Linear Dose-response Function Research Articles

Spatial Resolution and Frequency Characteristics for Dose Modulation on the TrueBeam Medical Accelerator

Purpose: To study the spatial resolution achievable by dose modulation in a water phantom using a multi-leaf collimator, jaws and their combination. To estimate the power spectrum density of the useful signal (dose distribution) and statistical noise, evaluate the frequency interval containing the useful signal.
 Material and methods: Using the Gafchromic EBT2 radiochromic film, nested squares dose patterns formed in a water-equivalent phantom by 6 and 15 MV photon beams of the TrueBeam medical accelerator, jaws, a multi-leaf collimator, and a combination of these devices were measured. Dose response to step function (ESF) data was extracted from the penumbra and the linear photon source dose response function (LSF) was calculated. To move to frequency domain, fast Fourier transform was performed over the obtained datasets, as well as over individual LSF peaks, and then power spectra densities were calculated. The Nyquist frequency associated with data sampling was 1.42 mm-1, the Hann window was used to minimize leakage effect.
 Results: The shape of the obtained LSF peaks was approximated by a sum of two Gaussian distributions with the same center positions but different widths. The LSF peak width at half maximum (FWHM) was 1.7-3.9 mm depending on the modulation device. No significant difference was observed in the peak widths at energies of 6 and 15 MV. In most cases, the width of the peak along the X-axis was wider than along the Y-axis. The power spectrum of the useful signal had a maximum near zero frequency, a 50 % level was near 0.09 mm-1 and its high frequency limit was about 0.4 mm-1. Above this value, only the spectrum of statistical noise was recorded, uniformly distributed over frequency.
 Conclusion: The obtained values of the LSF peak width in the range 1.7-3.9 mm characterize the ability of dose modulation by the considered devices or their combination, which can be significant for treatment of small targets (less than 3-4 cm), where these limits of spatial resolution can be reached. The obtained relationships in frequency domain can be used for optimal removal of statistical noise using Wiener filters from profiles or two-dimensional dose distributions.

Oral intake exposure to phthalates in vegetables produced in plastic greenhouses and its health burden in Shaanxi province, China

Phthalate exposure from Vegetables grown in Plastic Greenhouses (VPGs) represents an important source of total daily phthalate exposure in China. However, quantified health risks of phthalates attributable to VPG intake have not been documented. To fill this gap, this study estimates phthalate exposure from VPG intake in western China and calculates the first assessment of the disease burden associated with phthalate exposure from VPG intake in China based on a simple steady-state exposure model and a linear dose-response function between human bio-monitoring phthalates and Type 2 Diabetes (T2D) prevalence. What we present in this paper is a problem identification and screening level risk assessment. We chose Shaanxi province as the research field site due to its large contribution to the total vegetable yield and consumption in western China. Phthalate concentration in VPG samples, phthalate exposure levels from VPG intake, and the T2D burden caused by phthalate attributable to VPG intake for adults were measured or calculated. Di-2-ethylhexyl phthalate (DEHP) was found to represent over 55% of the total phthalate concentration in VPGs, followed by di-n-butyl phthalate (DnBP) and di-isobutyl phthalate (DiBP). Phthalate exposure from VPG intake for urban adults was higher than the level for rural adults. The share of DEHP exposure from VPG intake to urinary total DEHP metabolites were nearly 8% and 15%, and the share of DnBP exposure caused by VPG intake to total daily DnBP metabolites were nearly 4% and 7%, for rural and urban adult populations in Shaanxi, respectively. The adult population with T2D attributable to phthalate exposure from VPG intake was 2561, nearly 6.4% to the T2D burden attributable to total phthalate exposure, and 0.4% to the total adult population with T2D in Shaanxi. The authors recommend policy interventions to protect populations from future risk of phthalate exposure.

