Multicomponent calibration

The most important techniques in multicomponent analysis are spectroscopy (of radiation of various wavelengths as well as of particles) and chromatography. Spectroscopic and chromatographic methods are able to analyze diverse species in a more or less selective way. For the determination of n species Q (i = 1,2,. ..,n), see 2.3, at least n signals must be measured, which should be well-separated in the ideal case. 

In analytical practice, the situation can be different as shown in Fig. 6.16 see Eckschlager and Danzer [1994] Danzer et al. [2004]. The given detail of a spectrum may show either well-separated signals as represented in (a) or signals that are overlapped to different degree see (b) and (c). 

In case (a) each species can be calibrated and evaluated independently from the other. In this fully selective case, the following equation system corresponds to the matrix A in Eq. (6.66)  

Multicomponent systems of the kind shown in Fig. 6.16b can be calibrated with a high degree of reliability when the preconditions mentioned above are valid. The uncertainties e, contain both deviations from the model and random errors. 

In the case of strongly overlapped signals, see Fig. 6.16c, multiple Unear calibration cannot be used for the following reasons  

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Depending on whether the spectra Y are calibrated as dependent on analyte amounts X or conversely, different methods of multicomponent calibration, as represented in Fig. 6.17, can be applied. 

The problem of multianalyte analysis is of high importance in different methods of analytical chemistry. The measurements with sensor arrays are not an exception they are always complicated by multicomponent calibrations, as the number of these calibrations, even if defined in accordance with the modem principles of experimental design, increases exponentially with the increase in the number of analytes. 

Hitchcock, K., Kalivas, J.H., and Sutter, J.M. (1992), Computer-Generated Multicomponent Calibration Designs for Optimal Analysis Sample Predictions, J. Chemom., 6, 85-96. 

A multicomponent calibrator is employed for calibrating the Seralyzer. Two calibrators enable a 2-point calibration. Human serum is used as initial material to which substances have been added by a special preparatory procedure. Thus one of each calibrator is available with concentrations (activities) in the low and in the high range. The concentrations (activities) were determined by means of routine wet chemical methods no details have been stated. Few studies are available on the frequency of calibration, i.e. on its constancy. The U.S. Food and Drug Administration prescribes a seven-day calibration rhythm that has been increased to 14 and 30 days, respectively, for some components. The manufacturer, Bayer Diagnostic, informs us that in future the calibration cycle will be 30 days. 

Eor multivariate calibration in analytical chemistry, the partial least squares (PLS) method [19], is very efficient. Here, the relations between a set of predictors and a set (not just one) of response variables are modeled. In multicomponent calibration the known concentrations of / components in n calibration samples are collected to constitute the response matrix Y (n rows, / columns). Digitization of the spectra of calibration samples using p wavelengths yields the predictor matrix X (n rows, p columns). The relations between X and Y are modeled by latent variables for both data sets. These latent variables (PLS components) are constructed to exhaust maximal variance (information) within both data sets on the one hand and to be maximally correlated for the purpose of good prediction on the other hand. From the computational viewpoint, solutions are obtained by a simple iterative procedure. Having established the model for calibration samples. comp>o-nent concentrations for future mixtures can be predicted from their spectra. A survey of multi-component regression is contained in [20],... 

The p and k matrix methods are two classical least squares approaches to multicomponent calibration. There are techniques based on factor analysis, however, that are increasingly popular these include the... 

To give an idea of the accuracy of multicomponent calibrations, this author has constructed calibrations for a mixture of three detergents in water, using ATR for recording spectra and PLS for the mathematical analysis. The accuracy of this analysis was as follows ... 

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