chapter  7
36 Pages

The Application of PBPK Modeling, the Bayesian Approach, and the Utilization of Markov Chain Monte Carlo Simulation in Risk Assessment

We make no attempt to “teach” PBPK modeling in this chapter as it is a very complex subject with well over a thousand publications in recent decades [1]. However, in an earlier book, Risk Assessment

for Environmental Health, Yang and Lu [2] had discussed the need for PBPK modeling in risk assessment from six different perspectives: (1) toxicological interactions of multiple chemicals, (2) minimizing animal experiments, (3) Food Quality Protection Act (FQPA) and the subsequent development of cumulative risk assessment at the USEPA, (4) internal dose, (5) exposure dose reconstruction and human biomonitoring, and (6) systems biology. Also included in that chapter is the line-by-line explanation of a sample PBPK model code in Berkeley Madonna software. The readers are encouraged to consult this earlier publication for a preliminary understanding of PBPK modeling. In-depth training related to PBPK modeling and its application to risk assessment is available through various PBPK modeling workshops (e.g., the ones offered by the lead author at Colorado State University, by the Hamner Institute and by the Health and Safety Laboratory, UK) or by reading the variety of review papers on the subject and the 2005 and 2012 books on PBPK by Reddy et al. and Peters, respectively [1, 3]. Likewise, the areas of Bayesian population PBPK modeling and MCMC simulation, though exceedingly important in modern risk assessment, are very complicated subjects. A detailed explanation and instruction of these areas is beyond the scope of this chapter. However, this chapter is specifically aimed toward those readers who do not intend to learn how to do PBPK/Bayesian population PBPK/MCMC but need to know how they are applied to risk assessment. Accordingly, a “minimal primer” is provided for each of these two areas (PBPK modeling and Bayesian population PBPK modeling/MCMC simulation) in as plain English as possible. 7.2 The Earlier Days of Risk Assessment of DCMThe development of the science of risk assessment, like any other field of science, has advanced from relatively simple and straight-forward methodologies to those with progressively more sophisti-cation. Thus, in the earlier days, because the available information usually consisted of laboratory animal toxicity studies, initial risk assessment of DCM by the USEPA was based on administered dose, from drinking water studies in rats and mice [4, 5], and exposure concentrations in inhalation studies in rats [6, 7]. From the days of the first on-line filing of DCM risk assessment in 1987, the USEPA

has made numerous updates as the science advances on DCM toxi-cology. At the time of writing this chapter in May 2013, the latest posting of the update on the IRIS summary was dated August 9, 2012. With the exception of published papers in scientific journals, only the most recent versions of the USEPA supporting documents are readily available. Some of the older USEPA documents are cited but are often difficult to locate. The initial chronic oral reference dose (RfD) was based on the critical effects of hepatic vacuolation, liver foci in the two-year F344 rat drinking-water bioassay [4]. The liver changes were observed after treatment for 78 weeks and persisted until week 104. Principally based on these findings, Serota et al. [4] suggested that 5 mg/kg-day was a no-observed-adverse-effect level (NOAEL) and 50 mg/kg-day was the lowest-observed-adverse-effect level (LOAEL) in male and female F344 rats exposed to DCM in drinking water for two years. Of course, the current chronic oral RfD in the IRIS summary has been updated on the basis of more recent science, and that will be discussed as part of our continuing DCM story. Likewise, the initial inhalation reference concentration (RfC) for DCM was based on data from rats in two chronic inhalation studies conducted at Dow Chemical Company [6, 7]. The authors of these papers [6, 7] indicated that even though the outcome of the two studies were similar, they placed more emphasis on Nitschke et al. [7] in their risk assessment because in this later study [7] they had examined a lower range of exposures. Nitschke et al. [7] reported that female rats exposed to 500 ppm methylene chloride had increased incidences of multinucleated hepatocytes and number of adenomas, fibromas, and fibroadenomas in the mammary gland. Their overall conclusion was that 200 ppm appeared to be the no-adverse-effect level for chronic inhalation exposure to Sprague-Dawley rats. On the basis of these studies, the USEPA did its initial risk assessment, and those values were since modified and updated from further studies appeared in the literature as discussed earlier. 7.3 The “Revolutionary” Paper: The Application

of PBPK Modeling in Risk AssessmentThe necessity for the application of PBPK modeling in risk assess-ment became evident as the science of toxicology advanced. One

of the most important advances was the consideration of “internal dose or target dose” instead of the then conventional external expo-sure dose. The pioneering work, as discussed in more details in the following text, was published by Andersen et al. [8]. Other needs for the utilization of PBPK modeling in toxicology and in risk assessment, summarized by Yang and Lu [2], included both scientific and regulatory reasons. These involved the consideration of toxicological interactions of multiple chemicals, minimizing animal experiments, the Food Quality Protection Act (FQPA) and the related development of cumulative risk assessment at the USEPA, and exposure dose re-construction and human biomonitoring. Finally, it should be noted that PBPK modeling, as a technology that integrates all relevant bio-logical information with computer simulation, captured the essence of systems biology [2]. 7.3.1 Physiologically Based Pharmacokinetic Modeling:

