Calibration Bracketing method

Standards should be analyzed contemporaneously for both determinative and confirmatory procedures. The method developer needs to describe fully the preparation of all the standards and the calibration procedure to be used, such as calibration prior to sample analysis, interspersed standards, or bracketing standards (confirmatory only). 

P-outine chemical analysis. This implies analysis of many samples, and use of calibration curves is an economic necessity. In general, the two-standard method, with standards bracketing each sample analyzed, is economical for the analysis of up to about 10 samples. Conventional least squares curve of best fit procedures are economical for analysis of 10 to 500 samples. The procedures described here are cost effective for the analysis of 500 samples or more. 

If the analytical method is required only to detect the presence of the analyte but not report a measurement result, then there will be no calibration relation to go from an indication of the measuring instrument to a concentration. In this case a number of independent measurements (at least 10) must be made at concentrations in a range that brackets the expected LOD. The fraction of positive and negative findings is reported for each concentration, and a concentration is then chosen as the LOD that gives an acceptable proportion of positive results. 

An analytical batch is a group of samples, extracts or digestates, which are analyzed sequentially using the same calibration curve and which have common analytical QC checks. These are the samples that are bracketed by the same CCVs, have the same instrument blanks, and other QC checks that may be required by the method (for example, the DDT and Endrin breakdown product check in organochlorine pesticide analysis by EPA Methods 8081). If the CCV or any of the analytical QC checks are outside the method acceptance criteria, the whole analytical batch or only the affected samples are reanalyzed. 

The calibration mode selected by the laboratory should also be carefully considered, i.e. standard additions, calibration curve and/or use of bracketing standards. All calibration methods suffer from typical sources of error or drawbacks, e.g. for standard additions non-linearity of the calibration curve, extrapolation difficulties, chemical form of calibrant added, etc. for external calibration (calibration curve) changes of the matrix affecting the linearity of the curve for bracketing standards time-consuming procedures for many routine laboratories, etc. (Quevauviller et al., 1996a Quevauviller, 1998b). 

Apart from the problem of nonlinearity, the calibration curve approach has another pitfall measured ion abundance ratios can change with time, leading to the possibility of significant errors since the calibration and sample measurements cannot be simultaneous (Schoeller, 1980). In order to minimize the effect of instrumental drift and to optimize precision, the National Bureau of Standards (NBS) proposed a bracketing protocol for the development of definitive (i.e., essentially bias-free and precise) IDMS methods (Cohen et al., 1980 White et al., 1982 Yap et al., 1983). It involves the measurement of each sample between measurements of calibration standards whose ion abundances most closely surround the ion abundance ratio of the sample. Measurements are made according to a strict protocol, used with samples prepared under restrictive conditions ... 

Apart from the fact that a linear calibration can be performed, bracketing offers excellent precision and accuracy. With the determination of serum cholesterol as an example, Cohen et al. (1980) showed that the replication error on five different serum pools was characterized by a CV of 0.17% with a set-to-set variability of 0.32%. For each serum average, a standard error (considering all causes of variability combined) of 0.16% CV was obtained. The undetected systematic error (bias) in this study was estimated to be smaller than 0.5%, while White et al. (1982), using two different IDMS methods, found serum glucose concentrations to agree within 1%. 

For metallicity distributions, one can examine lower spectral resolution diagnostics. The most useful of these has been the Ca II triplet indicator (Armandroff Da Costa 1991), which uses the combined equivalent width of the Ca II triplet near 8500 A, calibrated with metallicities of globular clusters, to infer the metallicity [Fe/H] (where the brackets denote the logarithmic abundance relative to that in the Sun). The main uncertainty of this method is that the Ca/Fe abundance ratio can vary depending on the star formation history, so the globular clusters may not provide the correct metallicity calibration for galaxies with a variety of star formation histories. Work needs to be done to calibrate the Ca II triplet with [Ca/H] rather than [Fe/H] to remove this ambiguity. 

External standardization methods are used for most quantitative assays. Solutions containing known concentrations of reference standards of the analytes are required to calibrate (standardize) the HPLC system. Bracketed standards injected before and after the samples set are preferred for improved accuracy. 

Determining the Relationship between Absorbance and Concentration 1 he method of external standards (sec Section ID-2) is most often used to establish the absorbance versus concentration relationship. After deciding on the conditions for the analysis, the calibration curve is prepared from a series of standard solutions that bracket the concentration range expected for the samples. Seldom, if ever, is it safe to assume adherence to Beer s law and use only a single standard to determine the molar ab,soq)tivity. It is never a good idea to base the results of an analysis on a literature value for the molar absorptivity. 

