If the equation relating to isotope dilution (11.15) is deducted not to material vol­ume (V), but to tracer volume (Vj), the reverse isotope dilution equation is obtained:

(11.24)

This equation is valid not only for volumes but also for the mass of materials.

When applying the reverse isotope dilution method (discussed in Section 10.1.6.2), the volume of the tracer is intended to determine. This requires knowledge of the total volume in which the radioactive tracer of known activity is mixed.

Such investigation is, for example, a wear study carried out with the radiotracer technique (Figure 11.16). The plug of a motor vehicle is a part that is particularly exposed to wear. For the study, a plug in its full mass is neutron-irradiated in the research reactor or locally irradiated with charged particles in a cyclotron, and then the radioactive part is inserted into the motor. Fine particles from the plug of the running motor get into the lubrication oil as the result of wearing. The oil volume/ mass and activity on the plug are measured prior to the test. This is followed by measuring the radioactive concentration/specific activity of the oil contaminated with worn particles. Then, using the equation related to reversed isotope dilution, either volume or mass of the radioactive tracer (worn particles in the oil) can be calculated.

In addition to wear studies, other corrosion processes can be tested by the reverse isotope dilution method. Such tests are wear of enamels, removal of surface degreasers at galvanization, and chromium loss at welding technologies.

Figure 11.16 A wear study of a radioactive plug built into the motor of a vehicle.

11.2.1 Groundwater Flow Studies

The linear velocity of groundwater can be determined by determining the dilution of a tracer as a function of time. Concentration decreases over time t at a ground­water flow with a Q flow rate according to the following equation:

dc _ Qc d t _ ~V

where V is the volume of the labeled water column, and c is the radioactive con­centration of the tracer at a time t.

Introducing an internal cross section of the well (A), the groundwater velocity v can be determined by integrating Eq. (11.25) as follows:

Consequently, for determining the flow velocity of groundwater, a continuous decrease of radioactive concentration of the tracer injected instantaneously into the well is measured (Figure 11.17).

A measuring probe automatically detects the residual concentration of the radio­active tracer diluted continuously with groundwater, while a connected meter records the concentration versus time plot (Figure 11.18).

To determine the direction of the groundwater flow, the intensity plot of the radioactive tracer escaping from the well is recorded for every direction. This can be done by rotating a probe sunken into the well which is collimated (opened) in one direction. The plot of a rotating probe is shown in Figure 11.19. The flow direction of the groundwater corresponds to the direction of the longest drawn tracer spot on the plot.

Groundwater flow velocity and flow direction studies serve typically to determine local conditions, while large field flow conditions are better determined by measuring

1— Scintillation detector

2— Lead shielding

3— Sealing balloon

4— Sealing balloon

5— Tracer injector

6— Tracer mixer

7— Rotating detector

8— Scaler

9—

Data logger

water level changes in several drilled wells. Mapping groundwater local flow condi­tions were executed in practice in the surrounding of industrial waste repositories.

As mentioned earlier, we may put together separate images to form a single whole- body view, without borderlines. However, this method works only for cameras with a rectangular field of view.

There is another way to construct whole-body images: by moving the table continu­ously, synchronized with the slab of the image matrix to where the acquired counts are added. (If the field of view is not rectangular, we have to correct for the differences in the effective acquisition time of each pixel.)

12.4.4.4 Reconstruction of Spatial (3D) Distribution

We already mentioned “tomography” (which means “slice imaging”) in Section 12.4.3. The mathematical procedure that calculates the distribution of cross sections from raw projections is called reconstruction.

In SPECT, the gamma camera detector(s) is moved on a 180° or 360° arc around the patient’s body and acquires 30—128 projection images of the distribu­tion of the radiopharmaceutical (see Figure 12.7). The movement (either continuous or “step and shoot”) is computer controlled.

There are advantages and disadvantages when comparing SPECT to X-ray trans­mission tomography (CT).

(C)

ft ft ft

Figure 12.7 The principle of SPECT data acquisition. (A) The detector(s) rotate around the patient. (B) With a dual-head camera, each detector covers 180°. (C) Many projection images are acquired. (Four of the brain projections are shown.)

12.4.4.5 Advantages of SPECT over CT

• Like all gamma camera methods, SPECT allows functional rather than structural imaging.

• We obtain images of a wide zone at once (the field of view is typically 30—40 cm along the body), so many slices can be reconstructed at once—and then slices in any slanting direction as well.

12.4.4.6 Limitations of SPECT

• As with gamma camera imaging in general, spatial resolution is relatively bad.

• Images are noisy because of the statistical nature of radioactive decay.

