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Simulating solute transport in a structured field soil: uncertainty in parameter identification and predictions.

Dual-permeability models have been developed to account for the significant effects of macropore flow on contaminant transport, but their use is hampered by difficulties in estimating the additional parameters required. Therefore, our objective was to evaluate data requirements for parameter identification for predictive modeling with the dual-permeability model MACRO. Two different approaches were compared: sequential uncertainty fitting (SUFI) and generalized likelihood uncertainty estimation (GLUE). We investigated six parameters controlling macropore flow and pesticide sorption and degradation, applying MACRO to a comprehensive field data set of bromide andbentazone [3-isopropyl-1H-2,1,3-benzothiadiazin-4(3H)-one-2,2dioxide] transport in a structured soil. The GLUE analyses of parameter conditioning for different combinations of observations showed that both resident and flux concentrations were needed to obtain highly conditioned and unbiased parameters and that observations of tracer transport generally improved the conditioning of macropore flow parameters. The GLUE "behavioral" parameter sets covered wider parameter ranges than the SUFI posterior uncertainty domains. Nevertheless, estimation uncertainty ranges defined by the 5th and 95th percentiles were similar and many simulations randomly sampled from the SUFI posterior uncertainty domains had negative model efficiencies (minimum of -3.2). This is because parameter correlations are neglected in SUFI and the posterior uncertainty domains were not always determined correctly. For the same reasons, uncertainty ranges for predictions of bentazone losses through drainflow for good agricultural practice in southern Sweden were 27% larger for SUFI compared with GLUE. Although SUFI proved to be an efficient parameter estimation tool, GLUE seems better suited as a method of uncertainty estimation for predictions.

Benzothiadiazines↗

Comparison of six phantoms for entrance skin dose evaluation in 11 standard X-ray examinations.

Entrance skin dose (ESD) is an important parameter for assessing the dose received by a patient in a single radiographic exposure. The most useful way to evaluate ESD is either by direct measurement on phantoms using an ionization chamber or using calculations based on a mathematical model. We compared six phantoms (three anthropomorphic, two physical, and one mathematical) in 11 standard clinical examinations (anterior-posterior (AP) abdomen, posterior-anterior (PA) chest, AP chest, lateral (LAT) chest, AP lumbar spine, LAT lumbar spine, LAT lumbo-sacral joint, AP pelvis, PA skull, LAT skull, and AP urinary tract) for two reasons: to determine the conversion factors to use for ESDs measured on different phantoms and to validate the mathematical model used. First, a comparison was done between the three anthropomorphic phantoms (Alderson Rando, chest RSD-77SPL, and 3M skull) and the two physical phantoms (Uniform and AAPM 31); for each examination we obtained "relative entrance skin dose factors." Second, we compared these five phantoms with the mathematical phantom: the overall accuracy of the model was better than 14%. Total mathematical model and total ionization chamber uncertainties, calculated by quadratic propagation of errors of the single components, were estimated to be on the order of +/-12% and +/-3%, respectively. To reduce the most significant source of uncertainty, the overall accuracy of the model was recalculated using new backscatter factors. The overall accuracy of the model improved: better than 12%. For each examination an anthropomorphic phantom was considered as the gold standard relative to the physical phantoms. In this way, it was possible to analyze the variations in phantom design and characteristics. Finally, the mathematical model was validated by more than 400 measurements taken on different phantoms and using a variety of radiological equipment. We conclude that the mathematical model can be used satisfactorily in ESD evaluations because it optimizes available resources, it is based on direct measurements, and it is an easy dynamic tool.

Algorithms↗

A comparison of three computer models for prediction of dose in acute amitriptyline overdose.

