Slope factor models

A second category of slope factor models employs Pb levels in some medium in combination with estimates of intakes, uptakes, and a simple biokinetic slope factor to estimate PbB levels. In a conceptual sense, the simpler slope factor approach, relating a medium Pb level like air lead to blood lead, is a variant of this second category. That is, an air Pb translating into intake and uptake quantities provides the same type of results as the earlier approach. 

Slope Factor Models with a Biokinetic Factor... 

Much of the interest in using predictive modeling of human Pb exposures concerns mechanistic, i.e., biokinetic, models. Biokinetic models differ from site-specific or multisite ad hoc/slope factor models in a number of important ways. Eirst, they are constructed (by definition) within a computational and biological/kinetic framework. That framework specifies inclusion of all identified parameters representing mechanisms by which environmental Pb is deposited in and removed from human organs and tissues. Mechanistic models are structured to be much more complex than the regression models... 

Bowers, T.S., Cohen, J.T., 1998. Blood lead slope factor models far adults comparisons of observations and predictions. Environ. Health Perspect. 106 (Suppl. 6), 1569—1576. 

Because risk at low exposure levels is difficult to tneasure directly either by animal experiments or by epidemiologic studies, the development of a slope factor generally entails applying a model to the available data set and... 

To.xicity values for carcinogenic effects can be e.xprcsscd in several ways. The slope factor is usually, but not always, the upper 95th percent confidence limit of the slope of the dose-response curve and is e.xprcsscd as (mg/kg-day). If the extrapolation model selected is the linearized multistage model, this value is also known as the ql. That is ... 

Because the slope factor is often an upper 95 percentile confidence limit of the probability of response based on experimental animal data used in tlie multistage model, tlie carcinogenic risk estimate will generally be an upper-bound estimate. Tliis means tliat tlie EPA is reasonably confident tliat tlie true risk will not exceed the risk estimate derived tlirough use of tliis model and is likely to be less than tliat predicted. 

The pH (or pI) term of the Nemst equation contains the electrode slope factor as a linear temperature relationship. This means that a pH determination requires the instantaneous input, either manual or automatic, of the prevailing temperature value into the potentiometer. In the manual procedure the temperature compensation knob is previously set on the actual value. In the automatic procedure the adjustment is permanently achieved in direct connection with a temperature probe immersed in the solution close to the indicator electrode the probe usually consists of a Pt or Ni resistance thermometer or a thermistor normally based on an NTC resistor. An interesting development in 1980 was the Orion Model 611 pH meter, in which the pH electrode itself is used to sense the solution temperature (see below). 

Kinetic Constants and Model Parameters in the O Flaherty Model 2-7 Residence Times in the Biokinetic Module of the IEUBK Model 2-8 Kinetic Constants and Model Parameters in the Leggett Model 2-9 Summary of Blood Slope Factors from Various Environmental Media 2-10 Genotoxicity of Lead In Vivo 2-11 Genotoxicity of Lead In Vitro... 

Olesen T, Moldrup P, Yamaguchi T, Rolston DE. 2001. Constant slope impedance factor model for predicting the solute diffusion coefficient in unsaturated soil. Soil Science 166 89-96. 

Risk-specific doses are derived from the slope factor or unit risk to estimate the dose associated with a specific risk level, for example a one-in-a-million (10 ) increased lifetime risk. Risk below the POD is typically approximated by multiplying the slope factor by an estimate of exposure, i.e., Risk = Slope Factor X Exposure. For exposure levels above the POD, the dose-response model is used instead of this approximation. 

If the substituent is situated on the central carbon the model fails to make a clear-cut prediction. This is because the effect of substitution on the gap and slope factor /are opposed. For example, an electron-withdrawing substituent (e.g. CH2C12 compared to CH3C1) is expected to decrease the gap and increase the slope factor, so that without more extensive informaton on the effect of the substituent on the above parameters, no definitive prediction is possible. A second limitation of the model is that it does not readily lend itself to treating mechanistic variations. Since its more detailed structure favours its application with just two state curves, in this case ground and charge transfer states, it is less readily extended to situations in which mechanistic variations are explicitly considered (e.g. the SN2-SN1 spectrum). 

The linearized multistage model (used by the EPA). This determines the cancer slope factor, which can be used to predict cancer risk at a specific dose. It assumes a linear extrapolation to a zero-dose threshold (Fig. 2.10). This factor is an estimate (expressed in mg/kg/day) of the probability that an individual will develop cancer if exposed to the chemical for 70 years. 

Assessment of Human Health Mixture RfD/RfC Hazard Quotient Hazard Index Dose-Response Modeling Cancer Slope Factors Epidemiological Measures Comparative Potency... 

The EPA uses the linearized multistage model (LMS)—illustrated in Figure 9.34—to conduct its cancer risk assessments. It yields a cancer slope factor, known as the ql (pronounced Ql-star), which can be used to predict cancer risk at a specific dose. The LMS assumes a linear extrapolation with a zero dose threshold from the upper confidence level of the lowest dose that produced cancer in an animal test or in a human epidemiology study. 

The U.S. EPA (1991) identified an "inhalation" unit risk of 8.5 x 10 per fig/w , derived from the Weibull time-to-tumor model, as the most appropriate estimate of the carcinogenic potency of sulfur mustard. This unit risk can be converted to a slope factor by normalizing the value for a 70 kg man inhahng 20 m of air per day. The resulting slope factor is 0.3 (ug/kg/day). ... 

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