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The use of a Diasonics DRF400 duplex ultrasound scanner to measure volume flow in arterio-venous fistulae in patients undergoing haemodialysis: an analysis of measurement uncertainties.

A pilot study to measure volume flow in arterio-venous fistulae in patients undergoing haemodialysis was undertaken to determine the accuracy and precision of values obtained using a modern duplex ultrasound scanner. A Diasonics DRF400 duplex ultrasound scanner was used with a small parts 10 MHz mechanical sector probe incorporating a 4.5 MHz Doppler transducer. Volume flow was measured in the brachial artery of 13 patients with surgically created arterio-venous fistulae in the distal circulation. Volume flow was also measured using a flow phantom in which the true volume flow was known. An analysis of the measurements made by the duplex scanner was performed to determine the sources of random and systematic uncertainty. Repeatability was improved with the probe clamped in position over the brachial artery giving a coefficient of variation in repeated measurements of volume flow in a patient of +/- 12%. Measured flows ranged from 884-3088 mL min-1. Comparison with measurements on the flow phantom showed these values from patients to be overestimated by 200-600 mL min-1. The values from the phantom should therefore be used to calibrate patient measurements. Analysis of uncertainties showed that precision was limited by random uncertainties in the measurement of vessel diameter and Doppler angle.

Aged↗

Uncertainty in dose estimation for gynecological implants.

One source of uncertainty in doses computed for intracavitary gynecological applications is the imprecision inherent in localizing the sources and the points of interest on radiographs of the implant and in transferring that data into the treatment planning computer. To quantify the effect of these activities on the accuracy of computed doses, five physicists and two dosimetrists performed computerized dose calculations on five applications chosen randomly from our patient files. For each of these applications, doses were computed at the traditional points A and B and at points in the bladder and rectum. Using identical sets of films, each planner located both the radioactive sources and points of interest, or only the sources, or only the points of interest. Another set of films was used to measure the accuracy of digitizing alone. Planners received no instructions on either the definition or the placement of the points of interest. Overall uncertainties in computed doses to points A and B and bladder were found to be about 7%. Uncertainty in dose to the rectum was on the order of 50%. Analysis of the results showed that about 1% of the error was due to digitization and about 2% to identification of source locations. Among the individual planners, almost all of the dose variation was from differences in placement of the points of interest on the implant radiographs. The results demonstrate the need for standard definitions and locations for points of calculation so that meaningful comparisons can be made among institutions.

Brachytherapy↗

The effect of setup uncertainties on the radiobiological advantage of fractionation in stereotaxic radiotherapy.

PURPOSE: There may be radiobiological advantages in administering stereotaxic radiation treatment in multiple fractions instead of by a single irradiation. However, a larger planning target volume may be required for fractionated stereotaxic radiotherapy than for a single session treatment, if decreased geometrical precision and increased setup uncertainty are associated with multiple-fraction treatments. This factor may partially offset the radiobiological gain. The purpose of this study is to estimate the potential therapeutic gain of fractionated treatments for brain tumors, and to assess the effect of increased setup uncertainty on the potential gain. METHODS AND MATERIALS: The concept of biologically effective dose (BED), based on the linear quadratic (LQ) model, was used to quantify the therapeutic efficacy of the respective treatment schema. Therapeutic gain (TG) was defined as the ratio of tumor BEDs, for multiple fractions and single treatment, respectively, for the same normal brain BED. To include the effect of increased planning volume in fractionated treatment, a power-law relationship was assumed for the volume dependence of prescription dose, and the TG was recalculated using the "volume-adjusted" doses. RESULTS: The therapeutic gain for fractionated treatment increases with fraction number, and is smaller for larger single treatment doses. For example, in going from 1 to 10 fractions, the TG is 1.40, 1.32, or 1.27 for single treatment dose of 20, 30, or 40 Gy, respectively. Also, the TG is more significant for the initial few fractions. The benefit of fractionation is diminished if larger planning volume is needed for multiple fraction treatments. For example, the above TG are reduced to 1.19, 1.11, or 1.06, if a 2 cm planning target volume in single fraction treatment is enlarged to 2.3 cm in fractionated treatment. CONCLUSION: Consideration of the therapeutic gain with fractionation should include estimates of setup uncertainty for multiple-fraction treatments, relative to that of single fraction radiosurgery.

