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Mathematical PK/PD modelling

The PKPDsim software package covers a broad range of topics related to antibiotics, pharmacokinetics and pharmacodynamics (PK/PD); from estimation of drug concentrations from zone diameters in a bio assay to simulation assisted design of experimental studies, e.g. optimum selection of dosage regimens for effect studies in mice.

The PKPDsim package consists of a number of programs:

• AssayDeterm estimates drug concentrations from measured zone diameters in a bio assay. The program also finds the assay error pattern, i.e. the standard deviation of the estimate as a function of the concentration. The results can be used as input for the initESTIM program. See examples 

• BinKin fits various mathematical expressions to experimental data for protein binding as a fuction of drug concentration in plasma. The estimated parameter values (e.g. the specific binding capacity and the product of binding affinity and mean time in bound state) are used in the other PKPDsim programs for calculation of the free fraction of drug. See examples

• initESTIM processes and formats PK data (concentration-time points) and generates the necessary input files for use in an external population PK parameter estimation program, e.g. NPAG¹. initESTIM also performs noncompartmental modelling and estimates entities such as C_peak, AUC, T>MIC and T½. See examples

• postESTIM extracts and processes information from an external data file (from the external program used for population PK parameter estimation, e.g. NPAG) for subsequent use in the program SIM. The quality of the parameter estimates is studies and presented in a number of graphs, and various parameter distributions (including nonparametic) can be obtained from the support points. See examples

• SIM is the core program of the PKPDsim package and built for Monte Carlo simulation with compartment models. The drug concentration (free or total) including lower and upper confidence bounds as a function of time, as well as the resulting microbial net growth and density, can be found for an arbitrary dosage regimen. SIM also estimates T>MIC, AUC, C_peak, probability of target attainment, MIC breakpoints, etc. SIM has a built-in library of predefined compartment models and support for user-specified models using the Delphi programming language. Some of the other programs in the PKPDsim package also call SIM silently as a simulation engine during their execution. See examples

• studyDESIGN is a tool mainly for optimum selection of dosage regimens for experimental effect studies (in mice). The program displays the interrelationship between T>MIC, AUC, C_peak, for a series of specified dosage regimens in tables and scatter plots. The corresponding concentration-time curves are also shown. Modelling of the various dosage regimens is based on a number of single bolus PK studies (up to five) with different dose size. These PK data can come from either initESTIM (noncompartmental description) or postESTIM (fitted compartment model). See examples

• studyEFFECT fits a sigmoid curve to the chosen measure of effect, e.g. Δlog(CFU)₂₄, as a function of T>MIC, AUC, C_peak , or total dose, respectively. The CFU effect data can be specified explicitly (experimental data) or generated internally (studyEFFECT will call SIM). studyEFFECT gets the information on T>MIC, AUC, C_peak, etc. from the studyDESIGN output file. See examples

The PKPDsim package runs on computers using Windows 7/XP/NT and requires Microsoft Office Excel 2003 (or newer) and Borland Delphi command-line compiler (Borland Delphi Professional Ver 7.0 or newer).

Originally, the PKPDsim package was developed exclusively for in-house research use. Therefore only little time has been spent on developing a standard Windows graphical interface for operating the software. Most of the input data including parameter values and program execution commands have to be specified in predefined templates (text and/or Excel files).

Several of the features in PKPDsim require generation of random numbers for which PKPDsim uses Knuth's portable subtractive generator² in the implementation described by Press et al³. Other necessary standard numerical algorithms such as singular value decomposition and the fourth-order Runge-Kutta method for integration of differential equations are also implemented as suggested by Press et al.

The various subprograms have been extensively tested on synthetic (simulation generated) data where the "correct answer" is known as well as the lab's own experimental data and - when available - also experimental data and simulation results from the literature.

References

1. BigWinPops, USC*PACK, Laboratory of Applied Pharmacokinetics, USC Keck School of Medicine.
2. Knuth, DE, The art of Computer Programming: Seminumerical Algorithms, Vol 2, 3rd Ed, 1997, Addison-Wesley.
3. Press, WH, et al., Numerical Recipes in Pascal, 1989, Cambridge University Press.