Uncertainties in Biologically-Based Modeling of Formaldehyde-Induced Respiratory Cancer Risk: Identification of Key Issues

In a series of articles and a health-risk assessment report, scientists at the CIIT Hamner Institutes developed a model (CIIT model) for estimating respiratory cancer risk due to inhaled formaldehyde within a conceptual framework incorporating extensive mechanistic information and advanced computational methods at the toxicokinetic and toxicodynamic levels. Several regulatory bodies have utilized predictions from this model; on the other hand, upon detailed evaluation the California EPA has decided against doing so. In this article, we study the CIIT model to identify key biological and statistical uncertainties that need careful evaluation if such two-stage clonal expansion models are to be used for extrapolation of cancer risk from animal bioassays to human exposure. Broadly, these issues pertain to the use and interpretation of experimental labeling index and tumor data, the evaluation and biological interpretation of estimated parameters, and uncertainties in model specification, in particular that of initiated cells. We also identify key uncertainties in the scale-up of the CIIT model to humans, focusing on assumptions underlying model parameters for cell replication rates and formaldehyde-induced mutation. We discuss uncertainties in identifying parameter values in the model used to estimate and extrapolate DNA protein cross-link levels. The authors of the CIIT modeling endeavor characterized their human risk estimates as "conservative in the face of modeling uncertainties." The uncertainties discussed in this article indicate that such a claim is premature.     

Benchmark Dose Risk Assessment for Formaldehyde Using Airflow Modeling and a Single-Compartment, DNA-Protein Cross-Link Dosimetry Model to Estimate Human Equivalent Doses

Formaldehyde induced squamous-cell carcinomas in the nasal passages of F344 rats in two inhalation bioassays at exposure levels of 6 ppm and above. Increases in rates of cell proliferation were measured by T. M. Monticello and colleagues at exposure levels of 0.7 ppm and above in the same tissues from which tumors arose. A risk assessment for formaldehyde was conducted at the CIIT Centers for Health Research, in collaboration with investigators from Toxicological Excellence in Risk Assessment (TERA) and the U.S. Environmental Protection Agency (U.S. EPA) in 1999. Two methods for dose-response assessment were used: a full biologically based modeling approach and a statistically oriented analysis by benchmark dose (BMD) method. This article presents the later approach, the purpose of which is to combine BMD and pharmacokinetic modeling to estimate human cancer risks from formaldehyde exposure. BMD analysis was used to identify points of departure (exposure levels) for low-dose extrapolation in rats for both tumor and the cell proliferation endpoints. The benchmark concentrations for induced cell proliferation were lower than for tumors. These concentrations were extrapolated to humans using two mechanistic models. One model used computational fluid dynamics (CFD) alone to determine rates of delivery of inhaled formaldehyde to the nasal lining. The second model combined the CFD method with a pharmacokinetic model to predict tissue dose with formaldehyde-induced DNA-protein cross-links (DPX) as a dose metric. Both extrapolation methods gave similar results, and the predicted cancer risk in humans at low exposure levels was found to be similar to that from a risk assessment conducted by the U.S. EPA in 1991. Use of the mechanistically based extrapolation models lends greater certainty to these risk estimates than previous approaches and also identifies the uncertainty in the measured dose-response relationship for cell proliferation at low exposure levels, the dose-response relationship for DPX in monkeys, and the choice between linear and nonlinear methods of extrapolation as key remaining sources of uncertainty.     

Symmetry, Identifiability, and Prediction Uncertainties in Multistage Clonal Expansion (MSCE) Models of Carcinogenesis

