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Resolving neighborhood scale in air toxics modeling: a case study in Wilmington, CA.

Air quality modeling is useful for characterizing exposures to air pollutants. Whereas models typically provide results on regional scales, new concerns regarding the potential for differential exposures among racial/ethnic populations and income strata within communities are driving the need for increasingly refined modeling approaches. These approaches need to be capable of resolving concentrations on the scale of tens of meters, across modeling domains 10-100 km2 in size. One approach for refined air quality modeling is to combine Gaussian and regional photochemical grid models. In this paper, the authors demonstrate this approach on a case study of Wilmington, CA, focused on diesel exhaust particulate matter. Modeling results suggest that pollutant concentrations in the vicinity of emission sources are elevated, and, therefore, an understanding of local emission sources is necessary to generate credible modeling results. A probabilistic evaluation of the Gaussian model application indicated that spatial allocation, emission rates, and meteorological data are important contributors to input and parameter uncertainty in the model results. This uncertainty can be substantially reduced through the collection and integration of site-specific information about the location of emission sources and the activity and emission rates of key sources affecting model concentrations.

Air Pollutants↗

Dynamic PET data analysis.

A general method for estimating the precision of parameters resulting from the use of various experimental designs (rate of injection and rate of tomographic data collection) in emission tomography studies is proposed. The sensitivity matrix of the study model and an estimate of the statistical uncertainty of the tomographic data are used to compute the covariance matrix of the parameters. The determinant of this covariance matrix (proportional to the total volume of uncertainty of the model parameters) serves as a criterion to be minimized. The method is applied to a three-compartment, three-transfer rate constant for glucose metabolism using dynamic positron emission tomography, and a comparison of various current protocols is made with simulated data. The results show that higher rates of injection and higher rates of tomographic data collection at early times lead to smaller statistical uncertainties for the estimates of rate constants. However, for the range of rate constants encountered in practice, differences are insignificant when an initial scan duration less than 30 s is used, without regarding the injection duration.

Deoxyglucose↗

Responding to sudden pollutant releases in office buildings: 1. Framework and analysis tools.

We describe a framework for developing response recommendations to unexpected toxic pollutant releases in commercial buildings. It may be applied in conditions where limited building- and event-specific information is available. The framework is based on a screening-level methodology to develop insights, or rules-of-thumb, into the behavior of airflow and pollutant transport. A three-stage framework is presented: (1). develop a building taxonomy to identify generic, or prototypical, building configurations; (2). characterize uncertainty and conduct simulation modeling to predict typical airflow and pollutant transport behavior; and (3). rank uncertainty contributions to determine how information obtained at a site might reduce uncertainties in the model predictions. The approach is applied to study a hypothetical pollutant release on the first floor of a five-story office building. Key features that affect pollutant transport are identified and described by value ranges in the building stock. Simulation modeling provides predictions and uncertainty estimates of time-dependent pollutant concentrations, following a release, for a range of indoor and outdoor conditions. In this exercise, we predict concentrations on the fifth floor to be an order of magnitude less than on the first, coefficients of variation greater than 2, and information about the HVAC operation and window position most reducing uncertainty in predicted peak concentrations.

Air Movements↗

Uncertainty in predicting riverbed erosion caused by urban stormwater discharge.

Ecologically based criteria require an integrated modeling approach. Due to the complexity of the system, the stochastic nature of loads, and the model abstractions, many uncertainties are involved. In this study, a simple integrated model is applied, which Swiss engineers employ to assess the impact of urban stormwater discharges on riverbed stability. In the course of a case study, an uncertainty analysis is carried out focusing on parameter uncertainties. The underlying context of the uncertainties is evaluated, and a variance-based sensitivity analysis is presented estimating the local uncertainty contribution of each parameter. The results reveal that the largest contributions stem from the model components describing the natural system. An experimental design is proposed that manages to reduce the output uncertainty significantly. Finally, we discuss the benefits of following the proposed procedure.

Cities↗

Model description of an alternately operated wastewater treatment plant--evaluation of the applicability of SimpleTreat.

