Cross-contributions

Isotope mass number Abundance, % Thermal neutron cross Contribution to the total cross ... 

The relative intensities of the peaks at M/z = 254 and 255 in the negative ion spectrum do not correlate well with those expected for CigHioO and C CisHjoO however, they do correlate rather well with C38H2o02 and C2 C36H2o02 if it is assumed that peak height is a direct measure of the ion intensity (i. e., there are no cross-contributions of the intensities of peaks, or that the resolution exceeds ca. 500.) With this same assumption the intensity of the M/z = 254,5 ion agrees very well with that to be expected for C C37H2o02. ... 

Figure 18 Calibration curves using an internal standard (IS). Analytes are quantified against an IS that has been added as early as possible in the analytical procedure. The ratios of detector responses for the analyte (fiA) and IS (R S) are plotted against the ratio of known amounts of analyte (A) and IS. When a sample is analyzed, the ratio Ra/Ris is measured. Then knowing the amount of IS added into the sample, the amount of analyte present in the sample can be estimated. Curves that do not pass through the origin of the graph or which are nonlinear are diagnostic of (a) chemical interference or sample carryover, (b) sample loss during the assay due to adsorption, and (c) saturation or cross-contribution between the IS and the analyte.

We calculate our theoretical isotropic spectmm as a convolution of the rotational stick spectra and the translational spectra. Our rotational stick spectra result from the first- and second-order DID light scattering mechanisms, and from the dipole-octopole (a ) and dipole-dipole-quadmpole (B0) multipolar light scattering mechanisms and their cross contributions. We then convolute,... 

The g-tensor (magnetogyric ratio tensor) appears as the crossing contribution to the energy... 

The cross-contribution phenomenon discussed above, with its implications for the need to adopt nonlinear regression in some form, can be a genuine difficulty for the analyst in real-world situations. Approaches used to mitigate the problem without having to resort to nonlinear regression are described in Section 9.4.5b. 

Figure 8.15 Examples of GC/EIMS calibration curves that are nonlinear as a result of cross-contributions between the analyte (butalbital) and SIS (butalbital-D5), both as the methylated derivatives. The SIS was present in all calibration solutions at a concentration of 200 ng mL . The mjz values (all for fragment ions) monitored were (a) analyte 196, SIS 201 (b) analyte 138, SIS 143. See main text for data on cross-contributions. In both cases the curves represent nonlinear least-squares regression fits of the data to Equation [8.89], accounting for cross-contributions in both directions. Reproduced from Whiting, /. Anal. Toxicol. 25, 179 (2001), with permission of Preston Publications, A Division of Preston Industries, Inc.

After the reference standard and SIS are received, a simple and rapid two compound chromatography-MS method (analyte and SIS) can be developed for screening these two compounds in solution. The two solutions can then be analyzed independently at relatively high concentration (S/B >100 for compound injected) as an initial indication for any potential cross-contribution from the... 

Obviously, a SIS with a sufficient degree of labeling and sufficient purity to eliminate the potential for crosscontribution would be the first choice for the analyst (Section 8.5.2c), but this ideal situation is not always what is found in real-world method development. However, even if there are cross-contributions between the analyte and SIS, it may be possible to circumvent the problem by making small modifications to the method. For instance, if a small cross-contribution is found from the analyte— IS due to insufficient isotope labeling, then the amount of SIS in the method can be increased and/or the ULOQ can be decreased. If, on the other hand, a small cross-contribution from the SIS- analyte is detected, the amount of SIS used in the method can be decreased. 

FDA work will tolerate an SIS cross-contribution of up to 20 % of the response of the analyte being quantified at the LLOQ concentration. Note that these fitness for purpose guidelines are based largely on practical experience without (thus far) any statistical justification. Ultimately this question should be settled by visual examination of the experimental calibration curve together with careful evaluation of the accuracy and precision over the entire range of analyte concentration for the specified SIS concentration used to generate the calibration. In any event, the cross-contributions (if any) must be carefully monitored during all phases of method validation and sample analysis and also must be fully discussed in the method description and final report. 

If the particular analog happens to be a structural isomer (Table 2.1), chromatographic resolution is necessary to distinguish the analytical signals for analyte and SIS (identical molecular masses) unless MS/MS is used and the isomers yield different product ions. Since the molecular mass of a homologous structure differs from that of the analyte by at least 14 Da, there is seldom any problem of cross-contributions arising from overlap of the isotopolog distributions (Section 8.5.2c). 

Just as for the analyte, the choice of product ion for MRM detection of the SIS requires the same considerations. In addition, usually the m/z value of the SIS precursor ion is different from that of the analyte, so there is no problem if the best choice of product ion turns out to be the same for both. This conclusion does not apply if there is appreciable overlap between the isotopic distributions of anal5h e and SIS, i.e. cross-contributions between the precursor ions (Section 8.5.2c), since the latter circumstance requires uniquely different product ions for there to be any hope of distinguishing the two. It is good practice to make a choice of product ion as the primary candidate for the MRM method, but also to choose one or two others as back-up candidates that should be independently optimized (collision energy etc.). Then, during subsequent stages of the overall method development, continue to use aU of these candidate ions until the final optimization, as an insurance against unforeseen selectivity problems with the primary candidate for the real-world samples. 

A possible approach to addressing nonlinearity that is not the result of cross-contributions between analyte and SIS (Section 9.4.5b) is to simply limit the range of reliable response to the linear region. While this is usually defensible with respect to negative deviations at high concentrations where the reasons are more clear-cut and reproducible, it could be problematic at the low end depending on the causes of the nonlinearity there since some of these will be intrinsically irieproducible. If the low end nonlinearity sets in at concentrations close to the desired LLOQ, it is advisable to undertake additional method development work to discover the cause and eliminate it... 

Figure 3.20b. The ratio of lycoctonine-type to ajaconine alkaloids in Delphinium ajacis. These results were obtained using the direct probe-mass spectrometer LKB-9000P and a crude alkaloid fraction. Major fragment ions that are characteristic of the compound and which have low cross contribution from the other compounds were selected. The cross contribution was determined as were the response factors from known amounts of pure compounds. Samples were then analyzed by repetitive scans in the high mass range (where most of the important fragment ions occur). The ion intensities of the interpretive fragment ions are plotted, and the area under each curve is determined and corrected for cross contributions and response factors to arrive at a total microgram estimation for each known compound. Unknowns are monitored by their characteristic fragment ions and estimated relative to the knowns (from Waller and Lawrence, 1975).

Table 12.1 Total electronic delocalization (5tot)> total electronic delocalization (5 ), and the corresponding crossed contributions to this latter for C4H4 and CgHg antiaromatic compounds...

Ae in terms of the low-density coefficients (equations (5.3) and (5.4)) accordingly contains additional terms. The first, kinetic contribution is the only important term at low densities and scales in time as for diffusion. The final term is the contribution from the potential part alone and the middle term is the cross contribution of the kinetic and potential part. The presence of these terms, and their functional dependence, can be demonstrated simply from a derivation of these expressions by the fluctuation-dissipation theorem, which gives the transport properties in terms of an autocorrelation function of the appropriate flux (see 5.4.1). For thermal conductivity, for example, the flux involves the sum of kinetic and potential eneigies. The autocorrelation of this flux involves the product of the flux at two different times, producing three different terms which can be shown to have the same dependence on density and g(a) as above. 

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