• Radiation attenuation occurs inside the patient’s body, and its extent depends on the depth of the organ as well as the structure of its environment.

• Radiation originating from an organ may scatter in the surrounding tissues, and the scat­tered photons may also be detected, further degrading spatial resolution.

As mentioned in Section 4.1.2, radioactivity is usually measured not by identifying the radioactive nuclei, but by counting the emitted particles. The absolute measure­ment of radioactivity means the measurement of the total activity, i. e., all radiating particles have to be counted in 4n spatial angles.

The detectors measuring the total activity are usually gas-filled detectors (as described in Section 14.1) and measured at a direct voltage where the alpha and

beta particles can be differentiated (Figure 14.3). During the measurements, it is assumed that every radioactive decay emits one particle, which is true for most decays.

The very thin layer of the radioactive sample is placed onto a very thin plastic sample holder (at most, 10 pg/cm2), and this sample is located in the middle of two half-sphere detectors. The produced sphere is purged continuously by the mixture of argon and methane gases. These types of detectors are called “4n-counters.” The signals produced in the two half-sphere detectors are added together after preamplifying.

The other method for the measurement of the total activity is the coincidence method. This method can be used for measuring two decay types. The first one is when an alpha particle and a gamma photon, or a beta particle and a gamma pho­ton, are emitted at the same time (within 10 7 s). In the other case, two gamma photons are emitted together (also within 10 7 s). The alpha/beta particle + gamma photon, or the two gamma photons, are measured by two detectors, which are con­nected in coincidence. This means that signals (/1+2) are obtained only when sig­nals are produced on the outputs of both detectors at the same time. In addition, the alpha/beta particles (/j) and gamma photons (/2) are counted separately. Similarly, when two gamma photons are detected, two independent gamma intensities are measured.

The total activity can be calculated as follows. The radioactive intensity (/) can be expressed by the product of the activities (A) and efficiencies (k). For the sepa­rately measured alpha/beta particles:

/1 — k A

For the gamma photon:

/2 — k2A

For the coincidence signals:

/1+2 — k^A (14.7)

By expressing the total activity:

The measurement of the total activity by the coincidence method seems to be very simple. In practice, however, efficiency corrections are required even for isotopes with the simplest decay schemes.

The total activity of radioactive sources with high activities can also be measured using calorimetry. The accuracy of the activity measurements can be improved by the application of differential calorimeters.

The most frequent sources of nuclear reactions generating artificial radioisotopes are neutrons produced through uranium fission. Based on their kinetic energy, these neutrons can be classified into three groups (as discussed in Section 6.2.1): thermal, epithermal, and fast neutrons, and each of these generate different nuclear reac­tions. The ratio of the neutrons belonging to the three groups is different at various points of the reactor core, so it is possible to select the neutron energy necessary for the required nuclear reaction either by selecting the appropriate irradiation channel or by shielding the target with cadmium foil.

Neutron flux in research reactors (i. e., in reactors not used for energy produc­tion) is typically in the range of 1012—1015 n cm-2 s-1. While in reactors at the lower end of this range, low-activity radioisotopes can be generated, and reactors with higher neutron flux result in products with high specific activity and provide a means of cost-effective radioisotope production. For example, a research reactor with 20 MW power has neutron flux in the range of 1—3 X 1015 n cm-2 s-1. Other, low-power reactors (e. g., training reactors) are not suitable for regular, technology — based isotope production, but only for physics measurements and neutron-activa­tion analysis.

Considerations for target selection were discussed in Section 8.5.2, while time — dependence of the neutron activation is found in Section 6.1. Besides, the irradia­tion time belonging to a given flux has to be calculated based on the activity to be achieved and on the target mass.

A very common task in analytical chemistry is the separation of the different com­ponents to be analyzed. The components are typically separated by distribution reactions using phase separation. For example, the precipitation, extraction, ion exchange, electrolysis, and different chromatographic methods are mentioned.

In order to have accurate analytical results, the distribution ratio (in other words, the yield of the separation procedure) must be determined. Radioactive tracers can assist in determining the yield. The application of the radioactive tracers is espe­cially useful in multicomponent systems if the radioactive isotopes of components have distinguishable radiation properties, such as different gamma energies.

