**Steady-state Equation for the Bicompartmental Model with Gamma Absorption. Application to Mycophenolate PK in Renal Transplant Patients**

M. Tod (1), B. Blanchet (2), A. Astier (2), A. Hulin (2)

(1) Laboratory of Toxicology, CHU Cochin, Paris, and ISPB, Claude Bernard University, Lyon, France, (2) Laboratory of Pharmacology, CHU Henri Mondor, Créteil, France

**Background: **The bicompartmental model with gamma-distributed absorption times is a useful empirical model for drugs whose absorption kinetics is not zero- or first-order. We derived for this model a steady-state equation, involving one parameter less than the previous derivation (1). The equation involves the incomplete gamma function P. An approximation (based on equivalence with a chi-squared distribution) is proposed in order to facilitate its implementation in NONMEM.

**Objectives: **To compare the population estimates obtained with NONMEM (approximate equation for P) and MONOLIX (no approximation for P) on real data.

**Methods:** Both approaches were compared for the estimation of mycophenolate (MPA) population parameters in 77 renal transplant patients treated with tacrolimus and mycophenolate mofetil. Three blood samples per patient were collected at steady-state at several occasions. Plasma concentrations were measured by HPLC. The two-compartment gamma absorption model was fitted to the data using NONMEM V (FOCE) and MONOLIX. The PK parameters were the volume of the central compartment V_{1}, the rate constant K_{21}, the slopes of the two phases Lam_{1}, Lam_{2}, the absorption rate constant Ka and the shape parameter, s. Goodness-of-fit was assessed by prediction discrepancies (2).

**Results:** Examination of prediction discrepancies plots revealed no lack of fit of the model. Fixed effects estimates obtained by both approaches were very similar and not significantely different. The typical mean absorption time (s / Ka) was 0.71 h while the typical variance of absorption time (s / Ka^{2}) was 0.094. Variance-covariance matrices of random effects differed. This may be due to differences in the calculation of the population likelihood in both softwares.

**Conclusion: **The new equation for the steady-state two-compartment model with gamma absorption and its approximation may be useful for NONMEM users.

**References:**[1] Premaud A et al. MAP bayesian estimation of MPA pharmacokinetics in renal transplant recipients at different postgrafting periods. Ther Drug Monit. 2005;27:354-361.

[2] Mentré F, Escolano S. Prediction discrepancies for the evaluation of non-linear mixed-effects models. J Pharmacokin Pharmacodyn. 2006;33:345-367.