Isotope dilution equation

A direct result of the ability to measure isotope ratios with ICP-MS is the technique known as isotope dilution analysis. This is done by spiking the sample to be analysed with a known concentration of an enriched isotopic standard, and the isotope ratio is measured by mass spectrometry. The observed isotope ratio (RJ of the two chosen isotopes can then be used in the isotope dilution equation (Eqn. 5.7) to calculate the concentration of the element in the sample ... 

Recall that NK and N are the numbers of atoms in the mixture due to sample and tracer, respectively. To convert them to weight requires use of the familiar Avo-gadro relationship and involves multiplying both sides of the equation by 1.0 twice, thereby introducing the atomic weights of sample and tracer (i.e., multiply each side by A JAS and A/At). Note that Avogadro s number appears on both sides of the equation and cancels out. As and Ar on the other hand, are not equal and do not cancel. The resulting equation is one form of the isotope dilution equation. 

Unfortunately, the natural product is heavier than its synthetic counterpart and it is relatively easy and not prohibitively expensive to add a small quantity of C enriched vanillin to the synthetic product. From this point of view, vanillin exlignin is preferred to vanillin ex-guaiacol since the quantity of labelled material required is lower. Applying isotopic dilution equations, it is apparent that less than one hundred milligrams of 99% 13C-labelled vanillin are required to transform 1kg vanillin ex-lignin into 1kg natural vanillin ... 

Once the internal standard is added to an extract, the isotope/endogenous substrate ratio is maintained, irrespective of sample losses encountered during purification. The amount of endogenous compound extracted from the plant tissue (Y) can, therefore, be calculated from the isotopic dilution equation ... 

By measuring in the blend the change in the Fe/ Fe ratio caused by adding the "spike" of other isotopic composition to the sample and by measuring the other isotopes to make appropriate corrections, one can determine the unknown amount of N of sample. The general Isotope dilution equation is ... 

The model [Eq. (7.2)] for the uncertainty calculations depicted in Figure 7.7 is based on the general isotope dilution equation of De Bievre [8] ... 

Isotope dilution analysis for protein quantification with ICP-MS is usually performed by linked techniques based on the coupling to an effective separation method, such as HPLC or CE. Generally, proteins to be analyzed should contain ICP-MS-detectable elements, including both naturally occurring and artificially labeled. After introduction of the spike that has different isotopic composition from the analyte, the elemental isotope ratio can be measured in ICP-MS and thus the detectable elements can be absolutely quantified by use of the isotope dilution equation. If proteins have been identified with biological mass spectrometry, or the elemental stoichiometric ratios of proteins have been known, the amount of proteins can be deduced from the elemental concentration of the proteins. 

The method of the species-unspecific modes is well described in literature. In brief, isotope ratios are monitored during the whole chromatographic procedure and corrected by the isobaric interference, dead time, and mass bias. Then the chromatogram of isotope ratios is transformed into the chromatogram of mass flow (mass versus time) using the following isotope dilution equation ... 

Calculate the original concentration or concentrations of the analytes from the isotope dilution equation, Eq. (7.4). 

The concentration of the species in the samples is calculated by applying the isotope dilution equation ... 

Equations 13.31 and 13.32 are only valid if the radioactive element in the tracer has a half-life that is considerably longer than the time needed to conduct the analysis. If this is not the case, then the decrease in activity is due both to the effect of dilution and the natural decrease in the isotope s activity. Some common radioactive isotopes for use in isotope dilution are listed in Table 13.1. 

The isotope dilution principle, first employed by Hevesy and Hobbie (133) in 1932 for the determination of lead in ores, was applied by Schoenheimer et al. (241) to the determination of amino acids. [Shemin and Foster (248) have reviewed this topic.] An N15-amino acid derivative was added to a protein hydrolyzate, a sample of the amino acid to be determined was isolated and purified, the excess N15 in this product was estimated with the mass spectrograph, and the grams of amino acid originally present were calculated from Equation 2. 

Conventional calibration MDRD equation [used only with those creatinine methods that have not been recalibrated to be traceable to isotope dilution mass spectrometry (IDMS)]... 