Linear and inverted U-shaped dose-response functions describe estrogen effects on hippocampal activity in young women

In animals, 17-beta-estradiol (E2) enhances hippocampal plasticity in a dose-dependent, monotonically increasing manner, but this relationship can also exhibit an inverted U-shaped function. To investigate E2’s dose-response function in the human hippocampus, we pharmacologically increased E2 levels in 125 naturally cycling women (who were in their low-hormone menstruation phase) to physiological (equivalent to menstrual cycle peak) and supraphysiological (equivalent to levels during early pregnancy) concentrations in a placebo-controlled design. Twenty-four hours after first E2 intake, we measured brain activity during encoding of neutral and negative pictures and then tested recognition memory 24 h after encoding. Here we report that E2 exhibits both a monotonically increasing relationship with hippocampal activity as well as an inverted U-shaped relationship, depending on the hippocampal region. Hippocampal activity exhibiting a U-shaped relationship inflects at supraphysiological E2 levels, suggesting that while E2 within physiological ranges stimulates hippocampal activity, supraphysiological ranges show opposite effects.

Daily mortality and ozone – which metric?

Background: Ozone is an aggressive gas but even worse it indicates a complex air pollution mixture. This highly reactive mixture of often only short-lived chemicals might even be better indicated not by the daily average ozone concentration but by the turn-over of ozone. We hypothesized that the daily variation in ozone concentration (the difference between night time low and early afternoon high half hour mean concentration) is a better predictor of health effects than the daily mean concentration. Methods: We performed a time series analysis on daily deaths (all causes, respiratory and cardiovascular causes as well as death in elderly 65+) in Vienna for the years 1991-2009. We controlled for seasonal and long term trend, day of the week, temperature and humidity using the same basic model for all pollutant metrics. Results: We found model ?t was best for same day variability of ozone concentration (calculated as the difference between daily hourly maximum and minimum) and hourly maximum. Of these the variability displayed a more linear dose-response function. Maximum 8h moving average and daily mean value performed not so well. Nitrogen dioxide (daily mean) in comparison performed better when previous day values were assessed. Same day ozone and previous day nitrogen dioxide effect estimates did not confound each other. Conclusion: Variability in daily ozone levels or peak ozone levels seem to be a better proxy of a complex reactive secondary pollutant mixture than daily average ozone levels in the Middle European setting. If this ?nding is con?rmed this would have implications for the setting of legally binding limit values.

Manual versus automated γ-H2AX foci analysis across five European laboratories: Can this assay be used for rapid biodosimetry in a large scale radiation accident?

The identification of severely exposed individuals and reassurance of the 'worried well' are of prime importance for initial triage following a large scale radiation accident. We aim to develop the γ-H2AX foci assay into a rapid biomarker tool for use in accidents. Here, five laboratories established a standard operating procedure and analysed 100 ex vivo γ-irradiated, 4 or 24h incubated and overnight-shipped lymphocyte samples from four donors to generate γ-H2AX reference data, using manual and/or automated foci scoring strategies. In addition to acute, homogeneous exposures to 0, 1, 2 and 4Gy, acute simulated partial body (4Gy to 50% of cells) and protracted exposures (4Gy over 24h) were analysed. Data from all laboratories could be satisfactorily fitted with linear dose response functions. Average yields observed at 4h post exposure were 2-4 times higher than at 24h and varied considerably between laboratories. Automated scoring caused larger uncertainties than manual scoring and was unable to identify partial exposures, which were detectable in manually scored samples due to their overdispersed foci distributions. Protracted exposures were detectable but doses could not be accurately estimated with the γ-H2AX assay. We conclude that the γ-H2AX assay may be useful for rapid triage following a recent acute radiation exposure. The potentially higher speed and convenience of automated relative to manual foci scoring needs to be balanced against its compromised accuracy and inability to detect partial body exposures. Regular re-calibration or inclusion of reference samples may be necessary to ensure consistent results between laboratories or over long time periods.

