Response index, determination

The linear dynamic range of the system was shown to be about four orders of magnitude as indicated by the curve in Figure 18. The response index determined for a series of compounds of different chemical types was found to be between 0.96 and 1.04. 

It is seen that, for a truly linear detector, the response index (a) will be unity and the experimentally determined value of (a) will be an accurate measure of the proximity of the response to strict linearity. It is also clear that (a) could be used to correct for any non-linearity that might occur in the detector and thus improve the accuracy of an analysis. 

Thus the slope of the Log/Log curve will give the value of the response index (r). If the detector is truly linear, r = 1 i.e. the slope of the curve will be sin 7r/4 =1). Alternatively, if suitable software is available, the data can be curved fitted to a power function and the value of (r) extracted from the results. The same data can be employed to determine the linear range as defined by the ASTM E19 committee. In this case, however, a linear plot of detector output against solute concentration at the peak maximum should be used and the point where the line deviates from 45° by 5% determines the limit of the linear dynamic range. 

Thus, the response index can be easily determined. However the accuracy of the measurement will depend on the flow rate remaining constant throughout the calibration, and consequently for a GC detector a precision flow controller must be employed and for an LC detector, a good quality solvent pump. Manufacturers do not usually provide the response indices for their detectors and so it is left to the analysts to measure it for themselves. 

Thus, the concentration of any (or all) of the components present in the mixture can be determined, providing they are adequately separated from one another. It is interesting to note that if the maximum accuracy and precision is required, and the data is to be corrected for a response index that is other than unity, either peak heights must be used or the chromatogram must be processed manually. For repeat analyses of the same type of mixture, the operating conditions can be maintained constant and, as there is no extreme change in sample composition, the response factors will usually need to be determined only once a day. 

Alternatively, according to the ASTM E19 committee report on detector linearity, the linear range may also be defined as that concentration range over which the response of the detector is constant to within 5%, as determined from a linearity plot. This definition is significantly looser than that using the response index. 

This method for defining detector linearity is satisfactory up to a point and ensures a minimum linearity from the detector and, consequently, an acceptable quantitative accuracy. However, the specification is significantly looser than that given above, and it is not possible to correct for any nonlinearity that may exist, as there is no correction factor provided that is equivalent to the response index. It is strongly advised that the response index should be determined for any detector that is to be used for quantitative analysis. In most cases, r need only be measured once, unless the detector undergoes some catastrophic event that is liable to distort its response, in which case, r may need to be checked again. 

The solution to the fractional diffusion equation is clearly dependent on fluctuations that have occurred in the remote past note the time lag k in the index on the fluctuations and the fact that it can be arbitrarily large. The extent of the influence of these distant fluctuations on the system response is determined by the relative size of the coefficients in the series. Using Stirling s approximation on the gamma functions determines the size of the coefficients in Eq. (25) as the fluctuations recede into the past, that is, as k — oo we obtain... 

FIGURE 5—4 Frequency distribution curves and quantal concentration-effect and dose-effect curves. A. Frequency distribution curves. An experiment was performed on 100 subjects, and the effective plasma concentration that produced a quantal response was determined for each individual. The number of subjects who required each dose is plotted, giving a log-normal frequency distribution (colored bars). The gray bars demonstrate that the normal frequency distribution, when summated, yields the cumulative frequency distribution—a sigmoidal curve that is a quantal concentration-effect curve. B. Quantal dose-effect curves. Animals were injected with varying doses of sedative-hypnotic, and the responses were determined and plotted. The calculation of the therapeutic index, the ratio of the to the ED q, is an indication of how selective a drug is in producing its desired effects relative to its toxicity. (See text for additional explanation.)... 

In a retrospective study including 46 patients with locally advanced or metastatic breast cancer, Takamura et al. evaluated the significance of [ Tc]MIBI uptake in early and delayed images in predicting tumor response to chemotherapy with epirubicin and cyclophosphamide or docetaxel [87]. Before starting chemotherapy, the patients underwent a [ Tc]MIBI SPECT study. The parameters extracted from SPECT images were the tumor-to-nor-mal tissue ratios (T/N) of [ Tc]MIBI uptake at 10 min (early phase) and at 180 min (delayed phase) and the retention index (RI) was calculated as follows RI = (T/N(d))/(T/N(e)). After chemotherapy, tumor response was determined by clinical examination. 

