Population pharmacokinetic analysis of nonlinear behavior of piperacillin during intermittent or continuous infusion in patients with cystic fibrosis

Abstract

The purpose of this study was to describe the nonlinear pharmacokinetics of piperacillin observed during intermittent infusion and continuous infusion by using a nonparametric population modeling approach. Data were 120 serum piperacillin concentration measurements from eight adult cystic fibrosis (CF) patients. Individual pharmacokinetic parameter estimates during intermittent infusion or continuous infusion were calculated by noncompartmental analysis and with a maximum iterative two-stage Bayesian estimator. To simultaneously describe concentration-time data during intermittent infusion and continuous infusion, nonlinear models were parameterized as two-compartment Michaelis-Menten models. Models were fit to the data with the nonparametric expectation maximization algorithm. The calculations were executed on a remote supercomputer. Nonlinear models were evaluated by log-likelihood estimates, residual plots, and R(2) values, and predictive performance was based on bias (mean weighted error [MWE]) and precision (mean weighted square error [MWSE]). A linear pharmacokinetic model could not describe combined intermittent infusion and continuous infusion data well. A good population model fit to the intermittent infusion and continuous infusion data was obtained with the constructed nonlinear models. Maximum a posteriori probability (MAP) Bayesian R(2) values for the nonlinear models were 0.96 to 0.97. Median parameter estimates for the best nonlinear model were as follows: K(m), 58 +/- 75 mg/liter (mean and standard deviation); V(max), 1,904 +/- 1,009 mg/h; volume of distribution of the central compartment, 14.1 +/- 3.0 liters; k(12), 0.63 +/- 0.41 h(-1); and k(21), 0.37 +/- 0.19 h(-1). The median bias (MWE) and precision (MWSE) values for MAP Bayesian estimation with the Michaelis-Menten model were 0.05 and 4.6 mg/liters, respectively. The developed nonlinear pharmacokinetic models can be used to optimize piperacillin therapy administered via continuous infusion in patients with CF and have distinct advantages over conventional linear models.

FIG. 1.

Two-compartment open model used to fit piperacillin data. IV, zero-order infusion rate; Vc, central compartment; Vp, peripheral compartment; Ke, first-order rate constant; Km, MM constant; Vmax, maximum excretion rate; k₁₂ and k₂₁, intercompartmental rate constants. Structural models evaluated in this study had either first-order elimination (Ke), MM elimination, or a combination of MM and first-order elimination.

FIG. 2.

Mean (and SD) piperacillin concentration-time profile during intermittent infusion (piperacillin, 4 g; tazobactam, 0.5 g; every 6 h) and continuous infusion (piperacillin, 16 g; tazobactam, 2 g; over 24 h) with the linear model. The solid line represents the fit with the linear model based on the intermittent pharmacokinetic data. For clarity, drug regimen crossover data are presented similarly (intermittent infusion followed by continuous infusion).

FIG. 3.

Mean (and SD) piperacillin concentration-time profile during intermittent infusion (piperacillin, 4 g; tazobactam, 0.5 g; every 6 h) and continuous infusion (piperacillin, 16 g; tazobactam, 2 g; over 24 h) with the MM model. The solid line represents the fit with the MM model based on the intermittent pharmacokinetic data.

FIG. 4.

Scatter plot of observed versus MAP Bayesian-predicted concentrations obtained with the population model median parameter estimates for the linear model and the best nonlinear model (MM model). (A) For the k_el model, the slope and the intercept of the line of best fit (solid line) are significantly different from 1.0 and 0.0 (broken line), respectively. The R² value is 0.88. (B) For the MM model, the slope and the intercept of the line of best fit (solid line) are not different from identity and 0.0 (broken line), respectively. The R² value is 0.97. pred. conc., predicted concentration; post., a posteriori.