Brain Neoplasms↗

Quantifying uncertainty in medical decisions.

Effective handling of uncertainty is one of the central problems in medical decision making. The sources and effects of uncertainty in medical decision making are examined and some new quantitative approaches for solving the associated problems are outlined. To handle uncertainty in the branching probabilities and node utilities for probability trees representing alternative treatment strategies, a public domain software package that can be used for the construction, analysis and comparison of probability trees with random parameters was developed. To facilitate specification of the random variables that arise in medical decision making problems, public domain software packages for both data-driven and subjective estimation of probability densities from the Johnson translation system of distributions have also been developed. For the analysis of complex problems that cannot be adequately represented by probability trees or by simple stochastic processes such as Markov chains, network simulation approaches that are oriented toward the sequence of activities seen by individual patients in the course of treatment are described.

Computer Simulation↗

Bayesian methodology incorporating expert judgment for ranking countermeasure effectiveness under uncertainty: example applied to at grade railroad crossings in Korea.

Transportation professionals are sometimes required to make difficult transportation safety investment decisions in the face of uncertainty. In particular, an engineer may be expected to choose among an array of technologies and/or countermeasures to remediate perceived safety problems when: (1) little information is known about the countermeasure effects on safety; (2) information is known but from different regions, states, or countries where a direct generalization may not be appropriate; (3) where the technologies and/or countermeasures are relatively untested, or (4) where costs prohibit the full and careful testing of each of the candidate countermeasures via before-after studies. The importance of an informed and well-considered decision based on the best possible engineering knowledge and information is imperative due to the potential impact on the numbers of human injuries and deaths that may result from these investments. This paper describes the formalization and application of a methodology to evaluate the safety benefit of countermeasures in the face of uncertainty. To illustrate the methodology, 18 countermeasures for improving safety of at grade railroad crossings (AGRXs) in the Republic of Korea are considered. Akin to "stated preference" methods in travel survey research, the methodology applies random selection and laws of large numbers to derive accident modification factor (AMF) densities from expert opinions. In a full Bayesian analysis framework, the collective opinions in the form of AMF densities (data likelihood) are combined with prior knowledge (AMF density priors) for the 18 countermeasures to obtain 'best' estimates of AMFs (AMF posterior credible intervals). The countermeasures are then compared and recommended based on the largest safety returns with minimum risk (uncertainty). To the author's knowledge the complete methodology is new and has not previously been applied or reported in the literature. The results demonstrate that the methodology is able to discern anticipated safety benefit differences across candidate countermeasures. For the 18 at grade railroad crossings considered in this analysis, it was found that the top three performing countermeasures for reducing crashes are in-vehicle warning systems, obstacle detection systems, and constant warning time systems.

Accidents, Traffic↗

On the uncertainty in activity measurements for samples containing "hot particles".

The uncertainty in activity measurements for samples containing hot particles is considered under three assumptions: (1) all activity in the samples is due to hot particles; (2) hot particle dimensions are log-normally distributed with the logarithm of the median radius m and the standard deviation of the logarithm of the particle radius s; and (3) the number of particles in the sample is a random quantity. It is shown that the measurement uncertainty grows when both s and m increase. Also, that for s < 0.25-0.3 the primary source of uncertainty is the randomness of the number of particles in the sample, and, if s exceeds 0.3, the "log-normality" effect becomes more dominant. The values of the variance/uncertainty estimated by the measurement of replicate aliquots from a single sample can be used for the estimation of the m and s relationship and boundary values of these parameters.

Computer Simulation↗

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↗

Estimation of uncertainty of analytical results based on multiple peaks.