The pharmacokinetics of amitriptyline in overdose have been reported not to fit conventional compartmental models. In this study, the dose-concentration-time relationships of amitriptyline in overdose were modeled with discriminant analysis, with an evolutionary heuristic search program, and with a decision-tree model based on the entropy of uncertainty of classification. The computer models all used the same data from dogs administered treatment (80 mg/kg), toxic (250 mg/kg), or fatal (500 mg/kg) doses directly into the surgically isolated duodenum. All the models achieved a high degree of success (77 to 93%) in assigning records to the high-, low-, or middle-dose groups. Two of the models gave a probability of the assignment. Results of this analysis suggest that blood amitriptyline and nortriptyline concentrations are most useful in estimating dose in acute amitriptyline overdose.

Amitriptyline↗

Methodological issues of using observational human data in lung dosimetry models for particulates.

INTRODUCTION: The use of human data to calibrate and validate a physiologically based pharmacokinetic (PBPK) model has the clear advantage of pertaining to the species of interest, namely humans. A challenge in using these data is their often sparse, heterogeneous nature, which may require special methods. Approaches for evaluating sources of variability and uncertainty in a human lung dosimetry model are described in this study. METHODS: A multivariate optimization procedure was used to fit a dosimetry model to data of 131 U.S. coal miners. These data include workplace exposures and end-of-life particle burdens in the lungs and hilar lymph nodes. Uncertainty in model structure was investigated by fitting various model forms for particle clearance and sequestration of particles in the lung interstitium. A sensitivity analysis was performed to determine which model parameters had the most influence on model output. Distributions of clearance parameters were estimated by fitting the model to each individual's data, and this information was used to predict inter-individual differences in lung particle burdens at given exposures. The influence of smoking history, race and pulmonary fibrosis on the individual's estimated clearance parameters was also evaluated. RESULTS: The model structure that provided the best fit to these coal miner data includes a first-order interstitialization process and no dose-dependent decline in alveolar clearance. The parameter that had the largest influence on model output is fractional deposition. Race and fibrosis severity category were statistically significant predictors of individual's estimated alveolar clearance rate coefficients (P < 0.03 and P < 0.01-0.06, respectively), but smoking history (ever, never) was not (P < 0.4). Adjustments for these group differences provided some improvement in the dosimetry model fit (up to 25% reduction in the mean squared error), although unexplained inter-individual differences made up the largest source of variability. Lung burdens were inversely associated with the miners' estimated clearance parameters, e.g. individuals with slower estimated clearance had higher observed lung burdens. CONCLUSIONS: The methods described in this study were used to examine issues of uncertainty in the model structure and variability of the miners' estimated clearance parameters. Estimated individual clearance had a large influence on predicted lung burden, which would also affect disease risk. These findings are useful for risk assessment, by providing estimates of the distribution of lung burdens expected under given exposure conditions.

Body Burden↗

Calibration and validation of an ASM3-based steady-state model for activated sludge systems--part I: Prediction of nitrogen removal and sludge production.

The steady-state model from Siegrist and Gujer (1994) which can be used for the design and optimisation of nitrogen-removing activated sludge plants is applied to the stoichiometrics and kinetics of a validated Activated Sludge Model No. 3. It considers the wastewater composition, the effect of the electron acceptor on the average sludge production, the oxygen input into anoxic volumes, denitrification in the secondary clarifier, the temperature and various operating conditions. The organic substrate for denitrification originates from readily degradable substrate from the influent, from the hydrolysis of slowly degradable particulate substrate along the activated sludge plant and from the endogenous respiration of the biomass. The model is calibrated and validated with data from long-term full-scale and pilot-plant experiments for Swiss municipal wastewater. The most sensitive parameters as well as the uncertainty of the model prognosis for various COD-to-nitrogen ratios from inlet water and anoxic volume fractions were calculated with the aid of sensitivity analyses and Monte-Carlo simulations. Excel spreadsheets of the model for different flow schemes are available from the corresponding author.

Biomass↗

Assessment of health economics in Alzheimer's disease (AHEAD) based on need for full-time care.

