Medical Physics. Ivan Tanev Ivanov. Thracianuniversity. 2016

Medical Physics. Ivan Tanev Ivanov. ThracianUniversity. 2016

CHAPTER 9. RADIOACTIVITY AND RADIOLOGY METHODS

9.1. Radioactivity. Alpha and beta radioactive decay. Alpha, beta and gamma rays

Radioactivity is the spontaneous ejection of high energy particles (rays, radiation) from the unstable nuclei of certain atoms. It is widely used in modern medicine for diagnosis and therapy. The proper use of radioactive rays for medical needs requires knowledge of their physical nature and mechanism of releasing.

The nuclei (nuclides) of atoms contain nucleons (protons and neutrons) which are linked by specific forces of attraction –forces ofnuclear interaction. At its vicinity each nucleon creates powerful nuclear forces of attracton, however, these forces strongly diminish wth the distance.

In contrast to neutrons, which are electrically neutral particles, the protons have a positive charge, so they repel each other by electrostatic forces. The latter forces are weeker however, they reach larger distances. The total nuclear binding energyof a given nucleus depends on the balance between the nuclear forces of attraction between the nucleons and the electrostatic forces of repulsion between the protons. Hence, it could have greater or lesser value depending on which forces dominate. Consequently, the stability ofa given nucleus depends on the ratio between the number of its protons and the number of its neutrons.

Fig. 9.1.1. Binding energy of nucleons in the nuclei of various isotopes.

The atomic nuclei are characterized by two numbers, the atomic number, Z, and the mass number, A,both of which determine the binding energy and stability of the nucleus. The atomic number, Z, equals the number of protons in the nucleus, which in turn is equal to the number of electrons orbiting around the nucleus. The mass number, A,represents the number of protons plus the number of neutrons in the nucleus. Atoms which have nuclei with the same atomic number, Z,but different mass number, A, are chemically indistinguishable isotopes of the same chemical element. Atoms whose nuclei have different atomic number, but the same mass number are called isobaric and atoms whose nuclei contain the same number of neutrons are called isotonic.

Radioactive nuclei are those which are unstable. What is the origin of this instability?

The nuclei of most atoms have too suitable ratio between the number of its protons and neutrons.By contrast the nuclei of other atoms have too small neutrons in respect to their protons or too many neutrons in respect to their protons. Such nuclei have low nuclear binding energyand are unstable. The unstable nuclei have a limited lifetime and spontaneously pass into a new stable form by releasing high-energy particles, ie, they demonstrate radioactivity. The unstable nuclei are designated as radioactive nuclei, or radionuclides. The transition of the radioactive nucleus from unstable state to a stable state represents a radioactive decay (transformation, disintegration) and according to the type of emitted particles, the decay is of two kinds:

1)  - radioactive decay. It is characteristic for the nuclei of the heavier elements (radium, radon, uranium, etc.). These radionuclides emit -rays (nuclei of helium atoms - two protons plus two neutrons) according to the following decay scheme

AХZ → A-4YZ-2 + 4He2

The symbole X indicates the initial, parent, nuclide and Y indicates the final, daughter, nuclide. The emitted particles have a large mass (four atomic mass units) and electric charge (two positive elementary charges). They are ejected with very high kinetic energy (several MeV), which has one or more discrete values. This means that the energy spectrum of the emitted  -rays is linear.

2)  - radioactive decay. It is characteristic for the radioactive isotopes from all parts of the periodic table. This decay is preceded by a change of a nucleon within the unstable nuclide: a neutron is converted into a proton or vice versa. The reasons for β - radioactive decay are the so called forces of weak interaction.Itcould proceed by the following three ways:

a) electron (-) decay:

AXZ → AYZ+1 + e- +

During this decay a neutron is converted into proton with the release of an electron. Interestingly enough, the energy of released electrons vary continuously from zero to some maximal value, Емах. Based on this unusual continuous energy spectrum of electron rays it was assumed that together with the electron an invisble particle is released which takes away a portion of the decay energy.This hypothesis was later confirmed and the newly discovered particle was called antineutrino, , which is the antiparticle of elementary particle neutrino, .

b) positron (+) decay:

AXZ → AYZ-1 + e+ + 

Here, the parent nuclide emits two elementary particles: positron (e+), which is the anti-particle of the electron, e-, and neutrino,. The mass and the electric charge of the positron, e+, are equal in magnitude to those of e-, but the sign of its charge is positive.

