Ga-67 is produced in cyclotrons (Eq. (8.26)).

Ga-68 can be obtained by reprocessing of spent fuel elements since it is a fission product.

Ge-68 is used in Ge-68/Ga-68 generators. The complexes of Ga-68 have medical applications.

8.6.11 Arsenic-76 (As-76)

As-76 is produced by the 75As(n, Y)76As nuclear reaction. When an organic arsenic compound is irradiated, an inorganic radioactive arsenic isotope is obtained as a result of the Szilard—Chalmers reaction. The inorganic arsenic can be separated by chemical procedures, so As-76 is carrier free.

The self-diffusion of water was studied using D, T, and 18O isotopes as tracers. The results of these experiments showed that the identity of the tracer hardly influ­ences the self-diffusion coefficient, which is about 2 X 10_5 cm2/s. The activation energy of the self-diffusion of water is 18 kJ/mol. In electrolytes, the self-diffusion coefficient of water slightly depends on the electrolyte concentration. The carrier — free isotopes diffuse via the self-diffusion of water molecules (see Section 9.3).

The irradiation with charged particles always means irradiation with positively charged particles ranging from protons to heavier nuclei. The most important inter­actions of the positively charged particles are similar to the interactions of the alpha particles with matter (see Table 5.2). For analytical purposes, protons are

% weight

used most frequently. In some cases, alpha particles are also applied. For example, in Rutherford spectroscopy, an example of which was presented in Section 5.2.2, the scattering of alpha particles from the nuclear field is used to obtain information on the sample.

Besides the interaction with the nuclear field, the interaction with the orbital electrons and the nucleus can be used in the analysis. The positively charged parti­cles, similar to X-ray and gamma photons, or electrons, can eject electrons from the K or L orbitals, providing qualitative and quantitative analytical tools. This ana­lytical method is particle-induced X-ray emission (PIXE; see Section 10.2.5.1).

The nuclear reactions of charged particles can be used for analytical purposes in the same way as NAA. The method is called “CPAA” or “charged particle-induced nuclear reaction analysis (CPINRA).” In addition, the prompt gamma photons of the nuclear reactions with charge particles can be measured in particle-induced gamma emission (PIGE; see Section 10.2.5.2).

Gamma radiation belongs to the family of electromagnetic waves. We utilize elec­tromagnetic waves of different energies (i. e., frequencies) every day, as shown in Figure 12.2.

The quantum of any kind of electromagnetic radiation is called a “photon.” Photons have both wave and particle properties (“wave—particle duality”). Photons

Figure 12.2 The electromagnetic spectrum and interactions with body tissue.

show wave-like phenomena, such as refraction by a lens, and destructive interfer­ence when reflected waves cancel each other out. On the other hand, it is regarded as a particle with zero rest mass and charge, unit spin, and energy equal to the product of the frequency of the radiation and the Planck constant.

Radiation is observed via the changes in matter interacting with radiation (Chapter 5). During the detection of radiation, ionization is the most important process. The ionization of matter causes changes in the electric properties. Some of the main detector types (gas-filled and semiconductor detectors) utilize the ioni­zation triggered by radiation. Scintillation of certain substances on the effect of radiation is another characteristic that is frequently used to detect radiation (scintil­lation detectors).

The chemical changes initiated by ionization provide another possibility to detect and measure radiation (autoradiography, chemical dosimeters, etc.). The thermal effects of the radiation, as well as nuclear reactions (e. g., detection of neu­trons), also can be used to detect radiation.

The instruments of radiation detection usually consist of two main parts: the detector and the signal-processing unit. In this textbook, detectors are discussed in detail; the signal-processing units are mentioned as needed in order to understand the operation of the detector and the mechanism of signal formation.

