Quantitation calibration methods

Haaland, D.M., Thomas, E.V., "Partial Least-Squares Methods for Spectral Analysis 1. Relation to Other Quantitative Calibration Methods and the Extraction of Qualitative Information" Anal. Chem. 1988 (60) 1193-1202. 

During the upcoming discussion of quantitative calibration methods, a specific example involving NIR transmission spectroscopy of 70 different styrene-butadiene copolymers [52] will be used help illustrate these methods. In this example, complete laboratory NMR analyses of all of the copolymers were available, which for each sample provided the concentrations of the four known chemical components di-butadiene, frani-butadiene, 1,2-butadiene, and styrene. The NIR spectra of these copolymer samples over the spectral range 1570-1850nm are shown in Figure 12.9. 

Haaland, D. M. and Thomas, E. V. (1988) Partial least-squares methods for spectral analyses. 1. Relation to other quantitative calibration methods and the extraction of qualitative information. Anal. Chem. 60, 1193-1202. 

A specific example is used to illustrate the MLR methods, as well as the other quantitative calibration methods discussed in this section. In this example, a total of 70 different styrene-butadiene copolymers were analyzed by NIR transmission spectroscopy.39 For each of these samples, four different properties of interest were measured the concentrations of czs-butadiene units, trans-butadiene units, 1,2-butadiene units, and styrene units in the polymer. The NIR spectra of these samples are overlayed in Figure 8.12. These spectra contain 141 X-variables each, which cover the wavelength range of 1570-1850 nm. 

Relation to other quantitative calibration methods and the extraction of qualitative information. Analytical Chemistry, 60, 1193-202. 

Often used quantitative calibration method in headspace analysis for matrix independent calibrations. 

An external standardization allows a related series of samples to be analyzed using a single calibration curve. This is an important advantage in laboratories where many samples are to be analyzed or when the need for a rapid throughput of samples is critical. Not surprisingly, many of the most commonly encountered quantitative analytical methods are based on an external standardization. 

We will explore the two major families of chemometric quantitative calibration techniques that are most commonly employed the Multiple Linear Regression (MLR) techniques, and the Factor-Based Techniques. Within each family, we will review the various methods commonly employed, learn how to develop and test calibrations, and how to use the calibrations to estimate, or predict, the properties of unknown samples. We will consider the advantages and limitations of each method as well as some of the tricks and pitfalls associated with their use. While our emphasis will be on quantitative analysis, we will also touch on how these techniques are used for qualitative analysis, classification, and discriminative analysis. 

D.M. Haaland, Multivariate Calibration Methods Applied to the Quantitative Analysis of Infrared Spectra, Chapter I in Computer-Enhanced Analytical Spectroscopy, Volume 3", edited by P.C. Jurs. Plenum Press, New York, 1992. 

The amounts of carfentrazone-ethyl, C-Cl-PAc, C-PAc, DM-C-Cl-PAc and HM-C-Cl-PAc were quantitated by the external standard calibration method. 

Quantitation was performed in all cases using the external calibration method. A series of standards were injected and the responses plotted against their known concentrations. Peak responses in samples were compared with the calibration plots to obtain the amount found (nanograms). A fresh calibration plot was generated with each analytical set of samples. 

The amounts of sulfentrazone, SCA (analyzed as DMS), and HMS were quantitated by an external standard calibration method. A computer spreadsheet program (Microsoft Excel) was used for calculation and reporting. 

Many characteristic molecular vibrations occur at frequencies in the infrared portion of the electromagnetic spectrum. We routinely analyze polymers by measuring the infrared frequencies that are absorbed by these molecular vibrations. Given a suitable calibration method we can obtain both qualitative and quantitative information regarding copolymer composition from an infrared spectrum. We can often identify unknown polymers by comparing their infrared spectra with electronic libraries containing spectra of known materials. 

Ibrahim et al. [30] described a fluorimetric method for the determination primaquine and two other aminoquinoline antimalarial drugs using eosin. Powdered tablets or ampule contents containing the equivalent of 50 mg of the drug was extracted with or dissolved in water (100 mL). A 10 mL aliquot was mixed with 10 mL of aqueous ammonia, 1 mL of 0.001% eosin (C.I. acid red 87) in dichloro-ethane, and dichloroethane was added to volume. Primaquine was determined fluorimetrically at 450 nm (excitation at 368 nm). Calibration graphs were rectilinear for 0.1-5 pg/mL of primaquine. Recoveries were quantitative. The method could be readily adapted for determination of the drug in biological fluids. 

Most of our discussion so far has centered on the use of the two-point-difference method of computing an approximation to the true derivative, but since we have already brought up the Savitzky-Golay method, it is appropriate here to consider both ways of computing derivatives, when considering how they behave when used for quantitative calibration purposes. 