Economic benefits of methylmercury exposure control in Europe: Monetary value of neurotoxicity prevention

BackgroundDue to global mercury pollution and the adverse health effects of prenatal exposure to methylmercury (MeHg), an assessment of the economic benefits of prevented developmental neurotoxicity is necessary for any cost-benefit analysis.MethodsDistributions of hair-Hg concentrations among women of reproductive age were obtained from the DEMOCOPHES project (1,875 subjects in 17 countries) and literature data (6,820 subjects from 8 countries). The exposures were assumed to comply with log-normal distributions. Neurotoxicity effects were estimated from a linear dose-response function with a slope of 0.465 Intelligence Quotient (IQ) point reduction per μg/g increase in the maternal hair-Hg concentration during pregnancy, assuming no deficits below a hair-Hg limit of 0.58 μg/g thought to be safe. A logarithmic IQ response was used in sensitivity analyses. The estimated IQ benefit cost was based on lifetime income, adjusted for purchasing power parity.ResultsThe hair-mercury concentrations were the highest in Southern Europe and lowest in Eastern Europe. The results suggest that, within the EU, more than 1.8 million children are born every year with MeHg exposures above the limit of 0.58 μg/g, and about 200,000 births exceed a higher limit of 2.5 μg/g proposed by the World Health Organization (WHO). The total annual benefits of exposure prevention within the EU were estimated at more than 600,000 IQ points per year, corresponding to a total economic benefit between €8,000 million and €9,000 million per year. About four-fold higher values were obtained when using the logarithmic response function, while adjustment for productivity resulted in slightly lower total benefits. These calculations do not include the less tangible advantages of protecting brain development against neurotoxicity or any other adverse effects.ConclusionsThese estimates document that efforts to combat mercury pollution and to reduce MeHg exposures will have very substantial economic benefits in Europe, mainly in southern countries. Some data may not be entirely representative, some countries were not covered, and anticipated changes in mercury pollution all suggest a need for extended biomonitoring of human MeHg exposure.

Which metric of ambient ozone to predict daily mortality?

It is well known that ozone concentration is associated with daily cause specific mortality. But which ozone metric is the best predictor of the daily variability in mortality? We performed a time series analysis on daily deaths (all causes, respiratory and cardiovascular causes as well as death in elderly 65+) in Vienna for the years 1991–2009. We controlled for seasonal and long term trend, day of the week, temperature and humidity using the same basic model for all pollutant metrics. We found model fit was best for same day variability of ozone concentration (calculated as the difference between daily hourly maximum and minimum) and hourly maximum. Of these the variability displayed a more linear dose–response function. Maximum 8 h moving average and daily mean value performed not so well. Nitrogen dioxide (daily mean) in comparison performed better when previous day values were assessed. Same day ozone and previous day nitrogen dioxide effect estimates did not confound each other. Variability in daily ozone levels or peak ozone levels seem to be a better proxy of a complex reactive secondary pollutant mixture than daily average ozone levels in the Middle European setting. If this finding is confirmed this would have implications for the setting of legally binding limit values. ► We performed a time-series analysis over 19 years of ozone and daily mortality. ► Within-day variability of ozone was the best predictors of same day mortality. ► Previous day nitrogen dioxide did not confound the results.

Economic evaluation of health consequences of prenatal methylmercury exposure in France

BackgroundEvidence of a dose–response relationship between prenatal exposure to methylmercury (MeHg) and neurodevelopmental consequences in terms of IQ reduction, makes it possible to evaluate the economic consequences of MeHg exposures.ObjectiveTo perform an economic evaluation of annual national benefits of reduction of the prenatal MeHg exposure in France.MethodsWe used data on hair-Hg concentrations in French women of childbearing age (18–45 years) from a national sample of 126 women and from two studies conducted in coastal regions (n = 161and n = 503). A linear dose response function with a slope of 0.465 IQ point reduction per μg/g increase in hair-Hg concentration was used, along with a log transformation of the exposure scale, where a doubling of exposure was associated with a loss of 1.5 IQ points. The costs calculations utilized an updated estimate of €2008 17,363 per IQ point decrement, with three hypothetical exposure cut-off points (hair-Hg of 0.58, 1.0, and 2.5 μg/g).ResultsBecause of higher exposure levels of women in coastal communities, the annual economic impacts based on these data were greater than those using the national data, i.e. € 1.62 billion (national), and € 3.02 billion and € 2.51 billion (regional), respectively, with the linear model, and € 5.46 billion (national), and € 9.13 billion and € 8.17 billion (regional), with the log model, for exposures above 0.58 μg/g.ConclusionsThese results emphasize that efforts to reduce MeHg exposures would have high social benefits by preventing the serious and lifelong consequences of neurodevelopmental deficits in children.

