This method is also known as saturation or displacement analysis:

Ab 1 L 1 L*2 Ab. L 1 Ab. L* (12.1)

The analyte to be measured (L) and its labeled version (L*) compete for occupy­ing a limited number of binding sites (Ab). The labeled component may be added some time later. The more (unlabeled) analyte is present in the reaction mixture, the less labeled ligand will be bound. The last step is the separation of bound from free ligand. If a radioactive tracer is used, the method is called radioimmunoassay (RIA). RIAs were first introduced in the 1960s by Yalow and Berson for insulin and by Ekins for thyroxin. The precise measurement of minute amounts of such a hormone was considered a breakthrough in endocrinology; Rosalyn Yalow, a biophysicist, received the Nobel Prize in medicine for the development of RIAs of peptide hormones in 1977.

The accuracy of a RIA is limited by both the competitive nature of the reaction and the efficiency of the separation method applied.

The first, catcher antibody (Ab1) is usually fixed to some solid phase (the wall of the vial, spheres, pearls, etc.). After reaction (12.2), unbound ligand is washed off, and then a second, tracer antibody (Ab2) is added that binds to the ligand molecules present and already fixed. The amount of the bound fraction of Ab2 increases with the ligand (L) concentration. Free Ab2 is washed off as well.

Sandwich methods usually apply excess amounts of the reagents as they are based on the occupation of, rather than competition for, the binding sites. Such methods allow fast, sensitive, and specific measurements. When applying radioac­tive labeling, the method is called immunoradiometric assay (IRMA). The accuracy of IRMA methods is superior to that of RIA and similar to the “alternative” meth­ods that do not apply radioactive tracers.

Semiconductor detectors operate similarly to ionization chambers (discussed in Section 13.1). This means that the charged particles produce negative and positive charge carriers, depending on the type of the semiconductor material, which move toward the oppositely charged electrodes. As a result, an electric impulse is formed. The main advantage of the semiconductor detector is that the energy producing the charge carriers (about 3.6 eV) is much less than that in the gas-filled tubes (^30 eV) of detectors or scintillation detectors (2—300 eV). Thus, the same radiation particles are able to produce more electric charges in the semiconductor detectors (by several orders of magnitude) than either in gas-filled tubes or in scintillation detectors.

The basic material of the semiconductor detectors is germanium or silicon. Their operation is usually explained by the theory of solids. This theory postulates that instead of having discrete energies as in the case of free atoms, the available energy states form bands. In the ground state, the electrons are in the valence band. Under the effect of radiation, the electrons can move from the valence band to the conduction band, increasing the conductivity. When an electron moves from the valence band into the conduction band, the produced vacancy, “the hole,” also takes part in the electric conduction because filling the hole with an electron of the adjacent atom requires a small amount of energy. The electrons and the holes move in opposite directions; the hole can be considered to be a positive charge.

When the basic material of the semiconductor (Si or Ge) is doped with an elec­tron donor (such as P, As, and Sb), or electron acceptor (e. g., Al, B, Ga, and In), an excess quantity of the electrons or holes, respectively, are produced. These types of semiconductors are called “n-type” (negative) or “p-type” (positive) semiconduc­tors, respectively. In these semiconductors, the excitation energy is even lower than in the pure germanium and silicon semiconductors.

Ge, Ge(Li), and Si(Li) semiconductor detectors are used for the measurement of gamma and X-ray radiations, respectively. The energy resolution of the Ge(Li) detectors widely applied in gamma spectroscopy is much better than that of scintil­lation detectors. For example, the half-width of the photoelectric peak of the 137mBa isotope (the daughter nuclide of Cs-137) (662 keV) is 2—3 keV (<0.5%) when measured with a semiconductor detector, while this value is 7—10% when measured with a scintillation detector. However, the efficiency of the semiconductor

Gamma energy (keV)

detectors is about one order of magnitude worse than that of the scintillation detec­tors. In addition, the semiconductor detector requires high-quality signal-processing units (e. g., charge and spectroscopic amplifiers). GeLi and SiLi semiconductor detec­tors have to be kept continuously at the temperature of liquid nitrogen because the thermal energy is enough to transfer the electrons from the valence band to the con­duction band, increasing the noise. Recently, high-purity germanium (HPGe) detec­tors also have been used, which can be allowed to warm up to room temperature when not in use.

