Cumulative exposure curve

Cumulative exposure curve for a population showing an exposure ( x axis) for a given percentile ( y axis) (Hoknes et al. 2005). 

It should be possible to derive a cumulative exposure curve for the whole of the population and, ideally, for consumers only. It is desirable to obtain estimates of exposure for any selected sub-set of the population, to ensure adequate protection of vulnerable groups. Depending upon the quality of the food consumption survey and associated data this may or may not be easy to achieve. If non-consumers are included in an exposure estimate, as is the case in typical per-capita estimates, then the estimate of exposure will be below the actual exposure and the amount of under-estimating will depend upon the ratio of non-consumers to consumers. 

Consistent with the human responses to arsine exposure, observations in several animal species (rats, mice, and hamsters) indicated hematologic involvement. Cumulative exposures of 540-1,800 ppm-min produced decreases in hematocrit levels, RBC counts, packed cell volumes, and increases in absolute and relative spleen weights (consistent with erythrocyte damage). For acute exposures, the exposure-response curve is steep generally less than a 10-fold difference between no-effect and lethality exposures. 

The lARC has concluded that epidemiological studies have established the relationship between benzene exposure and the development of acute myelogenous leukemia and that there is sufficient evidence that benzene is carcinogenic to humans. Although a benzene-leukemia association has been made, the exact shape of the dose-response curve and/or the existence of a threshold for the response is unknown and has been the source of speculation and controversy. Some risk assessments suggest exponential increases in relative risk (of leukemias) with increasing cumulative exposure to benzene. At low levels of exposure, however, a small increase in leukemia mortality cannot be distinguished from a no-risk situation. In addition to cumulative dose other factors such as multiple solvent exposure, familial connection, and individual sus-... 

Both variability and uncertainty in threshold and exposure data can be taken into account by using probability distributions to represent the input variables instead of point estimates. The data are plotted in a cumulative distribution curve. For example, threshold data and intake data can be plotted as probability distributions. By combining the threshold distribution and the intake distribution, the output distribution will describe the probability that a part of the population will be exposed at such levels and under such circumstances that adverse effects may occur. Consequently, an approximation of the percentage of the population likely to experience adverse effects at various exposure levels can be made. 

Thus, the type of exposure, continuous for lifetime versus intermittent or short-term exposure, appears to strongly influence the low dose-response curve. The cumulative exposure of 2 mmol/kg yielded a 92% liver cancer incidence... 

Sanders Do non-cumulative dos response studies have any effect on your Ca2+ force curves In other words, do you bias your data by doing cumulative doso-response curves towards Ca2+ sensitization When there is a short exposure to the compound do you get a shift ... 

Although the data are not sufficient to define the shapes of the dose incidence curves in most instances, a markedly increased risk of cancer has been noted in a number of more heavily exposed populations (Ikble 6.5). In 2-naphthylamine distillers, for example, the latency and incidence of bladder cancer have been observed to vary systematically in relation to the duration of exposure (Figure 6.2). In those with exposures lasting more than five years, the cumulative incidence approached 100 percent (Figures 6.2 6.3). 

Model predictions have been made of the disposition of butadiene and epoxybutene in rodents and humans. Kohn and Melnick (1993) predicted that the cumulative body burden of epoxybutene after a 6-h exposure to 100 ppm butadiene (area under the epoxybutene versus time curve from 0 to 6 h) in humans would be 7- and 35-fold lower than in rat and mouse, respectively. For a 12-h exposure to 10 ppm butadiene, the model... 

When variability and uncertainty are propagated separately (e.g. by two-dimensional or 2D Monte Carlo), they can be shown separately in the output. For example, the output can be presented as three cumulative curves a central one representing the median estimate of the distribution for variation in exposure, and two outer ones representing lower and upper confidence bounds for the distribution (Figure 2). This can be used to read off exposure estimates for different percentiles of the population, together with confidence bounds showing the combined effect of those uncertainties that have been quantified. 

Figure 14 Example of cumulative distribution for variability of exposure between consumers (thick curve), with 95% confidence intervals (thin curves) showing uncertainty for each percentile consumer. Other confidence intervals (e.g. 90% or 99%) could be shown, depending on the level of confidence wanted by risk managers, bw = body weight.

Permeation Properties. The data shown in Figure 2 are the toluene permeation rates of the fluorinated and untreated containers g. toluene/container per day are plotted vs. the time of toluene exposure on a logarithmic scale. These cumulative permeation rates were calculated based on the cumulative weight loss over the time of toluene exposure, as opposed to the differential permeation rates based on the differential weight loss over each time interval. The room temperature permeation rates for the in-situ fluorinated containers were less than 0.01 g./day and, hence, have been rounded up to 0.01 g./day for illustrative purposes. In Figure 2, the,flat portion of the curves for the untreated containers yielded the steady state permeation rates. From these values, the permeability coefficients (P) for the untreated containers were calculated using Equation 1. 

Fig. 7. A cumulative spectral sensitivity curve for the decrease in elongation at break of (ethylene-carbon monoxide 1%) copolymer sheets on exposure to a filtered xenon source for 219 h at 60 °C. determined by the cut-on filter technique. The error bars show the standard error of the mean [133]...

The quantal dose-effect curve provides a guide to toxic effect frequencies relative to exposure under the conditions of the laboratory toxicity test. Doses corresponding to other toxic effect frequencies may be extrapolated from cumulative dose-effect curves. For example, the 10% toxic dose, or TD,q, represents a dose corresponding to a cumulative-effect incidence of 10% of the test population it is determined by finding the dose that corresponds to a 10% cumulative-effect frequency (in the sigmoidal curve) or 3.7 probit units (in the probit plot). The 75% toxic dose, or TD75, is the dose corresponding to 75% cumulative-effect incideuce or 5.8 probits. 

These analyses focused on four lead exposure variables prenatal (maternal) blood lead (PbBPre) as an index of prenatal exposure 10-day neonatal blood lead (PbBl) as another index of prenatal exposure and maximum first-year blood lead (MaxPbB) and cumulative 12-month blood lead (CumPbB) as indices of postnatal exposure. MaxPbB was the highest postnatal PbB value recorded for each infant at any assessment between 3 and 12 months of age. CumPbB was derived from calculation of the area under the curve of each child s PbB profile from 10 days to 12 months. This integrated index was used to characterize historical postnatal lead exposure in assessing developmental effects. 

---