OBJECTIVE: To develop a framework for estimating the long-term health and economic consequences of AD based on patient characteristics at a given point in time. METHODS: A pharmacoeconomic model (Assessment of Health Economics in Alzheimer's Disease, AHEAD) was developed based on equations that relate the probability of needing full-time care (FTC) over time to patient characteristics summarized in index scores. These equations were developed from published data on interquartile times until FTC is needed and until death, using nonlinear regressions of the resulting index-specific hazards. These equations were then incorporated into a hidden Markov framework that allows for calculation of expected time to FTC and to death, as well as of the economic consequences of disease progression. There are three major states in the model: not requiring FTC ("pre-FTC"), requiring FTC, and death. RESULTS: Outcomes for five sample patients are derived to illustrate application of the AHEAD model. The impact of altering disease markers in these patients is also considered. CONCLUSION: The need for a generally applicable tool to forecast long-term outcomes based on relatively short-term data is becoming increasingly acute with the advent of new therapies for AD. The AHEAD model provides a relatively simple framework for the prediction of time to FTC requirement based on short-term observed data such as those from clinical trials. Although subject to the uncertainties inherent in modeling, the model nevertheless provides a standard estimation technique that may facilitate comparisons between existing and emerging therapies.

Aged↗

Global warming and thermohaline circulation stability.

The Atlantic thermohaline circulation (THC) plays an important role in global climate. Theoretical and palaeoclimatic evidence points to the possibility of rapid changes in the strength of the THC, including a possible quasi-permanent shutdown. The climatic impacts of such a shutdown would be severe, including a cooling throughout the Northern Hemisphere, which in some regions is greater in magnitude than the changes expected from global warming in the next 50 years. Other climatic impacts would likely include a severe alteration of rainfall patterns in the tropics, the Indian subcontinent and Europe. Modelling the future behaviour of the THC focuses on two key questions. (i) Is a gradual weakening of the THC likely in response to global warming, and if so by how much? (ii) Are there thresholds beyond which rapid or irreversible changes in the THC are likely? Most projections of the response of the THC to increasing concentrations of greenhouse gases suggest a gradual weakening over the twenty-first century. However, there is a wide variation between different models over the size of the weakening. Rapid or irreversible THC shutdown is considered a low-probability (but high-impact) outcome; however, some climate models of intermediate complexity do show the possibility of such events. The question of the future of the THC is beset with conceptual, modelling and observational uncertainties, but some current and planned projects show promise to make substantial progress in tackling these uncertainties in future.

Atlantic Ocean↗

Mapping indoor radon-222 in Denmark: design and test of the statistical model used in the second nationwide survey.

In Denmark, a new survey of indoor radon-222 has been carried out, 1-year alpha track measurements (CR-39) have been made in 3019 single-family houses. There are from 3 to 23 house measurements in each of the 275 municipalities. Within each municipality, houses have been selected randomly. One important outcome of the survey is the prediction of the fraction of houses in each municipality with an annual average radon concentration above 200 Bq m(-3). To obtain the most accurate estimate and to assess the associated uncertainties, a statistical model has been developed. The purpose of this paper is to describe the design of this model, and to report results of model tests. The model is based on a transformation of the data to normality and on analytical (conditionally) unbiased estimators of the quantities of interest. Bayesian statistics are used to minimize the effect of small sample size. In each municipality, the correction is dependent on the fraction of area where sand and gravel is a dominating surface geology. The uncertainty analysis is done with a Monte-Carlo technique. It is demonstrated that the weighted sum of all municipality model estimates of fractions above 200 Bq m(-3) (3.9% with 95%-confidence interval = [3.4,4.5]) is consistent with the weighted sum of the observations for Denmark taken as a whole (4.6% with 95%-confidence interval = [3.8,5.6]). The total number of single-family houses within each municipality is used as weight. Model estimates are also found to be consistent with observations at the level of individual counties. These typically include a few hundred house measurements. These tests indicate that the model is well suited for its purpose.

Air Pollutants, Radioactive↗

Prediction of the benefits from dose-escalated hypofractionated intensity-modulated radiotherapy for prostate cancer.

