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Physiologically-based pharmacokinetic modelling
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What is a PBPK model?

Physiologically based pharmacokinetic (PBPK) modeling is a mathematical modeling technique for predicting the absorption, distribution, metabolism and excretion (ADME) of synthetic or natural chemical substances in humans and other animal species. PBPK modeling is used in pharmaceutical research and drug development, and in health risk assessment
Risk assessment
Risk assessment is a step in a risk management procedure. Risk assessment is the determination of quantitative or qualitative value of risk related to a concrete situation and a recognized threat...

 for cosmetics or general chemicals.

PBPK models strive to be mechanistic by mathematically transcribing anatomical, physiological, physical, and chemical descriptions of the phenomena involved in the complex ADME processes. A large degree of residual simplification and empiricism is still present in those models, but they have an extended domain of applicability compared to that of classical, empirical function based, pharmacokinetic models. PBPK models may have purely predictive uses, but other uses, such as statistical inference, have been made possible by the development of Bayesian
Bayesian statistics
Bayesian statistics is that subset of the entire field of statistics in which the evidence about the true state of the world is expressed in terms of degrees of belief or, more specifically, Bayesian probabilities...

 statistical tools able to deal with complex models (see Gelman et al. 1996). That is true for both toxicity risk assessment and therapeutic drug development.

PBPK models try to rely a priori on the anatomical and physiological structure of the body, and to a certain extent, on biochemistry. They are usually multi-compartment model
Multi-compartment model
A multi-compartment model is a type of mathematical model used for describing the way materials or energies are transmitted among the compartments of a system. Each compartment is assumed to be a homogenous entity within which the entities being modelled are equivalent...

s, with compartments corresponding to predefined organs or tissues, with interconnections corresponding to blood or lymph flows (more rarely to diffusions). A system of differential equations for concentration or quantity of substance on each compartment can be written, and its parameters represent blood flows, pulmonary ventilation rate, organ volumes etc., for which information is available in scientific publications. Indeed the description they make of the body is simplified and a balance needs to be struck between complexity and simplicity. Besides the advantage of allowing the recruitment of a priori information about parameter values, these models also facilitate inter-species transpositions or extrapolation from one mode of administration to another (e.g., inhalation to oral). An example of a 7-compartment PBTK model, suitable to describe the fate of many solvents in the mammalian body, is given in the next Figure.

History

It is interesting to note that the first pharmacokinetic model described in the scientific literature (see Teorell 1937) was in fact a PBPK model. It led, however, to computations intractable at that time. The focus shifted then to simpler models, for which analytical solutions could be obtained (such solutions were sums of exponential terms, which led to further simplifications.) The availability of computers and numerical integration algorithms marked a renewed interest in physiological models in the early 1970s. By 2010, hundred of scientific publications have described and used PBPK models, and at least two private companies are basing their business on their expertise in this area.

Uses of PBPK modeling

PBPK models are compartmental models like many others, but they have a few advantages over so-called "classical" pharmacokinetic models, which are less grounded in physiology. PBPK models can first be used to abstract and eventually reconcile disparate data (from physico-chemical or biochemical experiments, in vitro
In vitro
In vitro refers to studies in experimental biology that are conducted using components of an organism that have been isolated from their usual biological context in order to permit a more detailed or more convenient analysis than can be done with whole organisms. Colloquially, these experiments...

 or in vivo
In vivo
In vivo is experimentation using a whole, living organism as opposed to a partial or dead organism, or an in vitro controlled environment. Animal testing and clinical trials are two forms of in vivo research...

 pharmacological or toxicological experiments, etc.) They give also access to internal body concentrations of chemicals or their metabolites, and in particular at the site of their effects, be it therapeutic or toxic. Finally they also help interpolation and extrapolation of knowledge between:
  • Doses: e.g., from the high concentrations typically used in laboratory experiments to those found in the environment
  • Exposure duration: e.g., from continuous to discontinuous, or single to multiple exposures
  • Routes of administration: e.g., from inhalation exposures to ingestion
  • Species: e.g., transpositions from rodents to human, prior to giving a drug for the first time to subjects of a clinical trial, or when experiments on humans are deemed unethical, such as when the compound is toxic without therapeutic benefit
  • Individuals: e.g., from males to females, from adults to children, from non-pregnant women to pregnant


Some of these extrapolations are "parametric" : only changes in input or parameter values are needed to achieve the extrapolation (this is usually the case for dose and time extrapolations). Others are "nonparametric" in the sense that a change in the model structure itself is needed (e.g., when extrapolating to a pregnant female, equations for the fetus should be added).

Limits and extensions of PBPK modeling

PBPK models rely and are bounded by chemical property prediction models (QSAR models or predictive chemistry models) on one hand. They also extend into, but are not destined to supplant, systems biology
Systems biology
Systems biology is a term used to describe a number of trends in bioscience research, and a movement which draws on those trends. Proponents describe systems biology as a biology-based inter-disciplinary study field that focuses on complex interactions in biological systems, claiming that it uses...

 models of metabolic pathways. They are also parallel to physiome
Physiome
The physiome of an individual's or species'physiological state is the description of itsfunctional behavior. The physiome describes the physiological dynamics ofthe normal intact organism and is built upon information and...

 models, but do not aim at modeling physiological functions beyond fluid circulation in detail. In fact the above four types of models can reinforce each other when integrated (Bois, 2009, 2010).

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