Physiologically based pharmacokinetic modeling: methodology, applications, and limitations with a focus on its role in pediatric drug development

Abstract

The concept of physiologically based pharmacokinetic (PBPK) modeling was introduced years ago, but it has not been practiced significantly. However, interest in and implementation of this modeling technique have grown, as evidenced by the increased number of publications in this field. This paper demonstrates briefly the methodology, applications, and limitations of PBPK modeling with special attention given to discuss the use of PBPK models in pediatric drug development and some examples described in detail. Although PBPK models do have some limitations, the potential benefit from PBPK modeling technique is huge. PBPK models can be applied to investigate drug pharmacokinetics under different physiological and pathological conditions or in different age groups, to support decision-making during drug discovery, to provide, perhaps most important, data that can save time and resources, especially in early drug development phases and in pediatric clinical trials, and potentially to help clinical trials become more "confirmatory" rather than "exploratory".

Figure 1

The concept for building a PBPK model modified according to Willmann et al. [13]. (a) Organisms (e.g., humans of different ages or populations) are the basis for the model. (b) The organism is divided into a number of compartments, each representing a single organ. To describe the distribution of compounds in the body, the organs are connected via their arteries and veins to the arterial and venous blood pool. Intercompartmental mass transport occurs via organ-specific blood flow rates. The organs are mathematically connected. (c) Division of each organ into three subcompartments representing the vascular space with blood cells and the interstitial and cellular space. The interstitial space is assumed to be in direct contact with the plasma. The exchange of substances between the cellular and interstitial compartment can occur by permeation across the membranes via passive diffusion as well as active influx and efflux transport processes by saturable Michaelis-Menten (MM) kinetics with V_max and K_m as parameters. Metabolism of substances (Meta1 and Meta2) occurs via active enzymes (MM kinetics). Finally, the model consists of a large number of coupled differential equations. (d) Output of the model : concentration time curves for the substances shown are simulated and observed ciprofloxacin concentrations in various organs after ciprofloxacin 5 mg/kg was intravenously applied to a rat.

Figure 2

Diagrams and equations for a perfusion rate-limited, one-compartment model (a) and a permeability rate-limited, two-compartment model with the permeability at the vascular membrane (b) of noneliminating organs, adapted from Nestorov et al. [15]. Q = blood flow; C = concentration; V = volume; Kp = tissue : plasma distribution coefficient; PS = permeability surface area coefficient; subscripts T, ART, VEN, V, and EV indicate tissue, arterial, venous, vascular compartment, and extravascular compartment, respectively.

Figure 3

Predicted and observed arithmetic mean (±SD) plasma concentration-time curves of alfentanil in (a) healthy controls and (b), (c) patients with liver cirrhosis. Figure is adapted from Edginton and Willmann [34].

Figure 4

Comparison of lidocaine predicted and observed mean plasma concentration-time curves in healthy controls (a) and patients with Child-Pugh class A (b) and class C liver cirrhosis (c). Model simulation results adapted from Edginton and Willmann [34].

Figure 5

Simulated midazolam maternal plasma concentration-time profile following postcaesarean IV bolus compared with two different set of observed data; adapted from Andrew et al. [32].

Figure 6

Predicted dose-normalized pediatric plasma concentration-time curves (lines) versus observed data (symbols) for (a) alfentanil and (b) morphine as reported in the original study by Edginton et al. [52]. Observed data was obtained from various studies in the literature.

Figure 7

Simulation results using the PK-Sim software of a PBPK model for sildenafil in children [53]. (a): Predicted age-dependent sildenafil hepatic clearance across different pediatric ages based on the clearance scaling module in PK-Sim software. (b): Age-related doses for oral sildenafil in children depending on the simulated age-related exposure (not shown) of sildenafil in a virtual pediatric population and the estimated exposure of the estimated doses of sildenafil in children between 3 months and 18 years. Potential pediatric doses based on simulations for sildenafil to achieve adult exposure: infants and children from 3 months to 4 years: 0.8 mg/kg; children from 5 to 8 years: 0.5 mg/kg; and children older than 8 years: 0.35 mg/kg as in adults. Box plots represent median, 25th, and 75th percentiles (box), 5th and 95th percentiles (error bar), and maximum and minimum values (x) of AUC_0−∞ from 1000 simulations in each age group.

Figure 8

Schematic drawing of a potential application of PBPK simulations for children of different ages to find optimal blood sampling time points for the pharmacokinetic investigations in a future pediatric trial according to Willmann [54]. Arrows indicate optimal sampling time for a 3-year-old child, a newborn, and an adult. LOQ: limit of quantification.