Extrapolation of data

The Z-concept permits scale-up between sinulat centrifuges solely on the basis of sedimentation performance. Other criteria and limitations, however, should also be investigated. Scale-up analysis for a specified sohds concentration, for instance, requires knowledge of sohds residence time, permissible accumulation of sohds in the bowl, G level, sohds conveyabihty, flowabihty, compressibihty, limitations of torque, and sohds loading. Extrapolation of data from one size centrifuge to another calls for the apphcation of specific scale-up mechanisms for the particular type of centrifuge and performance requirement. 

The chart shown in Fig. 10-25 is for pure liqmds. Extrapolation of data beyond the ranges indicated in the graph may not produce accurate results. Figure 10-25 shows the variation of vapor pressure and NPSH reductions for various hydrocarbons and hot water as a function of temperature. Certain rules apply while using this chart. When using the chart for hot water, if the NPSH reduction is greater than one-half of the NPSH reqmred for cold water, deduct one-half of cold water NPSH to obtain the corrected NPSH required. On the other hand, if the value read on the chart is less than one-half of cold water NPSH, deduct this chart value from the cold water NPSH to obtain the corrected NPSH. 

The behaviour of samples under the actual conditions of service is the final criterion, but unfortunately such observations take a long time to collect and assess, and the cautious extrapolation of data from accelerated tests must be relied on for forecasting the behaviour of anodised aluminium in any new environment. 

FIGURE 4.11 The extrapolation of data like those in Fig. 4.10 for a number of gases suggests that the volume of all gases should become 0 at T = 0 (—273°C). Extrapolated data are shown in gray. In practice, all gases condense to liquids before that temperature is reached. 

Often, it will be found that currents for a given reaction cannot be measured at all metals at the same value of potential. At some metals the currents would be too low for a reliable, sufficiently accurate determination at others they might be too high for a satisfactory experimental realization. A comparison will then be possible only after an extrapolation of data obtained in a different region of potentials, to the value of selected for comparison. This extrapolation may not be sufficiently reliable where the Tafel section of the polarization curve is too short or indistinct. 

In addition, as a final caution, it must be remembered that each site is unique, and must be carefully evaluated individually and not by generic extrapolation of data from other sites or studies. 

H.A. Guess and K.S. Crump. "Low Dose Extrapolation of Data from Animal Carcinogenicity Experiments - Analysis of a New Statistical Technique." Math. Biosciences, 32, 1976, pp. 15-36. 

Estimates of exposure levels posing minimal risk to humans (MRLs) have been made, where data were believed reliable, for the most sensitive noncancer effect for each exposure duration. MRLs include adjustments to reflect human variability and extrapolation of data from laboratory animals to humans. 

While 1,2,5-thiadiazole 1,1-dioxide has not yet been prepared, extrapolation of data on the known 3,4-dimethyl-l,2,5-thiadiazole 1,1-dioxide 23 <1998JP091> indicated that the nonaromatic or antiaromatic 1,2,5-thiadiazole 1,1-dioxide has a more delocalized structure than its isomeric thiadiazole 1,1-dioxide anologues <1997JMT119, 2001JMT285>. 

Extrapolation of data from any and all of these tests to large scale must be made with care. 

For small vessels and slow reactions, corrections must be made because of the heat content of the reaction vessel itself. For large-scale reaction vessels and for rapid reactions, the system will be close to adiabatic operations. This aspect must be taken into account in scale-up. In effect, the extrapolation of data obtained in small-scale equipment has limitations as discussed in [193]. In case of a runaway, the maximum temperature in the reaction system is obtained from the adiabatic temperature rise, that is, Tmax = (Tr + ATad). In reality, the adiabatic temperature rise is significantly underestimated if other exothermic reaction mechanisms occur between Tr and (Tr + ATad). Therefore, a determination must be made to see if other exothermic events, which may introduce additional hazards during a runaway, occur in the higher temperature range. This can determine if a "safe operating envelope" exists. 

Thermal ageing in air, followed by extrapolation of data to lower temperatures using Arrhenius formula, has been applied widely in the design of electrical insulation for use at service temperatures, typically between 80 °C and 150 °C. The methodology is defined in detail in IEC 60216 [9]. 

Thiophene-1-oxide and 1 -substituted thiophenium salts present reduced aromaticity.144 A variety of aromaticity criteria were used in order to assess which of the 1,1-dioxide isomers of thiophene, thiazole, isothiazole, and thiadiazole was the most delocalized (Scheme 46).145 The relative aromaticity of those molecules is determined by the proximity of the nitrogen atoms to the sulfur, which actually accounts for its ability to participate in a push-pull system with the oxygen atoms of the sulfone moiety. The relative aromaticity decreases in the series isothiazole-1,1-dioxide (97) > thiazole-1,1 -dioxide (98) > thiophene-1-dioxide (99) then, one has the series 1,2,5 -thiadiazole-1,1 -dioxide (100) > 1, 2,4-thiadiaz-ole-1,1-dioxide (101) > 1,2,3-thiadiazole-1,1 -dioxide (102) > 1,3,4-thiadiazole-l,1-dioxide (103) in the order of decreasing aromaticity. As 1,2,5-thiadiazole-1,1-dioxide (100) was not synthesized, the approximations used extrapolations of data obtained for its 3,4-dimethyl-substituted analogue 104 (Scheme 46). 