When we talk about detection and measurement of radiation, it includes deter­mining the type, the energy, or the energy distribution of the emitted particle or electromagnetic radiation, as well as the different decay rates (activity or intensity). The type of the particle or electromagnetic radiation and the energy gives informa­tion on the radioactive isotope that emitted the radiation (qualitative analysis). The activity or intensity (see Section 4.1.2) gives the number of radioactive nuclides (quantitative analysis). The detectors are characterized based on the following properties:

• The type (or the energy) of the particles, which can be detected by the detector.

• Dead time: the time needed to detect a novel particle after detecting the previous one. Shorter dead time is better. When the dead time is long, the measured activities or intensities have to be corrected; the correction, however, is the source of uncertainty. The dead time determines the maximum activity or intensity, which can be measured by a detector.

• The signal-to-noise ratio should be optimal. The increase of the sensitivity usually increases the noise too.

• The amplitude of the signals in the detector may be proportional to the energy of the particles or electromagnetic radiation or not. This factor determines whether the

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© 2012 Elsevier Inc. All rights reserved.

energy of the particles can be measured, i. e., qualitative analysis can be done or not. The amplitude of the signal is proportional to the energy only in the case of some detector types. Other types of detectors produce signals independent of the energy of the radiation. This, however, can be advantageous for situations such as dose measurement.

• The signals should be easily treatable by the signal-processing unit. In the case of the most important detector types (gas-filled tubes, scintillation counters, and semiconductor detectors), this is usually not a problem because in all these detectors, electric impulses are formed under the effect of the radiation, which can be amplified and discriminated easily. The signals with different amplitudes belong to well-determined energies and can be discriminated by using the so-called channels. The number of channels defines how many different groups can be divided from the signals with different amplitudes. When all signals are equal or the total activity has to be measured (no qualitative analysis is needed), the signals are not discriminated and a one-channel analyzer is applied. In the case of the particles or electromagnetic radiations with energy that is not uniform, the detector produces signals with different amplitudes, where the number of channels can be up to several thousand. The increase in the channel numbers obviously makes the instruments more complicated and expensive. Thus, the detectors and the signal­processing units must be constructed in accordance.

• When the detector is able to produce signals with different amplitudes, the resolution is an important property of the detector. The resolution indicates the distance of two signals (energy of radiation), which can be separated from each other. Of course, the high resolu­tion of a detector is useful only when the number of the channels in the signal-processing unit is high enough.

• The resolution is significantly affected by the half-width of the signals (Figure 14.1). The half-width is composed from the natural width of the spectrum lines (Eq. (5.98)) and the interactions of radiation with the matter in the detector.

• The efficiency of the detector indicates the ratio of the particles or photons that are detected.

Since detectors score differently in each of the above categories, the detector has to be chosen carefully and adapted to the given task. In the next sections, the most important types of radiation detectors will be discussed.

Isotope production technologies developed on the principles discussed in Section 8.5.2 consists of the following typical steps: IAEA TECDOC-1341 (2003) and IAEA Technical Reports Series No.63 (1966).

1. selection of the optimal physical and chemical form, as well as the isotope abundance of the target,

2. calculation of the irradiation time and selection of the irradiation parameters,

3. selection of a research reactor or a cyclotron for the irradiation,

4. cooling of the short-lived contamination isotopes,

5. opening and dissolution of the irradiated target,

6. separation of the target radionuclide from the contaminating radionuclides (if necessary),

7. chemical processing of the target, developing the necessary chemical form,

8. purification of the product (if necessary),

9. adjustment of the radioactive concentration of the product,

10. dispensing and sterilization of the product (the latter for radiopharmaceuticals only).

Of course, not all these steps are necessary for each production technology; the actual details of the procedure are determined by the product being sought.

The dissolution of the target generally requires the use of a strong acid or alka­line. However, such an aggressive chemical medium is often not desired in the final formulation; so to eliminate the acid or alkaline, a frequently used method is dry evaporation of the solution. Dry evaporation and the following dissolution of the

dry residue in an arbitrary liquid composition (e. g., buffer or isotonic solution) are simple, and they allow adjustment of the chemical form of the product as required.

