Pharmacodynamic Parameters of Pharmacokinetic/Pharmacodynamic (PK/PD) Integration Models

Abstract

Pharmacokinetic/pharmacodynamic (PK/PD) integration models are used to investigate the antimicrobial activity characteristics of drugs targeting pathogenic bacteria through comprehensive analysis of the interactions between PK and PD parameters. PK/PD models have been widely applied in the development of new drugs, optimization of the dosage regimen, and prevention and treatment of drug-resistant bacteria. In PK/PD analysis, minimal inhibitory concentration (MIC) is the most commonly applied PD parameter. However, accurately determining MIC is challenging and this can influence the therapeutic effect. Therefore, it is necessary to optimize PD indices to generate more rational results. Researchers have attempted to optimize PD parameters using mutant prevention concentration (MPC)-based PK/PD models, multiple PD parameter-based PK/PD models, kill rate-based PK/PD models, and others. In this review, we discuss progress on PD parameters for PK/PD models to provide a valuable reference for drug development, determining the dosage regimen, and preventing drug-resistant mutations.

Keywords: MIC; PD parameter; PK/PD integration model; dosage regimen; kill rate; multi-drug resistance; mutant prevention concentration; time-kill curve.

Figure 1

Antimicrobial PK, PD, and PK/PD parameters based on MIC (minimum inhibitory concentration) and MPC (mutant prevention concentration). The most commonly applied PK/PD parameters are AUC/MIC (area under the curve of antibacterial concentration divide MIC) or AUC/MPC, C_max/MIC (maximum drug concentration divide MIC) or C_max/MPC, and T > MIC (the time of the drug concentration above MIC during the dosage interval) or T > MPC (the time of the drug concentration above MPC during the dosage interval). MSW (mutant selection window) is the drug concentration between MIC and MPC. T_MSW (dash area) is the time that the antibacterial concentration inside MSW during the dosage interval.

Figure 2

The possible changes of bacterial population and sensitivity under different antibacterial concentrations in low (10⁵ CFU/mL) and high (10¹⁰ CFU/mL) inoculums based on MSW theory. ◦, susceptible bacteria. •, natural mutant bacteria. ♢, first step mutant bacteria. ♦, multiple step mutant bacteria. MIC, minimum inhibitory concentration. MPC, mutant prevention concentration. MSW, mutant selection window, is the drug concentration between MIC and MPC. In low inoculum, the bacterial population will be gradually reduced with the drug concentrations added from MIC to MPC, and the bacterial sensitivity may be decreased because of the emergence of first step resistant mutation during MSW. In high inoculum, a natural mutant bacteria may exist in the initial population. The total population will be decreased but the mutant subpopulations may be increased when the drug concentrations below MPC. The sensitivity may be obviously decreased because of the emergence of first step and multiple step mutant bacteria during MSW.

Figure 3

The relationship curves between kill rate and concentration of concentration-dependent (dotted line) and time-dependent (solid line) drugs. For concentration-dependent drugs, the kill rate will gradually increase with the concentration added. For time-dependent drugs, the kill rate was smaller compared to concentration-dependent drugs and rapidly reach a plateau that the value have little change with the concentration increased.