The Mann et al. (1985) study is limited in that too few animals were used, organs other than the liver were not adequately evaluated, and only males were studied. Although an adequate acute-duration oral study would be useful to corroborate or refute the thyroid effects seen in the Mann et al. (1985) study, this does not represent a data need, since an acute oral MRL has been derived. Ingestion of contaminated drinking water is expected to be the predominant route of exposure for individuals living in the vicinity of hazardous waste sites. However, acute-duration inhalation and dermal studies in animals are needed to assess the potential toxicity of di- -octylphthalate following exposure via these routes because there are insufficient pharmacokinetic data available to support the extrapolation of data obtained after oral administration to other routes of exposure. 

The degree of exposure of the fetus to a particular substance can be best assessed in human subjects, but concerns of fetal safety have restricted the use of this approach. Moreover, clinical studies cannot elucidate the various mechanisms that contribute to transplacental transport of a particular compound. There are many structural differences between the human placenta and the placenta of other mammalian species, which complicates extrapolation of data obtained from in vivo animal models to humans [7], Thus, several ex vivo and in vitro techniques have been developed to study the placental role in drug transfer and metabolism during pregnancy and there are some excellent articles that discuss these systems in detail [7], Both isolated tissues and various cell culture techniques are currently in use and these have been summarized below. 

Biocatalysis has traditionally been performed in aqueous environments, but this is of limited value for the vast majority of nonpolar reactants used in chemical synthesis. For a long time it was assumed that all organic solvents act as denaturants, primarily based on the flawed extrapolation of data obtained from the exposure of aqueous solutions of enzyme to a few water-miscible solvents, such as alcohols and acetone, to that of all organic sol vents. 

Solubility data for mucus are not available, but Table 7-1 indicates that the Henry s law constant for ozone in water under the conditions of the lung is 9,700. Solubility data for pure ozone and other physical properties are available from various sources. Air Quality Criteria for Photochemical Oxidants reports an ozone solubility of 0.494 ml/ 100 ml of water at 0 C for ozone at 760 mm Hg extrapolation of data from Thorp indicates 1.09 g/liter of water at 0 C and approximately 0.31 g/liter of water at 37 C for 100% ozone. The value for 37 C agrees closely with the solubility calculated from the Henry s law constant for pure ozone at 760 mm Hg. 

The advantages of in vitro assays are (1) the ability to control the assay variables, (2) the potential opportunity to study the various steps within the complete process, (3) cellular and molecular events can be more carefully monitored and (4) the costs and the duration of the experiments are often lower than those of in vivo assays. The disadvantages of in vitro assays are that the cells, reagents and conditions used in different laboratories are not standardized and that the in vitro effects seen, do not always match the activities observed in vivo. This has been demonstrated for e.g. TNFa, which inhibits angiogenesis in vitro, but induces angiogenesis in vivo [6]. Particularly in the light of the possible influence of various cells of the immune system on angiogenesis, extrapolation of data from in vitro to in vivo needs to be carefully addressed. 

A relatively stable aqua complex or protonated hypoastatous acid [H20At] has been assumed similarly, a protonated hypoiodous acid has been reported to exist in aqueous solutions (15). The equilibrium constant for the deprotonation reaction [Eq. (9)] has been estimated by extrapolation of data accrued from the lighter halogens to be < 10" (80), indicating that [H20At]" is a fairly weak acid. Another structure, the symmetric diaqua cationic complex [H20-At-0H2]", has also been proposed (79, 80). 

Extrapolation of data from studies in experimental animals to the human situation involves two steps a first step is to adjust the dose levels applied in the experimental animal studies to human equivalent dose levels, i.e., a correction for differences in body size between laboratory animals and humans. A second step involves the application of an assessment factor to compensate for uncertainties inherent in toxicity data as well as the mterspecies variation in biological susceptibility. These two steps are addressed in the following sections. 

One aspect in the extrapolation of data from smdies in experimental animals to the human simation is, as mentioned above, a correction of the dose levels in experimental animal smdies to equivalent human dose levels, e.g., a NOAEL derived from an animal study to the equivalent human NOAEL. 

In the following text, various studies will be described, which attempt to establish a scientific rationale for the selection of the interspecies assessment factor. Based on these studies, it can be concluded that a species-specific default factor based on differences in caloric requirement (see Table 5.4) should be used for interspecies extrapolation regarding metabolic size. The remaining interspecies differences should preferentially be described probabilistically, or a deterministic default factor of 2.5 could be used for extrapolation of data from rat studies to the human situation. 

For extrapolation of data from animal studies to humans, account should be taken of species-specific differences between animals and humans. 

No default factor has been suggested for route-to-route extrapolation. It is generally recommended that whether an extrapolation of data is justified in a given situation should be decided on a case-by-case basis, based on expert judgment of scientific information. 

TNO has, for differences between experimental conditions and exposure patterns for workers, suggested a number of default values (Hakkert et al. 1996). For extrapolation of data from subacute-to-subchronic exposure and from subchronic-to-chronic exposure, the factor ranges generally... 

The first step, extrapolation of data from experimental animals to the human simation, is similar to the interspecies extrapolation described in detail for threshold effects (Section 5.3). The second step, evaluation of a carcinogen s mechanism(s) or mode of action(s), is very important for the choice of model for the risk assessment, i.e., non-threshold or threshold this issue is addressed in Section 4.9. The third step, quantitative dose-response assessment, is the main focus of this chapter and is addressed in more detail in the following text. 

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