For medical applications (explained in later chapters), we usually need rather short­lived radionuclides that have to be artificially produced because we cannot separate them economically from natural sources. We can produce radioactive materials in the following ways (also see Chapter 8):

• In nuclear reactors, where irradiation channels are formed through the nuclear reactor shield to put the target in the way of high neutron flux. The neutrons induce nuclear transformations.

• The other possibility is to use accelerators, especially cyclotrons, invented by Ernest Lawrence (1901 — 1958) at Berkeley, who was awarded the Nobel Prize in physics in 1939. In 2005, there were about 130 cyclotrons in the European Union, 80% of which were dedicated to routine medical radioisotope production.

• The daughter element of a radionuclide may also be radioactive; this fact is utilized in radioisotope generators (see later in this chapter and Section 8.7.1.4).

From a practical point of view, the most important difference is that radioisotopes produced in nuclear reactors are usually cheaper than cyclotron products. We shall list some other aspects next.

The radioactivity in the hydrosphere also has natural and artificial sources. The most important natural radioactive isotope in the hydrosphere is 40K, which, in the form of a potassium ion, is mostly found dissolved in water. Because of the lower salt concentration, the radioactivity of rivers is much less than that of seawater. For example, the mean radioactivity of the Danube River is 70—90 mBq/dm3, and the activity of seawater is about 10—15 Bq/dm3. Among the artificial radioactive pollu­tions, Sr, Cs, I, and I dissolve well in water, so the natural water mainly contains these artificial isotopes.

Of course, the radioactive isotope of hydrogen, tritium, is also present in natural waters as tritiated water. As mentioned in Section 7.3, tritium is formed in nuclear

power plants in 14N(n,3 4He)T and 14N(n, T)12C reactions. The emission of the nuclear power plants raised the tritium concentration by 1—2 orders of magnitude above the natural level. The tritium activity is generally expressed in tritium units (TUs). One tritium unit means that the ratio of the hydrogen (1H) and tritium (3H) atoms in 1018:1. The radioactivity of 1 TU is 0.1184 Bq/dm3.

The vegetation in water accumulates dissolved radioactive isotopes. The accu­mulation depends on the composition of water and the species present. The humus formed from the decomposition of the vegetation also uptakes the radioactive iso­topes, which in this way transfers to the lithosphere.

Sr-85 is produced by the spallation of molybdenum (natural Mo(p, spallation)85Sr). Its half-life is 65 days, and it disintegrates with electron capture and gamma radiation.

Sr-89 is produced in the 88Sr(n, Y)89Sr nuclear reaction. Its half-life is 50 days, в _-emitter.

Sr-90 is obtained as a fission product. Its half-life is 29 years, в — emitter. Its daughter nuclide is the 90Y isotope, which can be obtained from 90Sr/90Y-genera — tors and used for palliative therapy.

8.6.13 Yttrium-90

Y-90 is the daughter nuclide of Sr-90, so the production has been discussed at strontium isotopes. The industrial production will be shown in Section 8.7.1.1.

8.6.14 Technetium-99m (Tc-99m)

Tc-99m is the most frequently used radioisotope in nuclear medicine. In medical laboratories, Tc-99m is obtained from Mo-99/Tc-99m generators (see Eq. (8.8)). The parent nuclide, Mo-99, is produced as a fission product in the reprocessing of spent fuel elements. For more information, see Section 8.7.1.4.

In this section, the kinetics of a heterogeneous isotope exchange reaction will be shown, the rate-determining step of which is the isotope exchange. As an example, the isotope exchange of potassium ions between blood plasma and red blood cells will be mentioned.

Let us assume that the mass of the potassium ions is mj and m2 in plasma and red blood cells, respectively. Potassium ions are exchanged continuously between the two phases, plasma and red blood cells, reaching steady state. In order to deter­mine the rate of the exchange in steady state, radioactive potassium ions are added to the plasma in such a small quantity that the steady-state exchange is not dis­turbed. The reaction is directed by the increase of the entropy (see Section 9.3.3.1).

