Response-factor approach

The response-factor approach is based on a method in which the response factors represent the transfer functions of the wall due to unit impulse excitations. The real excitation is approximated by a superposition of such impulses (mostly of triangular shape), and the real response is determined by the superposition of the impulse responses (see Figs. 11.33 and 11.34). ... 

Taking into account that a certain percentage of VOCs cannot usually be identified, Clausen et al. (1991) have combined the individual calibration approach and the average response factor approach. They defined the TVOC value as the sum of the correctly measured masses of identified VOCs plus the amount of non-identified peaks in the chromatogram, using the response factor of toluene. The EU-ECA working group recommend this approach. 

Cifkova, E., Holcapek, M., Lisa, M., Ovcacikova, M., Lycka, A., Lynen, F. and Sandra, P. (2012) Nontargeted quantitation of lipid classes using hydrophilic interaction liquid chromatography-elecirospray ionization mass spectrometry with single internal standard and response factor approach. Anal. Chem. 84, 10064-10070. 

The aim of all the foregoing methods of factor analysis is to decompose a data-set into physically meaningful factors, for instance pure spectra from a HPLC-DAD data-set. After those factors have been obtained, quantitation should be possible by calculating the contribution of each factor in the rows of the data matrix. By ITTFA (see Section 34.2.6) for example, one estimates the elution profiles of each individual compound. However, for quantitation the peak areas have to be correlated to the concentration by a calibration step. This is particularly important when using a diode array detector because the response factors (absorptivity) may considerably vary with the compound considered. Some methods of factor analysis require the presence of a pure variable for each factor. In that case quantitation becomes straightforward and does not need a multivariate approach because full selectivity is available. 

When the test for related substances is a limit test, the peaks of the impurities in the chromatogram of the test solution can be compared to the peak of the test substance in the chromatogram of a dilution of the test solution at the limiting concentration. The approach is vahd provided that the response factors of the impurities and the test substance are equivalent using the detector conditions described, otherwise correction factors need to be applied. 

The limitations of derivatization are that derivatization reactions only approach completion and never attain it, that the conditions of derivatization sometimes cause degradation, and that even very similar compounds are derivatized to different extents. Use of derivatization, therefore, requires a careful study of recovery of known components. A limitation common to the use of specialized detectors and derivatization is the response factor problem. The detector responds to different compounds to a greater or lesser extent. Measurement of correction factors to account for this is one of the most time-consuming aspects of analysis. 

Lucic, B., Trinajstic, N., Sild, S., Karelson, M., Katritzky, A. R. J. Chem. Inf. Comput. Sci. 39, 1999, 610-621. A new efficient approach for variable selection based on multiregression Prediction of gas chromatographic retention times and response factors. 

Where the specific impnrity is unavailable or is too costly, the use of composite or degraded samples is possible. This approach involves the nse of a dirty sample of a drug substance or the creation of a mixture of impurities through the in situ forced degradation method. Both of these approaches are best nsed for qualitative uses. In each of these mixtures, the impurities are present in unknown quantities. The real benefit of this type of impnrity standard is the low cost and the ability to unequivocally identify the peak loci of the impurities. When these mixtures are used in conjunction with a compendial standard and a well-developed set of relative response factors the resnlts will meet most analytical needs. 

Historically, the so-called safety factor approach was introduced in the United States in the mid-1950s in response to the legislative needs in the area of the safety of chemical food additives (Lehman and Fitzhugh 1954). This approach proposed that a safe level of chemical food additives could be derived from a chronic NOAEL from animal studies divided by a 100-fold safety factor. The 100-fold safety factor as proposed by Lehman and Fitzhugh was based on a limited analysis of subchronic/chronic data on fluorine and arsenic in rats, dogs, and humans, and also on the assumption that the human population as a whole is heterogeneous. Initially, Lehman and Fitzhugh reasoned that the safety factor of 100 accounted for several areas of uncertainty ... 

