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2. 2. Activity • The quantity of radioactive material, expressed as the number of radioactive atoms undergoing nuclear transformation per unit time, is called activity (A) • Traditionally expressed in units of curies (Ci), where 1 Ci = 3.70 x 1010 disintegrations per second (dps) • The SI unit is the becquerel (Bq) – 1 mCi = 37 MBq
3. 3. Decay Constant • Number of atoms decaying per unit time is proportional to the number of unstable atoms • Constant of proportionality is the decay constant (λ) -dN/dt = λ N A = λ N
4. 4. Physical Half-Life • Useful parameter related to the decay constant; defined as the time required for the number of radioactive atoms in a sample to decrease by one half λ = ln 2/Tp1/2 = 0.693/Tp1/2 • Physical half-life and decay constant are inversely related and unique for each radionuclide
5. 5. Fundamental Decay Equation Nt = N0e-λt or At = A0e-λt where: Nt = number of radioactive atoms at time t At = activity at time t N0 = initial number of radioactive atoms A0 = initial activity e = base of natural logarithm = 2.71828… λ = decay constant = ln 2/Tp1/2 = 0.693/Tp1/2 t = time
6. 6. Nuclear Transformation • When the atomic nucleus undergoes spontaneous transformation, called radioactive decay, radiation is emitted – If the daughter nucleus is stable, this spontaneous transformation ends – If the daughter is unstable, the process continues until a stable nuclide is reached • Most radionuclides decay in one or more of the following ways: (a) alpha decay, (b) beta-minus emission, (c) beta-plus (positron) emission, (d) electron capture, or (e) isomeric transition.
7. 7. Alpha Decay • Alpha (α) decay is the spontaneous emission of an alpha particle (identical to a helium nucleus) from the nucleus • Typically occurs with heavy nuclides (A > 150) and is often followed by gamma and characteristic x-ray emission energyntransitioHeYX 24 2 4A 2Z A Z ++→ +− −
8. 8. Beta-Minus (Negatron) Decay • Beta-minus (β- ) decay characteristically occurs with radionuclides that have an excess number of neutrons compared with the number of protons (i.e., high N/Z ratio) • Any excess energy in the nucleus after beta decay is emitted as gamma rays, internal conversion electrons or other associated radiations energyβYX -A 1Z A Z +++→ + ν
9. 9. Beta-Plus Decay (Positron Emission) • Beta-plus (β+ ) decay characteristically occurs with radionuclides that are “neutron poor” (i.e., low N/Z ratio) • Eventual fate of positron is to annihilate with its antiparticle (an electron), yielding two 511-keV photons emitted in opposite directions energyβYX A 1-Z A Z +++→ + ν
10. 10. Electron Capture Decay • Alternative to positron decay for neutron-deficient radionuclides • Nucleus captures an orbital (usually K- or L-shell) electron • Electron capture radionuclides used in medical imaging decay to atoms in excited states that subsequently emit detectable gamma rays energyYeX A 1-Z -A Z ++→+ ν
11. 11. Isomeric Transition • During radioactive decay, a daughter may be formed in an excited state • Gamma rays are emitted as the daughter nucleus transitions from the excited state to a lower-energy state • Some excited states may have a half-lives ranging up to more than 600 years energyXX A Z Am Z +→
12. 12. Decay Schemes • Each radionuclide’s decay process is a unique characteristic of that radionuclide • Majority of pertinent information about the decay process and its associated radiation can be summarized in a line diagram called a decay scheme • Decay schemes identify the parent, daughter, mode of decay, intermediate excited states, energy levels, radiation emissions, and sometimes physical half-life
13. 13. Generalized Decay Scheme
14. 14. Radionuclide Production • All radionuclides commonly administered to patients in nuclear medicine are artificially produced • Most are produced by cyclotrons, nuclear reactors, or radionuclide generators
15. 15. Cyclotrons • Cyclotrons produce radionuclides by bombarding stable nuclei with high-energy charged particles • Most cyclotron-produced radionuclides are neutron poor and therefore decay by positron emission or electron capture • Specialized hospital-based cyclotrons have been developed to produce positron-emitting radionuclides for positron emission tomography (PET) – Usually located near the PET imager because of short half-lives of the radionuclides produced
16. 16. Nuclear Reactors • Specialized nuclear reactors used to produce clinically useful radionuclides from fission products or neutron activation of stable target material • Uranium-235 fission products can be chemically separated from other fission products with essentially no stable isotopes (carrier) of the radionuclide present • Concentration of these “carrier-free” fission- produced radionuclides is very high
17. 17. Neutron Activation • Neutrons produced by the fission of uranium in a nuclear reactor can be used to create radionuclides by bombarding stable target material placed in the reactor • Process involves capture of neutrons by stable nuclei • Almost all radionuclides produced by neutron activation decay by beta-minus particle emission
18. 18. Radionuclide Generators • Technetium-99m has been the most important radionuclide used in nuclear medicine • Short half-life (6 hours) makes it impractical to store even a weekly supply • Supply problem overcome by obtaining parent Mo-99, which has a longer half-life (67 hours) and continually produces Tc-99m • A system for holding the parent in such a way that the daughter can be easily separated for clinical use is called a radionuclide generator
19. 19. Transient Equilibrium • Between elutions, the daughter (Tc-99m) builds up as the parent (Mo-99) continues to decay • After approximately 23 hours the Tc-99m activity reaches a maximum, at which time the production rate and the decay rate are equal and the parent and daughter are said to be in transient equilibrium • Once transient equilibrium has been reached, the daughter activity decreases, with an apparent half- life equal to the half-life of the parent • Transient equilibrium occurs when the half-life of the parent is greater than that of the daughter by a factor of ~10
20. 20. Secular Equilibrium • If the half-life of the parent is very much longer than that of the daughter (I.e., more than about 100× longer), secular equilibrium occurs after approximately five to six half-lives of the daughter • In secular equilibrium, the activity of the parent and the daughter are the same if all of the parent atoms decay directly to the daughter • Once secular equilibrium is reached, the daughter will have an apparent half-life equal to that of the parent
21. 21. Ideal Radiopharmaceuticals • Low radiation dose • High target/nontarget activity • Safety • Convenience • Cost-effectiveness
22. 22. Mechanisms of Localization • Compartmental localization and leakage • Cell sequestration • Phagocytosis • Passive diffusion • Metabolism • Active transport
23. 23. Localization (cont.) • Capillary blockade • Perfusion • Chemotaxis • Antibody-antigen complexation • Receptor binding • Physiochemical adsorption
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