10.1.1 The Measurement of Concentration Using Natural Radioactive Isotopes

The quantity of an element present in the same sample can be determined if the rel­ative abundance of its isotopes is constant, and among these isotopes, there is at least one natural radioactive isotope with a long half-life. Such elements are potas­sium, rubidium, samarium, lutetium, rhenium, and uranium. In these concentration measurements, the activity of the radioactive isotopes is measured. When we know the relative abundance of the radioactive isotopes, the quantity of the element that is present can be calculated from Eq. (4.12), taking into account the relative abun­dance of the radioactive isotopes.

As an example, the data required for the quantitative measurement of lutetium is illustrated in Table 10.1. The 176Lu isotope, which is in the natural lutetium in 2.59%, is used for the measurements. As calculated from the data in Table 10.1, 10 4 mol of lutetium provide about 100 dpm of activity. This activity can be mea­sured easily by a 4n-counter (as described in Section 14.6). If other types of nuclear detectors are used, the measuring efficiency has to be included in the correction. Unfortunately, the half-lives of these very long-lived radioactive isotopes are fre­quently determined with a relatively high number of errors; thus, the quantitative measurements may have a high level of uncertainty.

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© 2012 Elsevier Inc. All rights reserved.

Table 10.1 The Data Required for the Quantitative Measurement of Lutetium Using

the 176Lu Isotope

Mass Number Relative Abundance (%) Half-life (min) Decay Constant (1/min)

175 94.71 Stable

176 2.59 2.02 X 10116 3.42 X 10“17

Flow parameters of substances processed in continuously operated chemical indus­trial systems are very important factors that influence chemical yield and product quality because the residence time of the substance in the system determines the contact time for reaction partners (namely, it defines the time of a chemical reaction).

If the residence time of a substance in an equipment is shorter than required, the chemical reaction will not be fully complete, but if it is unnecessarily long, the equipment efficiency will decrease. In addition to the length of time, there is the question of whether the full substance volume is involved in the entire reaction or only a part of it. This latter option may be due to dead spaces that have been formed with stagnating substances in the equipment, which also helps determine the efficiency.

A possible way to determine the important parameters of the chemical engineer­ing behavior of equipment and substances is to investigate and evaluate the mate­rial flow characteristics in an equipment or system. Material flows can be well studied by means of the radioisotope tracer technique using outer detectors. For such studies, a radioactive tracer is instantaneously injected into the inlet stream, and detector(s) are installed outside the system at the outlet stream. Detectors con­tinuously measure radioactive concentration of the tracer as count/time and plot the count rate versus time function. For obtaining chemical engineering parameters, these plots are evaluated.

Basic models of flow types are shown in Figure 11.9.

By quantitative evaluation of plots obtained from a radiotracer test, the follow­ing chemical engineering parameters can be determined:

• Average residence time of the substance.

• Extension of dead spaces.

In addition to quantitative parameters, the shape of plots provides important information on the character and deformation of flows.

The theoretical (designed) and actual (measured) residence time of a substance are determined on the basis of the following formulas:

V ml Qml/s

N

t, c(t)dt

Jo______

* N

c(t)dt

o where c(t) is the radioactive concentration. ml/s (milliliter/second) is the measuring unit.

The residence time of the substance in a chemical reactor corresponds to the reaction time for the chemical reaction. Optimally, the residence time is identical to the chemical reaction time. When designing continuously operated chemical reactors, the volume of the vessel and the flow rate of the substance passing
through the vessel are matched to the optimal residence time. The radioactive tracer test reveals if the experimentally measured residence time corresponds to the theo­retically designed residence time or not.

The theoretical residence time refers to the total volume of a vessel, while the experimental residence time obtained from the radiotracer test gives the active vol­ume of the vessel in which the material flow really takes place. The remaining space (difference of the theoretical and experimental) is the dead space where the material is stagnating, meaning that this material does not participate in the chemical reaction.

Vholtter = Velm — Veff (11-20)

Vholtter = Velm — ^ki’sS (11-21)

If there are dead space(s) in a vessel, average residence time becomes shorter and reaction volume and reaction efficiency will decrease.

