During preclinical trials for a new drug, its therapeutic dose needs to be determined for safe clinical phase tests. Dose estimation experiments are typically performed on laboratory animals like rats, dogs or non-human primates. It is important that all mechanisms of drug kinetics and metabolism are understood, before a new drug can be safely administered to humans. The necessary interspecies scaling of the therapeutic drug dose levels is often obtained by weight-based extrapolation, thus introducing large uncertainties about the global transport mechanisms, the clearances and mass balance errors.
This paper proposes an algorithmic method for the parameter estimation and model selection of physiologically-based pharmacokinetics (PBPK) in a flexible vasculature model of an organism. The methodology consists of the following steps:
1. Construction of the simplified, closed vasculature flow network for each analyzed species
2. Selection of the organ-specific PBPK models
3. Automatic solution of the time-concentration profiles in each organ after drug delivery
4. Obtaining experimental data related to drug delivery in each organ
5. Parameter estimation; comparison of the resulting concentration profiles with experiments
6. (Re)evaluation of the quality of each PBPK model
The PBPK model typically defines a set of ordinary differential equations reflecting the drug accumulation in each physiological compartment. These equations are a function of blood perfusion, drug clearance, receptor binding as well as the dosing method. For parameter estimation, a set of experimentally measured concentration profiles after drug delivery is needed for each modeled subsystem, such as plasma, blood and tissue. The minimum least squares distance between experimental and predicted concentrations determine the optimal parameters for each PBPK model. The advantages of using analytic sensitivity information for the inversion problem will be highlighted in this paper. In addition, we show that kinetic inversion problems often exhibit solution multiplicity. Therefore, we deploy global optimization techniques that can locate all minima in the least square error surface. The solution of the parameter estimation gives the desired kinetic constants and drug clearance for each organ in the organism. Our modeling framework also allows for evaluation of model quality, so that proper model selection among various PBPK models can be performed in an automated fashion.
In conclusion, this contribution presents a method for semi-automated physiologically-based pharmacokinetic model selection and parameter estimation based on experimental datasets from drug response curves. The results include time-dependent drug concentrations in each organ and provide valuable insights into the mechanics of drug transport in a modeled organism. The successful application of the proposed methods will lead to better design of preclinical trials, more knowledge gain from animal experimentation and eventually lead to shorter drug development times.
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