The sources of the uncertainty of GC and HPLC analysis of pesticide residues, which consist of several components, and three methods applicable for the estimation of the uncertainty of the results are described. Different scenarios for estimating the uncertainty of measurements of multi-component residues are identified.

Chromatography, Gas↗

Analysis of natural gas by gas chromatography reduction of correlated uncertainties by normalisation.

The results of gas chromatographic analysis of natural gas mixtures reveal strong correlations (Pearson correlation coefficient of >0.96) between the uncertainty of each component and variations in the ambient pressure. Although correction for ambient pressure variations can reduce this variability, normalisation of the results of each analysis using the assumption that the sum of all component amount fractions is unity provides significantly greater reductions in the uncertainty of each measured component. We show that the uncertainty in normalised components can be estimated approximately using the correlation coefficient as a measure of the correlation present in the measurements, or exactly using a full calculation of the variance/covariance (V/C) structure of the data.

Chromatography, Gas↗

Robust interpretive optimisation in high-performance liquid chromatography considering uncertainties in peak position.

In the context of interpretive chromatographic optimisation, robustness is usually calculated by introducing deliberated shifts in the nominal optimal conditions and evaluating their effects on the monitored objective function, mimicking thus the experimental procedures used in method validation. However, such strategy ignores a major source of error: the uncertainties associated to the modelling step, that may give rise to deceiving results when conditions that were expected to yield baseline separation are reproduced in the chromatograph. Two approaches, based on the peak purity concept, are here proposed to evaluate the robustness of the objective function under the perspective of measurement errors and modelling. The first approach implements these uncertainties as an extra band broadening for each chromatographic peak. The second one implements them as peak fluctuations in simulated replicated assays, which gives rise to a distribution of peak purities, easily computed through Monte-Carlo simulations. Both approaches predict satisfactorily a decreased separation capability, with respect to the conventional approach, for those situations where the uncertainties in peak position make the objective function critical. The first approach is less optimistic and formally less rigorous than the second one, but its computation is simpler. It can be used to map the critical resolution regions, to be comprehensively appraised further by the slower, although more rigorous, Monte-Carlo approach.

Amino Acids↗

Determination of lanthanides in international geochemical reference materials by reversed-phase high-performance liquid chromatography using error propagation theory to estimate total analysis uncertainties.

The weighted least-squares (WLS) regression method was successfully applied to establish calibration curves with variable amounts of lanthanides ranging from 0.002 to 0.430 microg. These curves were employed for the analysis of 13 lanthanides (La-Nd, Sm-Tb, and Ho-Lu) in 12 international geochemical reference materials (IGRM). The separation of the lanthanide group was achieved in approximately 15 min. Dysprosium could not be determined in IGRM because of its co-elution with Yttrium. A linear gradient program of alpha-HIBA eluent with a concentration ranging from 0.05 to 0.5 M (0.1 M OS, pH 3.8 with NH(4)OH, and a flow-rate of 1.0 ml/min) was employed. The detection was performed with a UV-vis system at 658 nm using a post-column reagent of Arsenazo III (0.5 ml/min). With this set of RP-HPLC conditions together with the use of both the ordinary least-squares (OLS) and the WLS regressions, we report the results of the measurements along with the total propagated uncertainties in individual concentration values. The uncertainties were obtained by combining standard errors in both regression parameters (slope and intercept) with those related to the chromatographic peak areas. The straight-line slopes and intercepts calculated by the WLS method provided not only considerably smaller errors than the conventional OLS method but also a much better estimation of the limits of detection. The concentrations calculated were compared with the "most probable" concentration values of these reference materials reported in the literature. Statistically significant agreement was consistently observed between the HPLC data and the literature values. The total uncertainties in estimated concentration values for the WLS were consistently smaller than the respective errors for the OLS.

Algorithms↗

The cerebellum and decision making under uncertainty.