A “Minimal Primer”Toxicology is a continuum of pharmacokinetics and pharmacodynamics. The former, pharmacokinetics, is what the body does to the chemical. Thus, how fast is the chemical absorbed, how rapidly is the chemical distributed to the tissues, what tissues, to what extent is the chemical metabolized, how long is the chemical retained in the body etc., are all areas of pharmacokinetics. The latter, pharmacodynamics, is what the chemical does to the body. Thus, does the chemical inhibit acetyl cholinesterase in the brain, does the chemical bind with the Ah receptor, what are the downstream event and toxicological consequences etc., are all possible subjects in the domain of pharmacodynamics. It is difficult to clearly distinguish where pharmacokinetics stop and pharmacodynamics begin. Similarly, toxicology is an overlapping continuum of pharmacokinetics and pharmacodynamics. It should be noted that there are people who prefer to use the terms of “toxicokinetics” and “toxicodynamics.” Simplistically, PBPK modeling is a computer simulation of “what the body does to the chemical,” based on physiology, biochemistry, and chemical engineering concepts. If we imagine our body as a

chemical plant, we have a pump (heart), a lot of pipes (blood vessels), and reactors (liver, kidney, etc.). The chemical has to get in the body first; therefore, we deal with “absorption” following the most usual ways of oral, inhalation, and/or dermal exposures. Once the chemical is in the body, the blood (and/or other body fluids) carries it to different parts of the body (distribution). The principal organ of metabolism is the liver in which various enzymes break down or modify the chemical, usually rendering it more water soluble to be excreted (metabolism). Of course, “elimination” of the chemical or its metabolites can be done via urine, feces, breath, or other means (e.g., loss of hair, cell). These four processes are termed “absorption, distribution, metabolism, and excretion,” or ADME-the principal elements of pharmacokinetics. PBPK modeling deals with these processes for a given system, which could be a single organ (e.g., the liver, the fat) or a collection of or lumped organs/tissues (e.g., richly or poorly perfused tissues). In each of these compartments, a mass balance differential equation integrates all the information in mathematic terms such as the general equation shown below:V dC

dt Q CA CVi

ij i j ij ij ij ij ij= - - - + -( ) lim PrMetab E Absorp Binding Such an equation could be easily “translated” into simple everyday English, and that is one of the beauties of PBPK modeling. To start with, i and j are, respectively, a given “tissue” and a given

“chemical,” and V, C, Q, CA, and CV are, respectively, “volume of the tissue,” “concentration of the chemical,” “flow rate of the blood to that tissue,” “concentration of the chemical in arterial blood,” and “concentration of the chemical in venous blood.” Thus, for example, VL is volume of the liver; CF,DCM is concentration of DCM in the fat. The meaning of this whole general mass balance equation, in simple English from left to right, is thus: the instantaneous rate of change of the amount (mass, which is resulted when concentration is multiplied by volume) of a given chemical (dC is an infinitesimal change of concentration; dt is an infinitesimal change of time) is equal to the blood flow rate to a given tissue multiplied by the differential concentration of that chemical between arterial and venous blood (i.e., input minus output), subtracting metabolism

(Metab), elimination (Elim), and protein binding (PrBinding) (because these processes take the chemical out of circulation) and adding absorption (Absorp). For a given tissue, or a group of tissues, not all the processes in this general equation are there so that the general equation would collapse into a simpler equation. Depending on your experimental needs, a collection of such mass balance equations, representing all relevant compartments included in the model, and their respective supporting equations formulate the PBPK model that is shown, conceptually, in Fig. 7.1. More details on PBPK modeling and its related analyses will be given in the “Minimal Primer” (Section 7.6.1) for Bayesian population PBPK modeling and MCMC simulation. 7.3.2 The “Revolutionary” Paper: Andersen et al. In 1987, Andersen et al. [8] published a paper describing their approach for applying PBPK modeling to the risk assessment of DCM. This was the beginning of a trailblazing effort for the application of PBPK modeling to toxicology and risk assessment; thus, it represented a “revolution” in the field of toxicology. In this paper, Andersen et al. [8] first pointed out that there were discrepancies among the results from three groups of chronic toxicity/carcinogenicity studies in laboratory animals; the three groups of studies were carried out, respectively, by Dow Chemical Company in rats and Syrian golden hamsters via inhalation exposure [6], Hazleton Laboratory America under the sponsorship of the National Coffee Association in rats [4] (original citation was from a 1984 workshop) and mice [5] (original citation was from a 1984 workshop) via drinking-water exposure, and rat inhalation studies conducted by the National Toxicology Program (NTP) [9] (original citation was a 1985 board draft of the NTP technical report). Andersen et al. [8] noted that while there was no evidence suggesting carcinogenicity of DCM in the Syrian golden hamster inhalation studies [6] and in rats and mice drinking-water studies [4, 5], inhalation of DCM resulted in increases in spontaneously occurring mammary gland tumors in the rat in both the Burek et al. [6] and the NTP [9] studies. In addition, low incidences of tumors in

the neck region and around salivary gland were noted in the male rats in the Burek et al. [6] study but not in the female rats in Burek et al. [6] nor in any rats of the NTP [9] studies. The most significant findings were in the studies by the NTP where the incidences of both benign and malignant tumors were elevated [9]. Thus, the NTP [9] concluded that under the inhalation study conditions, there was some evidence for carcinogenicity of DCM for male rats (an increased incidence of benign neoplasms of the mammary gland), clear evidence for carcinogenicity of DCM for female rats (increased incidences of benign neoplasms of the mammary gland), and clear evidence for both male and female mice (increased incidences of alveolar/bronchiolar neoplasms and hepatocellular neoplasms).