Alternately operated wastewater treatment plants (WWTPs) are fundamentally different compared to conventional activated sludge WWTPs with respect to flow patterns and aeration in the biological reactors. Several model applications exist for conventional WWTPs, e.g. SimpleTreat, and in this study the effect of substituting a complex discontinuous operation, involving alternating degradation and flow conditions between two reactors, with one single bioreactor with continuos flow (SimpleTreat) has been investigated by setting up two models representing the respective operation schemes. The discontinuous operation induces fluctuations in the outlet concentrations that are not modelled with the single bioreactor model, however, the fluctuations and the associated uncertainties were found to be insignificant compared to the influence of the input parameter uncertainties on the model results. An empirical relationship between an aggregate pseudo-1st order degradation rate for the single bioreactor model and realistic aerobic and anoxic 1st order degradation rates, respectively, has been established. When using this aggregate degradation rate in the single bioreactor model an outlet concentration can be calculated that deviates no more than 2% from the mean outlet concentration from the alternating operation model. For substances with aerobic half-lives longer than approximately 2 h, which is valid for many chemical substances, the aggregate 1st order degradation rate can be set equal to the aerobic 1st order degradation rate.

Bioreactors↗

Sensitivity analysis for healthcare models fitted to data by statistical methods.

After fitting complex models to data using statistical methods, a sensitivity analysis can be carried out. This determines which parts of a model are causing the bulk of the uncertainty in the model predictions (model "output"), and is a decision-support tool for the modeller who contemplates refining a model further or collecting additional data. A simple methodology for carrying out a sensitivity analysis is described. It is envisaged that such a relatively quick insight-generating step would precede the use of a more formal decision-theoretic approach that would address specific questions. Its use is illustrated using a model for breast cancer screening previously published in this journal. A simpler 3-parameter screening model is used in a simulation study of the error of the method as a function of sample size.

Breast Neoplasms↗

Linking indoor air and pharmacokinetic models to assess tetrachloroethylene risk.

Physiologically based pharmacokinetic (PBPK) models describing the uptake, metabolism, and excretion of xenobiotic compounds are now proposed for use in regulatory health-risk assessments. In this study we investigate the extent of PCE metabolism arising from domestic respiratory exposure to tetrachloroethylene (PCE) from ground water, as predicted using a PBPK model. Indoor exposure patterns we use as input to the PBPK model are realistic ones generated from a three-compartment model describing volatilization of PCE from domestic water into household air. Values we use for the metabolic parameters of the PBPK model are estimated from data on urinary metabolites in workers exposed to PCE. It is shown that for respiratory PCE exposure due to typical levels of PCE in ground water, use of time-weighted average air concentrations with a steady-state PBPK model yields estimates of total metabolized PCE similar to those obtained using completely dynamic modeling, despite considerable uncertainty in key exposure- and metabolic-model parameters. These findings suggest that, for PCE, risk estimation taking pharmacokinetics into account may be accomplished using a simple analytic approach.

Air Pollutants↗

Predicting the potential public health impact of disease-modifying HIV vaccines in South Africa: the problem of subtypes.

Current HIV vaccines in development appear unlikely to prevent infection, but could provide benefits by increasing survival; such vaccines are described as disease-modifying vaccines. We review the current status of vaccines and modeling vaccines. We also predict the impact that disease-modifying vaccines could have in South Africa, where multiple subtypes are co-circulating. We model transmissibility/fitness differences among subtypes. We used uncertainty analyses to model vaccines with four characteristics: (i) take, (ii) duration of immunity, (iii) reduction in transmissibility/fitness, and (iv) increase in survival. We reconstructed, and forecasted, the South African epidemic from 1940 to 2140 (assuming no vaccination). We predict that: (i) incidence will peak in 2014, decline, and stabilize, (ii) prevalence will continue to rise, and (iii) the AIDS death rate curve will peak in 2022. Our predictions show that (over the next 135 years) the epidemic in South Africa will switch from a predominantly Subtype C epidemic to an epidemic driven by other subtypes. We predict that the epidemic could remain unchanged, even with mass vaccination with a vaccine that is equally effective against all co-circulating subtypes. However, if the non-C subtypes are less (or equally) transmissible as Subtype C then disease-modifying vaccines could result in eradication. Thus, in countries where multiple-subtypes are co-circulating it is critical to realize that small biological differences among subtypes will have dramatic consequences for the effectiveness of HIV vaccination campaigns. A slight difference in fitness will determine whether a disease-modifying vaccine has almost no impact on the epidemic or can achieve eradication.