This study aimed to identify the neural basis of probabilistic reasoning, a type of inductive inference that aids decision making under conditions of uncertainty. Eight normal subjects performed two separate two-alternative-choice tasks (the balls in a bottle and personality survey tasks) while undergoing functional magnetic resonance imaging (fMRI). The experimental conditions within each task were chosen so that they differed only in their requirement to make a decision under conditions of uncertainty (probabilistic reasoning and frequency determination required) or under conditions of certainty (frequency determination required). The same visual stimuli and motor responses were used in the experimental conditions. We provide evidence that the neo-cerebellum, in conjunction with the premotor cortex, inferior parietal lobule and medial occipital cortex, mediates the probabilistic inferences that guide decision making under uncertainty. We hypothesise that the neo-cerebellum constructs internal working models of uncertain events in the external world, and that such probabilistic models subserve the predictive capacity central to induction.

Adolescent↗

Human variability in the renal elimination of foreign compounds and renal excretion-related uncertainty factors for risk assessment.

Renal excretion is an important route of elimination for xenobiotics and three processes determine the renal clearance of a compound [glomerular filtration (about 120 ml/min), active renal tubular secretion (>120 ml/min) and passive reabsorption (<120 ml/min)]. Human variability in kinetics has been quantified using a database of 15 compounds excreted extensively by the kidney (>60% of a dose) to develop renal-excretion related uncertainty factors for the risk assessment of environmental contaminants handled via this route. Data were analysed from published pharmacokinetic studies (after oral and intravenous dosing) in healthy adults and other subgroups using parameters relating primarily to chronic exposure [renal and total clearances, area under the plasma concentration time-curve (AUC)] and acute exposure (Cmax). Interindividual variability in kinetics was low for both routes of exposure, with coefficients of variation of 21% (oral) and 24% (intravenous) that were largely independent of the renal processes involved. Renal-excretion related uncertainty factors were below the default kinetic uncertainty factor of 3.16 for most subgroups analysed with the exception of the elderly (oral data) and neonates (intravenous data) for whom renal excretion-related factors of 4.2 and 3.2 would be required to cover up to 99% of these subgroups respectively.

Administration, Oral↗

Modeling field-scale multiple tracer injection at a low-level waste disposal site in fractured rocks: effect of multiscale heterogeneity and source term uncertainty on conceptual understanding of mass transfer processes.

Multiple factors may affect the scale-up of laboratory multi-tracer injection into structured porous media to the field. Under transient flow conditions and with multiscale heterogeneities in the field, previous attempts to scale-up laboratory experiments have not answered definitely the questions about the governing mechanisms and the spatial extent of the influence of small-scale mass transfer processes such as matrix diffusion. The objective of this research is to investigate the effects of multiscale heterogeneity, mechanistic and site model conceptualization, and source term density effect on elucidating and interpreting tracer movement in the field. Tracer release and monitoring information previously obtained in a field campaign of multiple, conservative tracer injection under natural hydraulic gradients at a low-level waste disposal site in eastern Tennessee, United States, is used for the research. A suite of two-pore-domain, or fracture-matrix, groundwater flow and transport models are calibrated and used to conduct model parameter and prediction uncertainty analyses. These efforts are facilitated by a novel nested Latin-hypercube sampling technique. Our results verify, at field scale, a multiple-pore-domain, multiscale mechanistic conceptual model that was used previously to interpret only laboratory observations. The results also suggest that, integrated over the entire field site, mass flux rates attributable to small-scale mass transfer are comparable to that of field-scale solute transport. The uncertainty analyses show that fracture spacing is the most important model parameter and model prediction uncertainty is relatively higher at the interface between the preferred flow path and its parent bedrock. The comparisons of site conceptual models indicate that the effect of matrix diffusion may be confined to the immediate neighborhood of the preferential flow path. Finally, because the relatively large amount of tracer needed for field studies, it is likely that source term density effect may exaggerate or obscure the effect of matrix diffusion on the movement of tracers from the preferred flow path into the bedrock.

Chemical Phenomena↗

IFRP: a hybrid interval-parameter fuzzy robust programming approach for waste management planning under uncertainty.