PURPOSE: To estimate the benefits of dose escalation in hypofractionated intensity-modulated radiotherapy (IMRT) for prostate cancer, using radiobiologic modeling and incorporating positional uncertainties of organs. MATERIALS AND METHODS: Biologically based mathematical models for describing the relationships between tumor control probability (TCP) and normal-tissue complication probability (NTCP) vs. dose were used to describe some of the results available in the literature. The values of the model parameters were then used together with the value of 1.5 Gy for the prostate cancer alpha/beta ratio to predict the responses in a hypofractionated 3 Gy/fraction IMRT trial at the Christie Hospital, taking into account patient movement characteristics between dose fractions. RESULTS: Compared with the current three-dimensional conformal radiotherapy technique (total dose of 50 Gy to the planning target volume in 16 fractions), the use of IMRT to escalate the dose to the prostate was predicted to increase the TCP by 5%, 16%, and 22% for the three dose levels, respectively, of 54, 57, and 60 Gy delivered using 3 Gy per fraction while keeping the late rectal complications (>/=Grade 2 RTOG scale) at about the same level of 5%. Further increases in TCP could be achieved by reducing the uncertainty in daily target position, especially for the last stage of the trial, where up to 6% further increase in TCP should be gained. CONCLUSIONS: Dose escalation to the prostate using IMRT to deliver daily doses of 3 Gy was predicted to significantly increase tumor control without increasing late rectal complications, and currently this prediction is being tested in a clinical trial.

Adenocarcinoma↗

Performance assessments of nuclear waste repositories: a dialogue on their value and limitations.

Performance Assessment (PA) is the use of mathematical models to simulate the long-term behavior of engineered and geologic barriers in a nuclear waste repository; methods of uncertainty analysis are used to assess effects of parametric and conceptual uncertainties associated with the model system upon the uncertainty in outcomes of the simulation. PA is required by the U.S. Environmental Protection Agency as part of its certification process for geologic repositories for nuclear waste. This paper is a dialogue to explore the value and limitations of PA. Two "skeptics" acknowledge the utility of PA in organizing the scientific investigations that are necessary for confident siting and licensing of a repository; however, they maintain that the PA process, at least as it is currently implemented, is an essentially unscientific process with shortcomings that may provide results of limited use in evaluating actual effects on public health and safety. Conceptual uncertainties in a PA analysis can be so great that results can be confidently applied only over short time ranges, the antithesis of the purpose behind long-term, geologic disposal. Two "proponents" of PA agree that performance assessment is unscientific, but only in the sense that PA is an engineering analysis that uses existing scientific knowledge to support public policy decisions, rather than an investigation intended to increase fundamental knowledge of nature; PA has different goals and constraints than a typical scientific study. The "proponents" describe an ideal, six-step process for conducting generalized PA, here called probabilistic systems analysis (PSA); they note that virtually all scientific content of a PA is introduced during the model-building steps of a PSA; they contend that a PA based on simple but scientifically acceptable mathematical models can provide useful and objective input to regulatory decision makers. The value of the results of any PA must lie between these two views and will depend on the level of knowledge of the site, the degree to which models capture actual physical and chemical processes, the time over which extrapolations are made, and the proper evaluation of health risks attending implementation of the repository. The challenge is in evaluating whether the quality of the PA matches the needs of decision makers charged with protecting the health and safety of the public.

Geological Phenomena↗

Modifying ADM1 to include formation and emission of odourants.

A mathematical model that is based upon the ADM1 structure has been developed to describe the formation and emission of odourous compounds in anaerobic sludge digestion. Special emphasis is given to the general mechanisms for the formation of common odorous sulfur compounds that are found in anaerobic digesters: methyl mercaptan, dimethyl sulfide and hydrogen sulfide, as well as volatile fatty acids and ammonia. The model includes multiple-reaction stoichiometry, microbial growth kinetics and conventional material balances for an ideally mixed reactor. Simulations that were performed with the model revealed that changes in common operational parameters such as temperature, HRT and sludge metal content can dramatically impact upon the gas phase concentrations of odourants. Additional research is required to reduce uncertainty in the model formulation.

