From: Garry Boswell" GBoswell@pcyc.com
Subject: [NMusers] Combined tissue and plasma concentration models
Date: Mon, March 29, 2004 8:39 pm
All,
I have plasma, liver, kidney, and tumor concentration data
from single and multiple dose IV administration of a drug to
groups of mice. I would like to develop a single NONMEM model
that I can use for predictive purposes to estimate concentrations
in theses matrices. I can fit the data to separate models
successfully but I would like to use a single model. Is this
possible and are there any references for such a model?
Garry Boswell
Combined tissue and plasma concentration models
From: Nick Holford n.holford@auckland.ac.nz
Subject: RE:[NMusers] Combined tissue and plasma concentration models
Date: Mon, March 29, 2004 11:04 pm
Garry,
There is no reason in principle why you should not be able to specify a model for 4
matrices. The most straightforward method would be to code a set of differential
equations defining a mammillary model (e.g. using ADVAN6). If the model is all first
order then you can specify the model in a somewhat more abstract way using ADVAN7 or
ADVAN5.
In practice you may find it harder to fit all the data as well to a single connected
model as you did with separate models. Fitting the data simultaneously is a good
stress test for the validity of the assumptions made about how the observed
concentrations are related to each other.
Nick
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
email:n.holford@auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556
http://www.health.auckland.ac.nz/pharmacology/staff/nholford/
From: musor000@optonline.net
Subject: RE:[NMusers] Combined tissue and plasma concentration models
Date: Tue, March 30, 2004 9:18 pm
Garry,
Your question is very general. General answer is yes. Here is a more specific
answer. Here a model based on PK6 example by Gabrielsson (analytical model and
similar differential equation model).
$PROBLEM PK6 - one subject, IV and oral dosing.
$INPUT TIME CP=DV EXPE DOSE=AMT EVID CMT PCMT
;EXPE-EXPERIMENT:
;1-BOLUS DOSE & BLOOD SAMPLE.
;2-BOLUS DOSE & URINE SAMPLE.
;3-ORAL DOSE & BLOOD SAMPLE.
;4-ORAL DOSE & URINE SAMPLE.
;CMT: 1-MOUTH, 2-BLOOD.
;PCMT: 2-BLOOD, 3-URINE.
;EVID: 0-OBSERVATION, 1-DOSE, 4-DOSE & RESET.
$DATA PK06DIF0.DA ;IGNORE #
$SUBROUTINES ADVAN6 TOL=3
;TOL - THE NUMBER OF ACCURATE DIGITS
$MODEL COMP=(DEPOT, INITIALOFF)
COMP=(CENTRAL)
COMP=(PERIPH,NODOSE)
$EST MAXEVAL=9999 SIG=5 NOABORT PRINT=10
$THETA
(50,250,900) ;VD -VOLUME OF DISTRIBUTION
(.1,5,15) ;CLE-CLEARENCE
(.1,0.9,2) ;BIO-BIOAVAILABILITY
(.05,0.5,5) ;KA -ABSORBTION COEFFICIENT
(0.01,0.3,5) ;TL -TIME LAG FOR ORAL DOSE
(.01,0.08,2) ;FE -FRACTION EXCRETED VIA URINE
;(287,287,287) ;VD -VOLUME OF DISTRIBUTION
;(5.76,5.76,5.76) ;CLE-CLEARENCE
;(1.09,1.09,1.09) ;BIO-BIOAVAILABILITY
;(0.437,0.437,0.437) ;KA -ABSORBTION COEFFICIENT
;(0.351,0.351,0.351) ;TL -TIME LAG FOR ORAL DOSE
;(0.0741,0.0741,0.0741) ;FE -FRACTION EXCRETED VIA URINE
;$OMEGA DIAGONAL(2) 20 10 ;CORR MATRIX OF ERRORS
$OMEGA 10 ;CORR MATRIX OF ERRORS
;NOTE: THERE ARE TOO MANY PARAMETERS IN THE MODEL.
;IF OMEGA HAS 2 ELEMENTS, THEN MOREL DOES NOT CONVERGE
;DUE TO ROUNDING ERRORS.
$COV
$PK
VD =THETA(1)
CLE=THETA(2)
BIO=THETA(3)
KA =THETA(4)
ALAG1 =THETA(5)
IF (EXPE.LE.2) ALAG1=0 ;TIME LAG EXIST FOR ORAL DOSE ONLY
FE =THETA(6)
KE = CLE/VD
IND=1 ;INDICATOR OF ORAL DOSE
IF (EXPE.LE.2) IND=0
S2=VD ;The amount A in the observation compartment
;at the time of observation, divided by the
;value of a parameter S, is used as the prediction.