The BoE has a duty to protect the interests of index-linked gilt investors (DMO 1999). This is a responsibility to determine whether any fntnre changes in the composition of the RPI index would be materially harmful to I-L gilt holders and to effect a redemption of any issue, via HM Treasury, if it feels any change had been harmful. 

It is seen from Table 1 that errors in the lower level component can be as much as 12.596 (1.25% absolute) for r = 0.94 and 9.5% (0.95% absolute) for r = 1.05. For most practical purposes r should lie between 0.98 and 1.02 if reasonable linearity is to be assumed. However, it should be pointed out that if r is known, then a correction can be applied, and thus take into account any non-linearity that may exist. This is the basic advantage of expressing linearity in terms of a response index. It should be emphasized that for the most accurate work the response index of the detector should be determined and applied where appropriate. 

Thus, the response index of the detector can be determined, but the accuracy of this determination will depend upon the constant nature of Q, the flow rate, and consequently, a good quality, constant flow pump should be employed. Manufacturers generally do not give the response index of their detectors, and, therefore, for highly accurate work its value needs to be determined. 

The first reported concentration is usually that which will provide a signal equivalent to twice the noise level and the second reported concentration is the limit at which the response factor was determined. At present, manufacturers do not usually differentiate between D and and do not quote a range for the response index r, however, it is hoped that in the future such data will be made available. Some manufacturers do mark the least sensitive setting of the detector as non-linear (N/L), which is a step towards a more rational approach to specifying linetu dynamic range. 

The Linear Dynamic Range - The linear dynamic range of a detector is that concentration range over which the detector response is linear within the restraints defined by the Response Index. It has been assigned the symbol Dl- The numerical value would be equal to the ratio of the maximum solute concentration, at which the response factor was determined, to the minimum detectable concentration or the detector sensitivity, the units of which will be dimensionless. It is useful to know the value of when analyzing a sample where the individual solutes present in the mixture cover a wide concentration range. 

Methods are described for determining the extent to which original natural color is preserved in processing and subsequent storage of foods. Color differences may be evaluated indirectly in terms of some physical characteristic of the sample or extracted fraction thereof that is largely responsible for the color characteristics. For evaluation more directly in terms of what the observer actually sees, color differences are measured by reflectance spectrophotometry and photoelectric colorimetry and expressed as differences in psychophysical indexes such as luminous reflectance and chromaticity. The reflectance spectro-photometric method provides time-constant records in research investigation on foods, while photoelectric colorimeters and reflectometers may prove useful in industrial color applications. Psychophysical notation may be converted by standard methods to the colorimetrically more descriptive terms of Munsell hue, value, and chroma. Here color charts are useful for a direct evaluation of results. 

Porosity (ej>) determination with NMR is a direct measurement as the response is from the fluid(s) in the pore space of the rock. The initial amplitude (before relaxation) of the NMR response of the fluid(s) saturated rock (corrected for hydrogen index) is compared with the amplitude of the response of bulk water having the same volume as the bulk volume of the rock sample. The 2 MHz NMR... 

Sample preparation, injection, calibration, and data collection, must be automated for process analysis. Methods used for flow injection analysis (FLA) are also useful for reliable sampling for process LC systems.1 Dynamic dilution is a technique that is used extensively in FIA.13 In this technique, sample from a loop or slot of a valve is diluted as it is transferred to a HPLC injection valve for analysis. As the diluted sample plug passes through the HPLC valve it is switched and the sample is injected onto the HPLC column for separation. The sample transfer time typically is determined with a refractive index detector and valve switching, which can be controlled by an integrator or computer. The transfer time is very reproducible. Calibration is typically done by external standardization using normalization by response factor. Internal standardization has also been used. To detect upsets or for process optimization, absolute numbers are not always needed. An alternative to... 

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