AIDS Vaccines↗

Modeling therapeutic strategies in rheumatoid arthritis: use of decision analysis and Markov models.

OBJECTIVE: The management of patients with rheumatoid arthritis (RA) is controversial, with a number of different proposed treatment strategies based on different conceptions of the natural history of the disease and different interpretations of the efficacy and effectiveness of the drugs used for treatment. We attempted to develop a theoretical framework to assess the effectiveness of different treatment regimens for RA. METHODS: We used decision analysis to structure the problem of comparing sequential monotherapy to a combination strategy. Subsequently, we used 3 different estimates of drug effectiveness: one from expert rheumatologists; a metaanalysis; and a recent nationwide survey of American rheumatologists, in a Markov model. Last, we utilized published duration of therapy data to model drug treatment over time. RESULTS: Estimates of drug effectiveness differed substantially among rheumatologists, but regardless of the estimates and the treatment strategy used, the model predicted over 90% of patients improved by the 3rd drug trial. Over time, treatment patterns in our model resemble the "sawtooth" pattern previously observed. CONCLUSION: Treatment strategies in RA are difficult to model because of uncertainty in both the structure of the model and the data needed to perform the analysis. These models tend to overestimate the effectiveness of drug sequences because of nonindependence between therapies, probably due to sequence effects, a change in responsiveness over time, or resistant subgroups. Our preliminary analysis suggests that the most effective agent, possibly methotrexate, should be used first if the objective is to get as many patients into remission as quickly as possible.

Arthritis, Rheumatoid↗

An intervention analysis for the reduction of exposure to methylmercury from the consumption of seafood by women of child-bearing age.

A previously developed exposure model was used [Risk Anal. 22 (2002) 689] to assess the effectiveness of various advisory scenarios on minimizing mercury (Hg) blood levels via the consumption of commercial seafood, both finfish and shellfish. This exposure model was developed to predict levels of Hg in blood in women of child-bearing age in the US based on the frequency of seafood consumption, the amount of seafood consumed per serving, and the types of seafood consumed. Steady-state relationships that employed descriptive statistics to account for toxicokinetic variation were used to predict levels of Hg in blood. The model incorporates an uncertainty dimension that is intended to represent the range of plausible interpretations of the data. The predictability of the model was confirmed via the use of National Health and Nutrition Examination Survey (NHANES) blood Hg data. In the present analysis, the model was used to predict the impact of limitations in the amount or types of seafood consumed on blood Hg levels. Specifically, simulations for various advisory scenarios were developed on the basis of limitations on total consumption of seafood, elimination of the consumption of certain species altogether, and/or a combination of both. In the baseline model, the median (uncertainty) estimates for the 50th, 95th, and 99th per capita population percentiles were 1.25, 8.2, and 16.1 ppb blood Hg, respectively. After restriction of seafood consumption to no more than 12 oz/week, the median (uncertainty) estimates for the 50th, 95th, and 99th per capita population percentiles were 1.22, 6.8, and 10.6 ppb blood Hg, respectively. Elimination of MeHg species, with average concentrations above 0.6 ppm, resulted in very modest decrements in Hg blood levels, in comparison to either the baseline or the reduced consumption scenarios. These results suggest that strategies to reduce MeHg exposure by reducing the amount of fish consumed (e.g., 12 oz/week) are more effective at eliminating the high end of the exposure distribution than are strategies intended to change the types of fish consumed.

Adult↗

Estimation of uncertainty and variability in bacterial growth using Bayesian inference. Application to Listeria monocytogenes.

The usefulness of risk assessment is limited by its ability or inability to model and evaluate risk uncertainty and variability separately. A key factor of variability and uncertainty in microbial risk assessment could be growth variability between strains and growth model parameter uncertainty. In this paper, we propose a Bayesian procedure for growth parameter estimation which makes it possible to separate these two components by means of hyperparameters. This model incorporates in a single step the logistic equation with delay as a primary growth model and the cardinal temperature equation as a secondary growth model. The estimation of Listeria monocytogenes growth parameters in milk using literature data is proposed as a detailed application. While this model should be applied on genuine data, it is highlighted that the proposed approach may be convenient for estimating the variability and uncertainty of growth parameters separately, using a complete predictive microbiology model.

Animals↗

Bootstrapping for pharmacokinetic models: visualization of predictive and parameter uncertainty.