Many models of exposure-related carcinogenesis, including traditional linearized multistage models and more recent two-stage clonal expansion (TSCE) models, belong to a family of models in which cells progress between successive stages-possibly undergoing proliferation at some stages-at rates that may depend (usually linearly) on biologically effective doses. Biologically effective doses, in turn, may depend nonlinearly on administered doses, due to PBPK nonlinearities. This article provides an exact mathematical analysis of the expected number of cells in the last ("malignant") stage of such a "multistage clonal expansion" (MSCE) model as a function of dose rate and age. The solution displays symmetries such that several distinct sets of parameter values provide identical fits to all epidemiological data, make identical predictions about the effects on risk of changes in exposure levels or timing, and yet make significantly different predictions about the effects on risk of changes in the composition of exposure that affect the pharmacodynamic dose-response relation. Several different predictions for the effects of such an intervention (such as reducing carcinogenic constituents of an exposure) that acts on only one or a few stages of the carcinogenic process may be equally consistent with all preintervention epidemiological data. This is an example of nonunique identifiability of model parameters and predictions from data. The new results on nonunique model identifiability presented here show that the effects of an intervention on changing age-specific cancer risks in an MSCE model can be either large or small, but that which is the case cannot be predicted from preintervention epidemiological data and knowledge of biological effects of the intervention alone. Rather, biological data that identify which rate parameters hold for which specific stages are required to obtain unambiguous predictions. From epidemiological data alone, only a set of equally likely alternative predictions can be made for the effects on risk of such interventions.     

A Cellular Dynamics Model of Experimental Bladder Cancer: Analysis of the Effect of Sodium Saccharin in the Rat

To make the methodology of risk assessment more consistent with the realities of biological processes, a computer-based model of the carcinogenic process may be used. A previously developed probabilistic model, which is based on a two-stage theory of carcinogenesis, represents urinary bladder carcinogenesis at the cellular level with emphasis on quantification of cell dynamics: cell mitotic rates, cell loss and birth rates, and irreversible cellular transitions from normal to initiated to transformed states are explicitly accounted for. Analyses demonstrate the sensitivity of tumor incidence to the timing and magnitude of changes to these cellular variables. It is demonstrated that response in rats following administration of nongenotoxic compounds, such as sodium saccharin, can be explained entirely on the basis of cytotoxicity and consequent hyperplasia alone.     

A Simple Toxicokinetic Model Exhibiting Complex Dynamics and Nonlinear Exposure Response

Uncertainty in model predictions of exposure response at low exposures is a problem for risk assessment. A particular interest is the internal concentration of an agent in biological systems as a function of external exposure concentrations. Physiologically based pharmacokinetic (PBPK) models permit estimation of internal exposure concentrations in target tissues but most assume that model parameters are either fixed or instantaneously dose-dependent. Taking into account response times for biological regulatory mechanisms introduces new dynamic behaviors that have implications for low-dose exposure response in chronic exposure. A simple one-compartment simulation model is described in which internal concentrations summed over time exhibit significant nonlinearity and nonmonotonicity in relation to external concentrations due to delayed up- or downregulation of a metabolic pathway. These behaviors could be the mechanistic basis for homeostasis and for some apparent hormetic effects.     

Impact of Acquired Immunity and Dose‐Dependent Probability of Illness on Quantitative Microbial Risk Assessment

Dose‐response models in microbial risk assessment consider two steps in the process ultimately leading to illness: from exposure to (asymptomatic) infection, and from infection to (symptomatic) illness. Most data and theoretical approaches are available for the exposure‐infection step; the infection‐illness step has received less attention. Furthermore, current microbial risk assessment models do not account for acquired immunity. These limitations may lead to biased risk estimates. We consider effects of both dose dependency of the conditional probability of illness given infection, and acquired immunity to risk estimates, and demonstrate their effects in a case study on exposure to Campylobacter jejuni. To account for acquired immunity in risk estimates, an inflation factor is proposed. The inflation factor depends on the relative rates of loss of protection over exposure. The conditional probability of illness given infection is based on a previously published model, accounting for the within‐host dynamics of illness. We find that at low (average) doses, the infection‐illness model has the greatest impact on risk estimates, whereas at higher (average) doses and/or increased exposure frequencies, the acquired immunity model has the greatest impact. The proposed models are strongly nonlinear, and reducing exposure is not expected to lead to a proportional decrease in risk and, under certain conditions, may even lead to an increase in risk. The impact of different dose‐response models on risk estimates is particularly pronounced when introducing heterogeneity in the population exposure distribution.     