Count rate versus time plots obtained from different measurements that used dif­ferent tracer activities can be compared to each other by converting them to stan­dard plots independent of the applied activity. This is performed by dividing each point (count rate) of the plot by the integrated count rate, i. e., the area under the curve on the plot.

This so-called density function (DE(t)) gives the relative frequency of the sub­stance portion, leaving the chemical reactor between t and the t + dt time interval. If values of the density function are integrated between 0 and t time-point, the so-called distribution function (DI(t)) is obtained, which represents the relative frequency of the occurrence of portions belonging to less than t time intervals. By combining the values of the density function and the distribution function, the so-called intensity function (I(t)) is obtained, which highlights flow irregularities (Figure 11.10). If an intensity function descends monotonously or has a maximum, these reflect a stagnating substance. In the case of ideal mixing or plug type flow, the intensity function is monotonously ascending.

From the shape of density, distribution, and intensity functions, the type of flow and flow irregularities can be concluded. On one hand, it can be determined if the flow pattern corresponds to the designed one or not (e. g., the tested flow is of plug or mixing type); on the other hand, it can be determined if deviation from the ideal flow pattern is significant or not and whether there are significant irregulaties in the flow pattern or not (Figure 11.11).

The plug flow characterizes chemical reactors where mixing of the substance portions representing different residence times is not needed. A simple physical example of this type of flow is the motion of heated water in a boiler passing through a drum without mixing with the entering cold water. However, there are several chemical reactors that operate on the principle of plug flow where reaction partners are introduced continuously into the reactor and only components repre­senting the same residence time are required to contact, and mixing with those portions entering or leaving the reactor earlier or later is not needed.

Figure 11.11 Ideal flows (plug flow and mixed flow) and a practical case.

Contrary to this flow pattern, mixing-type chemical reactors ensure intensive mixing among substances of various residence times, e. g., entering and leaving the reactor in various timepoints. A typical example of this is the so-called equalization basin, which collects wastewater from various chemical plants with the aim of ega — lizing concentration peaks and fluctuations of various wastewaters by mixing and dilution.

None of these ideal flow types exists in pure form in practice. The actual flow pattern is always a combination of plug flow and mixing-type flow. It is important to know which type of theoretical flow pattern resembles the measured quantity and to what extent. To determine this, flow models are developed that provide quantitative parameters for expressing the extent of adequacy to one or the other basic flow type. In such models, compartments of ideal type flow are combined until an adequate description of the actual flow pattern is found.

The cascade model is built from n number of mixed tanks with identical volumes, connected to each other in series. In chemical engineering, by connecting an infinite number of mixed tanks in series, a plug flow pattern is obtained. When fitting a cascade model to the actual plot obtained for the measured system, the question is how many mixed tanks are necessary to connect in series to obtain a density function that fits well with the actual measured plot.

Figure 11.12 demonstrates density functions corresponding to cases when con­necting mixed tanks of n = 1, n = 2, n = 3, n = 4, n = 5, n = 6, n = 7 numbers. It is seen that as the number of mixed tanks connected in series increases, the density function gets closer and closer to the density function describing a plug type flow. NB: residence time of the moving substance is identical for each case.

The cascade model is based on mixed type flow compartments and quantita­tively gives the extent of deviation from the ideally mixed flow pattern with an increasing number of cascades (e. g., the number of mixed tanks). The higher the n number of tanks, the greater the deviation of the actual flow from the ideally mixed flow pattern. The cascade model is applied for equipment designed for mixed type flow (Figure 11.12).

The density function of the cascade model is found as follows:

where D is the dispersion coefficient and D/uL is the inverse of the Peclet number.

Mixed models combine the number, size, and connection way of plug flow and mixed tank units. As an example, one plug flow unit is connected to one mixed tank unit in a series in Figure 11.14. More complicated models can also be con­structed where the number, size, and method of connection (in series or parallel) of the units are varied until the density function of the theoretical model fits best to the plot measured with the radiotracer technique.

