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EPA-Expo-Box (A Toolbox for Exposure Assessors)

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Exposure Reconstruction
(Biomonitoring and Reverse Dosimetry)

Pharmacokinetic Models

Pharmacokinetic (PK) models can be used to help characterize exposure when used in conjunction with biomonitoring data to relate exposure to internal dose (predictive analysis), or vice-versa to relate internal dose to exposure (reconstructive analysis).

In exposure assessment, PK models can be used to characterize the internal dose by identifying and evaluating the relationship between an intake dose and biomonitoring data, enable route-to-route extrapolation of the internal dose, and reconstruct exposure when used in combination with data from epidemiological studies (U.S. EPA, 2006).

PK models provide insights into the body burdens that result from specific exposures, but require specific knowledge of model parameters and of the relationship between exposure and internal dose.

There are advantages and limitations to using PK models. After studying what happens to a chemical once it is absorbed, a PK model can be used to back-calculate the level of exposure based on biomonitoring data. Using PK models in this way for exposure reconstruction is potentially a very powerful application; however, detailed input parameters for the PK model must be known for the model to be reliable. Most importantly, the relationship between exposure and dose, including bioavailability, needs to be well understood, which is not always the case.

PK models vary in complexity. The simplest PK model is a one-compartment, first order model that assumes immediate distribution of a chemical within a single “compartment” such as blood or body lipids or even the whole body of the organism. The creatinine correction model is an example of a simple PK model that is applicable for contaminants that are excreted in urine within hours following intake. In comparison to these simple models, a physiologically based PK (PBPK) model is a complex, multi-compartment model that accounts for an organism’s physiology and the chemical properties of the contaminant.

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Simple

A simple one-compartment, first-order PK model estimates the change in concentration (C) in one compartment over time given a specified exposure or intake. It takes what comes in, the Dose; subtracts what goes out via an elimination rate constant (k); and calculates the change in concentration of a chemical (the body burden) over time (t).

Expression

Simple models have minimal overall data requirements, but do not model the fate of the chemical in the body and cannot, therefore, address target organ dose which is often necessary for a toxicology study. A one-compartment PK model is most often applied for contaminants that bioaccumulate in body tissues. Bioaccumulative contaminants typically have overall elimination half-lives on the order of years (e.g., lead, dioxin, DDT).

Diagram of Simple, One-Compartment Model
One-Compartment Model

The compartment might also be referred to as the "volume of distribution", or V, and might represent the entire body or a part of the body (e.g., the blood). The elimination rate constant, k, is related to the elimination half-life of the chemical, specifically k = 0.693/half-life.

The simple one-compartment PK model can be applied in an iterative mode, meaning that it can be applied in the context of a computer model structure where the key input parameters, the Dose, the volume of distribution V, and the elimination rate constant k, can vary over time. Another common application is to assume steady state conditions, where these inputs do not vary over time. Mathematically, this can be used to:

Solve for Concentration given Dose   Solve for Dose given Concentration
Expression   Expression

Creatinine Correction Model

Many contaminants do not bioaccumulate, but rather are eliminated from the body, mostly by urine excretion, within a matter of hours following intake (e.g., some pesticides, bisphenol A, perchlorate, and phthalates). The most common model for reconstructing dose for contaminants that are eliminated via urine is the creatinine correction model. Muscles excrete creatinine daily in urine and simple functions exist to estimate the expected daily creatinine excretions adjusted for sex, age, body weight, height, and race (Mage et al., 2008; Mage et al., 2004; Cockcroft and Gault, 1976). Creatinine is regularly measured along with urine-excreted contaminants in surveys like NHANES where contaminant concentrations are expressed in terms of mass contaminant/mass creatinine. 

Reconstructing dose using the creatinine correction approach is only applicable if exposure is ongoing and daily excretion is assumed to be directly correlated to daily exposure.

One reason creatinine is measured is to normalize urine concentrations. Specifically, there are situations where high contaminant concentrations occur because of low urine volume (urine volume is a function of hydration), not high excretion of the contaminant. Creatinine excretion is expected to be more uniform and not a function of hydration, hence a creatinine concentration tends to be more stable than a volume-based concentration.

For purposes here, the creatinine correction approach can be used to estimate the daily intake of the contaminant assuming that exposure is ongoing and daily and that most of the contaminant or metabolites of the contaminant are excreted in urine. Assuming these conditions are true, then daily contaminant excretions can be estimated using this equation:

Expression

where CR is creatinine excretion and CT is the contaminant or the contaminant metabolite excretion. Rearranging this equation allows daily excretion of a contaminant (i.e., CT daily) to be calculated.

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Complex

Actual exposures and human body physiology are more complicated than what is captured in a one-compartment, first-order steady-state model. The first-order model can be adapted to a temporal (unsteady-state) framework where the chemical in only one compartment of the body is modeled, but the dose, rate constant, and even the volume through which the chemical is distributed can change over time. More complex PK models account for an organism’s physiology in their equations and are called physiologically based pharmacokinetic (PBPK) models.

PBPK models require parameterization to simulate the movement and fate of chemicals within the body, considering transfers between tissues and organs, metabolism, and storage. Parameters might be physiological, physiochemical, or biochemical in nature (see the figure below). There are often practical limitations to using PBPK models for exposure reconstruction due to the lack of valid parameters for the numerous transfer and rate constants for human exposure scenarios.

Parameters used in a PBPK model to determine intake
dose from biomarker concentration (Moir, 1999)

Figure 3:  Parameters used in a PBPK model to determine intake dose from biomarker concentration (Moir 1999)

Multiple-compartment models are more complex and typically include the organs and tissues relevant for the specific chemical distribution, metabolism, or toxicity. These models might specify venous movement of blood (away from organs and back to the heart and lungs) and arterial movement of blood (away from the heart and lungs to the rest of the body). More complex models can also describe the formation and transport of metabolites. Creating these mathematical models requires specific physiological data, such as blood flow rate to individual compartments, rate of metabolism, knowledge of whether processes are saturable, and partition coefficients (which describe how chemicals distribute in various tissues). For many chemicals, such data is often unavailable to build these more complex models.

Complex PBPK model adapted from pg 13 of 1,4-dioxane IRIS (U.S. EPA, 2010).
Complex PBPK model adapted from pg 13 of 1,4-Dioxane IRIS (U.S. EPA 2010).


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