Quantitative response, method optimization

Partial chemical information in the form of known pure response profiles, such as pure-component reference spectra or pure-component concentration profiles for one or more species, can also be introduced in the optimization problem as additional equality constraints [5, 42, 62, 63, 64], The known profiles can be set to be invariant along the iterative process. The known profile does not need to be complete to be used. When only selected regions of profiles are known, they can also be set to be invariant, whereas the unknown parts can be left loose. This opens up the possibility of using resolution methods for quantitative purposes, for instance. Thus, data sets analogous to those used in multivariate calibration problems, formed by signals recorded from a series of calibration and unknown samples, can be analyzed. Quantitative information is obtained by resolving the system by fixing the known concentration values of the analyte(s) in the calibration samples in the related concentration prohle(s) [65],... 

During method optimization, initially qualitative responses, related to the quality of the separation, are considered. On the other hand, during robustness testing, first quantitative responses are studied. Nevertheless, all types of responses can be evaluated during both method optimization and robustness testing. 

During robustness testing, in a first instance, the considered responses usually represent quantitative aspects of the method (5,16). An analytical method is considered robust if no significant effects are found on the response(s) describing the quantitative aspect of the method. Although during method optimization usually quantitative responses are initially not considered, they can, however, be studied. 

To continue to optimize compounds and quantitatively assess improvements in affinity requires specialized methods and/or special mathematical handling of concentration-response data. 

Table 8.7). Thus, intensity and concentration are directly proportional. However, the intensity of a spectral line is very sensitive to changes in flame temperature because such changes can have a pronounced effect on the small proportion of atoms occupying excited levels compared to those in the ground state (p. 274). Quantitative measurements are made by reference to a previously prepared calibration curve or by the method of standard addition. In either case, the conditions for measurement must be carefully optimized with reference to the choice of emission line, flame temperature, concentration range of samples and linearity of response. Relative precision is of the order of 1-4%. Flame emission measurements are susceptible to interferences from numerous sources which may enhance or depress line intensities. 

Selection of the form of an empirical model requires judgment as well as some skill in recognizing how response patterns match possible algebraic functions. Optimization methods can help in the selection of the model structure as well as in the estimation of the unknown coefficients. If you can specify a quantitative criterion that defines what best represents the data, then the model can be improved by adjusting its form to improve the value of the criterion. The best model presumably exhibits the least error between actual data and the predicted response in some sense. 

A new HP-TLC method has been applied for the quantitative analysis of flavonoids in Passiflora coerulea L. The objective of the experiments was the separation and identification of the compound(s) responsible for the anxiolytic effect of the plant. Samples were extracted with 60 per cent ethanol or refluxed three times with aqueous methanol, and the supernatants were employed for HPTLC analysis. Separation was performed on a silica layer prewashed with methanol and pretreated with 0.1 M K2HP04, the optimal mobile phase composition being ethyl acetate-formic acid-water (9 1 l,v/v). It was established that the best extraction efficacy can be achieved with 60 - 80 per cent aqueous methanol. The HPTLC technique separates 10 different flavonoids, which can be used for the authenticity test of this medicinal plant [121],... 

In reference 88, response surfaces from optimization were used to obtain an initial idea about the method robustness and about the interval of the factors to be examined in a later robustness test. In the latter, regression analysis was applied and a full quadratic model was fitted to the data for each response. The method was considered robust concerning its quantitative aspect, since no statistically significant coefficients occurred. However, for qualitative responses, e.g., resolution, significant factors were found and the results were further used to calculate system suitability values. In reference 89, first a second-order polynomial model was fitted to the data and validated. Then response surfaces were drawn for... 

Procaine was indirectly determined by Minami et al. using atomic absorption spectrometry [51]. Nerin et al. also used indirect atomic spectrometiy to determine procaine, with their method involving the formation of an ion-pair with Co(SCN)4 and extraction of the ion pair into 1,2-dichloroethane [52. Quantitation of the Co response was effected using the atomic absorption at 241 nm, and optimal pH conditions and the linear regions of the calibration graphs were reported. 