PURPOSE: We explore use of "bootstrapping" methods to obtain a measure of reliability of predictions made in part from fits of individual drug level data with a pharmacokinetic (PK) model, and to help clarify parameter identifiability for such models. METHODS: Simulation studies use four sets (A-D) of drug concentration data obtained following a single oral dose. Each set is fit with a two compartment PK model, and the "bootstrap" is employed to examine the potential predictive variation in estimates of parameter sets. This yields an empirical distribution of plausible steady state (SS) drug concentration predictions that can be used to form a confidence interval for a prediction. RESULTS: A distinct, narrow confidence region in parameter space is identified for subjects A and B. The bootstrapped sets have a relatively large coefficient of variation (CV) (35-90% for A), yet the corresponding SS drug levels are tightly clustered (CVs only 2-9%). The results for C and D are dramatically different. The CVs for both the parameters and predicted drug levels are larger by a factor of 5 and more. The results reveal that the original data for C and D, but not A and B, can be represented by at least two different PK model manifestations, yet only one provides reliable predictions. CONCLUSIONS: The insights gained can facilitate making decisions about parameter identifiability. In particular, the results for C and D have important implications for the degree of implicit overparameterization that may exist in the PK model. In cases where the data support only a single model manifestation, the "bootstrap" method provides information needed to form a confidence interval for a prediction.

Computer Simulation↗

Estimating environmental exposures to sulfur dioxide from multiple industrial sources for a case-control study.

This paper first discusses how population exposures to environmental pollutants are estimated from environmental monitoring data and the problems that are encountered in estimating risk from pollutants on the basis of ecologic studies. We then present a technique of estimating individualized exposures to an atmospheric pollutant, sulfur dioxide (SO2), through atmospheric transport modeling for a case-control study. The transport model uses the quantities of SO2 released from 30 geographically identified industrial facilities and meteorological data (wind speed and direction) to predict the downwind ground-level concentrations of SO2 at geographically identified residences, receptors, of 797 study subjects. A distribution of facility SO2 emissions, uncertainties in effective stack height, and model uncertainty are incorporated to examine the uncertainty in the predicted versus ambient monitoring SO2 levels, and to generate an exposure uncertainty distribution for both the cases and controls. The transport model's accuracy is evaluated by comparing recorded ambient measurements of SO2 with the model's predicted SO2 estimates at geographically identified ambient monitoring stations.

Air Pollutants↗

Model comparison for risk assessment: a case study of contaminated groundwater.

Many environmental multimedia risk assessment models have been developed and widely used along with increasing sophistication of the risk assessment method. Despite of the considerable improvement, uncertainty remains a primary threat to the credibility of and users' confidence in the model-based risk assessments. In particular, it has been indicated that scenario and model uncertainty may affect significantly the assessment outcome. Furthermore, the uncertainty resulting from choosing different models has been shown more important than that caused by parameter uncertainty. Based on the relationship between exposure pathways and estimated risk results, this study develops a screening procedure to compare the relative suitability between potential multimedia models, which would facilitate the reduction of uncertainty due to model selection. MEPAS, MMSOILS, and CalTOX models, combined with Monte Carlo simulation, are applied to a realistic groundwater-contaminated site to demonstrate the process. It is also shown that the identification of important parameters and exposure pathways, and implicitly, the subsequent design of uncertainty reduction and risk management measures, would be better-formed.

Animals↗

Surveillance of Barrett's oesophagus: exploring the uncertainty through systematic review, expert workshop and economic modelling.