The photoelectric peaks of the Ra-226 and its daughter nuclides measured by semi­conductor and scintillation detectors are shown in Figure 14.7. This figure illustrates the differences in the gamma spectra obtained by scintillation and semiconductor detectors. As seen, semiconductor detectors have a higher resolution but a lower efficiency than the scintillation detectors.

Since radioactivity has been discovered as a natural phenomenon, only natural radioactive isotopes were available for the first studies. The basic concepts of radioactivity and radioactive indicators were developed using the natural radioac­tive isotopes; thus, these isotopes have mainly historical importance. From the late 1940s, artificial radioactive isotopes have been produced in cyclotrons, and later in nuclear reactors. Recently, the artificial radioactive isotopes are dominant in radio­tracer studies. Natural radioactive isotopes are used only in the environmental isotope transport modeling.

Neutron irradiation of the 235U nuclide generates a wide variety of fission products, which are then stabilized through в_-decays or transformed to radionuclides with

QQ 131 137 85

longer half-lives, suitable for various applications. The Mo, I, Cs, and Kr fission products have practical importance. Among them, QQMo is very significant because its daughter element, the QQmTc radionuclide, is appropriate for isotope generation (a “cow,” as discussed in Section 8.3), is the most important radioiso­tope of the medical diagnostics IAEA TECDOC-1065 (1QQQ).

The common feature of this group is that individual fission products can be extracted from the mixture with multistep separation methods. They are noncarrier added radionuclides, but they contain many potentially contaminating radionu­clides; thus, sophisticated purification is required to obtain sufficiently pure isotopes.

Half-life: 66 h.

Decay mode and energy: [3_ (keV) 1214 and y (keV) 740.

For the preparation of 99Mo/99mTc isotope generator

Enriched uranium containing 45% 235U in aluminum alloy.

In high-flux research reactors, with thermal neutrons, for some days.

A 235U(n, f) mixture of fission products (99Mo content 6%).

Dissolution of the target in NaOH with addition of oxidizing agent (e. g., H2O2), in order to assist dissolution and to provide an oxidized medium.

When dissolving the target in alkaline, beside 99Mo, only a few other elements will be found in the solution. These contaminating elements are separated in two ion — exchange columns and in another column filled with a chelating agent. 99Mo is eluted from the third column; the eluent is evaporated to dry and dissolved again in NaOH. To lower the reduction effect of radiolysis, an oxidizing agent (hypochlorite) is added to the solution.

In alkaline solution, the chemical species is sodium molybdate (Na299MoO4). This solution with very high activity is transported in depleted uranium containers that have a much higher attenuation coefficient against radiation than lead containers.

With a nuclear reaction of 98Mo(n, y), 99Mo can also be obtained, but specific activity is much lower.

The production of the 99Mo radionuclide in fission nuclear reaction is followed by subsequent (3_ — decays:

(8.24)

The activity of 99Mo represents only approximately 6% of the fission mixture. Its extraction from the isotope mixture and its production as sodium molybdate is carried out in steps described in Table 8.13.

Considering the fact that the portion of the 99Mo in the mixture of fission pro­ducts is low (6%), producers supply several users, and users apply several orders of magnitude of TBq 99Mo activity for generator production; the total activity pro­duced is extremely high. Moreover, the 99Mo radionuclide has high gamma energy; thus, the production of 99Mo requires hot cells with very thick (40- 50 cm) lead shielding and results in a huge amount of radioactive waste.

Recently, five countries (Canada, France, Belgium, the Netherlands, and South Africa) produced 99Mo in good quantity, which satisfies these high technical requirements and from which users (99Mo/99mTc generator producers) are supplied.

The extracted 99Mo is used for preparing 99Mo/99mTc radionuclide generators. The principle of isotope generators is described in Section 8.3. Because the half­lives of the parent (99Mo) and daughter (99mTc) nuclides are within the same orders of magnitude, transient equilibrium will develop (see Section 4.1.6). The activity of the system will be directed by the parent nuclide decay. The daughter nuclide is separated from its parent on the place of use. As this separation is made not in the generator production facility but at the user (e. g., in hospitals), it is important that the separation should be simple. From this aspect, chromatographic separation— where the daughter nuclide is eluted from its parent fixed on a chromatographic column—is the most beneficial.

