First principles pharmacokinetic modeling: A quantitative study on Cyclosporin
Highlights
► An approach to develop whole-body PK models based on first principles is proposed. ► To solve the parameter estimation problem, a rigorous inversion algorithm is used. ► Advantages of our methodology are demonstrated with a case study on Cyclosporin. ► Drug kinetics and transport are determined using only in vivo dose–response data. ► Results establish Cyclosporin biodistribution dynamics in all organs and tissues.
Introduction
The effect of novel drugs on targeted organs is typically studied in animal drug dosing trials. Pharmacokinetic models establish relationships between drug dosage, bioaccumulation and clearance utilizing dose–response measurements. Classical pharmacokinetic (PK) models relate anatomy and physiology parametrically to dose–response data while fitting exponential functions with multiple adjustable constants or exponential coefficients ([Buss and Stepanek, 1993], [Legg and Rowland, 1987], [Ursino et al., 1992]). The resulting black-box formulae permit the computation of the area under the curve (AUC), the plasma half-life of elimination (t1/2) or the intrinsic clearance rates. Limitations are observed when fitted relations are used to extrapolate drug concentration profiles for different doses (Ring et al., 2011).
Non-mechanistic, classical PK methods derive very little information about reaction kinetics and biotransport phenomena. It is reportedly difficult to scale or extrapolate information among laboratory animals or to predict drug fate for different dosing regimes (Nestorov, Hadjitodorov, Petrov, & Rowland, 1999). Hence, large sets of dose–response data have to be acquired in extensive animal trials in rats, then dogs and monkeys, until finally arriving at reasonably safe specifications for human trials. Prediction accuracy in PK models could be greatly improved by the incorporation of conservation laws, and fundamental transport and biochemical reaction mechanisms, which is beyond the scope of black-box approaches.
The efficacy of novel drugs can be studied more systematically with mechanistic biochemical models. Several authors have proposed whole body physiologically based pharmacokinetic (PBPK) prediction and modeling techniques ([Gueorguieva et al., 2006], [Kawai et al., 1994], [Kawai et al., 1998], [Tanaka et al., 2000]). A thorough review of whole body physiologically based pharmacokinetic models (Edginton, Theil, Schmitt, & Willmann, 2008) recognizes the need for methods linking modeling, simulation, drug approval and rigorous experimental data analysis. Previous work commonly deployed compartments, typically encompassing several biological subsystems such as blood, plasma, red blood cells, interstitial fluid, the lymphatic system, the central nervous system, tissues and organs (De Buck et al., 2007).
One possible scenario for drug fate modeling in the whole body is to determine the drug transport parameters by in vitro measurements, for instance with tissue-to-plasma partitioning coefficients ([Haritova and Fink-Gremmels, 2010], [Schmitt, 2008]). However, these compartmental models typically do not account for the physiologically consistent blood perfusion or lymphatic fluid exchange patterns.
Several authors have recently used first principles modeling to elucidate the biochemical reaction mechanisms of new drugs in vivo ([Espié et al., 2009], [Garg and Balthasar, 2007], [Lüpfert and Reichel, 2005], [Laplanche et al., 2007], [Peters and Hultin, 2008], [von Kleist and Huisinga, 2007], [von Kleist and Huisinga, 2009], [Yates, 2006]). Although mechanistic, the underlying algorithms commonly infer systemic circulation with a set of continuity and conservation differential equations. Every part of the whole body flow network has to be entered manually. This soon leads to infeasibility if multiple animal models need to be tested.
In contrast, our improved workflow ensures that for arbitrarily complex PBPK networks with hundreds of biological “compartments”, corresponding differential equations are automatically generated and validated. This allows for testing various circulatory system configurations with greater detail as more data become available on the drug–organ interactions. Given solid data describing individual pharmacokinetic processes, the selection of an accurate but general mechanistic model still remains a scientific challenge.
In this article a rigorous engineering approach based on first principles of mass, species and momentum conservation is proposed to build upon the advances in classical PK modeling. The presented work aims at determining drug reaction kinetics and transport phenomena from actual experimental dose–response measurements. To scientifically examine drug fate in living organisms, we emphasize the need for a closed loop iterative methodological approach: (i) obtaining experimental data, (ii) constructing first principle models, (iii) estimating parameters and (iv) gaining insights from comparing working hypotheses with experimental sets.
We will demonstrate the advantages of our methodology with a case study on the immunosuppressant Cyclosporin. Our advanced mechanistic model results in a rigorous analysis of biodistribution after a bolus iv injection into a rat. The model will also be used to assess different administration regimes, which in the case of Cyclosporin have been shown to enormously affect interactions with physiology, cardiovascular dynamics and pharmacology ([Kawai et al., 1994], [Kimura et al., 2010], [Kovarik et al., 2008], [Omar and El-Mas, 2004]). We hope to contribute an improved level of understanding in such a complex topic.
This paper is organized as follows. Section 2 lays out the conceptual foundation: (i) steady state systemic blood circulation model, (ii) mechanistic transport, mass transfer and biochemical reaction parameters, and (iii) a parameter estimation technique for determining the unknown model parameters from actual animal experiments. The application of this concept is demonstrated with a case study on Cyclosporin in Section 3. Results are discussed in section four.
Section snippets
Mathematical Formulation of Whole Body Pharmacokinetics
This section introduces our PBPK model with inherent first principles intraspecies scaling, an overview of which is shown in Fig. 1. We present a living system model which predicts the drug biodistribution among individual subjects of the same species, in an organism, organs, tissues and cells.
- 1.
Intraspecies scaling is accomplished by application of physiological and morphological differences onto the underlying first principles PBPK model.
- 2.
Whole body drug dynamics results from application of
Results: case study on Cyclosporin
This section presents the case study on Cyclosporin. It shows the systemic blood circulation model of a rat followed by a formulation of the mechanistic PBPK transport and biochemical reaction model. Finally, the nonlinear parameter estimation technique will be used to determine the unknown PBPK model parameters with individual confidence interval estimates to assess model quality. Specifically, the results demonstrate a parameter estimation technique for therapeutic bolus injection of 6 mg/kg
Discussion
One model fits all dosing regimes. The presented mechanistic physiological workflow determines fundamental transport and reaction mechanisms of Cyclosporin in an entire organism.
A key outcome of this study is that the bioaccumulation of Cyclosporin can be predicted for a wide of range of different doses with a mechanistic model, whose parameters were estimated from a single dose experiment. In the case study, the unique set of mechanistic parameters, k, was determined rigorously from
Conclusions
This first principles PBPK framework allows modeling of drug dose–response curves for a wide range of variations such as physiology, pathology and selected administration routes in all organs of a rat. These results are derived from a single laboratory dose experiment dataset combined with constant physiological data. The case study is a proof-of-concept of first principles modeling which is expected to lead to novel insights about the biodistribution, bioaccumulation and elimination of
Acknowledgements
Financial support from NSF CBET 0730048 is gratefully acknowledged. C.H. was supported by a fellowship from the NSF Research Experience for Undergraduates Site on Novel Processes and Materials in Biomedical Engineering and Medicine (NSF REU EEC 0754590).
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