The following two examples demonstrate how this method can be used to deter­mine distribution ratios. First, the separation of the 90Sr—90Y parent—daughter pair is mentioned. These are fission products of 235U in nuclear reactors (see Figure 6.5 and Section 7.3). Since their fission yield is relatively high, and 90Sr has a rela­tively long half-life, it is important to be able to determine precisely the activity concentration of 90Sr in different samples. However, as a result of the negative beta decay of 90Sr, 90Y is formed:

90 Sr! 90Y! 90Zr

30 years 64 h

Both isotopes have pure negative beta radiation, and the maximum beta energies are 546 and 2284 keV for 90Sr and 90Y, respectively. As a result, the activity of the parent nuclide, 90Sr, can be measured directly only in secular equilibrium (as discussed in Section 4.1.6). The time needed to reach the secular equilibrium is determined by the half-life of the daughter nuclide, 90Y. This is 64 h, so the secular equilibrium is reached after about a month, which is too long to obtain the analyti­cal result. To avoid this problem, 90Sr and 90Y isotopes are separated chemically using several different procedures. Each separation procedure requires the determi­nation of the yield of separation. This can be done easily using the 85Sr isotope as a tracer that has beta and gamma radiation. Since neither 90Sr nor 90Y has gamma radiation, the gamma radiation of 85Sr (514 keV) is used for the analysis. 85Sr with

Solid sample

I

Tracers: 242Pu, 243Am, 232U, (229Th)

I

Digestion: cc. HNO3/(HF) Dissolution: 8 M HNO3

I

Extraction chromatography by UTEVA resin

known activity/intensity is added to the mixture of 90Sr—90Y before the separation. The yield is calculated on the activity/intensity measurement of the pure strontium fraction after the separation.

The other example illustrating the use of radioactive isotopes to determine sepa­ration yields is the analysis of the uranium (sometimes thorium) and transuranium elements. As discussed in Section 6.2.1 (Eqs. (6.22) and (6.23)), these isotopes are produced from 238U in nuclear reactors. For their quantitative analysis, precipita­tion, extraction, and ion exchange separations are used. The separation yields are determined by radioactive tracers that are not present in the samples, i. e., nonfission products, such as 242Pu, 243Am, 232U, and 229Th. An example for the separation and sample preparation is shown in Figure 10.1.

In these two examples, the radioactive tracers are applied in radioactive samples. Obviously, similar procedures can be applied for nonradioactive samples. The sepa­ration yield of different processes (precipitation, gravimetry, extraction, ion exchange, chromatography, etc.) can be determined using radioactive tracers, both in the analytical and in the preparative scale. The traditional analytical methods coupled with radioactive tracers include radiogravimetry, radiochromatography, and so on.

Before we go into further details, we must first answer this question: what justifies the application of radioactive substances in medicine at all? Quite frequently, very low concentrations of substances have to be measured either in the body or in biological samples, or we have to follow the physiological or pathological metabolic, secretory, or excretory processes, making otherwise invisible phenomena observable by applying suitable tracers.

12.2.1 Comparison of Methods for In Vitro Measurement of Concentrations

Although more and more accurate laboratory (photometric, fluorometric, and enzymatic) methods had been developed for the measurement of concentrations in biological fluids, about two decades ago, there was still no method apart from RIA and immunoradiometric assay (IRMA; for more details about this, see Section 12.3), which were simple and cheap enough for routine measurements of concentrations in the nmol/L range.

Note that recently various “alternative” (nonradiotracer) methods have been intro­duced that have similar sensitivity to that of IRMA. However, in vitro nuclear diag­nostic methods are still indispensable parts of laboratory medicine (and probably will be for a long time), primarily due to their low cost. (From an environmental point of view, the waste produced by the alternative assays is no less hazardous than the radiotracer.)

Both natural and artificial radioactive isotopes are present in the environment (Table 13.1) in the atmosphere, hydrosphere, lithosphere, and living organisms, including the plant—animal—human food chain. The radioactive isotopes in the environment give the external radiation dose to human organisms, while the iso­topes incorporated by breathing, feeding, and so on are the source of the internal radiation dose (see Sections 13.4.1 and 13.4.3).

Radioactive isotopes, similar to stable isotopes, continuously circulate among the different parts of the environment, as illustrated in Figure 13.2. The radioactive isotopes in compartments are in direct exchange; in other words, they may pass through to other compartments. The distribution of radioactive isotopes in different compartments is mainly determined by their chemical properties. In nature, radio­active isotopes may react with different components of air (oxygen, nitrogen, car­bon dioxide, and aerosols), may dissolve in water, or may be sorbed on the solid phases of the spheres, especially the lithosphere. The chemical reactions of radioac­tive isotopes produce chemical species, which then distribute in the different com­partments in order to approach the thermodynamic equilibria. In nature, of course,

Table 13.1 The Most Important Radioactive Isotopes, Including Natural and Artificial Ones,

in the Environment

Radioactive Isotope

the thermodynamic equilibria are never reached; therefore, only the tendencies of the chemical reactions and the tendency of the distribution of the radioactive iso­topes can be discussed.