Deviation from ideal flow models can predict the types and effectiveness of the processes as well as expected quality of the material produced in the equipment.

In the case of serious deviations, the shape of the plots gained from the radio­tracer test itself refers to flow disturbances. Such serious flow disturbances are shown in Figure 11.15, demonstrating (a) plug type flow as designed with higher residence time than expected, (b) three channels formed within one flow, and (c) two channels within one flow.

Radiotracer investigations of such flow tests are justified partly by their simple technical implementation, partly because they do not require previous calibrations,

and partly because of significant information can be obtained about the efficiency of chemical reactors and expected product quality.

To cite a practical example, a chemical factory operates a mixed tank type basin for equalizing wastewater effluents originating from several plants. Flow tests car­ried out with the radiotracer technique resulted a much shorter residence time than calculated and test plots indicated a multichannel type flow. This test revealed that due to gradual sludge deposition, wastewater flows through several channels with­out the intended intensive mixing and dilution. A consequence of the radiotracer test was dredging and repeating the test.

Further industrial examples for the qualification of material flows include:

• Flow testing of the slurry in autoclaves digesting bauxite in an alumina factory.

• Measuring whitening reaction (residence) time of cellulose fibers in the pulp industry.

• Mixing of the benzine and gasoline fractions during flow in an oil pipeline.

• Mixing of the cold and warm water in electric boilers during flow.

• Testing the flow of melt in a bath furnace of a plate glass factory.

For instance, quantitative comparison of the activity uptake of left and right organs or lobes is possible. Figure 12.5 demonstrates how we measure relative kidney function.

12.4.4.2 Information Extraction

A dynamic image series may contain a huge amount of information. During a hepa­tobiliary study, for example, 110—120 images are typically taken, each represented by a 128 X 128 matrix—a matter of nearly 2 million numbers that is impossible to analyze entirely by the human eyes. We need computers to extract useful infor­mation from the raw data that can be related to the function of the investigated organ. Figure 12.6 demonstrates the possible solutions:

• By drawing the contours of the organs (ROI = “region of interest”), time—activity curves from the counts inside these regions are generated, and some parameters are calculated from them.

• Alternatively, we may calculate a parameter from the time—activity curve of each pixel, reinsert its value to the respective element of a matrix, and display the resulting “parametric image” as a pseudocolor image.

The two methods can also be combined: parametric images may help with outlining the appropriate regions.

Figure 12.5 Split renal function calculated from the geometric mean of the posterior (PA) and anterior (AP) images (left: 14%, right: 86%).

Parametric images

Figure 12.6 Methods for processing a dynamic image series. (Images of the kidneys are shown.)

12.4.4.3 Archiving

Traditionally, X-ray films were used to display and archive medical images; however, this method is rather expensive. Nowadays, it is cheaper by two orders of magnitude to archive the image series of nuclear medicine on CD or DVD.

The radiation detectors mentioned previously detect radiation by physical and chemical interaction with the substance of the detector. Neutrons, however, have only scattering interactions and initiate nuclear reactions with the nuclei; thus, the detection of the neutrons is problematic and have only a small amount of efficiency.

The nuclear reactions can be used for the detection and measurement of neu­trons. Two nuclear reactions are mentioned: 10B(n, a)7Li and 6Li(n, a)3H. Boron and lithium are present in the form of boron trifluoride or lithium glass, respectively. In both cases, the emitted alpha particles are detected. The intensity of the alpha radia­tion is proportional to the number of absorbed neutrons. BF3 gas is placed into a proportional counter, i. e., a gas-filled tube is used to detect the alpha particles. In the case of Li-glass, its scintillation property is used up in the detection.

The neutrons are detected by an LiF + ZnS combined detector. In the 6Li (n, a)3H nuclear reactions, two charged particles (the alpha particle and the tritium nucleus) are formed, inducing scintillation of zinc sulfide.