This procedure involves making measurements on each sample between measurements on two calibration standards prepared such that their ion abundances fall just above and below the ion abundances of the sample. Analyte concentration is calculated by linear interpolation between bracketing standards and good precision and accuracy can be achieved using this procedure. This is a specialised version of the graphical method and, again, is mostly used for organic IDMS. 

Initially, an estimate of the concentration of the analyte in the sample is made. This can be made by using either a conventional IDMS analysis (calibration, graph or bracketing) or by some alternative method such as conventional GC-MS or ICP-MS analysis with an internal standard. 

This simple-looking inversion of the concentration-absorbance relationship has rather important consequences. It is possible, by use of the "P" matrix approach, to quantify the composition of mixtures in the presence of variable amounts of "impurities", without being able to specify the composition or concentration of those impurities. The only requirement is that the impurities must be present in the calibration standards in amounts that bracket the concentrations of these impurities in the unknown samples. This property of the "P" matrix method makes it feasible to generate calibration spectra of plasma or whole blood containing known amounts of the proteins of interest (albumin, gamma-globulins, fibrinogen, fibronectin, transferrin. . . ) and the remainder of the blood components can be treated as impurities. 

The use of pre-extraction spiking is particularly important when the presence of matrix co-extractives modifies the response of the analyte as compared with analytical standards. It is increasingly common in methods for veterinary drug residues in foods to base the quantitative determination on a standard curve prepared by addition of standard to known blank representative matrix material at a range of appropriate concentrations that bracket the target value (the analytical function). Use of such a tissue standard curve for calibration incorporates a recovery correction into the analytical results obtained. 

Extrapolation of the bias function from the masses of the reference isotopes to the masses of the analytes of interest is typically kept as small as is practical. Ideally, the analytes of interest are bracketed by the mass bias calibration isotopes, i.e., the bias correction is interpolated. For example, a T1 isotopic standard is used to correct unknown Pb ratios, but T1 would not be a good choice for correction of Pu isotopes. If appropriate isotopic abundance reference materials are available and appropriate care is used, MC-ICP/MS is among the most versatile (applies to most of the Periodic Table) and accurate methods for determining unknown isotopic composition. 

In this method two standards are selected so that their concentrations closely bracket the expected value for the analyte. This means that only a small section of the calibration graph is used. The concentration of the analyte in the sample is calculated according to the equation ... 

A standard procedure for the temperature calibration of differential thermal analysers and differential scanning calorimeters has been published as ASTM E 967 (1999). In the two point method two calibrants are chosen to bracket the temperature range of interest. It is assumed that the correct temperature T is related to the experimental temperature Texp by the relationship,... 

A more ideal situation is where the matrix is of constant composition and only the trace element concentrations vary from specimen to specimen. Here, only the constant matrix absorption needs to be considered for each element. Interelement effects can be ignored, and a simple linear equation such as Eq. (11.8) can be used to relate concentration to measured intensity separately for each element. Probably the most desirable method for generating the calibration curves is making up standards of known composition. Several standards are required for each element, bracketing the expected range of concentration. Since trace elements are involved, the set of standards for one element can include the range of concentrations for all the elements. Consequently, somewhere between 4 and 10 standards are adequate. 

It is best to calibrate the instrument at a pH near to that of the sample or at two pH values that bracket the sample pH. If necessary, calibration can be performed at multiple pH levels, such as pH 4.00, 7.00, and 10.00 to check the linearity of the system. The use of a calibration curve gives the best empirical relationship between voltage and concentration, but the accuracy depends on matching the ionic strength of the sample to that of the standards to avoid differences in activity coefficients. This can be difficult to do in high-ionic-strength samples and complex matrices. In these cases, the method of standard additions (MSA), discussed subsequently, may be nsed to advantage. 

Flame instability can cause large errors in flame photometric anedysis. It is, therefore, essential that all assays be carried out in triplicate. Calibration curves should be checked or reconstructed when the assays are carried out. If high accuracy is desired, a standard solution containing more or less the same concentration of the element as the sample solution, is assayed immediately before and after the sample solution. This method is known as bracketting. Very frequently, internal standards are used and the choice element for this purpose is usually lithium. 

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