Methodology for Determining the Appropriateness of a Linear Dose‐Response Function

Microbial food safety risk assessment models can often at times be simplified by eliminating the need to integrate a complex dose-response relationship across a distribution of exposure doses. This is possible if exposure pathways lead to pathogens at exposure that consistently have a small probability of causing illness. In this situation, the probability of illness will follow an approximately linear function of dose. Consequently, the predicted probability of illness per serving across all exposures is linear with respect to the expected value of dose. The majority of dose-response functions are approximately linear when the dose is low. Nevertheless, what constitutes "low" is dependent on the parameters of the dose-response function for a particular pathogen. In this study, a method is proposed to determine an upper bound of the exposure distribution for which the use of a linear dose-response function is acceptable. If this upper bound is substantially larger than the expected value of exposure doses, then a linear approximation for probability of illness is reasonable. If conditions are appropriate for using the linear dose-response approximation, for example, the expected value for exposure doses is two to three logs(10) smaller than the upper bound of the linear portion of the dose-response function, then predicting the risk-reducing effectiveness of a proposed policy is trivial. Simple examples illustrate how this approximation can be used to inform policy decisions and improve an analyst's understanding of risk.

Ionizing Radiation and Leukemia Mortality among Japanese Atomic Bomb Survivors, 1950–2000

This paper provides the first comprehensive report on mortality by type of leukemia among the Japanese atomic bomb survivors in the Life Span Study (LSS). Analyses include 310 deaths due to leukemia during the period 1950-2000 among 86,611 people in the LSS. Poisson regression methods were used to evaluate associations between estimated bone marrow dose and leukemia mortality. Attention was given to variation in the radiation dose-leukemia mortality association by time since exposure, age at exposure, city and sex. The excess relative rate per gray of acute myeloid leukemia was best described by a quadratic dose-response function that peaked approximately 10 years after exposure. Acute lymphatic leukemia and chronic myeloid leukemia mortality were best described by a linear dose-response function that did not vary with time since exposure. Adult T-cell leukemia was not associated with estimated bone marrow dose. Overall, 103 of the 310 observed leukemia deaths were estimated to be excess deaths due to radiation exposure. In the most recent decade of observation (1991-2000), the estimated attributable fraction of leukemia deaths among those survivors exposed to >0.005 Gy was 0.34, suggesting that the effect of the atomic bombings on leukemia mortality has persisted in this cohort for more than five decades.

Lung Fibrosis and Lung Cancer Incidence in Beagle Dogs that Inhaled 238PuO2 or 239PuO2

Determination of radiation protection guidelines for persons working with plutonium has been complicated by limited human data on the biological behavior and subsequent health effects from internally deposited plutonium. One solution has been the use of animal models to predict likely health effects in humans. To compare the relationships between plutonium inhalation and lung fibrosis and lung cancer, data from life-span studies of beagle dogs given a single exposure to either plutonium-238 dioxide (238PuO2) or plutonium-239 dioxide(239PuO2) were analyzed. Estimates of the cumulative hazard of lung fibrosis and lung cancer after exposure to either were generated. The hazard of lung fibrosis was not consistent with a linear no-threshold model, although the magnitude of the threshold differed by radionuclide. In dogs given 239PuO2,the best model of lung fibrosis incorporated a linear dose response function; a linear-quadratic dose-response function fit the data better in dogs given 238PuO2. At any given cumulative dose, the lung fibrosis hazard was greater for dogs given 238PuO2. In dogs given 238PuO2, with or without covariates, aquadratic dose-response function for lung cancer hazard fit better than a linear no-threshold model. In dogs given 239PuO2, models of lung cancer with the dose-response function as the sole predictor variable were consistent with a linear no-threshold model; however, a quadratic dose-response function with a cell-killing term fit better. These findings have implications for radiation protection because, while lung cancer hazard was dependent on cumulative dose, regardless of isotope, the lung fibrosis hazard depended on both cumulative dose and isotope.