Except the matter, there is also antimatter in the nature. The animatter is made up of so called antiparticles, which are analogous to the corresponding elementary particles of the matter and are produced by certain radioactive decays, nuclear reactions or collision between high-energy particles. Each antiparticle lives until it meets its particle-antipode. On the meeting both particles disapper, annihilate, and two high-energy photons (electromagnetic gamma quants) emerge on their place. In medicine, theannihilation of electrons and positrons, resulting in the appearance of gamma-quant pairs,is used in the positron computer tomography.

c) The -decayalso includes the so called electron capture, when the unstable nucleus captures one electron from the nearest electron shells, the K-shell, L-shells ect. If the captured electron originates from the K-layer the decay is referred to as K-capture. The captured electron "neutralizes" one proton to a neutron resulting in the emittance ofneutrino. On the other hand, the place of the captured electron, called vacancy, is occupied by an electron coming down from the upper orbits and having higher energy. The excess energy is released in the form of Ro-ray photons, which have a linear energy spectrum, characteristic for the type of decaying atoms.

The emitted β-rays represent a stream of e- or e+. The accompanying flows of antineutrino, , or neutrino, , have no medical importance, due to their extremely weak interaction with the atoms and molecules.

During thedecaytransition,theunstable parent nucleustransforms into a stable daughter nucleus. However, some tiny portion of excess energy remains in the daughter nucleus. Therefore, the newly formed daughter nucleus is initially in an excited state, occupying discrete energylevels above the stable ground level. To descend to the stable ground state the excited daughter nucleus emits gamma rays. Gamma rays are electromagnetic quanta (photons) with energy larger than that of X-ray photons. They have no electrical charge and mass at rest and travel at the speed of light. Because the gamma rays are emitted when the excited daughter nucleus descends between two quantized energy levels, they have discreet energy, ie, the energy spectrum of gamma rays is linear.

Most often, gamma-radiation is emitted immediately after the formation of the daughter nuclei. In this case, the gamma radiation accompanies the-, and -radioactive decay of unstable nuclei. This is undesirable in the medical application of radioisotopes, as it makes the radioisotopes more harmful to the patient. In some cases the entire quantity of the radioisotopedecays in a short time, and the resulting daughter nuclei remain in the excited state for years. Such an excited state with very long lifetime is called a metastable state and the transition into such state is called isomeric transition. It is clear that after a certain interval of time these daughter nuclei will emit gamma rays only. In medicine, such metastable radionuclides are preferred over conventional radionuclides which emit mixed (-gamma) or (-gamma) radiation because the gamma rays are much less harmful than  and -rays. In medicine the most frequently used radionuclide of this kind is the metastable technetium 99Tc (99mTc).

The mass spectrometer is a device for detecting different isotopes in a sample by comparing the mass of its atoms. The sample is firstly evaporated (atomized) and a flow of high energy electrons is passed through the vapour to fully ionize the atoms. The obtained ions (bare atomic nulei) are accelerated by the electric field of a positively charged electrode and are passed through a thin slit to form a narrow beam of parallel-moving ions. Finally, the ion beam is deviated by a strong electric field and fall onto a photographic plate. Ions having the same mass and charge fallalong the same line (the image of the slit) on the plate. Ions of the same element with the same charge but different mass will form several closely spaced lines, each corresponding to a different isotope of this element. Thus, the plate will contain several groups of lines, each group corresponding to a given element and its isotopes. The intensity of each line will correspond to the concentration of its corresponding isotope in the sample. By substituting the photographic plate with a photomultiplier, the sensitivity of the mass spectrometer is increased, and even multiple separate single atoms can be detected. The mass spectrometer is used to identify the isotopic composition of the different samples and a molecular formula of the compounds.