Other results obtained from the ruggedness test are the definition of optimized method conditions for the factors and of system suitability criteria for a number of responses. System suitability parameters [6,17] are defined as an interval in which a response can vary for a rugged method. The system suitability criteria are the range of values between which a response (e.g. retention time, capacity factor, number of theoretical plates, resolution) can vary without affecting the quantitative results of the analysis. For instance, a design is performed and the retention time of the main substance varies between 200 s and 320 s without affecting the quantitative determination of the substances. The system suitability criteria for the retention time is then defined as the interval 200 s - 320 s. 

Problems of choosing responses of complex research subjects have been analyzed. The optimization parameter is, in fact, a reaction or response to factor level changes that define the status of a research subject. Responses may be economic, technoeco-nomic, technical-technological, statistical, psychological, etc. A response should be quantitative, singular, statistically effective, universal, physically real, simple and easily measurable. For responses with no quantitative measurement, the ranking method is used. Out of all responses typical for a research subject, only one or a general response is taken. Other responses are used as constraints. 

The interlot or intersample differences can also cause variations in the recovery for an analyte and its internal standard. For example, in a method based on liquid-liquid extraction for p-hydn)x y-a(< >r vastatin, the recovery of internal standard varied from 67.19 to 89.99 % (1.5-fold) for the four subjects tested despite the fact that the ratios of analyte to IS were relatively independent of subject sources, i.e., no impact on the quantitation [36], It should be borne in mind that a method is usually optimized aiming the maximum recovery for an analyte, i.e., not for any matrix components. In case where a matrix component causes matrix effect and the optimal extraction conditions happen to be an unreliable extraction condition for the matrix component, variable IS response is very likely. 

Cocaine has been extracted from coca leaves and the optimization procedure was investigated by means of a central composite design [17]. Pressure, temperature, nature, and percentage of polar modifier were studied. A rate of 2 mL/min CO2 modified by the addition of 29 % water in methanol at 20 M Pa for 10 min allowed the quantitative extraction of cocaine. The robustness of the method was evaluated by drawing response surfaces. The same compound has also been extracted by SEE from hair samples [18-20]. 

The responses of main interest are different during both applications. In optimization, responses related to the separation of peaks (Section 6.2) are modelled. In robustness testing the quantitative aspect (the content determination) of the method is of most interest, since it is the one that should remain unaffected by small variations in the variables. Responses related to the separation (resolution, relative retention) or describing the general quality of the chromatogram (capacity factors, analysis times, asymmetry factors, and column efficacy) are often also studied. As recommended by the ICH guidelines the results of a robustness test can be used to define system suitability test limits for some of the responses [82]. 

The responses of main interest also are different in method development and robustness testing. In development, the considered responses are related to the quality of the separation (l),such as, for electrophoretic methods, migration times, peak shapes, and the resolutions between neighboring peaks. When the separation is optimized and the method is validated, thus also in robustness testing, the responses of main interest are related to the quantitative aspects of the method, such as contents, concentrations, or recoveries. The responses considered during development occasionally are considered in a second instance, for example, as system suitability test (SST) parameters. 

Validation of Optimized Conditions. Once the relationship between the experimental parameters and the response has been modeled and the optimum conditions predicted, experiments should be performed to verify that the response is in fact the desired one. Most commonly, the resolution among the peaks should meet a quantitative requirement. Another method of verification is to compare the predicted response (dehned by the model-predicted optimal conditions) to the actual experimental response. In the case of Nielsen et al., the experimental response fell within the conhdence intervals of the predicted response, and therefore, the model used to optimize the separation of fungal metabolites was a success (66). In the case of the MEKC separation of anionic metal complexes by Breadmore et al., in which the model predicted the electrophoretic mobility of each complex, the model-predicted separation was overlaid with an actual separation, shown in Figure 5.4. Inspection of the coinciding peaks shows that the prediction was, in fact, accurate. Once the separation is deemed optimized, validation of criteria by figures of merit such as precision, dynamic range, selectivity, limit of detection, limit of quantitation, and robustness (see Table 5.1) are typically performed to ensure reproducible and secure results (34). 

---