In this study, an interval-parameter fuzzy-robust programming (IFRP) model is developed and applied to the planning of solid waste management systems under uncertainty. As an extension of the existing fuzzy-robust programming and interval-parameter linear programming methods, the IFRP can explicitly address system uncertainties with complex presentations. Parameters in the IFRP model can be represented as interval numbers and/or fuzzy membership functions, such that the uncertainties can be directly communicated into the optimization process and resulting solution. Furthermore, highly uncertain information for the lower and upper bounds of interval parameters that exist due to the complexity of the real world can be effectively handled through introducing the concept of fuzzy boundary interval. Consequently, robustness of the optimization process and solution can be enhanced. Results of the case study indicate that useful solutions for planning municipal solid waste management practices can be generated. They reflect a compromise between optimality and stability of the study system. Willingness to pay higher costs will guarantee the system stability; however, a desire to reduce the costs will run the risk of potential instability of the system. The results also suggest that the proposed hybrid methodology is applicable to practical problems that are associated with highly complex and uncertain information.

Algorithms↗

Predicting streamflow response to fire-induced landcover change: implications of parameter uncertainty in the MIKE SHE model.

Fire is a primary agent of landcover transformation in California semi-arid shrubland watersheds, however few studies have examined the impacts of fire and post-fire succession on streamflow dynamics in these basins. While it may seem intuitive that larger fires will have a greater impact on streamflow response than smaller fires in these watersheds, the nature of these relationships has not been determined. The effects of fire size on seasonal and annual streamflow responses were investigated for a medium-sized basin in central California using a modified version of the MIKE SHE model which had been previously calibrated and tested for this watershed using the Generalized Likelihood Uncertainty Estimation methodology. Model simulations were made for two contrasting periods, wet and dry, in order to assess whether fire size effects varied with weather regime. Results indicated that seasonal and annual streamflow response increased nearly linearly with fire size in a given year under both regimes. Annual flow response was generally higher in wetter years for both weather regimes, however a clear trend was confounded by the effect of stand age. These results expand our understanding of the effects of fire size on hydrologic response in chaparral watersheds, but it is important to note that the majority of model predictions were largely indistinguishable from the predictive uncertainty associated with the calibrated model - a key finding that highlights the importance of analyzing hydrologic predictions for altered landcover conditions in the context of model uncertainty. Future work is needed to examine how alternative decisions (e.g., different likelihood measures) may influence GLUE-based MIKE SHE streamflow predictions following different size fires, and how the effect of fire size on streamflow varies with other factors such as fire location.

California↗

An expression of within-plate uncertainty in sandwich ELISA.

This paper puts forward a method to describe an equation of the within-plate uncertainty (relative standard deviation (R.S.D.) of measurements) as a function of analyte concentration in sandwich enzyme-linked immunosorbent assay (ELISA). A kit for thyroid stimulating hormone is taken as an example. The pipetting procedures of analyte solution and chromogen-substrate solution and absorbance inherent to the wells of a microplate are identified as major error sources and their variability is included as parameters in the uncertainty equation. These parameters can be determined by the experiments with distilled water. The theoretical R.S.D. is shown to be in good agreement with the results of the repeated experiments using the real samples. Since the theory gives a continuous plot of R.S.D. against concentration, the uncertainty structure of the ELISA kit can be recognized over a wide concentration range and the detection limit and quantitation range can easily be determined on the plot.

Enzyme-Linked Immunosorbent Assay↗

Probabilistic methods for addressing uncertainty and variability in biological models: application to a toxicokinetic model.

Population variability and uncertainty are important features of biological systems that must be considered when developing mathematical models for these systems. In this paper we present probability-based parameter estimation methods that account for such variability and uncertainty. Theoretical results that establish well-posedness and stability for these methods are discussed. A probabilistic parameter estimation technique is then applied to a toxicokinetic model for trichloroethylene using several types of simulated data. Comparison with results obtained using a standard, deterministic parameter estimation method suggests that the probabilistic methods are better able to capture population variability and uncertainty in model parameters.

Animals↗