The occurrence of radioactive isotopes in the different spheres is discussed on the basis of Figure 13.2.

In this chapter, the radioactive tracers of the individual elements and their produc­tion are sketched briefly. In the case of tritium and C-14, the nuclear reactions, as well as the chemical syntheses of labeled organic compounds, are outlined.

Ion source

Figure 8.8 The scheme of a linear accelerator. Protons fly through the tubes operated with alternating voltage supply. The length of the tube is adjusted in relation to the frequency of alteration that the protons meet an accelerating voltage whenever they pass from one tube to the next.

8.6.1 Tritium

Tritium (3H) is the isotope of hydrogen and emits negative beta particles with 18.6 keV maximal energy. Its half-life is 12.3 years. Tritium is produced by the 6Li(n, a)3H nuclear reaction. A foil from an MgLi alloy is used as target; tritium is separated by heating. Tritium is applied as T2 gas or tritiated water (T2O) in the syntheses of different organic compounds.

• Alkanes can be produced by isotope exchange reactions of hydrogen in organic compounds:

Pd, heating

R — H 1 T2O ——— > R — T 1 THO (8.18)

• Alkane (methane) can be prepared in the reaction of tritiated water with aluminum carbide:

R — CHOH — COOH — NaO! CHI3 1 R21 (COOH)2 (8.19)

• Alkanes are formed in the Grignard reaction:

RMgX 1 T2O! RT 1 MgOTX (8.20)

• Double bonds can be saturated by tritium gas.

• Alcohols can be obtained by the reduction of carbonyl compounds with NaBT4 or LiAlT4:

4R2CO 1 NaBT4 1 2H2O! 4R2CTOH 1 NaBO2 (8.21)

• By the exchange of the labile hydrogen of malonic acid and decarboxylation, acetic acid is produced. In addition, the labeled malonic acid can be used in many organic syntheses.

• By the reaction of calcium carbide and tritiated water, tritium-labeled acetylene can be prepared, which can be a starting material in many organic syntheses.

Equation (9.24), expressing the ratio of the radioactive and inactive atoms at the maximum mixing entropy, has another meaning. When the nominator of Equation
(9.24) is multiplied by the decay constant of the radioactive isotope (A), the denom­inator is divided by Avogadro number (NA) and multiplied by the molar mass (M), the equation is obtained as follows:

0 A’

n a_

n +N M

Na,

where — is the radioactivity of the tracer, m is the mass of the ith component, including the tracer and the inactive carrier, and the -/m ratio is the specific activity.

On the basis of the specific activity, the tracer studies are classified into two groups:

1. The specific activity is constant, which means that the mixing entropy of the system is maximal during the whole period of the studies. In this case, the activity is measured at different places of the system and at different times, the ratio of the activities quantita­tively gives the distribution of the substance. This method is applied, for example, for the determination of the solubility of very insoluble salts (such as in Hevesy’s first tracer experiments, described in Section 8.1) or for the study of the efficiency of electrolysis.

2. The specific activity changes because the radioactive isotope is diluted with the stable isotope of the same element. In these studies, the specific activity has to be deter­mined before and after the dilution. The change in specific activity gives information on the quantity of the diluting substance. This principle is applied to isotope dilution methods, including some important medical applications (such as RIA, described in Section 12.3).

The principle of the isotope dilution methods is discussed here. Let us suppose a radioactive substance with activity -:

— = An (9.26)

where n is the number of radioactive nuclides and A is the decay constant. The ini­tial specific activity before dilution (a0) is:

An 1

a0 = П+N M

Na

where N is the number of the inactive nuclides (carrier), M is the molar mass, and Na is Avogadro number (see also Eq. (9.25)). If N0 inactive carrier nuclides are added to this system (dilution), the total activity (—) remains the same (a closed system); the specific activity (a0), however, decreases:

Since the activity (A) is the same, from Eqs. (9.27) and (9.28), we obtain:

A 5 An 5 aQ(n 1N) = a! (n 1N 1 N0) (9.29)

From here,

N0 5 (n 1 N)0 — l) (9.30)

Since n«N, the number of the radioactive nuclides can be disregarded. The quan­tity of the diluting substance can be calculated when we know N, and the specific activities before (a0) and after (a0) the dilution.

According to the classification by the specific activity, group l (constant specific activity, the mixing entropy is maximal) contains, for example, the determination of solubility, a part of diffusion studies (self-diffusion is not included), radiometric analysis, and autoradiography. Group 2 (specific activity changes, the mixing entropy increases) contains, for example, the determination of specific surface area, the different types of isotopic dilution methods, substoichiometric analysis, RIA, the study of isotopic exchange reactions, self-diffusion, and the determination of exchange current.