9.2. Activity and half-life of a radioactive source. Physical basis of the radionuclide diagnostics

Unstable nuclei of atoms undergo radioactive decay with emition of α-, β- and γ-rays. In medicine, the radioactive source means a body, which contains atoms with radioactive nuclei - radionuclides.

Let ΔN denotes the number of nuclides in the radioactive source that have decayed over the time interval, Δt. The ratio ΔN/Δt = A defines the activity of the radioactive source, ie, it represents the average number of decayed nuclei per unit time. The radioactive decay of individual nuclides is a random and spontaneous event which is independent of any external conditions (temperature, pressure, etc.). Let λ indicates the probability that a given radioactive nucleus will decay over a unit time interval. This quantity depends only on the type of the unstable nucleus, thus it is also called aradioactivedecay constant.

The activity, A, of a given radioactive source is proportional to the total number, N, of radioactive nuclei in the source and to the probability, λ, for individual decay, ie, A = ΔN/Δt = λ.N. The solution of this differential equation indicates how N will decrease with the time, t: N = No. exp (-λ.t). Similar equation describes the decrease of radioactivity of the source with the time: A = Ao. exp (-λ.t). Here No and Ao represent the initial number of unstable atoms and the initial activity of the source. The above equations express the law of radioactive decay, which states that the activity of a radioactive source decreases exponentially with the time.

The radioactive decay law is illustrated in Fig. 9.2.1 where the decay rates of two different radioactive sources with different decay constants,λ1λ2, are compared. It can be seen that the greater is the decay constant the higher will be the decay rate. Furthermore, the activity never becomes zero, but after a sufficiently long time it becomes less than a givenaffordable limit.

An important parameter for each radionuclide is the half-life, T1/2, which is defined by the time at which the number of unstable atoms, respectively, the activity of the source, it reduced by half. Fig.9.2.1 shows that sources with greaterλ, will have smaller T1/2. The exact relationship is T1/2 = 0.69/λ. Concequently, the radioactive decay law can be writenin the following form: A = Ao. exp (- 0.69.t /T1/2).Fig. 9.2.2 indicates how the half-life times, T1/2, of various isotopes depend on the proton / neutron ratio of nucleons in the nucleus.

Radioactive diagnosis is a branch of medicine which uses radioactive tracer atoms. The traceratom is a radioactive isotope (P, C, O,ect) which replaces a stable chemical element in a compound. The radiolabeled compound could be tracked through one or more reactions orpaths by means of a radiation detector. The radiolabeled compound (nutrient, drug, hormone,aminoacid, ect) is called radiopharmaceutical when it is introduced into the body for the study of compound's metabolism, distribution, and passage through the human body.The chemical compound, containing radioactive isotope do not differ in its chemical behavior from the same compound containing a stable isotope of the same chemical element. So, by virtue of itsradioactivitythe tracer can be used to explore the mechanism of biochemical reactions and physiological pathways by tracing the transfer of the radioisotope from the initial reactants to the final products.

Fig. 9. 2. 1. Time dependence of the activity of two radioactive sources with different constants of radioactive decay.

The radioactive tracer atoms can be separated from the stable isotope or obtained by suitable nuclear reactions. The most frequently used nuclear reaction is thecaptureof low energy (thermal) neutrons by the nuclei of a stable isotope, yielding an unstable isotope.The radiopharmaceuticals are usually labeled with metastable Technetium-99m (99mTc), which is aγ-emitter with a half-life of 6 hours.

The location and concentration of radiopharmaceuticals in a body can be determined measuring the radioactive radiation of their tracer atoms. The emitted radioactive rays are detected by means of suitable radioactive detectors - particle counters, ionization chambers, scintillation detectors, ect. These detectors are very sensitive instruments capable of detecting traces of radioactivity, which allows use harmless amounts of radiopharmaceuticals.