The activity of the radioactive potassium ions is I and can be expressed as:

where a01 is the initial (t = 0) specific activity of potassium ions in the plasma. After the addition of radioactive potassium ions to plasma, the radioactive potas­sium ions enter red blood cells as a result of the potassium exchange. After an arbi­trary t amount of time, the radioactivity of the plasma will be Ib and the specific activity of the potassium ions will be a1:

І1 = ma (9-62)

Similarly, for the radioactivity (I2) and the specific activity (a2) of the red blood cells:

І2 = m2a2 (9-63)

Since the system is closed for potassium ions (no potassium ions, including radio­active and inactive, are added later):

I = І1 112 (9-64)

In the time period dt, dm2’1 of potassium ions goes from the plasma to the red blood cells, and simultaneously, dm1’2 of potassium ions goes from the red blood cells to the plasma. As a result, the change of the potassium ions in the red blood cells is:

dm2 = dm2’1 — dm1′

and conversely, the change of the potassium ions in the plasma is:

dm1 = dm1’2 — dm2′ (9-66)

Mathematically, the change of the radioactivity both in the red blood cells and in the plasma can be expressed by the total differential quotient of the radioactivity:

dl2 = m2 da2 1 a2 dm2 (9-67)

dI1 = m1 da1 1 a1 dm1 (9-68)

Also, the change of the radioactivity can be expressed by the transport (Eqs. (9.65) and (9.66)) and the specific activities of potassium ions:

dl2 = a1 dm2’1 — a2 dm’2 (9-69)

dl1 = a2 dm1’2 — a1 dm2’1

By comparing Eqs. (9.67) and (9.69) with Eqs. (9.68) and (9.70), we arrive at the following two equations:

Я1 dm2’1 — «2 dm1’2 = m2 d«2 + a2 dm2 (9-71)

Я2 dm1’2 — «1 dm2’1 = m1 d«1 + «1 dm1 (9-72)

Now, let us study the change of the mass of the potassium ions in a period of time, dt, in the red blood cells:

dm2’1 m2 з d«2

dt Я1 — Я2 dt

and in the plasma:

dm1’2 m1 з d«1

dt Я2 — Я1 dt

As mentioned previously, the system is under steady-state conditions, i. e., the trans­port rate of the (inactive) potassium ions is the same in both directions, from the plasma to the red blood cells and vice versa. Let us denote this transport rate with C:

dm2’i dmi’2 „

— = — = C (9-81)

Using Eqs. (9.79) and (9.80), we obtain:

d^2 = — (a — Я2) (9.82)

dt m2

da^ = — (a2 — ai) (9.83)

dt m1

Since the system is closed for potassium ions (see Eqs. (9.62)—(9.64)), the total radioactivity at any time t is the sum of the radioactivities of the plasma and red blood cells:

I = miai 1 m2«2 (9.84)

Equation (9.84) can also be expressed to mean specific activity (a):

I = m{a 1 m{a (9.85)

From Eqs. (9.84) and (9.85), we get:

m1a1 1 m2a2 = m{a 1 m{a (9.86)

In Eqs. (9.82) and (9.83), there are two variables, a2 and ai, which depend on each other. For the solution of these equations, one of the variables must be eliminated. In order to do this, from Eq. (9.86), the specific activities, a2 and ai, and their differences, ai — a2 and a2 — ai, are expressed:

Then, Eqs. (9.89) and (9.90) are substituted into Eqs. (9.82) and (9.83), thus:

da2 C mi 1 m2

= dt

a — a2 m2 mi

dai C mi 1 m2

= dt

a — ai mi m2

The solution of Eqs. (9.91) and (9.92) is:

— ln(a — Я2) = (—m11 mA 11K (9.93)

m2 m1

-ln(a — *1) = (11K (9.94)

m1 m2

where K and Kare integration constants.