Calculating the P/S ratio from the corresponding peak area ratios or by using one point calibration method leads to erroneous interpretations [54] because the P/S ratio depends on sample dilution. An accurate quantitation of FA is thus needed to evaluate this important parameter correctly. 

Method validation is defined in the international standard, ISO/IEC 17025 as, the confirmation by examination and provision of objective evidence that the particular requirements for a specific intended use are fulfilled. This means that a validated method, if used correctly, will produce results that will be suitable for the person making decisions based on them. This requires a detailed understanding of why the results are required and the quality of the result needed, i.e. its uncertainty. This is what determines the values that have to be achieved for the performance parameters. Method validation is a planned set of experiments to determine these values. The method performance parameters that are typically studied during method validation are selectivity, precision, bias, linearity working range, limit of detection, limit of quantitation, calibration and ruggedness. The validation process is illustrated in Figure 4.2. 

In many cases of practical interest, no theoretically based mathematical equations exist for the relationships between x and y we sometimes know but often only assume that relationships exist. Examples are for instance modeling of the boiling point or the toxicity of chemical compounds by variables derived from the chemical structure (molecular descriptors). Investigation of quantitative structure-property or structure-activity relationships (QSPR/QSAR) by this approach requires multivariate calibration methods. For such purely empirical models—often with many variables—the... 

This example belongs to the area quantitative structure-property relationships (QSPR) in which chemical-physical properties of chemical compounds are modeled by chemical structure data—mostly built by multivariate calibration methods as described in this chapter und using molecular descriptors (Todeschini and Consonni... 

Their increased application in light food and drink products has given a new impetus to develop fast and accurate method for their determination. Among computer-controlled instruments multivariate calibration methods and derivative techniques are playing very important role in the multicomponent analysis of mixtures by UV-VIS molecular absorption spectrophotometry [2]. Both approaches ate useful in the resolution of overlapping band in quantitative analysis [3, 4]. 

Quantitative PCR has been widely used to determine the amount (number of molecules) of DNA molecules in a test sample. The best quantitative PCR method involves the addition of known amounts of a similar DNA or RNA fragment, such as one containing a short deletion or specific mutation, to the test sample before amplification. Such internal standards must be precisely calibrated to ensure that they are amplified and detected in a form and manner that are similar to the test sample. The ratio of the internal standard and the targeted template will depend on the amount of internal standard added and allows for the determination of the amount of the targeted molecule in the test sample. Therefore, the ideal standard for quantitative amplification based assays should have a structure that is comparable to the template of interest and which allows for the simultaneous amplification of both template and standard using a single primer pair. 

This classification method [78,79] actually uses the quantitative regression method of PLS (described earlier) to perform qualitative analysis. This is done by populating one or more y variables not with reference property values, but rather with zeros or ones, depending on the known class membership of the calibration samples. For example, if there are only two possible classes and four calibration samples, a single y variable can be constructed as follows ... 

In Section 12.3.2, the fundamental differences between direct and inverse modeling methods were discussed. As will be discussed here, this distinction is not just a convenient means for classifying quantitative regression methods, but has profound implications regarding calibration strategy and supporting infrastructure. 

E.V. Thomas and D.M. Haaland, Comparison of multivariate calibration methods for quantitative spectral analysis. Anal. Chem., 62, 1091-1099 (1990). 

In Section 5.2, the two classical calibration methods, direct and indirect CLS, are discussed. These methods work well with simple systems that adhere to a linear model (e.g., Beer s Law). Calibrating involves determining the spectra of the pure components and quantitation is achieved using regression. The distinction between these methods is in how the pure-component spectra are obtained. With DCLS they are measured directly with ICLS they are estimated from spectra of miiaures of the components. 

Internal standard (IS) calibration requires ratioing of an analytical signal to an IS which has very similar characteristics to that of the analyte of interest (an element which is similar to the analyte either in mass, ionisation potential or chemical behaviour). Quantitative analysis applying internal standardisation is the most popular calibration strategy in ICP-MS, as improvements in precision are obtained when the technique is appropriately used. Of course, the validity of this calibration method requires that one ensures a good selection of the correct internal standard. For this purpose it is possible to resort to chemometric methods [16]. 

The multivariate quantitative spectroscopic analysis of samples with complex matrices can be performed using inverse calibration methods, such as ILS, PCR and PLS. The term "inverse" means that the concentration of the analyte of interest is modelled as a function of the instrumental measurements, using an empirical relationship with no theoretical foundation (as the Lambert Bouguer-Beer s law was for the methods explained in the paragraphs above). Therefore, we can formulate our calibration like eqn (3.3) and, in contrast to the CLS model, it can be calculated without knowing the concentrations of all the constituents in the calibration set. The calibration step requires only the instrumental response and the reference value of the property of interest e.g. concentration) in the calibration samples. An important advantage of this approach is that unknown interferents may be present in the calibration samples. For this reason, inverse models are more suited than CLS for complex samples. 

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