In biochemistry and physiology, radiopharmaceuticals are used to elucidate the metabolic pathways for degradation of a compound and the use of its parts in the synthesis of other compounds. Also, one can trace the biological mechanism by which the radiopharmaceutical is taken up, processed and removedby an organism, tissue or cell. The biological mechanism for the removal of a substance is characterized by its biological half-life, Tb. During the removal of a given radiopharmaseutical, its radioactivity within the bioorganism will decrease due to both its removal and radioactive decay. In such a case, the effective period, Teff,for thehalf decrease in radioactivity is shorter and is given by the expression

1/Teff = 1/Tb + 1/T1/2

The radiopharmaceuticals are used for diagnosis of pathological tissue or for radiation therapy of tumors. The following diagnostic techniques are most frequently applied:

1. In the functional radiodiagnosis, the radiopharmaseutical is introduced into the organism by inhalation, orally or through injection into the blood. Next, the times for its accumulation, retention and removal from the body are measured. For example, 53J131 (γ-radioactive iodine with half-life of eight days) preferentially concentrates in the thyroid gland, providing a measure of its function. Other suitable radiopharmaceuticals are 15P32 (beta radioactive phosphorus) which accumulates in the bone marrow of hollow bones and Tl201 (gamma radioactive thallium), which accumulates in the myocardium. In case of pathology the times for the accumulation and retention of tracer atoms in the tested organ are different in respect to norm. In this examination, the detector of radioactivity (scintillation probe) is placed close to the skin against the tested organ and its readings are recorded over time. This method is also known as dynamic autoradiography.

This method allows the admission and accumulation of iron in some human organs (heart, liver and bone marrow) to be examined. A standard quantity of a radioactive isotope of iron is introduced in the patient, and a few days later the growth of radioactivity in the respective organ is non-ivasively measured by a proper radiometer.

Fig. 9. 2. 2. Half-life time (T1/2) of various isotopes with Z protons and N neutrons.

2. Localization diagnostics (scintigraphy) uses a highly collimated detector of radioactivity to measure the equilibrium distribution of a radiopharmaceutical in the tested organ or in the whole body of patient. Important examples are the distribution of radioiodine (53J131) in the follicles of the thyroid gland or in kidney, the distribution of 201Tl (radioactive thallium) in the myocardium. After reaching the equilibrium distribution of the tracer atoms, the radioactivity detector (linear scanner) is moved consistently in parallel linesforming a rectangle over the examined organ. Along with the detectorthe recording device is also moved depicting the two-dimensional distribution of radioactivity (scintigram).

A similar result can be obtained with gamma camera, which has the important advantage to obtain the result without using a mechanical system for scanning of the examined surface. The gamma camera uses computer processing of the data instead of mechanical scanning. It has another advantage as the computer processing allows the change in radioactivity at each point to be traced over time, which is in fact a functional examination of the organ.

To establish pernicious anemia the patient is given food containing radioactively labeled vitamin B12 and the radioactivity of the liver is measured. If the radioactivity is not growing at sufficient rate, a conclusion could be drawn that the intestines cannot properly absorb vitamin B12and the patient has pernicious anemia.

3. The tracer atoms found diverse applications in a variety of radioimmunoassay methods. Radioimunoassay is used to directly and accurately measure the traces of biologically active substances in the blood - antigens and antibodies, enzymes, hormones, amino acids, markers for pregnancy, allergens, drugs, markers of various diseases, including cancer. For example, one can use a solution of antigen labeled with a suitable radioisotope, e.g. J125. After mixing this solution with the blood plasma of the patient the antigen becomes bound to the antibodies of the plasma. The produced complexes of antigen-antibody are next isolated, for example by precipitation or centifugation, and the radioactivity of the obtained product measured. Other methods use antibodies, labeled with a radioisotope,and the binding of these antibodies to an allergen is measured radiometrically. The radioimunoassay methods are very sensitive because they combine the high specificity of antigen-antibody reaction with the high sensitivity of the radioactivity measurements.