Isotope dilution analysis is a method of determining the quantity of chemical substances. In its most simple conception, the method of isotope dilution comprises the addition of known amounts of isotopically enriched substance to the analyzed sample. Mixing of the isotopic standard with the sample effectively "dilutes" the isotopic enrichment of the standard and this forms the basis for the isotope dilution method. Isotope dilution is classified as a method of internal standardisation, because the standard (isotopically enriched form of analyte) is added directly to the sample. In addition, unlike traditional analytical methods which rely on signal intensity, isotope dilution employs signal ratios. Owing to both of these advantages, the method of isotope dilution is regarded among chemistry measurement methods of the highest metrological standing.[1]
Isotopes are variants of a particular chemical element which differ in neutron number. All isotopes of a given element have the same number of protons in each atom. The term isotope is formed from the Greek roots isos (ἴσος "equal") and topos (τόπος "place"), meaning "the same place"; thus, the meaning behind the name is that different isotopes of a single element occupy the same position on the periodic table.
Analytical application of the radiotracer method is a forerunner of isotope dilution. This method was developed in the early 20th century by George de Hevesy for which he was awarded the Nobel Prize in Chemistry for 1943.
An early application of isotope dilution in the form of radiotracer method was determination of the solubility of lead sulphide and lead chromate in 1913 by George de Hevesy and Friedrich Adolf Paneth.[2] In the 1930s, US biochemist David Rittenberg pioneered the use of isotope dilution in biochemistry enabling detailed studies of cell metabolism.
Isotope dilution is analogous to the mark and recapture method, commonly used in ecology to estimate population size.
For instance, consider the determination of the number of fish (nA) in a lake. For the purpose of this example, assume all fish native to the lake are blue. On their first visit to the lake, an ecologist adds five yellow fish (nB = 5). On their second visit, the ecologist captures a number of fish according to a sampling plan and observes that the ratio of blue-to-yellow (i.e. native-to-marked) fish is 10:1. The number of fish native to the lake can be calculated using the following equation:
nA=nB x
10 | |
1 |
=50
nA=nB x
RB-RAB | |
RAB-RA |
x
1+RA | |
1+RB |
Isotope dilution is almost exclusively employed with mass spectrometry in applications where high-accuracy is demanded. For example, all National Metrology Institutes rely significantly on isotope dilution when producing certified reference materials. In addition to high-precision analysis, isotope dilution is applied when low recovery of the analyte is encountered. In addition to the use of stable isotopes, radioactive isotopes can be employed in isotope dilution which is often encountered in biomedical applications, for example, in estimating the volume of blood.
Isotope dilution notation | ||
---|---|---|
Name | Symbol | |
Analyte | A | |
Isotopic standard (Spike) | B | |
Analyte + Spike | AB |
Consider a natural analyte rich in isotope iA (denoted as A), and the same analyte, enriched in isotope jA (denoted as B). Then, the obtained mixture is analyzed for the isotopic composition of the analyte, RAB = n(iA)AB/n(jA)AB. If the amount of the isotopically enriched substance (nB) is known, the amount of substance in the sample (nA) can be obtained:[3]
nA=nB
RB-RAB | |
RAB-RA |
x
x(jA)B | |
x(jA)A |
For elements with only two stable isotopes, such as boron, chlorine, or silver, the above single dilution equation simplifies to the following:
nA=nB
RB-RAB | |
RAB-RA |
x
1+RA | |
1+RB |
In a simplified manner, the uncertainty of the measurement results is largely determined from the measurement of RAB:
2 | |
u(n | |
A) |
\propto\left({
\partial{nA | |
ur(n
2 | |
A) |
\propto
| ||||||||||||||||||
|
2 | |
u(R | |
AB) |
ur(nA)min\mapsto\partial\left(
(RA-RB) | |
(RA-RAB)(RAB-RB) |
RAB\right)/\partialRAB=0
RAB=\sqrt{RARB
The single dilution method requires the knowledge of the isotopic composition of the isotopically enriched analyte (RB) and the amount of the enriched analyte added (nB). Both of these variables are hard to establish since isotopically enriched substances are generally available in small quantities of questionable purity. As a result, before isotope dilution is performed on the sample, the amount of the enriched analyte is ascertained beforehand using isotope dilution. This preparatory step is called the reverse isotope dilution and it involves a standard of natural isotopic-composition analyte (denoted as A*). First proposed in the 1940s[9] and further developed in the 1950s,[10] reverse isotope dilution remains an effective means of characterizing a labeled material.
Isotope dilution notation | ||
---|---|---|
Name | Symbol | |
Analyte | A | |
Natural standard | A* | |
Isotopic standard (Spike) | B | |
Analyte + Spike | AB | |
Standard + Spike | A*B |
Reverse isotope dilution analysis of the enriched analyte:
nB=nA*
RA*-RA*B | |
RA*B-RB |
x
x(jA)A* | |
x(jA)B |
nA=nB
RB-RAB | |
RAB-RA |
x
x(jA)B | |
x(jA)A |
nA=nA*
RA*-RA*B | |
RA*B-RB |
x
RB-RAB | |
RAB-RA |
nA=nA* (RA*B=RAB\landRA*=RA)
To avoid contamination of the mass spectrometer with the isotopically enriched spike, an additional blend of the primary standard (A*) and the spike (B) can be measured instead of measuring the enriched spike (B) directly. This approach was first put forward in the 1970s and developed in 2002.[12]
Many analysts do not employ analytical equations for isotope dilution analysis. Instead, they rely on building a calibration curve from mixtures of the natural primary standard (A*) and the isotopically enriched standard (the spike, B). Calibration curves are obtained by plotting measured isotope ratios in the prepared blends against the known ratio of the sample mass to the mass of the spike solution in each blend. Isotope dilution calibration plots sometimes show nonlinear relationships and in practice polynomial fitting is often performed to empirically describe such curves.[13]
When calibration plots are markedly nonlinear, one can bypass the empirical polynomial fitting and employ the ratio of two linear functions (known as Padé approximant) which is shown to describe the curvature of isotope dilution curves exactly.[14]