For the calculation of the integration constants K and K, we assume that at t = 0, a2 = a20, and я1 = a10:

K = — ln(a — a20) (9.95)

K = — ln(a — a10) (9.96)

By substituting Eqs. (9.95) and (9.96) into Eqs. (9.93) and (9.94):

The Kinetics of the Change of the Radioactivity in Red Blood Cells (a2) Since at t = 0 and a20 = 0 (radioactive potassium ions were added to the plasma), from Eq. (9.97), we obtain:

a — a2 C m1 1 m2 ln =—■ t

a m2 m1

After equivalent mathematical transformations:

C m1 1 m2

a — a2 = a exp —————— 1

m2 m1

C m1 1 m2

a2 = a — a exp — t

m2 m1

Since at t = 0, a20 = 0, and a1 = a0, from Eq. (9.86):

a0m1 = amj 1 am2

From here:

a (9.103)

m1 1 m2

Substituting Eq. (9.103) into Eq. (9.101), after mathematical transformation, we obtain:

Я0 m1 1 m2 m2 m1

The Kinetics of the Change of Radioactivity in Plasma (aa) As mentioned previ­ously, at t = 0, radioactive potassium ions were added only to the plasma; thus, a10 = a0. Substituting this into Eq. (9.98), we get:

in = _c_mL±m. t (9.105)

a — Я0 m1 m2

Similar to the transformations done previously for red blood cells, the change of radioactivity in the plasma can be expressed as follows:

(m1=m1 1 m2 )a0 — a1 (jm/m1 1 m2) —I

(m,1/m1 1 m2 )a0 — a0 (m1/m1 1 m2)

(m1/m1 1 m2) — (a1 /aQ) C m1 1 m2

(m1=m1 1 m2) — 1 m1 m2

m1 a1 m1 C m1

— = — 1 exp —

m1 1 m2 a0 m1 1 m2 m1

a1 m1 m1 C m1

= — — 1 exp —

a0 m1 1 m2 m1 1 m2 m1

when reaching equilibrium (t! 00), from Eqs. (9.104) and (9.109), we obtain: m1

a1 = a2 = ——- a0 (9.110)

m1 1 m2

This means that the specific activity is the same in the whole system; that is, the mixing entropy reached the absolute maximum.

Of course, this discussion can also be applied to other cases of heterogenous iso­tope exchange systems on the condition that the system has a component that can exchange freely between the phases.

Thus, we conclude that the heterogeneous isotope exchange allows us to study transport processes between phases under equilibrium conditions. Similar to the McKay equation (see Section 9.3.3.1) describing homogeneous isotope exchange, Eqs. (9.104) and (9.109) also show pseudo first-order kinetics, depending on the quantities in the two phases (mj and m2). The rate of the transport (C) can be mea­sured when the isotope exchange is the rate-determining process and the quantities in the two phases (mj and m2) are known. Moreover, it is enough to know only one of the two quantities (m1 and m2) because there are two kinetic equations, one for each phase. Thus, the quantity in the unknown phase also can be calculated. To provide an example of this latter application, we can mention the determination of the quantity of the exchangeable phosphate ions in soils. By the usual analytical methods, the total phosphate quantity present in the soil can be measured; however, only a portion of this phosphate can be dissolved in the soil solution. When the phosphate quantity of the soil solution is measured (it can be considered as m1), and the heterogeneous phosphate exchange between the soil solution and the soil is studied by adding radioactive phosphate to the soil solution, based on the kinetic studies, the quantity of the exchangeable phosphate of soil (m2) and the rate of iso­tope exchange (C) can be determined from Eqs. (9.104) and (9.109). The value of m2 can be calculated from the equilibrium-specific activities too (see Eq. (9.110)).

The heterogeneous isotope exchange clearly illustrates the most important aspects and advantage of the radiotracer methods: systems in thermodynamic equi­librium can be studied without disturbing equilibrium. The rate of processes in equilibrium can be given quantitatively. To do this, the isotope tracer method is the only option.

The rate of the isotope exchange reaction can also be determined at different temperatures. From the obtained values, the binding energy between the atoms par­ticipating in the isotope exchange can be calculated using the Arrhenius equation.

Nowadays, isotope exchange reactions are frequently used to study the rate of biological metabolisms and to determine the binding energy in heterogeneous cata­lytic reactions. In addition, the study of isotope exchange reactions provides useful information in geology (see Section 3.4).