Isotope dilution analysis, 134-135 equation, 134 overspiking, 134.135(f) practical exercise, 176-182 precision, 134... 

The reverse isotope dilution technique can be applied for accurate determination of the Mg contents in a sample, sample, on applying equation 7, by measuring the isotope ratio of a selected pair of stable isotopes, in a weighed mixmre of the sample with an isotopically enriched CRM. The average atomic masses m and the isotopic ratios R of Mg in the enriched CRM and in nature are known. The method was applied for determination of Mg in plant material using a CRM isotopically enriched with Mg, measuring with an ICP/MS instruments. ... 

The isotope dilution results in Table II are on fuel source samples obtained from NBS which were considered homogeneous. The results in Table III are from the sampling points indicated in Figure 4. These summarized results are mostly by the SSMS general scan technique which has an estimated accuracy of better than 50%. The isotope dilution measurements are limited by the emulsion detector to 3-5%. The results are in grams of metal flow per minute. The mass balance for the various elements was computed by the following equations ... 

This is the basic equation of direct isotope dilution analysis. The unknown amount x of material A is given in terms of the amount y of added labeled material A and the two measured specific activities Si and S2. 

The above equation is the basic equation of inverse isotope dilution analysis and indicates that the unknown amount q of active material A can be deduced by adding r... 

The title compound, 1,3-dideuteriated malondialdehyde, MDA-46, formed in a lipid peroxidation process involved in the pathogenesis of many human diseases45,46, has been needed for quantitative determination of MDA in human blood or urine by isotope dilution mass spectrometry. It has been synthesized47 by condensation of deuteriated butyl vinyl ether with deuteriated triethyl orthoformate in the presence of montmorillonite clay K-10 (equation 18). 

In the laboratory, the isotope dilution procedure involves adding a known amount of spike of known isotopic composition to a known amount of sample of known isotopic composition the mixture of spike and sample is equilibrated the ratio of the sample isotope to the spike isotope is then measured and the resulting R is inserted into the equation. For replicate analyses, this is the only parameter... 

The title compound 220, a potent broad spectrum antibiotic but showing bone marrow toxicity292, has been synthesized293 according to equation 137. The pure 220 was used as internal standard in an isotope dilution-gas chromatographic-mass spectrometric (ID-GC-MS) method of quantification of chloramphenicol in biological samples (edible tissues)293. 

When isotope dilution is used to determine total mineral content, two ratios are measured. The following two equations are used to determine the two unknowns, (1) the total natural mineral content of the sample ( ) and (2) the amount of isotope spike ( N) recovered in feces ... 

This relationship can also be used to establish the accuracy of the Se spike concentration, which Is most conveniently added as a solution. Employing accurately prepared samples of natural selenium (Sen known) spiked with known amounts of the 2se solution, R is then measured and Equation 4 solved for Sega This is basically an inverse Isotope dilution procedure. When performed on the same Instrument to be used for subsequent measurements. It has the added advantage of cancelling out any mass discrimination by the Instrument. 

In addition to isotope dilution of the DIN pools, DON can be released during the course of the experiment. The DON pool can be isolated so that the amount of N released to the pool can be quantified. This recently released N was taken up by the cells and so should be included in the uptake calculation. This rate is referred to as a gross uptake rate, Pq, and is the sum of measured uptake plus any N that was taken up and released as DON. The difference between gross and the traditionally measured net uptake rates results from the release of N-label to the DON pool. When N-labeled DON is released to the extra cellular DON pool, it is no longer in the pool and so is not included in the traditional calculation of N uptake (Bronk and Ward, 2000 Bronk et al., 1994). The following equation is used to calculate a gross N uptake rate p(Pc) ... 

As with the equations for transfer between two compartments Eqs. (31.1—31.4), the same equation for isotope dilution (GHbert et al., 1982) applies to any single compartment that can be measured (see Section 2). 

It should be mentioned that the same kind of equations hold if stable isotopes are applied for labelling of the elements or compounds to be determined by isotope dilution analysis. In this application, isotope ratios are taking the place of specific activities and they are preferably measured by mass spectrometry. 

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