Anaerobiosis↗

The application of physiologically based pharmacokinetic modeling in human health risk assessment of hazardous substances.

Physiologically based pharmacokinetic (PBPK) modeling is an important tool for improving the accuracy of human health risk assessments for hazardous substances in the environment. The proper use of PBPK modeling can reduce uncertainties that currently exist in risk assessment procedures by providing more scientifically credible extrapolations across species and routes of exposure, and from high experimental doses to potential environmental exposures. Current applications of PBPK models range from relatively straightforward uses for the extrapolation of chemical kinetics across species, route, and duration of exposure to much more demanding chemical risk assessment applications requiring a description of complex pharmacodynamic phenomena such as mitogenicity and hyperplasia secondary to cytotoxicity. PBPK modeling helps to identify the factors that are most important in determining the health risks associated with exposure to a chemical, and provides a means for estimating the impact of those factors both on the average risk to a population and on the specific risk to an individual. The chief challenge in the application of PBPK modeling in human health risk assessment lies in the need to generate chemical-specific data to support the development and validation of the models. Extensive use of rapidly developing in vitro and structure-activity relationship techniques is needed to provide the data required for the large number of hazardous chemicals currently contaminating the environment.

Animals↗

A biokinetic model for predicting the retention of 3H in the human body after intakes of tritiated water.

Scarce published data on the long-term excretion of tritiated water from the human body have been re-evaluated in order to develop a biokinetic model describing the retention in the human body of 3H from tritiated water (HTO) that could be used for both prospective and retrospective radiation protection. A three-component exponential function is proposed to describe the elimination of 3H from HTO with biological half-times of 10 d (99.00%), 40 d (0.98%) and 350 d (0.02%) respectively. The model predicts a committed effective dose of 1.7 x 10(-11) Sv Bq(-1), comparable with that of the current ICRP Publication 56 and 72 models, and estimates the retention of 3H to within a factor of about 2 of the measured values up to 40 d after intake and about 5 at times longer than 100 d. The derivation of the model and the uncertainties associated with the various parameters are discussed.

Absorption↗

Time-resolved study of biofilm architecture and transport processes using experimental and simulation techniques: the role of EPS.

Cellular material and extracellular polymeric substances are the basic structural elements in biofilm systems. The structure and role of EPS for biofilm development and metabolic processes have not been precisely determined and, therefore, have not yet been included as a necessary element in modelling and simulation studies. This is due to the difficulty of experimentally detecting the extracellular polymeric substances in situ and differentiating them from cellular material on the one hand, and to the subsequent uncertainty about appropriate models--e.g. rigid hindrances, porous microstructure or visco-elastic structure--on the other hand. In this work, we report on the use of confocal laser scanning microscopy to monitor the development of a monoculture biofilm of Sphingomonas sp. grown in a flow cell. The bacterial strain was genetically labelled resulting in strong constitutive expression of the green fluorescent protein. The development of extracellular polymeric substances was followed by binding of the lectin concavalin A to cell exopolysaccharides. The growth of the resulting strain was digitally recorded by automated confocal laser scanning microscopy. In addition, local velocity profiles of fluorescent carboxylate-modified microspheres were observed on pathlines throughout the biofilm. The CLSM image stacks were used as direct input for the explicit modelling and three-dimensional numerical simulation of flow fields and solute transport processes based on the conservation laws of continuum mechanics. At present, a strongly simplifying EPS-model is applied for numerical simulations. The EPSs are preliminarily assumed to behave like a rigid and dense hindrance with diffusive-reactive solute transport.

Biofilms↗

Economic evaluation of health effects with preference imprecision.