For tracer studies carried out with open radioisotopes, the material or materials to be tested are labeled with a radioactive isotope prior to the investigation. During

Nuclear and Radiochemistry. DOI: http://dx. doi. org/10.1016/B978-0-12-391430-9.00011-1

© 2012 Elsevier Inc. All rights reserved.

the test, radiation of the isotope is detected outside the equipment, which identifies disposition of the labeled material or its rate of distribution among several branches of pipes or equipment. At the same time, intensity of the radioactive tracer is pro­portional to the quantity of the material or its concentration. With suitable calibra­tion, the intensity can be corresponded with the quantitative mass or volume of the material.

Most isotope diagnostic methods for concentration measurement belong to the family of “protein binding assays.” Generally, they have the following main components:

• The specimen from which the concentration of a constituent (L, “ligand,” “analyte,” or “antigen”) is to be measured.

• A substance (e. g., antibody, Ab) specifically binding the ligand (L).

• A tracer, which can be either:

• The labeled version of the ligand (L*, in case of competitive assays) or

• A second, labeled antibody (Ab*, in excess amount) against the ligand to be measured.

• A method to separate the bound and free tracers.

In immunoassays, the specific binding material is a monoclonal or polyclonal antibody. Labeling may use a radioisotope, enzyme, chemiluminescent, or fluores­cent tracer.

Immune binding reactions are greatly influenced by a number of conditions (temperature, reaction times, pH, etc.); therefore, standards with known concentra­tions of the analyte are included in each series of measurements. A calibration curve based on these standards is used to calculate the concentration from the signal measured from an unknown sample.

In practice, various combinations of tracers, labeled components, competitive or sequential reactions, limited or excess amounts of components, and separation methods are used. The basic principles of the two most widespread methods are summarized next.

The light emitted by the scintillator molecules is transferred as electric impulses by a photomultiplier. The main parts of the photomultiplier are the photocathode and the multiplying system (dynodes). In the scintillation detector, the scintillation crys­tal and the photomultiplier are coupled together (Figure 14.6). Very good optical connection is required between the scintillator and the photocathode, which is pro­vided by silicon oil with high viscosity.

The operation of the photomultiplier is as follows. The light emitted by the scintil­lator produces electrons (photo electrons) in the photocathode. The photocathode is usually located onto the inner wall of the input window. It is semipermeable for the input light. Most frequently, antimony or its compounds are used as photocathodes. The antimony is evaporated and deposited onto the inner wall. Then it is treated with alkali metals or little oxygen. The photocathode SbCsO is an example, with the high­est sensitivity at a 440 nm wavelength. This is close to the wavelength of the light emitted by most scintillators (about 400 nm). As mentioned previously, the addition of a secondary scintilator can modify the wavelength of the light if required.

The electrons emitted by the photocathode are transmitted to the dynodes of the multiplying system. The dynodes have an increasingly higher voltage, and the dif­ference between the adjacent dynodes is about 80—150 V; thus, the quantity of the electrons is multiplied from one dinode to another. At the end of the dynode sys­tem, the quantity of the electrons (i. e., the current) is high enough to be detected directly by the usual electronic devices. The sensitivity of the photomultipliers (namely, the signal-to-noise ratio) is very good.

The quantity of the electrons can be multiplied even by a factor of 108. The mul­tiplication factor of the electrons depends on the number, the geometry, and the voltage of the dynodes. Usually, 8—15 dynodes are applied. The multiplication factor is limited by the dark current of the photocathode, which is caused by the spontaneous electron emission of the photocathode. Cooling the photocathode decreases the dark current.

The electric impulse outputs from the photomultiplier are attenuated, discrimi­nated, and registered.

In complex molecules (e. g., in organic compounds), it is important to know the posi­tion of the labeling atom, and in some cases, such a compound has to be synthesized where the labeling atom is in a desired position. In this latter case, the position of the radioactive atom also has to be determined because the chemical reactions initiated by the radiation (Szilard—Chalmers reactions, discussed in Section 6.4) can influence its position.