A Quantitative Microbial Risk Assessment Model for Legionnaires'' Disease: Animal Model Selection and Dose-Response Modeling

Legionnaires' disease (LD), first reported in 1976, is an atypical pneumonia caused by bacteria of the genus Legionella, and most frequently by L. pneumophila (Lp). Subsequent research on exposure to the organism employed various animal models, and with quantitative microbial risk assessment (QMRA) techniques, the animal model data may provide insights on human dose-response for LD. This article focuses on the rationale for selection of the guinea pig model, comparison of the dose-response model results, comparison of projected low-dose responses for guinea pigs, and risk estimates for humans. Based on both in vivo and in vitro comparisons, the guinea pig (Cavia porcellus) dose-response data were selected for modeling human risk. We completed dose-response modeling for the beta-Poisson (approximate and exact), exponential, probit, logistic, and Weibull models for Lp inhalation, mortality, and infection (end point elevated body temperature) in guinea pigs. For mechanistic reasons, including low-dose exposure probability, further work on human risk estimates for LD employed the exponential and beta-Poisson models. With an exposure of 10 colony-forming units (CFU) (retained dose), the QMRA model predicted a mild infection risk of 0.4 (as evaluated by seroprevalence) and a clinical severity LD case (e.g., hospitalization and supportive care) risk of 0.0009. The calculated rates based on estimated human exposures for outbreaks used for the QMRA model validation are within an order of magnitude of the reported LD rates. These validation results suggest the LD QMRA animal model selection, dose-response modeling, and extension to human risk projections were appropriate.     

Model Averaging in Microbial Risk Assessment Using Fractional Polynomials

The alleviation of food-borne diseases caused by microbial pathogen remains a great concern in order to ensure the well-being of the general public. The relation between the ingested dose of organisms and the associated infection risk can be studied using dose-response models. Traditionally, a model selected according to a goodness-of-fit criterion has been used for making inferences. In this article, we propose a modified set of fractional polynomials as competitive dose-response models in risk assessment. The article not only shows instances where it is not obvious to single out one best model but also illustrates that model averaging can best circumvent this dilemma. The set of candidate models is chosen based on biological plausibility and rationale and the risk at a dose common to all these models estimated using the selected models and by averaging over all models using Akaike's weights. In addition to including parameter estimation inaccuracy, like in the case of a single selected model, model averaging accounts for the uncertainty arising from other competitive models. This leads to a better and more honest estimation of standard errors and construction of confidence intervals for risk estimates. The approach is illustrated for risk estimation at low dose levels based on Salmonella typhi and Campylobacter jejuni data sets in humans. Simulation studies indicate that model averaging has reduced bias, better precision, and also attains coverage probabilities that are closer to the 95% nominal level compared to best-fitting models according to Akaike information criterion.     

Issues Related to Time Averaging of Exposure in Modeling Risks Associated with Intermittent Exposures to Lead

Typical exposures to lead often involve a mix of long-term exposures to relatively constant exposure levels (e.g., residential yard soil and indoor dust) and highly intermittent exposures at other locations (e.g., seasonal recreational visits to a park). These types of exposures can be expected to result in blood lead concentrations that vary on a temporal scale with the intermittent exposure pattern. Prediction of short-term (or seasonal) blood lead concentrations arising from highly variable intermittent exposures requires a model that can reliably simulate lead exposures and biokinetics on a temporal scale that matches that of the exposure events of interest. If exposure model averaging times (EMATs) of the model exceed the shortest exposure duration that characterizes the intermittent exposure, uncertainties will be introduced into risk estimates because the exposure concentration used as input to the model must be time averaged to account for the intermittent nature of the exposure. We have used simulation as a means of determining the potential magnitude of these uncertainties. Simulations using models having various EMATs have allowed exploration of the strengths and weaknesses of various approaches to time averaging of exposures and impact on risk estimates associated with intermittent exposures to lead in soil. The International Commission of Radiological Protection (ICRP) model of lead pharmacokinetics in humans simulates lead intakes that can vary in intensity over time spans as small as one day, allowing for the simulation of intermittent exposures to lead as a series of discrete daily exposure events. The ICRP model was used to compare the outcomes (blood lead concentration) of various time-averaging adjustments for approximating the time-averaged intake of lead associated with various intermittent exposure patterns. Results of these analyses suggest that standard approaches to time averaging (e.g., U.S. EPA) that estimate the long-term daily exposure concentration can, in some cases, result in substantial underprediction of short-term variations in blood lead concentrations when used in models that operate with EMATs exceeding the shortest exposure duration that characterizes the intermittent exposure. Alternative time-averaging approaches recommended for use in lead risk assessment more reliably predict short-term periodic (e.g., seasonal) elevations in blood lead concentration that might result from intermittent exposures. In general, risk estimates will be improved by simulation on shorter time scales that more closely approximate the actual temporal dynamics of the exposure.     