The radiotracer methods can also be classified based on the field of applications, such as physicochemical, analytical, biological, medical, and industrial applica­tions. Physicochemical applications include, for example, the determination of sol­ubility, the study of diffusion, the distribution of substance between phases, and the study of reaction mechanisms. It is important to note that radiotracer methods are widely used in the study of interfacial processes because of the high sensitivity of radioindicators. Analytical applications include the radiometric analysis, isotopic dilution methods (including RIA), autoradiography, neutron activation analysis, and all analytical methods based on the interaction of radiation with matter (see the discussion of this in Chapter 10).

Isotope labeling can also be done by stable isotopes, in which case the natural abundance of a given element is altered. In other words, a stable isotope is enriched. The concentration of the stable isotopes can be determined in two ways:

• The samples are activated after the studies and the number of isotopes is determined on

the basis of the produced radioactive nuclides.

• The number of isotopes can be determined by mass spectrometry, infra spectrometry, and

so on.

These methods, however, are much more complicated than simple radioactivity measurement methods.

Of course, the basic concepts of labeling by stable isotopes are just the same as those of radioactive isotopes, only the detection methods are different. Therefore, all of the principles and relation mentioned above for radioactive isotopes apply to stable isotopes.

As mentioned previously, during the activation by neutrons, a (n, Y) reaction takes place. This reaction produces radionuclides that can also emit gamma photons. This means that two gamma photons are formed as expressed by the following scheme:

Target nuclide (n, Y) radioactive nuclide! radiation of gamma photon.

NAA (see Section 10.2.2.1) provides analytical information using the gamma photons irradiated by the radioactive nuclide. The gamma photons formed in the nuclear reaction itself are called “prompt gamma photons” because they are formed within 1014 s after neutron capture. PGAA detects these gamma photons and pro­vides analytical information independent of whether the product nuclide is stable or radioactive. Similar to NAA, the energy of gamma photons gives qualitative infor­mation, while the activity or intensity provides quantitative information. The kinet­ics of activation is also the same.

The prompt gamma photons can be detected only during irradiation, i. e., the excited nucleus formed by neutron capture, called a “compound nucleus” (see Section 6.1) emits gamma photons. The excitation energy is in the range of
the binding energy of neutrons (7—8 MeV). The de-excitation (i. e., the emission of gamma photons) can happen in one step or in several steps, emitting one gamma photon with high energy or a cascade of gamma photons with low energies. For this reason, the prompt gamma spectra are rather complicated.

PGAA has the same advantageous properties as NAA. In addition, PGAA can detect all elements because prompt gamma photons as emitted photons are pro­duced in every (n, Y) reaction. (In NAA, only radioactive product nuclides with suitable half-lives can be measured after irradiation.) Thus, PGAA is especially important in the analysis of light elements (such as H, B, and N; see Table 10.4). Because of its high sensitivity, it is a very useful method to use in the analysis of elements in tracer quantities (Cd, Hg, etc.). The disadvantage of this method, how­ever, is that the gamma photons have to be measured directly in the neutron beam. This results in high background radiation. In addition, to detect the prompt gamma photons, the neutron beam has to exit the nuclear reactor, which significantly decreases the neutron flux. Since gamma photons can be produced as cascades of photons with low energy, the gamma spectra are usually very complicated and require special evaluation procedures. At the same time, PGAA is an expensive method, which restricts its widespread application.

As seen in Figure 6.4, the cross section of the nuclear reaction with neutrons is inversely proportional to the neutron energy. Thus, by decreasing the energy of the neutrons (i. e., using cold neutrons (see Section 5.5.3)), the cross section can increase by as much as two orders of magnitude. This increases the number of nuclear reactions, improving the sensitivity of PGAA. The application of the cold neutrons in PGAA is the most important supplement to the traditional NAA. When irradiating with cold neutrons, the background intensity is significantly smaller, providing a possibility for in vivo applications.

The detection limit of this method is in the range of 10_5—10_9 g, depending on the cross section of the (n, Y) reaction of the isotopes of the elements. It is applied in the analysis of the following:

• Light elements (H, B) for which NAA cannot be used.

• Main (Si, Al, H, C), trace — (Cu, Cd, Hg, Pb) and indicator (B, Rb, Sm, Gd) elements in geological formations.

• Toxic elements (Cd, Hg)—macro — (H, C, O, Ca) and microelements (Cu, Zn, Fe) in bio­logical, medical samples.

In Figure 10.8, a prompt gamma activation spectrum of a standard cement sample taken using a high-purity germanium detector (HPGE) with Compton suppression is shown.