- Open Access
A generalized physiologically-based toxicokinetic modeling system for chemical mixtures containing metals
© Sasso et al; licensee BioMed Central Ltd. 2010
Received: 18 February 2010
Accepted: 2 June 2010
Published: 2 June 2010
Humans are routinely and concurrently exposed to multiple toxic chemicals, including various metals and organics, often at levels that can cause adverse and potentially synergistic effects. However, toxicokinetic modeling studies of exposures to these chemicals are typically performed on a single chemical basis. Furthermore, the attributes of available models for individual chemicals are commonly estimated specifically for the compound studied. As a result, the available models usually have parameters and even structures that are not consistent or compatible across the range of chemicals of concern. This fact precludes the systematic consideration of synergistic effects, and may also lead to inconsistencies in calculations of co-occurring exposures and corresponding risks. There is a need, therefore, for a consistent modeling framework that would allow the systematic study of cumulative risks from complex mixtures of contaminants.
A Generalized Toxicokinetic Modeling system for Mixtures (GTMM) was developed and evaluated with case studies. The GTMM is physiologically-based and uses a consistent, chemical-independent physiological description for integrating widely varying toxicokinetic models. It is modular and can be directly "mapped" to individual toxicokinetic models, while maintaining physiological consistency across different chemicals. Interaction effects of complex mixtures can be directly incorporated into the GTMM.
The application of GTMM to different individual metals and metal compounds showed that it explains available observational data as well as replicates the results from models that have been optimized for individual chemicals. The GTMM also made it feasible to model toxicokinetics of complex, interacting mixtures of multiple metals and nonmetals in humans, based on available literature information. The GTMM provides a central component in the development of a "source-to-dose-to-effect" framework for modeling population health risks from environmental contaminants. As new data become available on interactions of multiple chemicals, the GTMM can be iteratively parameterized to improve mechanistic understanding of human health risks from exposures to complex mixtures of chemicals.
Physiologically based toxicokinetic (PBTK) models are an important class of dosimetry models that are useful in estimating internal and target tissue doses of xenobiotics for risk assessment applications . PBTK models employ mass balances on compartments within a human or animal body, for the purpose of estimating the time-course profiles of toxicant concentrations in tissues and fluids. These models are also useful for understanding therapeutic outcomes from internal tissue exposures to pharmaceuticals . In conjunction with epidemiological and demographic data, and models of environmental pollution and exposure, PBTK models are applied to assess population health risks and provide a scientific basis for regulating the production and use of chemicals . PBTK models provide a critical mechanistic linkage between exposure models and biologically-based dose-response models. Thus, PBTK models for complex mixtures should form a central component of any human exposure and health risk modeling framework that aims to address multiple contaminants .
Humans are typically exposed to multiple xenobiotic chemicals, such as pharmaceuticals, cosmetics, alcohols, metals, solvents, pesticides, volatile and semi-volatile organic compounds, etc., simultaneously. For this reason, there have been efforts to incorporate metabolic interactions in PBTK models for mixtures of selected chemicals . Concurrently, there have been increasing numbers of applications involving "whole-body" physiologically-based toxicokinetic (WBPBTK) models that aim to reduce model uncertainties and better characterize inter-individual variabilities . These whole-body models account for all major tissues and exposure pathways, and are capable of incorporating detailed physiological data. However, comprehensive mixture modeling efforts have not been pursued in the field of toxic metal compounds, and there are currently no available PBTK models for mixtures of metals. Indeed, toxicokinetic models have only focused on individual metals separately, despite evidence of interactions of toxic metals with other toxic metals , with essential metals , and even with nonmetal pollutants . Recent developments in the field of molecular biomarkers have identified toxic interactions among metals such as arsenic, lead, and cadmium (including some toxic effects that are not seen in relation to single component exposures) . Though, in the long term, there is a need for developing mechanistic toxicodynamic models for mixtures of metal compounds, in the short term there is a need for a PBTK modeling system that is capable of simulating multiple interacting metals and nonmetals simultaneously. Such a system should also incorporate realistic whole-body physiology of members of both the general and of susceptible populations.
Toxicological interactions among metals
Due to their similarities to essential metals, toxic metals are transported and eliminated through many common cellular mechanisms by "molecular mimicry" . As a result, there exist toxicokinetic and toxicodynamic interactions among toxic and essential metals [7, 8]. Metal absorption, elimination, and toxicokinetics should therefore be considered highly correlated for exposed individuals, with susceptibilities resulting in differential effects of multiple metals. Population susceptibilities resulting from essential element status are often a significant source of uncertainty and variability for metals risk assessment . For example, iron inhibits lead and cadmium intestinal uptake due to shared absorption mechanisms ; conversely, toxic metals may inhibit essential element absorption . Cadmium and zinc are also known to have a variety of interactions due to the metal-binding protein metallothionein . Selenium may potentially alter both arsenic and methylmercury toxicity . Other nutrients such as antioxidants, Vitamins A/C/E, magnesium, phosphorus, riboflavin, and methionine are also known to impact toxic metal susceptibility .