OBJECTIVES: To assess what is known about the effectiveness, safety, affordability, cost-effectiveness and organisational impact of endoscopic surveillance in preventing morbidity and mortality from adenocarcinoma in patients with Barrett's oesophagus. In addition, to identify important areas of uncertainty in current knowledge for these programmes and to identify areas for further research. DATA SOURCES: Electronic databases up to March 2004. Experts in Barrett's oesophagus from the UK. REVIEW METHODS: A systematic review of the effectiveness of endoscopic surveillance of Barrett's oesophagus was carried out following methodological guidelines. Experts in Barrett's oesophagus from the UK were invited to contribute to a workshop held in London in May 2004 on surveillance of Barrett's oesophagus. Small group discussion, using a modified nominal group technique, identified key areas of uncertainty and ranked them for importance. A Markov model was developed to assess the cost-effectiveness of a surveillance programme for patients with Barrett's oesophagus compared with no surveillance and to quantify important areas of uncertainty. The model estimates incremental cost--utility and expected value of perfect information for an endoscopic surveillance programme compared with no surveillance. A cohort of 1000 55-year-old men with a diagnosis of Barrett's oesophagus was modelled for 20 years. The base case used costs in 2004 and took the perspective of the UK NHS. Estimates of expected value of information were included. RESULTS: No randomised controlled trials (RCTs) or well-designed non-randomised controlled studies were identified, although two comparative studies and numerous case series were found. Reaching clear conclusions from these studies was impossible owing to lack of RCT evidence. In addition, there was incomplete reporting of data particularly about cause of death, and changes in surveillance practice over time were mentioned but not explained in several studies. Three cost--utility analyses of surveillance of Barrett's oesophagus were identified, of which one was a further development of a previous study by the same group. Both sets of authors used Markov modelling and confined their analysis to 50- or 55-year-old white men with gastro-oesophageal reflux disease (GORD) symptoms. The models were run either for 30 years or to age 75 years. As these models are American, there are almost certainly differences in practice from the UK and possible underlying differences in the epidemiology and natural history of the disease. The costs of the procedures involved are also likely to be very different. The expert workshop identified the following key areas of uncertainty that needed to be addressed: the contribution of risk factors for the progression of Barrett's oesophagus to the development of high-grade dysplasia (HGD) and adenocarcinoma of the oesophagus; possible techniques for use in the general population to identify patients with high risk of adenocarcinoma; effectiveness of treatments for Barrett's oesophagus in altering cancer incidence; how best to identify those at risk in order to target treatment; whether surveillance programmes should take place at all; and whether there are clinical subgroups at higher risk of adenocarcinoma. Our Markov model suggests that the base case scenario of endoscopic surveillance of Barrett's oesophagus at 3-yearly intervals, with low-grade dysplasia surveyed yearly and HGD 3-monthly, does more harm than good when compared with no surveillance. Surveillance produces fewer quality-adjusted life-years (QALYs) for higher cost than no surveillance, therefore it is dominated by no surveillance. The cost per cancer identified approaches pound 45,000 in the surveillance arm and there is no apparent survival advantage owing to high recurrence rates and increased mortality due to more oesophagectomies in this arm. Non-surveillance continues to cost less and result in better quality of life whatever the surveillance intervals for Barrett's oesophagus and dysplastic states and whatever the costs (including none) attached to endoscopy and biopsy as the surveillance test. The probabilistic analyses assess the overall uncertainty in the model. According to this, it is very unlikely that surveillance will be cost-effective even at relatively high levels of willingness to pay. The simulation showed that, in the majority of model runs, non-surveillance continued to cost less and result in better quality of life than surveillance. At the population level (i.e. people with Barrett's oesophagus in England and Wales), a value of pound 6.5 million is placed on acquiring perfect information about surveillance for Barrett's oesophagus using expected value of perfect information (EVPI) analyses, if the surveillance is assumed to be relevant over 10 years. As with the one-way sensitivity analyses, the partial EVPI highlighted recurrence of adenocarcinoma of the oesophagus (ACO) after surgery and time taken for ACO to become symptomatic as particularly important parameters in the model. CONCLUSIONS: The systematic review concludes that there is insufficient evidence available to assess the clinical effectiveness of surveillance programmes of Barrett's oesophagus. There are numerous gaps in the evidence, of which the lack of RCT data is the major one. The expert workshop reflected these gaps in the range of topics raised as important in answering the question of the effectiveness of surveillance. Previous models of cost-effectiveness have most recently shown that surveillance programmes either do more harm than good compared with no surveillance or are unlikely to be cost-effective at usual levels of willingness to pay. Our cost--utility model has shown that, across a range of values for the various parameters that have been chosen to reflect uncertainty in the inputs, it is likely that surveillance programmes do more harm than good -- costing more and conferring lower quality of life than no surveillance. Probabilistic analysis shows that, in most cases, surveillance does more harm and costs more than no surveillance. It is unlikely, but still possible, that surveillance may prove to be cost-effective. The cost-effectiveness acceptability curve, however, shows that surveillance is unlikely to be cost-effective at either the 'usual' level of willingness to pay ( pound 20,000-30,000 per QALY) or at much higher levels. The expected value of perfect information at the population level is pound 6.5 million. Future research should target both the overall effectiveness of surveillance and the individual elements that contribute to a surveillance programme, particularly the performance of the test and the effectiveness of treatment for both Barrett's oesophagus and ACO. In addition, of particular importance is the clarification of the natural history of Barrett's oesophagus.

