Supplementary Materials 1. Kagan L, Turner MR, Balu

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Supplementary Materials
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ADAPT-5 code for mPBPK model (human prediction):
**********************************************************************
C
ADAPT
*
C
Version 5
*
C**********************************************************************
C
*
C
MODEL
*
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
NSParam
NVparam
NSecPar
NSecOut
Ieqsol
Descr
= 4
! Enter # of Diff. Eqs.
= 5
! Enter # of System Parameters.
= 2
! Enter # of Variance Parameters.
= 0
! Enter # of Secondary Parameters.
= 0 ! Enter # of Secondary Outputs (not used).
= 1 ! Model type: 1 - DIFFEQ, 2 - AMAT, 3 - OUTPUT only.
= ' mPBPK Model human PK prediction'
CC
C----------------------------------------------------------------------C
C
Enter Symbol for Each System Parameter (eg. Psym(1)='Kel')
C
C----c-----------------------------------------------------------------C
Psym(1)='sigma_1'
Psym(2)='sigma_2'
Psym(3)='Kp'
Psym(4)='a1'
Psym(5)='m1'
CC
C----------------------------------------------------------------------C
C
Enter Symbol for Each Variance Parameter {eg: PVsym(1)='Sigma'}
C
C----c-----------------------------------------------------------------C
PVsym(1)='intercept'
PVsym(2)='Slope'
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'
Real*8 T,X(MaxNDE),XP(MaxNDE),sigma_1,Kp,CLp,ISF,Vp,L
Real*8 sigma_2,VL,sigmaL,a1,m1
CC
C----------------------------------------------------------------------C
C
Enter Differential Equations Below {e.g. XP(1) = -P(1)*X(1) }
C
C----c-----------------------------------------------------------------C
ISF = 18.2-2.6
Vp = 2.6
L = 2.9/24
VL = 5.2
sigmaL = 0.2
sigma_1 = P(1)
sigma_2 = P(2)
Kp = P(3)
a1 = P(4)
m1 = P(5)
CLp=a1*70**m1
if (P(1) .GT. 1 .OR. P(2) .GT. 1) Then
XP(1)=0
Else
c
c
XP(1)= R(1)-X(1)/Vp*(CLp+0.33*L*(1-sigma_1)+ 0.67*L*(1-sigma_2))
+ X(4)*(L/VL)
Endif
XP(2)= X(1)/Vp*(0.33*L)*(1-sigma_1)
- X(2)/(0.65*ISF*Kp)*(0.33*L)*(1-sigmaL)
XP(3)= X(1)/Vp*(0.67*L)*(1-sigma_2)
- X(3)/(0.35*ISF*Kp)*(0.67*L)*(1-sigmaL)
XP(4)=X(2)/(0.65*ISF*Kp)*(0.33*L)*(1-sigmaL) + X(3)/(0.35*ISF*Kp)
C *(0.67*L)*(1-sigmaL) - X(4)*(L/VL)
c
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),Vp
CC
C----------------------------------------------------------------------C
C
Enter Output Equations Below
{e.g. Y(1) = X(1)/P(2) }
C
C----c-----------------------------------------------------------------C
Vp = 2.6
Y(1) = X(1)/Vp
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
C
Subroutine COVMOD(Pmean, ICmean, PC)
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
NCparam = 0
! Enter # of Covariate Parameters.
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
C
Subroutine POPINIT(PmeanI,ICmeanI,PcovI,ICcovI, PCI)
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
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
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
C
Subroutine PRIOR(Pmean,Pcov,ICmean,ICcov)
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
Phoenix code for mPBPK model (human):
MODEL
remark ******************************************************
remark This code is for mPBPK with allometric scaling
remark ******************************************************
COMMANDS
NFUNCTIONS 1
NDERIVATIVES 4
NPARAMETERS 4
PNAMES 'sigma1','sigma2','a', 'm'
NCONS 1
NSECO 0
END
TEMPORARY
T=X
Dose = CON(1)
ISF = 18.2 - 2.6
Vp = 2.6
L = 2.9/24
VL = 5.2
Kp = 0.8
CLp= a1*70**m1
Duration = 1
IF T>Duration THEN
Rinf = 0
ELSE
Rinf = Dose/Duration
ENDIF
END
START
Z(1)=0
Z(2)=0
Z(3)=0
Z(4)=0
END
DIFFERENTIAL
IF sigma1 > 1 THEN
DZ(1) = 0
ELSE
DZ(1)= Rinf -Z(1)/Vp*(CLp+0.33*L*(1-sigma1)+ 0.67*L*(1-sigma2))+ Z(4)*(L/VL)
ENDIF
IF sigma2 >1 THEN
DZ(1) = 0
ELSE
DZ(1)= Rinf -Z(1)/Vp*(CLp+0.33*L*(1-sigma1)+ 0.67*L*(1-sigma2))+ Z(4)*(L/VL)
ENDIF
DZ(2)= Z(1)/Vp*(0.33*L)*(1-sigma1) - Z(2)/(0.65*ISF*Kp)*(0.33*L)*0.8
DZ(3)= Z(1)/Vp*(0.67*L)*(1-sigma2) - Z(3)/(0.35*ISF*Kp)*(0.67*L)*0.8
DZ(4)= Z(2)/(0.65*ISF*Kp)*(0.33*L)*0.8 + Z(3)/(0.35*ISF*Kp)*(0.67*L)*0.8 - Z(4)*(L/VL)
END
FUNCTION 1
F=Z(1)/2.6
END
EOM
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