Low essential element status or illnesses may result in higher absorption of multiple metals . This has direct implications for PBTK applications to population risk assessment, since failing to account for high correlations in the absorption of individual metals may lead to misinterpretations of biomarker data. In cases where susceptible individuals are exposed to mixtures of toxic metals while exhibiting high absorption, there is a greater likelihood of toxic effects, either due to additive or synergistic interactions. This is particularly important since some metals exhibit common toxic effects such as hepatic, renal, and neurological toxicity. Molecular biomarkers of toxic metal health effects are becoming sensitive enough to detect some toxic interactions . Synergistic toxic interactions in the liver and kidneys between arsenic and cadmium , and lead and cadmium  have been observed in exposed human populations.
Toxicological interactions among metals and nonmetals
Selected interactions between metals and CYP450 enzymes in humans and animals
Halogenated aliphates, triazines, organophosphates, VOCs, drugs
Drugs, organophosphates, triazines
Inhibited 1A2 (rats)
Arylamines, organophosphates, triazines, VOCs, PCBs, drugs
Induced 1A1 (rats)
PAHs, VOCs, PCBs, triazines
Altered 1A1/2 induction by PAHs/TCDD (rats)
PAHs, VOCs, PCBs, triazines, organophosphates, drugs
General model structure
Matrices indexed by both tissue and chemical are defined as follows: A is the matrix of chemical amounts in the different tissues; Q is the matrix of tissue flow rates; Cin is the matrix of inlet concentrations to the tissues (typically the concentrations in the arterial blood streams, but may also be a volume-weighted average of multiple inlet streams); Cout is the matrix of outlet concentrations; R is the matrix of net rates of metabolism for all the chemicals considered (negative values indicate formation of chemical); and T is the matrix of net rates of transport of all chemicals considered via additional processes (i.e. excretion, absorption, or inter-compartmental transfer). While the blood flows are assumed to be independent of the chemical under consideration, a chemical-specific formulation allows for selective lumping of the compartments for some chemicals.
In the above equation, superscripts E and C denote extracellular and cellular space, respectively. P i,j is the tissue:blood partition coefficient, H i,j is the lumped permeability-area coefficient (volume/time), and is the permeation rate of chemical through the diffusive layer (mass/time). The outlet concentration is equal to the extracellular concentration . PBTK models sometimes differ in how the driving force for diffusion is defined. If more complex transport mechanisms other than diffusion occur (i.e. carrier-mediated transport), alternative expressions for are required.
For the perfusion-limited assumption, the outlet concentration is equal to C i,j /P i,j . Depending on the physicochemical properties of the contaminant, PBTK models may consist entirely of diffusion- or perfusion-limited compartments, or a combination of both.
Equations for metabolism
where i and k denote the metabolizing and inhibiting chemical species, respectively; Vmax,iis the maximum reaction velocity (mass/time); Km,iis the Michaelis constant (mass/volume); Ik,iis the competitive inhibition constant for chemical k inhibiting the metabolism of chemical i (mass/volume). Similar generalized equations are applicable to describe reductions in Vmax due to noncompetitive inhibition, or increases in Vmax or Γ due to enzyme induction.
The modeling system that is presented here, GTTM (Generalized Toxicokinetic Modeling System for Mixtures) was implemented in the Matlab programming environment, that has previously been reviewed as a useful tool for PBPK applications , and includes various toolboxes for parameter identification and visualization. Multiple diverse PBTK models may be incorporated into a common workspace, allowing for simultaneous, interacting simulations. In order to accommodate multiple chemicals and a large number of potential interactions, the GTMM utilizes matrix-based formulations. For example, every tissue is assigned a first-order reaction network matrix as shown in Equation 4, and analogous matrices address other types of reaction and transport rates. The mass balances of multiple chemicals in all the tissues are represented by a matrix of ordinary differential equations (ODEs), that are solved by the ode15s stiff ODE solver of Matlab. The inputs to the GTMM are exposure profiles, and physiological and biochemical parameters. The outputs are the time-concentration profiles of different chemicals in the various tissues. Physiological variability in the population may be consistently considered across the models for all chemicals by linking with biological databases that provide physiological values for a majority of the tissue groups. GTTM offers the option to obtain parameters from databases for the general population (i.e. the P3M physiological database ) and for susceptible populations (i.e. the elderly and health-impaired ). Other sources of whole-body physiology include the PK-Pop scaling algorithm used by PK-Sim , and the polynomial relationships used by PostNatal . The Matlab environment allows the GTMM to generate "virtual individuals" with consistent physiology using any of the above databases.
The GTMM was evaluated with respect to its ability to predict toxicokinetics of multiple toxic metals "individually" (i.e. "one metal at a time"). Predictions of biomarkers by the GTMM were compared with the estimates from the corresponding single-metal PBTK models, using the same input data as the original literature evaluation studies of these models. For the case studies involving individual metals, the major physiological parameters for the GTMM were set to the values used in these original modeling case studies, so as to ensure direct comparison. Evaluations were performed for four toxic metals (cadmium, arsenic, lead, chromium), and a toxic metal compound (methylmercury). In all cases, the GTMM explained the available data and replicated the predictions of the various metal-specific formulations. Subsequently, the GTMM was applied to a hypothetical case involving interactions between metals and nonmetals.