The estimation of economic benefits of health effects through direct methods, such as contingent valuation, presents the problem of preference imprecision. This paper deals with this problem by proposing an elicitation method that allows the subject to state an interval for willingness to pay, without inducing any specific amount as a response. The paper also analyzes the effects of the context where changes in health occur on the associated imprecision level and the estimates, by comparing a situation without context with another in which effects are due to atmospheric pollution. The econometric modelling develops a Bayesian estimation method for censored intervals, which models the existing uncertainty between the lower and upper limits derived from the elicitation process. Results prove that data dispersion is significantly higher for the non-contextual scenario, and increases for the most severe symptoms.

Bayes Theorem↗

Factors that modify risks of radiation-induced cancer.

The collective influence of biologic, physical, and other factors that modify risks of radiation-induced cancer introduces uncertainties and assumptions that limit precision of estimates of human cancer risk that can be calculated for populations exposed to low-dose radiation. The important biologic characteristics include the tissue sites and cell types, baseline cancer incidence, latent periods, time-to-tumor recognition, and individual host (e.g., age and sex) and competing etiologic influences. Physical factors include radiation dose, dose rate, and radiation quality. Statistical factors include time-response projection models, risk coefficients, and dose-response relationships. Sources that modify risk also include other carcinogens and biologic factors (e.g., hormonal conditions, immune status, hereditary factors). Discussion includes examples of known influences that modify radiation-associated cancer risks and how they have been dealt with in the risk-estimation process, including extrapolation to low doses, use of relative risk models, and other uncertainties.

Cocarcinogenesis↗

Using the W&H integrated uncertainty analysis framework with non-initiated experts.

The W&H (Walker and Harremoës) integrated uncertainty analysis framework was put forward with the aim of providing a conceptual basis for the systematic treatment of uncertainty in model-based decision support activities such as policy analysis, integrated assessment and risk assessment. It provides a heuristic tool that can be applied in decision support exercises to classify and report the various dimensions of uncertainty. The intention is to stimulate better communication among analysts as well as between them and policymakers and stakeholders. The framework successfully articulates diverse scholarly understandings of 'uncertainty', 'ignorance', and 'quality' in science for policy, Nevertheless, experience with the W&H framework has revealed that many of the concepts put forward are relatively unfamiliar--and perhaps somewhat controversial--to experts practising decision support. Thus, efforts are required to communicate the W&H framework to experts in such a way that their knowledge of uncertainty is elicited adequately, without them being overly intimidated or confused by the novelty of the concepts presented to them. After introducing the W&H conceptual framework, this paper presents the methodology that was used in applying the W&H framework in expert elicitations on uncertainty in the risk assessment of genetically modified crops. Experiences with the use of this methodology are discussed and recommendations for further improvement are given.

Decision Support Techniques↗

Modeling of the dispersion of depleted uranium aerosol.

Depleted uranium is a low-cost radioactive material that, in addition to other applications, is used by the military in kinetic energy weapons against armored vehicles. During the Gulf and Balkan conflicts concern has been raised about the potential health hazards arising from the toxic and radioactive material released. The aerosol produced during impact and combustion of depleted uranium munitions can potentially contaminate wide areas around the impact sites or can be inhaled by civilians and military personnel. Attempts to estimate the extent and magnitude of the dispersion were until now performed by complex modeling tools employing unclear assumptions and input parameters of high uncertainty. An analytical puff model accommodating diffusion with simultaneous deposition is developed, which can provide a reasonable estimation of the dispersion of the released depleted uranium aerosol. Furthermore, the period of the exposure for a given point downwind from the release can be estimated (as opposed to when using a plume model). The main result is that the depleted uranium mass is deposited very close to the release point. The deposition flux at a couple of kilometers from the release point is more than one order of magnitude lower than the one a few meters near the release point. The effects due to uncertainties in the key input variables are addressed. The most influential parameters are found to be atmospheric stability, height of release, and wind speed, whereas aerosol size distribution is less significant. The output from the analytical model developed was tested against the numerical model RPM-AERO. Results display satisfactory agreement between the two models.

Aerosols↗