Reassessing Benzene Cancer Risks Using Internal Doses

Human cancer risks from benzene exposure have previously been estimated by regulatory agencies based primarily on epidemiological data, with supporting evidence provided by animal bioassay data. This paper reexamines the animal-based risk assessments for benzene using physiologically-based pharmacokinetic (PBPK) models of benzene metabolism in animals and humans. It demonstrates that internal doses (interpreted as total benzene metabolites formed) from oral gavage experiments in mice are well predicted by a PBPK model developed by Travis et al. Both the data and the model outputs can also be accurately described by the simple nonlinear regression model total metabolites = 76.4x/(80.75 + x), where x = administered dose in mg/kg/day. Thus, PBPK modeling validates the use of such nonlinear regression models, previously used by Bailer and Hoel. An important finding is that refitting the linearized multistage (LMS) model family to internal doses and observed responses changes the maximum-likelihood estimate (MLE) dose-response curve for mice from linear-quadratic to cubic, leading to low-dose risk estimates smaller than in previous risk assessments. This is consistent with the conclusion for mice from the Bailer and Hoel analysis. An innovation in this paper is estimation of internal doses for humans based on a PBPK model (and the regression model approximating it) rather than on interspecies dose conversions. Estimates of human risks at low doses are reduced by the use of internal dose estimates when the estimates are obtained from a PBPK model, in contrast to Bailer and Hoel's findings based on interspecies dose conversion. Sensitivity analyses and comparisons with epidemiological data and risk models suggest that our finding of a nonlinear MLE dose-response curve at low doses is robust to changes in assumptions and more consistent with epidemiological data than earlier risk models.     

Pharmacokinetic Principles for Dose-Rate Extrapolation of Carcinogenic Risk from Genetically Active Agents

Neither experimental animal exposures nor real-life human exposures are delivered at a constant level over a full lifetime. Although there are strong theoretical reasons why all pharmacokinetic processes must "go linear" at the limit of low dose rates, fluctuations in dose rate may produce nonlinearities that either increase or decrease actual risks relative to what would be expected for constant lifetime exposure. This paper discusses quantitative theory and specific examples for a number of processes that can be expected to give rise to pharmacokinetic nonlinearities at high dose rates–including transport processes (e.g., renal tubular secretion), activating and detoxifying metabolism, DNA repair, and enhancement of cell replication following gross toxicity in target tissues. At the extreme, full saturation of a detoxification or DNA repair process has the potential to create as much as a dose² dependence of risk on dose delivered in a single burst, and if more than one detoxification step becomes fully saturated, this can be compounded. Effects via changes in cell replication rates, which appear likely to be largely responsible for the steep upward turning curve of formaldehyde carcinogenesis in rats, can be even more profound over a relatively narrow range of dosage. General suggestions are made for experimental methods to detect nonlinearities arising from the various sources in premarket screening programs.     

Extending the Stochastic Two-Stage Model of Carcinogenesis to Include Self-Regulation of the Nonmalignant Cell Population

One of the challenges of introducing greater biological realism into stochastic models of cancer induction is to find a way to represent the homeostatic control of the normal cell population over its own size without complicating the analysis too much to obtain useful results. Current two-stage models of carcinogenesis typically ignore homeostatic control. Instead, a deterministic growth path is specified for the population of "normal" cells, while the population of "initiated" cells is assumed to grow randomly according to a birth-death process with random immigrations from the normal population. This paper introduces a simple model of homeostatically controlled cell division for mature tissues, in which the size of the nonmalignant population remains essentially constant over time. Growth of the nonmalignant cell population (normal and initiated cells) is restricted by allowing cells to divide only to fill the "openings" left by cells that die or differentiate, thus maintaining the constant size of the nonmalignant cell population. The fundamental technical insight from this model is that random walks, rather than birth-and-death processes, are the appropriate stochastic processes for describing the kinetics of the initiated cell population. Qualitative and analytic results are presented, drawn from the mathematical theories of random walks and diffusion processes, that describe the probability of spontaneous extinction and the size distribution of surviving initiated populations when the death/differentiation rates of normal and initiated cells are known. The constraint that the nonmalignant population size must remain approximately constant leads to much simpler analytic formulas and approximations, flowing directly from random walk theory, than in previous birth-death models.(ABSTRACT TRUNCATED AT 250 WORDS)     

