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| INITIAL STEADY STATE EXAMPLE |
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This is an example of the use of the Initial Steady State (I_SS)
reserved variable in $PK. It was provided by Nick Holford, Dept Phar-
macology & Clinical Pharmacology, University of Auckland.
Glucose and insulin are both endogenous substances, whose rates of
formation are given by terms RGLU and RINS in the differential equa-
tions. In the absence of dose events, both glucose and insulin are
assumed to be at steady state levels. Exogenous doses of both glucose
and insulin are also present in the first subject's data.
It is possible to intialize the steady state condition with a dose
record having AMT=0, RATE=0, SS=1, but this is artificial. The ini-
tial condition that the system is at steady state is a feature of the
model, not of the data. In this example, the $PK block contains the
statement I_SS=1. This causes the system to be initialized appropri-
ately. The statement I_SS=1 could also have been placed among the
$MODEL statements. However the initialization is performed, the
result is the same: non-zero concentrations GLU and INS are computed
at TIME=0.
The SS data item need not be present in the data set for the I_SS com-
putation. It is present in this example in order to demonstrate that
SS may also be computed using a dose record (see the third and fourth
subjects' data).
Note that SIGMA and OMEGA are fixed to 0 for purposes of illustration,
so that the simulated values are exactly equal to those that arise
from the model without the random variability due to ETA and EPS.
NONMEM issues warning messages ("INITIAL ESTIMATE OF WITHIN INDIVIDUAL
VARIANCE IS ZER0"). These may be ignored.
This example also illustrates the use of A(n) on the right in the
$ERROR block to obtain the compartment amounts that are used for the
computation of concentrations GLU and INS.
$PROB nicksiss6.ctl I_SS=1 in $PK ADVAN6
$DATA Nicksiss.dat
$INPUT ID TIME CMT AMT RATE SS DV
$SIM (200070927) ONLYSIM NSUB=1
;Silber HE, Jauslin PM, Frey N, Gieschke R, Simonsson US, Karlsson MO.
;An integrated model for glucose and insulin regulation in healthy
;volunteers and type 2 diabetic patients following intravenous glucose
;provocations. J Clin Pharmacol. 2007 Sep;47(9):1159-71.
$THETA
40 ; POP_RGLU MMOL/H/70KG - glucose input rate
40 ; POP_VGLU L/70KG - volume of distribution for glucose
5 ; POP_CLGLU L/H/70KG - glucose clearance
1 ; POP_EMXGLU - EMAX for effect of glucose on insulin input
10 ; POP_C50GLU MMOL/L - EC50 for effect of glucose on Insulin input
5 ; POP_HILGLU - Hill parameter for effect of glucose on Insulin input
5000 ; POP_RINS PMOL/H/70KG - insulin input rate
5 ; POP_VINS L/70KG - volume of distribution for insulin
70 ; POP_CLINS L/H/70KG - insulin clearance
2 ; POP_EMXINS - EMAX for effect of insulin on glucose clearance
50 ; POP_C50INS PMOL/L - EC50 for effect of insulin on glucose clearance
2 ; POP_HILINS - Hill parameter for effect of insulin on glucose clearance
$OMEGA
0 FIX ;PPV_RGLU
0 FIX ;PPV_RINS
$SIGMA
0 FIXED ;0.1 ;G_EXP_RUV
0 FIXED ;1 ;G_ADD_RUV MMOL/L
0 FIXED ;0.1 ;I_EXP_RUV
0 FIXED ;1 ;I_ADD_RUV PMOL/L
$SUBR ADVAN6 TOL=3
$MODEL
COMP (GLUCOSE)
COMP (INSULIN)
$PK
I_SS=1
; GLUCOSE
RGLU=THETA(1)*EXP(ETA(1))
VGLU=THETA(2)
CLGLU=THETA(3)
EMXGLU=THETA(4)
C50GLU=THETA(5)
HILGLU=THETA(6)
;INSULIN
RINS=THETA(7)*EXP(ETA(2))
VINS=THETA(8)
CLINS=THETA(9)
EMXINS=THETA(10)
C50INS=THETA(11)
HILINS=THETA(12)
S1=VGLU
S2=VINS
$DES
DGLU=A(1)/VGLU
DINS=A(2)/VINS
DGLUH=DGLU**HILGLU
DGEFF=EMXGLU*DGLUH/(C50GLU**HILGLU+DGLUH) ; effect of glucose on insulin
DINSH=DINS**HILINS
DIEFF=EMXINS*DINSH/(C50INS**HILINS+DINSH) ; effect of insulin on glucose
DADT(1)=RGLU - CLGLU*(1+DIEFF)*DGLU ; glucose
DADT(2)=RINS*(1+DGEFF)- CLINS*DINS ; insulin
$ERROR
GLU=A(1)/VGLU ; glucose concentration
INS=A(2)/VINS ; insulin concentration
IF (CMT.EQ.1)THEN
Y=GLU*(1+ERR(1))+ERR(2)
ENDIF
IF (CMT.EQ.2)THEN
Y=INS*(1+ERR(3))+ERR(4)
ENDIF
$TABLE ID TIME CMT AMT RATE SS GLU INS
ONEHEADER NOPRINT FILE=nicksiss6.tab
The data (Nicksiss.dat) follows.
#ID,TIME,CMT,AMT,RATE,SS,DV
1 0 1 0 0 0 .
1 0 2 0 0 0 .
1 .1 1 25 0 0 .
1 1.0 2 10 0 0 .
1 3 1 0 0 0 .
1 3 2 0 0 0 .
1 100 1 . . . .
1 100 2 . . . .
2 0 1 0 0 0 .
2 0 2 0 0 0 .
2 100 1 . . . .
2 100 2 . . . .
3 0 1 0 0 1 .
3 100 1 . . . .
3 100 2 . . . .
4 0 1 0 0 1 .
4 100 1 . . . .
4 100 2 . . . .
(See Initial Steady State,I_SS,ISSMOD)
(See i_ss, initial_condition).
REFERENCES: none.
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