Linear and Non-Linear Dose-Response Functions Reveal a Hormetic Relationship between Stress and Learning

Over a century of behavioral research has shown that stress can enhance or impair learning and memory. In the present review, we have explored the complex effects of stress on cognition and propose that they are characterized by linear and non-linear dose-response functions, which together reveal a hormetic relationship between stress and learning. We suggest that stress initially enhances hippocampal function, resulting from amygdala-induced excitation of hippocampal synaptic plasticity, as well as the excitatory effects of several neuromodulators, including corticosteroids, norepinephrine, corticotropin-releasing hormone, acetylcholine and dopamine. We propose that this rapid activation of the amygdala-hippocampus brain memory system results in a linear dose-response relation between emotional strength and memory formation. More prolonged stress, however, leads to an inhibition of hippocampal function, which can be attributed to compensatory cellular responses that protect hippocampal neurons from excitotoxicity. This inhibition of hippocampal functioning in response to prolonged stress is potentially relevant to the well-described curvilinear dose-response relationship between arousal and memory. Our emphasis on the temporal features of stress-brain interactions addresses how stress can activate, as well as impair, hippocampal functioning to produce a hormetic relationship between stress and learning.

An integer programming model for optimizing shoulder rehabilitation.

Strength restoration is one goal of shoulder rehabilitation following rotator cuff repair surgery. However, the time spent in a physical rehabilitation setting is limited. The objective of this study was to develop a novel mathematical formulation for determining the optimal shoulder rehabilitation exercise protocol to restore normal shoulder strength given a time-constrained rehabilitation session. Strength gain was modeled using a linear dose-response function and biomechanical parameters of the shoulder musculature. Two different objective functions were tested: (1) one based on a least squares support vector machine using healthy and pathologic shoulder strengths (normative objective function), and (2) one which seeks to match the strength of the contralateral shoulder (contralateral objective function). The normative objective function was subject-independent and the optimal protocol consisted of four sets each of adduction and external rotation. The contralateral objective function was subject-specific and the typical optimal protocol consisted of various set combinations of abduction and internal and external rotation. These results are only partially consistent with current practice. Improvement of the current model is dependent on a better understanding of strength training adaptation and shoulder rehabilitation.

Marine ecotoxic effect of pulse emissions in life cycle impact assessment

Characterization factors for ecotoxicity in life cycle impact assessment are traditionally calculated as the product of effect and fate factors. Steady-state multiple compartment models are used to calculate the fate factor, while effect factors are derived from species sensitivity distributions (SSDs) for multiple substances using average or marginal gradients. Others have shown that steady-state multicompartment models can be used to calculate characterization factors if linear dose-response functions are used. Average gradients are linear dose-response functions per definition. Marginal gradients are first-order Taylor approximations of the effect function and require marginal exposure at all points of the compartment. Instantaneous mixing, giving marginal exposure within compartments, is an implicit assumption of the multicompartment model. This paper investigates if the assumption of marginal exposure results in significant errors for the characterization factor. Ecotoxic effect of pulse emissions is simulated in a transient three-dimensional single compartment model of the marine aquatic environment. Results show that the error in characterization factors for the Taylor approximation is less than a factor of two for multisubstance SSDs assuming concentration addition only in the aggregation of toxic effect of substances. Assuming a combination of response and concentration addition may result in a deviation of several orders of magnitude.

