Experience With Nonmem: Population Pharmacokinetics Of Propofol

H. Ihmsen, J.Schüttler

Institut für Anästhesiologie der Rheinischen Friedrich-Wilhelms-Universität Bonn, W-5300 Bonn 1, Germany

Introduction: Population pharmacokinetics is an important tool in anaesthesiology, it allows to estimate not only the mean pharmacokinetic parameters of a drug for a normal patient but in addition the influence of such concomitant variables like age, weight or sex. Besides this the population analysis gives estimates for the interindividual variability of the main pharmacokinetic parameters like clearance or central volume of distribution and makes it possible to calculate not only the mean concentration for a given infusion, but also the expected range (e.g. the 68% confidence interval). We are using pharmacokinetic data for the controlling of infusion pumps, so we need the results of population pharmacokinetics to adjust our model to the individual patient as good as possible.

Configuration: We use NONMEM Version III Level 1.2 with double precision. Due to our requests we wrote our own PRED-subroutine, in which the predicted blood levels are calculated as well as the partial derivatives for inter- and intraindividual variability; so we have not installed PREDPP and NM-TRAN. We run NONMEM under CMS on an IBM 3481 main frame computer of the university hospital. Until now the speed of 3 MIPS has been sufficient for our problems. The largest data set (64 individuals, 1364 measurements, 3-compartment model with interindividual variability of Cl and Vc and 3 additional parameters for several influences) needed of about 6000 seconds CPU-time (including the covariance step). We wrote subroutines to read and store the infusion schemes and to produce output files which can immediatly be used for graphs.

Pharmacokinetic model: We used an open two or three compartment model with elimination from the central compartment; parameters to fit were the transfer constants k12, k21, k13, k31, the total body clearance Cl and the central volume of distribution Vc. We assumed an interindividual variability of Cl and Vc following the “constant coefficient of variation” principle. The same assumption was made for the remaining intraindividual variability.

Data set: The complete data are shown in table 1; all data are from the university hospital of Bonn, except the group of old patients, whose data we kindly got from R. Larsen. In most cases the continous infusion was computer-controlled, that means the infusion rate changed once per minute. For nearly all groups the sampling time was in such a order that a two-compartment-model was sufficient; only for the bolus-infusion-group a three compartment model was superior.

Group

Application

Number of cases

Number of data sets

Sampling time [min]

Age [years]

Weight [kg]

Sex

Propofol + Alfentanil

continous

infusion

11 patients

327

140-240

197±36

16-43

28±9

57-67

62±4

2 m

9 f

Propofol + Fentanyl

continous

infusion

10 patients

182

75-250

150±64

21-45

37±11

52-74

61±7

1 m

9 f

Propofol + Ketamin

continous

infusion

13 patients

125

50-270

110±71

25-4

34±6

55-82

62±8

0 m

13 f

Bolus- Infusion

single

bolus

8 patients

8 volunteers

332

480-720

585±122

20-51

31±10

57-94

69±10

8 m

8 f

Triple-Slope Infusion

continous

infusion

7 volunteers

298

267-558

362±102

24-28

25±2

57-82

70±9

5 m

2 f

Old patients

continous

infusion

10 patients

98

30-70

53±12

66-82

73±6

51-73

62±8

4 m

6 f

Children

continous

infusion

18 patients

47

60-300

120±57

0.1-8

3±2

3-27

13±7

8 m

13 f

Table 1: Total Data set of Propofol (85 cases; 1409 individual data sets)

Regression procedure: A stepwise regression was performed in the following way: if possible (that means more than 10 measurements for one individual) we first made single fits of every individual to get a first look on the data and to reject outliers. The next step was to fit groupwise and at least to fit two or more groups simultaneously. To find out the influence of concomitant parameters we proceeded in a way which was similar to that described by Maître and al. in their study of Alfentanil (1). We made a first fit constraining the concerning factor to the null-hypothesis-value (e.g. 1 for a multiplicative parameter), then we fitted the data with the parameter free to be estimated. To decide wether the additional parameter improves the model (i.e. wether the concerning influence is significant) one has the following criteria:

  1. The difference in objective function which is approximately chi-square-distributed; that means, that a difference of 7.8 corresponds to p < 0.005 for one degree of freedom.
  2. The residual plots should be better with the additional parameter, that means they should not show any structure or “pattern”.
  3. If the additional parameter is related to a kinetic parameter, whose interindividual variability is estimated (e.g. Cl or Vc), this variability should decrease if one adds the parameter to the model.
  4. The standard error of the mean of the additional parameter should be of such order that the confidence interval does not include the null-hypothesis-value.

Results: The mean kinetic parameters and variabilities of the different groups are shown in table 2. For all groups Cl and Vc are proportional to the bodyweight; so we normalized both with respect to bodyweight. The additionally applicated drugs have an influence on nearly all parameters. The volume of distribution is much smaller for infants even if it is normalized to the bodyweight. The difference in Vc between the triple-slope-group and the bolus-group is due to the distribution process which is better “seen” with a slow infusion than with a bolus application.

Group

k12

[min-1]

k21

[min-1]

k13

[min-1]

k31

[min-1]

Vc

[1/kg]

Cl

[l/min/kg]

inter. Variab.

Cl

inter. Variab. Vc

intra. Variab.

Propofol+ Alfentanil

0.092 (0.026)

0.036 (0.006)

–

–

0.69 (0.09)

0.039

(0.002)

21 %

33%

17%

Propofol+ Fentanyt

0.043 (0.005)

0.013 (0.003)

–

–

0.49 (0.06)

0.039

(0.001)

14%

26%

17%

Propofol+ Ketamin

0.066 (0.009)

0.009 (0.002)

–

–

0.52 (0.09)

0.017

(0.003)

66%

42%

22%

Bolus- Infusion

0.22 (0.04)

0.061 (0.011)

0.026 (0.006)

0.004 (0.001)

0.37 (0.08)

0.030

(0.001)

12%

28%

26%

Triple-Slope Infusion

0.13 (0.02)

0.019 (0.002)

–

–

0.28 (0.02)

0.023

(0.002)

11 %

24%

22%

Old patients

0.12 (0.03)

0.034 (0.015)

–

–

0.41 (0.04)

0.031

(0.004)

67%

35%

14%

Children

0.32 (0.16)

0.008 (0.002)

–

–

0.11 (0.01)

0.042

(0.005)

60%

33%

30%

Table 2: Pharmacokinetic parameters of the different groups (Mean, SEM)

At least we have found an influence of age and sex; for individuals older than 60 years, Vc and Cl decrease linearly:

Vci = Vc*(1 -fl*(agei-60)) f1 = 0.024 ± 0.008

Cli = Cl * (1 – f2*(agei – 60)) f1 = 0.023 ± 0.009

where Vc and Cl are the mean pharmacokinetic values and i marks the ith individual.

For females we have found a central distribution of volume which is a bit higher than for males:

VCfemale = Vc* f3 f3 = 1.2 ± 0.1

Conclusion: We have found several factors which have an influence on the pharmacokinetics of Propofol, so we can estimate the expected pharmacokinetic for an individual patient. These factors have also been implemented in the model used for the control of our infusion pumps and with these devices we are now performing anaesthesia with new patients of different age and ASA risk classes to valid our results.

Reference:
(1) P.Maître, S. Vozeh, J. Heykants, D. Thomson, 0. Stanski: Population pharmacokinetics of Alfentanil: the average dose-plasma concentration relationship and interindividual variability in patients. Anesthesiology 66:3-12, 1987

Reference: PAGE 1 (1992) Abstr 894 [www.page-meeting.org/?abstract=894]

Poster: oral presentation