Although many types of isotope generators exist, only some of them have practi­cal importance; e. g., 188W/188Re, 90Sr/90Y, 113Sn/113mIn, 82Sr/82mRb, and 99Mo/99mTc for medical use, and 137Cs/137mBa for industrial use. Among them, the 99Mo/99mTc isotope generator has the highest significance because it provides the most important radionuclide (99mTc) used for isotope diagnostics in nuclear medicine. As much as 80% of the isotope diagnostic investigations in medicine are made with this radionuclide; for this reason, this system is described in detail next.

The dominant role of the 99Mo/99mTc isotope generator can be attributed not only to the ideal nuclear characteristics of the 99mTc daughter nuclide (with gamma energy, which can penetrate through body tissues and with an ideal half-life), but also to its desirable chemical properties. The technetium as transition metal can be bound with several organ-specific complexes, which transfer the labeling isotope to the intended organ. Consequently, the same radionuclide with its beneficial nuclear features is suitable for investigating various organs by varying the linked chemical chelating agent.

In addition to these benefits, the 99mTc radionuclide can be easily extracted (eluted) from the 99Mo/99mTc isotope generator on site if this isotope mixture is adsorbed on a chromatographic column. The chromatographic separation is based on the different retention coefficient of the two radionuclides. Molybdate ions form so-called oligomer aggregates in acidic solutions, so they adsorb stronger in the alumina column than single pertechnetate ions. This binding is strengthened further by higher charges of the molybdate ions. The chemical composition of molybdate and pertechnetate ions present in various pH ranges is summarized in Table 8.14.

The best chromatographic separation is achieved when both the 99Mo parent and the 99mTc daughter nuclides are maintained in the highest oxidation state. This means that the isotope mixture must be maintained under strongly oxidized condi­tions during the whole production.

However, the high activity of the isotope mixture and the resulting dose cause permanent radiolysis (chemical decomposition caused by radiation effect) in the water solution, causing chemical reduction. As a result, the radiation of the isotope mixture has a countereffect against maintaining an oxidizing medium and a good separation because oligomers cannot be separated in lower oxidation states.

To maintain a permanent oxidized state with suitable redox potential in the solu­tion, an oxidizing agent, such as hydrogen peroxide and bubbled air, must be added to the isotope mixture.

Based on these considerations, the production of the 99Mo/99mTc isotope genera­tor from fission molybdenum (Na299MoO4) is carried out through steps described in Table 8.15.

The total activity of 99Mo in the generator production plants is in the TBq range at production time. Activities dispensed to individual generators are in the range of 37—370 GBq. Activity to be dispensed to the generator column can be chosen by the user when ordering the generator. As the dose rate constant of the parent nuclide is high, processing the total activity needs hot cells with a lead wall thick­ness of 15 cm, while shielding of the generators requires a lead pot with a lead wall thickness of 5 cm.

The half-life of the daughter nuclide (99mTc) is relatively short (6 h), so it will decompose shortly after the diagnostic investigation. At the same time, the longer half-life (66 h) of the parent nuclide provides comfortable access for the daughter nuclide at least for a week. In practical terms, this means that a hospital laboratory can perform around 100 diagnostic investigations with the daughter nuclide by ordering fresh isotope generator every week and by eluting it once a day.

The principal operation scheme of the 99Mo/99mTc isotope generator is demon­strated in Figure 8.4. The two tubes of the chromatographic column end in injection needles for which the elution agent solution and a vacuumed ampoule are attached by piercing. A vacuum will suck the eluent through the column, which desorbs the generated 99mTc daughter nuclide from the column.

The activity versus time functions of the 99Mo parent nuclide decay and of the 99Tc daughter nuclide generation are shown in Figure 8.11. The process leads to transient equilibrium. It should be noted that the daughter activity reaches its maxi­mum at 24 h, which coincides with the hospital practice, e. g., the elution of the generator once a day guarantees the daily maximum activity for the elution.