Testing the Dose–Response Specification in Epidemiology: Public Health and Policy Consequences for Lead

Statistical evaluation of the dose–response function in lead epidemiology is rarely attempted. Economic evaluation of health benefits of lead reduction usually assumes a linear dose–response function, regardless of the outcome measure used. We reanalyzed a previously published study, an international pooled data set combining data from seven prospective lead studies examining contemporaneous blood lead effect on IQ (intelligence quotient) of 7-year-old children (n = 1,333). We constructed alternative linear multiple regression models with linear blood lead terms (linear–linear dose response) and natural-log–transformed blood lead terms (log-linear dose response). We tested the two lead specifications for nonlinearity in the models, compared the two lead specifications for significantly better fit to the data, and examined the effects of possible residual confounding on the functional form of the dose–response relationship. We found that a log-linear lead–IQ relationship was a significantly better fit than was a linear–linear relationship for IQ (p = 0.009), with little evidence of residual confounding of included model variables. We substituted the log-linear lead–IQ effect in a previously published health benefits model and found that the economic savings due to U.S. population lead decrease between 1976 and 1999 (from 17.1 μg/dL to 2.0 μg/dL) was 2.2 times ($319 billion) that calculated using a linear–linear dose–response function ($149 billion). The Centers for Disease Control and Prevention action limit of 10 μg/dL for children fails to protect against most damage and economic cost attributable to lead exposure.

Prenatal intravenous cocaine and the heart rate-orienting response: a dose–response study

Attentional dysfunction is a persistent behavioral abnormality that is emerging as one of the cardinal features in the investigations of the teratogenic effects of cocaine in humans and rodents. The present study sought to extend this work by using a dose-response design with an alternate strain of rat. Virgin Long-Evans female rats, implanted with an IV access port prior to breeding were administered saline, 0.5, 1.0, or 3.0 mg/kg of cocaine HCl from gestational day (GD) GD8-21 (1x per day-GD8-14, 2x per day-GD15-21). Cocaine had no significant effect on maternal or litter parameters. At 14-15 days of age, 1 male and 1 female from each litter were tested to evaluate the heart rate orienting response (HR-OR). Following 20 min for acclimation, pups were presented an olfactory stimulus for 20s per trial, across four trials, and with an intertrial interval of 2 min. The initial baseline HR was not significantly different across the treatment groups, although cocaine did alter the stability of the QRS complex duration. The magnitude of the HR-OR averaged across trials increased as a linear function of dosage of cocaine. A more complex (quadratic) interaction between cocaine dose and sex of the offspring was also noted. When examined across trials, the controls failed to display any significant within-session variation in the HR-OR; in contrast all of the prenatal cocaine treated groups displayed either sensitization (low and high dose) or habituation of the response (middle dose). Analysis of the peak HR-OR confirmed that the controls were indeed displaying the response on at least one trial of the session, albeit not consistently on any specific trial. The more vigorous HR-OR of the prenatal cocaine groups, relative to vehicle controls, most likely reflects an alteration in development of the neural basis of response; as previously shown, the most vigorous response to the olfactory stimulus is seen early (12 days of age) and progressively decreases across the preweaning period. In sum, prenatal exposure to cocaine, at least when administered by the IV route, provides reproducible alterations in attentional processes, as indexed by the noradrenergically-mediated HR-OR. The documentation of a linear dose-response function suggests that there is likely no threshold for the drug-induced alteration. Moreover, the sex of the animal also appears to play some role in the nature of the expression of the altered HR-OR.

The GABAB receptor agonists baclofen and CGP44532 decreased nicotine self-administration in the rat.