Physiologically Based Liver Modeling and Risk Assessment

Because of the inherent complexity of biological systems, there is often a choice between a number of apparently equally applicable physiologically based models to describe uptake and metabolism processes in toxicology or risk assessment. These models may fit the particular data sets of interest equally well, but may give quite different parameter estimates or predictions under different (extrapolated) conditions. Such competing models can be discriminated by a number of methods, including potential refutation by means of strategic experiments, and their ability to suitably incorporate all relevant physiological processes. For illustration, three currently used models for steady-state hepatic elimination--the venous equilibration model, the parallel tube model, and the distributed sinusoidal perfusion model--are reviewed and compared with particular reference to their application in the area of risk assessment. The ability of each of the models to describe and incorporate such physiological processes as protein binding, precursor-metabolite relations and hepatic zones of elimination, capillary recruitment, capillary heterogeneity, and intrahepatic shunting is discussed. Differences between the models in hepatic parameter estimation, extrapolation to different conditions, and interspecies scaling are discussed, and criteria for choosing one model over the others are presented. In this case, the distributed model provides the most general framework for describing physiological processes taking place in the liver, and has so far not been experimentally refuted, as have the other two models. These simpler models may, however, provide useful bounds on parameter estimates and on extrapolations and risk assessments.     

Model Uncertainty and Risk Estimation for Experimental Studies of Quantal Responses

Experimental animal studies often serve as the basis for predicting risk of adverse responses in humans exposed to occupational hazards. A statistical model is applied to exposure-response data and this fitted model may be used to obtain estimates of the exposure associated with a specified level of adverse response. Unfortunately, a number of different statistical models are candidates for fitting the data and may result in wide ranging estimates of risk. Bayesian model averaging (BMA) offers a strategy for addressing uncertainty in the selection of statistical models when generating risk estimates. This strategy is illustrated with two examples: applying the multistage model to cancer responses and a second example where different quantal models are fit to kidney lesion data. BMA provides excess risk estimates or benchmark dose estimates that reflects model uncertainty.     

Modeling for Risk Assessment of Neurotoxic Effects

The regulation of noncancer toxicants, including neurotoxicants, has usually been based upon a reference dose (allowable daily intake). A reference dose is obtained by dividing a no-observed-effect level by uncertainty (safety) factors to account for intraspecies and interspecies sensitivities to a chemical. It is assumed that the risk at the reference dose is negligible, but no attempt generally is made to estimate the risk at the reference dose. A procedure is outlined that provides estimates of risk as a function of dose. The first step is to establish a mathematical relationship between a biological effect and the dose of a chemical. Knowledge of biological mechanisms and/or pharmacokinetics can assist in the choice of plausible mathematical models. The mathematical model provides estimates of average responses as a function of dose. Secondly, estimates of risk require selection of a distribution of individual responses about the average response given by the mathematical model. In the case of a normal or lognormal distribution, only an estimate of the standard deviation is needed. The third step is to define an adverse level for a response so that the probability (risk) of exceeding that level can be estimated as a function of dose. Because a firm response level often cannot be established at which adverse biological effects occur, it may be necessary to at least establish an abnormal response level that only a small proportion of individuals would exceed in an unexposed group. That is, if a normal range of responses can be established, then the probability (risk) of abnormal responses can be estimated. In order to illustrate this process, measures of the neurotransmitter serotonin and its metabolite 5-hydroxyindoleacetic acid in specific areas of the brain of rats and monkeys are analyzed after exposure to the neurotoxicant methylene-dioxymethamphetamine. These risk estimates are compared with risk estimates from the quantal approach in which animals are classified as either abnormal or not depending upon abnormal serotonin levels.     

Risk Analysis for Invasive Species: General Framework and Research Needs

A joint workshop was convened by the Society for Risk Analysis Ecological Risk Assessment Specialty Group and the Ecological Society of America Theoretical Ecology Section to provide independent scientific input into the formulation of methods and processes for risk assessment of invasive species. In breakout sessions on (1) the effects of invasive species on human health, (2) effects on plants and animals, (3) risk analysis issues and research needs related to entry and establishment of invasive species, and (4) risk analysis issues and research needs related to the spread and impacts of invasive species, workshop participants discussed an overall approach to risk assessment for invasive species. Workshop participants agreed on the need for empirical research on areas in which data are lacking, including potential invasive species, native species and habitats that may be impacted by invasive species, important biological processes and phenomena such as dispersal, and pathways of entry and spread for invasive species. Participants agreed that theoretical ecology can inform the process of risk assessment for invasive species by providing guidelines and conceptual models, and can contribute to improved decision making by providing a firm biological basis for risk assessments.     