When the binding energy of the bond between the labeling atom and the neigh­boring atom is relatively low, an exchange reaction can take place between the differently labeled species. For example, when labeling diiodine methane with radioactive iodine isotope (e. g., 131I), three types of molecules are formed:

CH2I2 + CH2131I232CH2I131I (8.9)

The equilibrium constant of the process is:

The equilibrium constant determines the ratio of the differently labeled molecules.

When the binding energy is high, the position of the labeling atom cannot always be changed. For example, in the case of 14C-labeled acetic acid, the carbon atoms of the methyl and carboxyl groups cannot change their positions; therefore, several labeled molecules can be produced. Specifically labeled compounds are synthetized when the labeling atom is at a well-defined position of the molecule. In the case of acetic acid, the radioactive isotope (14C) can be in the methyl group (14CH3COOH) or the carboxyl group (CH314COOH). When every carbon atom is labeled (in acetic acid, this means two labeling 14C isotopes, 14CH314COOH), the molecule is universally labeled. A compound is generally labeled when the labeling atoms are statistically positioned; every labeled atom has the same specific activity, independent of the position in the molecule. In the case of acetic acid, half of the 14C atoms are in the methyl group, the other half are in the carboxyl group, and the substance is the mixture of 14CH3COOH and CH314COOH in 1:1. The different types of specifically labeled compounds can be produced only when the chemical bonds are strong enough. If not, an exchange can take place between the different labeled molecules, which always results in a generally labeled compound.

The preparation of the different types of the labeled compounds demands suitable labeled reagents and synthetic procedures. Generally labeled organic com­pounds can be prepared from 14C-labeled carbon dioxide or acetylene. When acety­lene contains only one labeled carbon atom (14CCH2, discussed in Section 8.6), generally labeled acetaldehyde can be produced by reacting labeled acetylene with water:

14CCH2 1 H2O! 14CH3CHO 1 CH314CHO (8.11)

From the generally labeled acetaldehyde, specifically labeled acetic acid can be produced in the following reactions. At first, acetaldehyde is transformed into methanol and carbon dioxide:

14CH3CHO ! 14CH3OH 1 CO2

CH314CHO ! CH3OH 114CO2 (8.12)

The carbon dioxide is eliminated, so methanol is obtained in which the ratio of the labeled (14CH3OH) and nonlabeled (CH3OH) molecules is 1:1. By carboxylation of methanol with the Grignard reagent in the presence of inactive carbon dioxide,

specifically labeled acetic acid can be obtained, and only the carbon atoms in the methyl groups are labeled (14CH3COOH):

Since half of the methanol molecules are not labeled, half of the acetic acid molecules are also not labeled, and the acetic acid is not carrier-free. The specific activity (radioactivity per mass of carbon) of the acetic acid will be half of the ini­tial, generally labeled acetic acid, since the half of the radioactive carbon atoms was previously lost as 14CO2.

Acetic acid labeled in the carboxyl group can also be prepared. For this, inactive methanol is carboxylated with labeled carbon dioxide (14CO2) in the same reaction (Eq. (8.13)). Universally labeled acetic acid can be synthetized from universally labeled acetylene (14C2H2).

The position of the labeling atom in the organic molecules can be determined by stepwise decomposition reactions. Some possible ways are as follows:

• Schmidt decomposition of carboxylic acids:

(8.14)

• Decarboxylation with copper chromite in boiling kinoline.

• Iodoform reaction, which cuts the bond of the methyl group next CO or CHOH:

R — CHOH — COOH CHI3 1 R—1 (COOH)2 (8.15)

• Oxidation of amino acids with ninhydrin:

ninhydrin

R — CHNH2 — COOH——————- y—— ! R — CHO 1NH3 1 CO2 (8.16)

The position of the labeling atom can be determined by the separation and radio­activity measurements of the products. The side reactions and the isotope exchange in the products, however, may present some difficulties.