;CALL INFN(ICALL,THETA,DATREC,INDXS,NEWIND)
$DES
DADT(1)=-KA*A(1)*IND
DADT(2)=-CLE/VD*A(2)+BIO*KA*A(1)*IND
DADT(3)=FE*CLE/VD*A(2)
A1=A(1)
A2S=A(2)/VD
A2=A(2)
A3=A(3)
$ERROR
CONC=F
IF (EXPE.EQ.1.OR.EXPE.EQ.3) Y=CONC*(1+ETA(1)) ;CONCENTRATION ERROR
IF (EXPE.EQ.2.OR.EXPE.EQ.4) Y=CONC*(1+ETA(1)) ;URINE AMT ERROR
IPRE=CONC ; individual-specific prediction
IRES=DV-IPRE ; individual-specific residual
IWRE=IRES/CONC ; individual-specific weighted residual
;CALL INFN(ICALL,THETA,DATREC,INDXS,NEWIND)
;$TABLE KE STH2 W FIRSTONLY NOAPPEND
$TABLE TIME DOSE PRED CMT PCMT A1 A2 A2S A3
$SCAT DV VS IPRE UNIT BY EXPE
$SCAT PRED VS TIME BY EXPE
$SCAT (IRES IWRE) VS TIME BY EXPE
0 . 1 12000 4 2 2
0.333 47.5 1 . 0 2 2
0.6667 46.2 1 . 0 2 2
1 46.5 1 . 0 2 2
2.0 42.9 1 . 0 2 2
3.0 45.9 1 . 0 2 2
4.0 44.8 1 . 0 2 2
6.0 40.5 1 . 0 2 2
8.0 38.0 1 . 0 2 2
24.0 26.3 1 . 0 2 2
24.0 340 2 . 0 3 3
48.0 14.2 1 . 0 2 2
48.0 550 2 . 0 3 3
72.0 8.8 1 . 0 2 2
96.0 5.7 1 . 0 2 2
168.0 1.5 1 . 0 2 2
0 . 3 25000 4 1 2
0.333 0.94 3 . 0 2 2
0.6667 13.1 3 . 0 2 2
1 27.9 3 . 0 2 2
2.0 38.0 3 . 0 2 2
3.0 71.9 3 . 0 2 2
4.0 76.1 3 . 0 2 2
6.0 83.9 3 . 0 2 2
8.0 75.0 3 . 0 2 2
24.0 51.6 3 . 0 2 2
24.0 705 4 . 0 3 3
48.0 34.9 3 . 0 2 2
48.0 1210 4 . 0 3 3
72.0 23.4 3 . 0 2 2
96.0 14.5 3 . 0 2 2
168.0 4.5 3 . 0 2 2
* ****************************************************;
$PROBLEM PK6 - one subject, IV and oral dosing.
$INPUT TIME CP=DV EXPE DO
$DATA PK06ANA1.DA ;IGNORE #
$EST MAXEVAL=9990 SIG=7 PRINT=5
$COV
$THETA
(.001,300,1000) ;VD
(.001,5,20) ;CLE
(.001,0.9,5) ;BIO
(.001,1.0,5) ;KA
(.001,0.2,5) ;TL
(.001,0.2,5) ;FE
$OMEGA DIAGONAL(2) 30 50 ;NEDIAGONALNAYA CORR MATRITSA
$PRED
VD =THETA(1)
CLE=THETA(2)
BIO=THETA(3)
KA =THETA(4)
TL =THETA(5)
FE =THETA(6)
KE = CLE/VD
IF (EXPE.EQ.1) THEN
DIV=DO
F = (DIV/VD)*EXP(-(CLE/VD)*TIME)
Y=F+ETA(1)
ENDIF
IF (EXPE.EQ.2) THEN
DPO=DO
F = ((BIO*DPO*KA)/(VD*(KA-KE)))*(EXP(-KE*(TIME-TL))-EXP(-KA*(TIME-TL)))
Y=F+ETA(1)
ENDIF
IF (EXPE.EQ.3) THEN
DIV=DO
F = FE*DIV*(1. - EXP(-(CLE/VD)*TIME))
Y=F+ETA(2)
ENDIF
IF (EXPE.EQ.4) THEN
DPO=DO
REST = (CLE/VD)*EXP(-KA*(TIME-TL))/(KA*(CLE/VD - KA))
F=FE*KA*BIO*DPO*(1/KA+EXP((-CLE/VD)*(TIME-TL))/(CLE/VD-KA)-REST)
Y=F+ETA(2)
ENDIF
IPRED=F ; individual-specific prediction
IRES=DV-IPRED ; individual-specific residual
IWRES=IRES/F ; individual-specific weighted residual
$TABLE EXPE TIME DO PRED DV RES WRES
$SCAT DV VS IPRED UNIT BY EXPE
0.333 47.5 1 12000
0.6667 46.2 1 12000
1 46.5 1 12000
2.0 42.9 1 12000
3.0 45.9 1 12000
4.0 44.8 1 12000
6.0 40.5 1 12000
8.0 38.0 1 12000
24.0 26.3 1 12000
48.0 14.2 1 12000
72.0 8.8 1 12000
96.0 5.7 1 12000
168.0 1.5 1 12000
0.333 0.94 2 25000
0.6667 13.1 2 25000
1 27.9 2 25000
2.0 38.0 2 25000
3.0 71.9 2 25000
4.0 76.1 2 25000
6.0 83.9 2 25000
8.0 75.0 2 25000
24.0 51.6 2 25000
48.0 34.9 2 25000
72.0 23.4 2 25000
96.0 14.5 2 25000
168.0 4.5 2 25000
24.0 340 3 12000
48.0 550 3 12000
24.0 705 4 25000
48.0 1210 4 25000
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