Figure 8.11 shows that daughter activity theoretically exceeds parent activity at transient equilibrium (dotted line). However, due to the branching decay of 99Mo (the value of branching factor = 0.96), the activity of the 99mTc daughter nuclide

remains systematically below the parent activity (continuous line). So, approximately 90% of the parent activity can be eluted as 99mTc in equilibrium (Figure 8.12). The activity curve corresponding to the hospital practice—daughter elution once a day—is demonstrated in Figure 8.13. 99Mo/99Tc radionuclide generators can be used economically for a week, with daily activities decreasing according to the parent decay.

99m^c

While 99mTc/99Mo generators are used for diagnostic purposes, another important generator (produced by high-flux reactor irradiation) is the 188W/188Re generator, which also serves a diagnostic purpose:

Irradiation: 186W(n, Y)187W(n, y)188W! 188W/188 Regenerator

In the simple isotope dilution method, the quantity of an inactive substance (m) is determined by the addition of a radioactive indicator. The labeled species (stan­dard) of the substance to be analyzed is added to the unknown samples. The quan­tity (m0 + mx) and the specific activity (a0) of the standard are exactly known. The system is homogenized, and the substance in question is selectively isolated as a well-defined compound; then it is purified to the required high level. As mentioned previously, the yield of isolation is unimportant. The specific activity of the com­pound obtained after the dilution (a) is determined.

If the quantity of the radioactive indicator can be disregarded (mx«m0), the quantity of the unknown substance from Eq. (9.30) is:

(a0 1 m = m0 — — 1 a

or is expressed by radioactive intensities:

m = m^-° — 1j (10.2)

Thus, the specific activity or intensity of the labeled substance has to be measured before and after the isotope dilution. The degree of the dilution is determined by the ratio of m to m0. The precision is usually suitable in the range of m = 0.01 X m0 to m0 = 0.01 X m. The simple dilution method is a fairly good option in all cases when the substance to be analyzed cannot be separated quantitatively.

In the case of permanent material thickness, the density of a material is determined on the basis of the principle of radiation absorption (Figure 11.23). For this, the so — called mass-absorption coefficient (p) should be introduced (see Eq. (5.48)), with which:

— = exp(—ppl) (11.28)

І0

The material density measured by radiation absorption can be determined by solving Eq. (11.28) for (p) density. Other members of the equation are identical to the parameters found in Eq. (11.27).

Typical application fields of both thickness and density measurements are paper industry, metal sheet rolling, and plastic foil production as well as measuring and

Figure 11.23 Material density determination based on radiation absorption.

continuous monitoring of the thickness of textiles, glass sheets, and laminated wooden sheets.

Industrial examples for the application of density measuring systems are:

• Density measurement of a streaming medium (such as crude oil, benzin, or petrol) in oil pipelines.

• Monitoring of chemical technology processes by measuring material density.

• Monitoring of efficiency in grinding machines by measuring the density of powder.

• Continuous monitoring of the density of materials transported on conveyors.

The second most frequent type of SPECT study is brain perfusion imaging, for similar reasons as those described at the beginning of the previous section. Although brain SPECT is used to assess several types of abnormalities of cere­bral circulation, an especially difficult task is to investigate epilepsy. The prob­lem is that the patient usually cannot remain still during seizure, so it is hard to take images of any kind. However, the radiopharmaceutical HMPAO (99mTc-D, L-hexamethylene-propyleneamine oxime) reaches an equilibrium distribution in the brain in only 1—2 min after injection, and then the distribution does not change for several hours. So if we succeed in administering HMPAO during sei­zure, we may take images 1—2 h following the seizure, when the patient is able to lie still for 20—30 min. An epileptic focus is hyperperfused during seizure, while it is hypoperfused in an interictal state.

P-32 is widely applied in biological and agricultural research. It is produced by irradiation of red phosphorus with neutrons in 31P(n,^)32P nuclear reaction. The half-life of 32P is 14.3 days, and it emits negative beta particles. By the dissolution of red phosphorus in water, phosphoric acid is formed. Therefore, the oxidation state of phosphorus is +5. When dissolving red phosphorus in hydrochloric acid, chloride and oxychloride are formed, the oxidation state of phosphorus is also 15. A 32P-labeled compound with a +3 oxidation state has not been produced yet. Carrier-free 32P can be produced from sulfur by the 32S(n, p)32P nuclear reaction. 32P can be gained as a H332PO4 solution by water vapor, and sulfur remains back as a solid. Another way to separate 32P is the dissolution of sulfur with an organic solvent (e. g., CS2), which makes the residue react with chlorine gas. The product is PCl5. For additional information, see Section 8.7.1.2.