The position of the labeling atom also can be determined using biological pro­cesses. For instance, the formation of carboxylic acid from carbohydrates (e. g., malonic acid, citric acid, or tartaric acid) can be mentioned. For example, tartaric acid can be dehydrogenized by tartaric acid dehydrogenase enzyme; the product of the reaction, fumarate, is then oxidized by potassium permanganate. Another possi­bility for determining the position of the labeled atoms in carbohydrates is through their decomposition by acetic acid bacteria, which decompose the carbohydrates to carbon dioxide, acetic acid, and propionic acid. By the separation and activity measurements of the products, the position of the labeled atom can be determined approximately.

Some plants and animals can synthesize labeled compounds. Canna indica can produce generally labeled carbohydrate from 14CO2; pigeons produce uric acid from 14C-labeled nutrients.

The number and position of the labeling atoms must be included in the nomen­clature of the labeled compounds. The International Union of Pure and Applied Chemistry (IUPAC) has recommendations for the formulas and names of the labeled compounds:

The formula of an isotopically substituted compound is written in the usual way except that appropriate nuclides symbols are used. When different isotopes of the same element are present in the same position, common usage is to write their sym­bols in order of increasing mass number.

The name of an isotopically substituted compound is formed by inserting in parentheses the nuclide symbol(s), preceded by any necessary locant(s), letters, and/or numerals, before the name or preferably before the denomination of that part of the compound that is isotopically substituted. Immediately after the paren­theses there is neither space nor hyphen, except that when the name, or a part of a name, includes a preceding locant, a hyphen is inserted. When polysubstitution is possible, the number of atoms substituted is always specified as a right subscript to the atomic symbol(s), even in case of monosubstitution.

Some examples are listed in Table 8.2.

In this group, there are isotope preparations that are made through the (n, p) nuclear reaction, followed by a decay mode causing a change in atomic number, and by the subsequent separation of the product from the irradiated target. Such products do not contain nonradioactive nucleus (carrier atoms), so their specific activity is high.

The I-131 radionuclide (see Table 8.11) can be listed in this group. Its typical production batch activity is around 740 GBq which—due to its high dose rate con­stant—needs thick shielding. Air exhausted from the production hot cell passes

through a charcoal filter impregnated with iodine absorbent. Both the filter and the absorbent material will be handled later as radioactive waste.

In addition to the 131I radioisotope, there is another iodine radioisotope suitable for in vitro investigations; namely, 125I (see Table 8.12) which also has low X-ray and gamma energy. It is produced from Xe gas, and the typical batch size is around 370 GBq. Its low gamma energy does not require high shielding. Air exhausted from the production hot cell passes through a charcoal filter impregnated with iodine absor­bent. (The third important iodine radioisotope, 123I, is a cyclotron product.)

In isotope dilution methods, radioactive isotopes are used as tracers. When diluting with a stable isotope, the specific activity decreases and the mixing entropy increases. Thus, the specific activity is measured before and after dilution; the quantity of the diluting substance is determined by the change of the specific activ­ity, as discussed in Section 9.2. Equations (9.26)—(9.30) are the basic formulas of the isotope dilution methods. In this section, the different isotope dilution methods and their applications will be discussed.

As seen in Eq. (9.30), specific activities provide the required analytical informa­tion, so the quantitative isolation of the studied substance is unnecessary. However, the isolated substance has to be pure (selective isolation) and must have a well — defined stoichiometry. In Eq. (9.30), mass or volume can replace the number of moles, so it is possible to determine these quantities as well. The absolute activity is frequently substituted by radioactive intensity (as discussed in Section 4.1.2). Of course, when we use intensities, we must ensure that the conditions of the measurements stay the same.

Isotope dilution methods are frequently applied to the measurement of the con­centration of substances which otherwise are difficult to analyze, such as the con­centration of a particular lantanoid element in the mixtures of rare earth elements or the concentration of a particular hydrocarbon in mixtures of hydrocarbons. The isotope dilution is suitable to measure the volume of substances in large tanks, such as molten metal in furnaces or mercury in electrolytic cells (see Section 11.2.4), in addition to the volume or flow rate of flowing liquids (blood, river, pipelines, etc.). A very important application of isotope dilution methods is the RIA in nuclear medicine (see Sections 12.2.1 and 12.3.1). The main types of isotope dilution methods will be discussed next.