Adenocarcinoma↗

A multimedia environmental model of chemical distribution: fate, transport, and uncertainty analysis.

This paper presented a framework for analysis of chemical concentration in the environment and evaluation of variance propagation within the model. This framework was illustrated through a case study of selected organic compounds of benzo[alpha]pyrene (BAP) and hexachlorobenzene (HCB) in the Great Lakes region. A multimedia environmental fate model was applied to perform stochastic simulations of chemical concentrations in various media. Both uncertainty in chemical properties and variability in hydrometeorological parameters were included in the Monte Carlo simulation, resulting in a distribution of concentrations in each medium. Parameters of compartmental dimensions, densities, emissions, and background concentrations were assumed to be constant in this study. The predicted concentrations in air, surface water and sediment were compared to reported data for validation purpose. Based on rank correlations, a sensitivity analysis was conducted to determine the influence of individual input parameters on the output variance for concentration in each environmental medium and for the basin-wide total mass inventory. Results of model validation indicated that the model predictions were in reasonable agreement with spatial distribution patterns, among the five lake basins, of reported data in the literature. For the chemical and environmental parameters given in this study, parameters associated to air-ground partitioning (such as moisture in surface soil, vapor pressure, and deposition velocity) and chemical distribution in soil solid (such as organic carbon partition coefficient and organic carbon content in root-zone soil) were targeted to reduce the uncertainty in basin-wide mass inventory. This results of sensitivity analysis in this study also indicated that the model sensitivity to an input parameter might be affected by the magnitudes of input parameters defined by the parameter settings in the simulation scenario. Therefore, uncertainty and sensitivity analyses for environmental fate models was suggested to be conducted after the model output was validated based on an appropriate input parameter settings.

Benzopyrenes↗

Predicting blood lead concentrations from lead in environmental media.

Policy statements providing health and environmental criteria for blood lead (PbB) often give recommendations on an acceptable distribution of PbB concentrations. Such statements may recommend distributions of PbB concentrations including an upper range (e.g., maximum and/or 90th percentile values) and central tendency (e.g., mean and/or 50th percentile) of the PbB distribution. Two major, and fundamentally dissimilar, methods to predict the distribution of PbB are currently in use: statistical analyses of epidemiologic data, and application of biokinetic models to environmental lead measurements to predict PbB. Although biokinetic models may include a parameter to predict contribution of lead from bone (PbBone), contemporary data based on chemical analyses of pediatric bone samples are rare. Dramatic decreases in environmental lead exposures over the past 15 years make questionable use of earlier data on PbBone concentrations to estimate a contribution of lead from bone; often used by physiologic modelers to predict PbB. X-ray fluorescent techniques estimating PbBone typically have an instrument-based quantitation limit that is too high for use with many young children. While these quantitation limits have improved during the late 1990s, PbBone estimates using an epidemiologic approach to describing these limits for general populations of children may generate values lower than the instrument's quantitation limit. Additional problems that occur if predicting PbB from environmental lead by biokinetic modeling include a) uncertainty regarding the fractional lead absorption by young children; b) questions of bioavailability of specific environmental sources of lead; and c) variability in fractional absorption values over a range of exposures. Additional sources of variability in lead exposures that affect predictions of PbB from models include differences in the prevalence of such child behaviors as intensity of hand-to-mouth activity and pica. In contrast with these sources of uncertainty and variability affecting physiologic modeling of PbB distributions, epidemiologic data reporting PbB values obtained by chemical analyses of blood samples avoid these problems but raise other issues about the validity of the representation of the subsample for the overall population of concern. State and local health department screening programs and/or medical evaluation of individual children provide PbB data that contribute to databases describing the impact of environmental sources on PbB. Overall, application of epidemiologic models involves fewer uncertainties and more readily reflects variability in PbB than does current state-of-the-art biokinetic modeling.

Animals↗