The general population is exposed to cadmium primarily through dietary ingestion and inhalation of cigarette smoke . Kidney damage is the primary health concern; other effects include alteration of enzyme levels, liver toxicity, cancer, and hypertension [31, 32]. Due to the long half-life of cadmium in humans, the PBTK formulation is different from typical PBTK formulations, as shown in Figure 1. The GTMM replicates the cadmium toxicokinetics described by the formulation by Kjellström and Nordberg (see Additional files 1 and 2) . Absorbed cadmium accumulates in the kidney and liver, and binds to metallothionein proteins. Elimination from the body occurs primarily through urinary excretion, which is a slow process in humans.
Application of the GTMM to a mixture of metals and non-metals
The hypothetical case study focuses on a 30-year old male experiencing continuous dietary exposure to metals (15 μg/day cadmium, 40 μg/day methylmercury, 70 μg/day lead, and 100 μg/day inorganic arsenic), and inhalation exposure to volatile organics (20 ppm toluene and 10 ppm benzene). Exposures continued for 500 days, reflecting an approximate steady state. However since the half-life of cadmium in the liver is extremely long, its corresponding steady state levels were estimated using a PBTK model run for an individual from birth to age 30, assuming a cadmium intake of 0.2 μg/kg/day (which is equivalent to 15 μg/day at age 30). The levels of cadmium in all tissues at age 30 were then used as the initial condition for the short-term simulations.
After 500 days, all metal intakes were increased by 40% of their baseline values in order to observe the dynamic (state transition) effects of a variable exposure. Exposure to toluene and benzene remained constant, and was not increased at day 500. Figure 8 (a) shows predicted liver concentrations of cadmium, lead, total arsenic, methylmercury, benzene, and toluene for the base-case (i.e. considering no interactions). Figure 8 (b) shows predicted liver benzene concentration for the base-case scenario and for different interaction assumptions. The increase in benzene concentration beyond day 500 is attributable to increased metal exposure. These results show that, depending on the types of metabolic interactions, there is the potential for substantial increases in the steady-state level of benzene in the liver. It must be noted that the precise relationships between toxic metal exposure and metabolic reaction rates of non-metals is not known and further study is needed in this area.
Discussion and Conclusions
The previous sections outlined the need, development, implementation, and evaluation of a Generalized Toxicokinetic Modeling system for Mixtures (GTTM), applicable to both metals and non-metals. At the evaluation stage, the implementations of the GTTM for individual chemicals (metals or metal compounds) employed assumptions that were used in the formulations or applications of literature models, but were harmonized via consistent whole body physiology. The GTMM is a step in the on-going development of an integrative toxicokinetic/toxicodynamic system that simulates binary and higher order metal interactions.
The GTMM provides a central component of a novel framework that aims to account for total exposures (cumulative and aggregate) of individuals and populations to mixtures of chemicals; these mixtures can arise from many sources and routes, including environmental releases, use of consumer products, and dietary intake. Specifically, the GTMM has been developed as a component of two complementary and evolving systems that provide the above-mentioned framework: the Modeling ENvironment for TOtal Risk studies (MENTOR) that addresses the "source-to-dose" steps in the exposure and risk modeling sequence , and the DOse Response Information ANalysis system (DORIAN) that addresses the biological "dose-to-effect" steps . In the case of MENTOR, the GTMM links to various multimedia/multipathway exposure modules for chemical mixtures, while in the case of DORIAN the GTMM has been designed to provide links to biologically-based dose-response (BBDR) modules for toxicodynamic processes, as these become available.
In addition to providing linkages of PBTK models for metal mixtures with biologically-based dose-response (BBDR) models for toxic effects, the framework should eventually also provide links with PBTK/BBDR models for essential elements. A manganese PBTK model for humans (which is in the early stages of development ) can be used to study interactions of toxic and essential metals via the GTMM. For mixtures of metals such as lead, cadmium, and arsenic, there is a need for BBDR models of renal and hepatic effects, because renal dysfunction impacts the elimination of essential and toxic metals in the plasma, and hepatic dysfunction may lead to potential interactions with organics, drugs, PCBs and pesticides. The magnitudes of these interactions in vivo are not currently known. However the GTMM can be used to study hypotheses regarding impacts of exposures from multiple metals and nonmetals, and to help identify priority areas for studying environmental health risks from exposures to complex chemical mixtures. The incorporation of whole-body physiology via linkages to up-to-date parameter databases is also useful in examining the distributions of risks within both the general population and selected susceptible subpopulations.
This work was supported primarily by USEPA-funded Environmental Bioinformatics and Computational Toxicology Center (ebCTC) under STAR Grant No. GAD R 832721-010, and the USEPA funded Center for Exposure and Risk Modeling (CERM) under Cooperative Agreement No. CR-83162501. Additional support was provided by the NIEHS sponsored UMDNJ Center for Environmental Exposures and Disease under Grant No. P30ES005022.
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