External Standard. In this approach, related substance levels are determined by calculation using a standard curve. The concentration of related substance is determined by the response (i.e., peak area of individual related substance) and the calibration curve. A reference standard of the drug substance is typically used in the calibration. Therefore, a response factor correction may be required if the response of related substance is very different from that of the drug substance. A single-point standard curve (Figure 3.4) is appropriate when there is no significant v-intercept. Otherwise, a multipoint calibration curve (Figure 3.5) has to be used. Different types of calibration are discussed in Section 3.2.3. 

For trace analysis, it is preferable to use a method that relies on the relative response factor for a compound against a reference compound. The areas of the compounds to be quantified are compared to the area of a reference compound, called an internal standard, present at a given concentration in each one of the samples (see Fig. 4.13). This approach can compensate for imprecision due to the injected volume and instrument instability between successive injections. It is superior to the preceding method where all of these factors influence the quantification. 

In this approach, one of the substances is considered for internal normalisation. For example, if compound 3 is used to determine the relative response factors K /3 and K2/3 of compounds 1 and 2 with respect to 3, one obtains ... 

With care internal normalization can be used where peak size is measured by height instead of area, though this is rare. The response factor is now subject to slight variations in column temperature, injection technique, carrier flow, and the like, all mentioned under peak height measurement previously. This approach requires that the standard mix for response factors to be run as close in time to the unknown as possible and new response factors to be determined each time. Note also that response factors determined from area measurement in no way are the same for those determined from peak height. 

VI. Practical Approaches to Solving Response Factor Problems. 195... 

Safety factor approach for chemicals that cause deterministic effects. Traditional toxicologic procedures for chemicals that can induce deterministic effects, which are assumed to have a threshold dose, define RfD for humans or animals as some fraction of NOAEL. This fraction is determined by establishing safety factors to account for weaknesses and uncertainties in the data and in the extrapolation from animals to humans. In the safety factor approach, doses below RfD are assumed not to result in a response because they are below the threshold of toxicity (Dourson and Stara, 1983 Renwick and Lazarus, 1998 Weil, 1972). 

There are two general approaches to the study of plant responses. One approach is the carefully designed greenhouse, field or pot experiments, where the observation of plant responses to soil factors are made. The alternative approach is the study of soils and plants in their natural environment. There are a number of drawbacks to the greenhouse experiments, for instance, reduction of time-scale in experiments creates uncertainty as to field relevance although reliable qualitative indications may be obtained (Folkeson et al., 1990). The responses of plants under artificial environmental conditions are usually not representative of the natural conditions (Irgolic and Martell, 1985). 

Another approach is the combination of SEC with multiple concentration detectors. If the response factors of the detectors for the components of the polymer are sufficiently different, the chemical composition of each slice of the elution curve can be determined from the detector signals. Typically, a combination of ultraviolet (UV) and refractive index (RI) detection is used another possibility is the use of a diode-array detector. In the case of non-UV-absorbing polymers, a combination of RI and density detection yields information on chemical composition [29-31]. 

The application of dual detection [UV and refractive index (RI)] to the SEC analysis of polystyrene-poly(methyl methacrylate) (PS-PMMA) has already been studied in this laboratory (2). Both MWD and CCD were determined using a methodology outlined by Runyon et al. (3). This approach relies on SEC column calibration with narrow polydis-persity standards for each of the homopolymers as well as a measure of the detector response factors for each homopolymer to produce a copolymer MWD. In the case of PS and PMMA this is feasible, but in other block copolymer systems the availability of suitable molecular weight standards may be more limited. In addition, this procedure does rely on true SEC and is not valid for block copolymers for which the universal calibration does not hold true for both blocks in a given solvent system. 

In addition to structural characterization, quantitative analysis of the various species is important in many application areas. Due to the effect of unsaturation on the relative abundance of the [M+H]" and mass discrimination effects in favour of the DAG fragment ion in a quadrupole mass analyser, determination of response factors for the various species is required for an accurate quantitative analysis [24]. Therefore, limiting the number of standards that are required in the analysis of complex TAG mixtures is an important topic in quantitation. From a comparison of four different approaches, Byrdwell et al. [24] concluded that the most accurate method involved the calculation of response factors from contributions from individual fatty acids to the TAG response. This approach was apphed with good results by others as well [17]. 

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