An assessment of methods for modelling regional pharmacokinetics – pooled data, pooled parameter estimates or NONMEM?

Aim: Understanding the clinical behaviour of drugs sometimes requires understanding the kinetics (and dynamics) of the drug in its target organ (e.g. the cerebral uptake of anaesthetics and analgesics). One method of studying regional (organ) kinetics is by simultaneously measuring the time-courses of the concentration of the drug in blood entering and leaving the organ. These data can provide sufficient information to define an appropriate model of the kinetics of the drug in the organ. However, there are number of ways of modelling these data, including analysis of pooled data, analysis of individual data followed by pooled parameter estimates or a population approach using NONMEM. These methods differ in their complexity and intended purpose. The aim of this study was to evaluate the accuracy of the parameters estimated using each method using simulated data for which the true parameter values were known.

Methods: The scenario analysed was similar to that used for an experimental study of the cerebral uptake of oxycodone (1). A simulated data set was made using Scientist for Windows (Micromath). Arterial concentrations were generated using a 2 compartment mamillary model. Regional venous concentrations were simulated assuming a 2 compartment membrane-limited model with three parameters V1 (volume of 1st organ compartment), PS (permeability term between organ compartments) and V2 (volume of 2nd organ compartment). Six studies were simulated, with model parameters having a random proportional error of 30%. A random proportional error of 8% was added to all concentrations to represent assay noise. The simulated data were analysed using three approaches: [1] Pooled data: The arterial and venous data were pooled (mean). Using “Scientist” software, pooled arterial concentrations were fitted to a forcing function, and the parameters of the membrane-limited model were estimated by fitting the pooled regional venous concentrations. [2] Pooled parameter estimates: As for 1, but the parameters of the membrane-limited model were estimated for each individual study. Parameter estimates were then pooled. [3] NONMEM: A membrane-limited model was fitted to the data for the 6 studies simultaneously, using NONMEM (FOCE with interaction, proportional and additive error model). Arterial concentrations were represented by linear interpolation of the data. The parameter estimates returned by each of the 3 methods were compared.

Results: The prediction error for the parameters V1, PS and V2 were -7.60, 3.88 and 14.98% for the pooled data approach [1], respectively. For the pooled estimates approach [2] these values were -11.30, 4.10 and 14.52%, respectively. For the NONMEM approach [3] these values were -1.13, 0.75 and 13.12%, respectively. All three methods slightly underestimated V2. While NONMEM was the most accurate method, all three gave acceptable estimates of the true parameter values. Simulations of the predicted “average” regional venous concentrations for the three methods produced time-courses that were essentially super-imposable.

Conclusion: The findings presented here are not general, but show that in this experimental scenario any of the three methods produced a similar model of drug kinetics in an organ or region. While on theoretical grounds the NONMEM approach is preferable, particularly if inter-subject variability is of interest, the pooled data approach is surprisingly effective if average parameter values are needed and time is short. The pooled estimates approach is as time-consuming as the NONMEM approach, but less useful.

Reference: 1. Villesen HH, Foster DJ, Upton RN, Somogyi AA, Martinez A, Grant C. Cerebral kinetics of oxycodone in conscious sheep. J Pharm Sci. 2006; 95:1666-76.