In this section, some examples of the diffusion of gases in solid media will be shown.

Diffusion of 222Rn in Soil

In porous media, the free volume can well be characterized by the diffusion of a gas that does not adsorb on the interfaces of the pores. For example, the diffusion of 222Rn gas is mentioned. Radon is a noble gas, and it has no interactions with the surrounding medium. Carrier-free ones can easily be produced (see Section 8.5.1) and their activity can be measured through the gamma radiation of its daughter nuclides. The diffusion of 222Rn has been studied in soil components, sand and clay, as porous media. The diffusion is described by the Fick’s laws; in this case, Fick’s second law, applied to linear diffusion, is used:

@C _ D

dt Sx2

where D is the diffusion coefficient (surface area/time), C is the concentration of the diffusing substance, and t is the time. When the concentration of the diffusing substance is measured by a radiotracer, the radioactive intensity (I) depends on the concentration, i. e.:

I _f (C)

Equation (9.32) does not have a general solution—only some solutions for special initial and boundary conditions. For linear diffusion at a constant temperature, a partial solution of Eq. (9.32) can be expressed by Eq. (9.34) when at t = 0, the total quantity of the diffusing substance is at a place x = 0 as a point source:

I = /° exp f—X ) (9.34)

4Dnt 4Dt

The diffusion coefficients can be determined in two ways. I values are measured as a function of time (t) at a given place (x = constant), or as a function of the dis­tance (x) at a given time (t = constant). This solution is frequently called “the para­bolic law of diffusion.” Depending on the method employed, the diffusion coefficients can be determined approximately from the slope of the ln I versus x2 or ln I versus 1/t, respectively. This gives a first-order relation; thus, it is a simple method for the determination of the diffusion coefficient. When, however, x = constant and t changes, a systematic error develops because the time is present in the intercept as well. Nowadays, computer programs are used for the estimation of diffusion coefficient from the original form of Eq. (9.34); in this way, this error can be ignored.

Simple laboratory equipment for the measurement of diffusion is shown in Figure 9.1, and the experimental results are plotted in Figure 9.2.

Figure 9.2 Linear diffusion of 222Rn gas in sand with different humidities. Humidity increases in the order: 1 > 2 > 3.

As seen in Figure 9.2, the volume of the free pores decreases when the humidity of sand increases, resulting in the decrease of migration rate of radon (Figure 9.3). Since the migration rate depends on the pore size, the determined diffusion coeffi­cient is a virtual diffusion coefficient.

Diffusion or migration measurements can be done in situ, under natural condi­tions. In this case, the solution of Eq. (9.32) applied to spatial diffusion has to be used. Under similar initial and boundary conditions as described in Eq. (9.34), the solution for spatial diffusion in an isotropic medium is:

Figure 9.4 Equipment for breaking a glass sphere containing 222Rn gas. (A) electric cable, (B) cap, (C) pushed spring,

(D) thin wire, (E) breaking iron disc, (F) gas outlet, and (G) glass sphere containing radon.

where r is the distance from the point source (considered as the origin of a sphere). In the studies of spatial diffusion, the diffusing gas (222Rn) is located as shown in Figure 9.4.

The spatial diffusion studies give similar results as linear diffusion studies, namely the virtual diffusion coefficient depends on the humidity—i. e., on the free volume of pores. Also, similar results are obtained in clay; however, clay contains less free volume pore space, and the virtual diffusion coefficients are about an order of magnitude smaller.

In Section 10.2.2.4, the principle of the diffraction of waves was discussed in detail. It is not repeated here; only the main differences of the X-ray and neutron diffraction studies are summarized in Table 10.7.

The X-ray diffraction is applied to the structural analysis of crystalline sub­stances. Correct structural analysis can be obtained on monocrystals from small inorganic compounds to complex macromolecules. The study of polycrystals and crystalline powders is frequently used to study the qualitative and semiquantitative analysis of crystalline substances when diffractograms of the unknown samples can be compared to those of standards. A very important application is the study of the mineral composition of rocks. An example is shown in Figure 10.20.