An Overview of a Multimedia Benchmarking Analysis for Three Risk Assessment Models: RESRAD, MMSOILS, and MEPAS

Multimedia modelers from the United States Environmental Protection Agency (EPA) and the United States Department of Energy (DOE) collaborated to conduct a detailed and quantitative benchmarking analysis of three multimedia models. The three models—RESRAD (DOE), MMSOILS (EPA), and MEPAS (DOE)—represent analytically-based tools that are used by the respective agencies for performing human exposure and health risk assessments. The study is performed by individuals who participate directly in the ongoing design, development, and application of the models. Model form and function are compared by applying the models to a series of hypothetical problems, first isolating individual modules (e.g., atmospheric, surface water, groundwater) and then simulating multimedia-based risk resulting from contaminant release from a single source to multiple environmental media. Study results show that the models differ with respect to environmental processes included (i.e., model features) and the mathematical formulation and assumptions related to the implementation of solutions. Depending on the application, numerical estimates resulting from the models may vary over several orders-of-magnitude. On the other hand, two or more differences may offset each other such that model predictions are virtually equal. The conclusion from these results is that multimedia models are complex due to the integration of the many components of a risk assessment and this complexity must be fully appreciated during each step of the modeling process (i.e., model selection, problem conceptualization, model application, and interpretation of results).     

Risk Assessment for Aflatoxin: III. Modeling the Relative Risk of Hepatocellular Carcinoma

Estimates have been made of the cancer potency of aflatoxin exposure among the U.S. population. Risk modeling is used to assess the dose-response relationship between aflatoxin exposure and primary liver cancer, controlling for hepatitis B virus (HBV), based on data provided by the Yeh et al. study in China. A relative risk model is proposed as a more appropriate alternative to the additive ("absolute" risk) model for transportation of risk coefficients between populations with different baseline rates. Several general relative risk models were examined; the exponential model provided the best fit. The Poisson regression method was used to fit the relative risk model to the grouped data. The effects of exposure to aflatoxin (AFB1) and hepatitis B infection were both found to be statistically significant. The risk of death from liver cancer for those exposed to AFB1 relative to the unexposed population, increases by 0.05% per ng/kg/day exposure of AFB1 (p less than 0.001). The results also indicated a 25-fold increase in the risk of death from liver cancer among those infected with hepatitis B virus, relative to noncarriers (p less than 0.0001). With a hepatitis prevalence rate of 1%, the aflatoxin intake level associated with liver cancer lifetime excess risk of 1 x 10(-5) for the U.S. population was estimated as 253 ng/day, based on a liver cancer baseline rate of 3.4/100,000/yr.     

A Bayesian Semiparametric Model for Radiation Dose‐Response Estimation

In evaluating the risk of exposure to health hazards, characterizing the dose‐response relationship and estimating acceptable exposure levels are the primary goals. In analyses of health risks associated with exposure to ionizing radiation, while there is a clear agreement that moderate to high radiation doses cause harmful effects in humans, little has been known about the possible biological effects at low doses, for example, below 0.1 Gy, which is the dose range relevant to most radiation exposures of concern today. A conventional approach to radiation dose‐response estimation based on simple parametric forms, such as the linear nonthreshold model, can be misleading in evaluating the risk and, in particular, its uncertainty at low doses. As an alternative approach, we consider a Bayesian semiparametric model that has a connected piece‐wise‐linear dose‐response function with prior distributions having an autoregressive structure among the random slope coefficients defined over closely spaced dose categories. With a simulation study and application to analysis of cancer incidence data among Japanese atomic bomb survivors, we show that this approach can produce smooth and flexible dose‐response estimation while reasonably handling the risk uncertainty at low doses and elsewhere. With relatively few assumptions and modeling options to be made by the analyst, the method can be particularly useful in assessing risks associated with low‐dose radiation exposures.