Previous work has indicated a potential role for gamma-aminobutyric acid-B (GABA(B)) receptor agonists in treating drug addiction in humans. Specifically, GABA(B) receptor agonists decreased cocaine, heroin and nicotine self-administration in rats. The purpose of the present studies was to extend previous findings by assessing the effects of additional GABA(B) receptor agonists on nicotine self-administration and food-maintained responding, under both fixed and progressive ratio schedules in rats. Male Wistar rats were exposed to a progressive ratio schedule where various nicotine doses were made available according to a within-subjects Latin Square design. Additional groups of rats were used to test the effects of the GABA(B) receptor agonists baclofen and CGP44532 on nicotine self-administration (0.01 and 0.03 mg/kg per infusion) and food-reinforced responding on fixed and progressive ratio (CGP44532 only) schedules. Nicotine maintained stable self-administration under a progressive ratio schedule with a linear dose-response function ( r=0.61). Both CGP44532 and (-)baclofen dose-dependently reduced nicotine self-administration on the fixed ratio schedule, and also decreased food-maintained responding at higher doses. Further, CGP44532 decreased breakpoints for nicotine and food at identical doses under the progressive ratio schedule. The present data demonstrate that administration of GABA(B) receptor agonists decreased intravenous nicotine self-administration under both fixed and progressive ratio schedules of reinforcement, possibly reflecting reduced rewarding effects of nicotine. Both baclofen and CGP44532 exhibited specificity for nicotine- versus food-maintained responding on the fixed ratio schedules but not on the progressive ratio schedule (CGP44532 tested only), indicating the potential usefulness of GABA(B) receptor agonists as therapeutics for smoking cessation.

The dose-response relationship at very low doses of acrylamide is linear in the flow cytometer-based mouse micronucleus assay

Acrylamide (AA) is genotoxic and has been classified as a probable human carcinogen. Human exposure to AA may be high by the consumption of starch-based food that has been treated at high temperature, e.g. potato chips and crisps. For risk assessment, extrapolation to the expected low doses to humans will be more reliable when data from low experimental doses can be used. We have registered the effects of a series of low doses in the sensitive flow cytometer-based micronucleus assay in mice, paying special attention to deviations from the expected linear dose-response function. Two experiments were performed with CBA mice, injected i.p. with different doses of AA. In one experiment the effects of 22 doses (two mice per dose) ranging from 0 to 100 mg/kg b.w. were studied. In the second experiment seven doses (five mice per dose) ranging from 0 to 30 mg/kg b.w. were used. In both experiments, a clear increase of the frequency of micronucleated erythrocytes was seen, already at the lowest doses used. The dose-response function was found to be linear with a tendency to have a steeper rise at the lowest doses. The low DNA content of the micronuclei indicated an absence of whole chromosomes, i.e. no aneugenic effect of AA.

Air pollution damage estimates: the cost per kilogram of pollutant

To optimise environmental regulations such as emission limits, pollution taxes or tradable permits, it is necessary to know the damage cost per kilogram of emitted pollutant. It is calculated by means of an impact pathway analysis which involves the calculation of the increased pollutant concentration in all affected regions due to an incremental emission (e.g. µg/m² of particles, using models of atmospheric dispersion and chemistry), followed by the calculation of physical impacts (e.g. number of cases of asthma due to these particles, using a concentration-response function) and multiplication by the corresponding cost. The numbers are summed over all receptors (population, crops, buildings, and so on) of concern. We show that in a uniform world (linear dose-response function, uniform receptor density and uniform atmospheric removal rate) conservation of matter implies a very simple formula for the total damage. The generalisation to secondary pollutants is straightforward. By detailed numerical evaluation, using real data for atmospheric dispersion and geographic receptor distribution, we demonstrate that this simple formula is an excellent representation of typical damages. Results are shown for the principal air pollutants emitted by smokestacks at industrial installations or by road transport.

Radiation dose dependences in the atomic bomb survivor cancer mortality data: a model-free visualization.

Chomentowski, M., Kellerer, A. M. and Pierce, D. A. Radiation Dose Dependences in the Atomic Bomb Survivor Cancer Mortality Data: A Model-Free Visualization. The standard approach to obtaining nominal risk coefficients for radiation-related cancer involves fitting linear or linear-quadratic dose-response functions. This is usually complemented by a more direct visualization where the data are subdivided into distinct dose categories and the effect level is quantified for each of these categories. Such model-free computations, however, can be quite dependent on the arbitrary choice of the cutpoints in dose. The method proposed here largely avoids this arbitrariness by choosing a dose category width-constant on a log scale-to obtain the desired degree of smoothing, and then superimposing results for all placements of the resulting log-dose grids. The method is applied to leukemia and solid cancer mortality of the A-bomb survivors.