI(15,15)=(PmeanI(15)*0.5)**2
        PcovI(16,16)=(PmeanI(16)*0.5)**2
        PcovI(17,17)=(PmeanI(17)*0.5)**2
        PcovI(18,18)=(PmeanI(18)*0.5)**2
        PcovI(19,19)=(PmeanI(19)*0.5)**2
        PcovI(20,20)=(PmeanI(20)*0.5)**2
        PcovI(21,21)=(PmeanI(21)*0.5)**2
        PcovI(22,22)=(PmeanI(22)*0.5)**2
        PcovI(23,23)=(PmeanI(23)*0.5)**2
       

CC
C----------------------------------------------------------------------C
C   Enter Values for Covariate Model Parameters                        C
C         {  e.g. PCI(1) = 2.0    }                                    C
C----c-----------------------------------------------------------------C
		
	
C----------------------------------------------------------------------C
C----------------------------------------------------------------------C
C
        Return
        End

C######################################################################C

        Subroutine PRIOR(Pmean,Pcov,ICmean,ICcov)
C       Parameter mean and covariance values for MAP estimation (ID,NPD,STS)
        Implicit None

        Include 'globals.inc'
        Include 'model.inc'

        Integer I,J
        Real*8 Pmean(MaxNSP+MaxNDE), ICmean(MaxNDE)
        Real*8 Pcov(MaxNSP+MaxNDE,MaxNSP+MaxNDE), ICcov(MaxNDE,MaxNDE)

CC
C----------------------------------------------------------------------C
C  Enter Nonzero Elements of Prior Mean Vector                         C
C          {  e.g. Pmean(1) = 10.0    }                                C
C----c-----------------------------------------------------------------C

	  
CC
C----------------------------------------------------------------------C
C   Enter Nonzero Elements of Covariance Matrix (Lower Triang.)       C
C         {  e.g. Pcov(2,1) = 0.25    }                                C
C----c-----------------------------------------------------------------C
		

C----------------------------------------------------------------------C
C----------------------------------------------------------------------C
C
        Return
        End

C######################################################################C

        Subroutine SPARAM(PS,P,IC)
        Implicit None

        Include 'globals.inc'

        Real*8 PS(MaxNSECP), P(MaxNSP+MaxNDE), IC(MaxNDE) 

CC
C----------------------------------------------------------------------C
C   Enter Equations Defining Secondary Paramters                       C
C           {  e.g.  PS(1) = P(1)*P(2)   }                             C
C----c-----------------------------------------------------------------C

        
C----------------------------------------------------------------------C
C----------------------------------------------------------------------C
C
        Return
        End
	  	  
C######################################################################C

        Subroutine AMAT(A)
        Implicit None

        Include 'globals.inc'
        Include 'model.inc'

        Integer I,J
        Real*8 A(MaxNDE,MaxNDE)

        DO I=1,Ndeqs
           Do J=1,Ndeqs
              A(I,J)=0.0D0
           End Do
        End Do

CC
C----------------------------------------------------------------------C
C   Enter non zero elements of state matrix  {e.g.  A(1,1) = -P(1) }   C
C----c-----------------------------------------------------------------C


C----------------------------------------------------------------------C
C----------------------------------------------------------------------C
C
        Return
        End

C######################################################################C
