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Imaging and Detectors for Medical Physics Lecture 4: Radionuclides

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Imaging and Detectors for Medical Physics Lecture 4: Radionuclides Joint CI-JAI advanced accelerator lecture series Imaging and detectors for medical physics Lecture 4: Radionuclides Dr Barbara Camanzi [email protected] Course layout Day AM 09.30 – 11.00 PM 15.30 – 17.00 Week 1 6th June Lecture 1: Introduction to Lecture 2: Detectors for medical imaging medical imaging 7th June Lecture 3: X-ray imaging 8th June Tutorial Week 2 13th June Lecture 4: Radionuclides 14th June Lecture 5: Gamma Lecture 6: SPECT cameras 16th June Lecture 7: PET Week 3 22nd June Tutorial Page 2/55 Books & references 1. N Barrie Smith & A Webb Introduction to Medical Imaging Cambridge University Press 2. Edited by M A Flower Webb’s Physics of Medical Imaging CRC Press 3. A Del Guerra Ionizing Radiation Detectors for Medical Imaging World Scientific 4. W R Leo Techniques for Nuclear and Particle Physics Experiments Springer-Verlag Nuclides live charts − http://www.nndc.bnl.gov/nudat2/ − https://www-nds.iaea.org/relnsd/vcharthtml/VChartHTML.html Page 3/55 Nuclear medicine imaging • Imaging of radioactive decay products of a radiopharmaceutical (radiotracer) introduced into the body → emission imaging (as opposed to X-ray imaging = transmission imaging) • Spatial distribution depends on how radiopharmaceutical interacts with tissues in the body • Administration of radiopharmaceutical: 1. Intravenous injection into bloodstream 2. Inhalation into lungs 3. Subcutaneous administration 4. Oral administration Page 4/55 Nuclear medicine imaging techniques • SPECT = Single Photon Emission CT = Single Photon Emission Computed Tomography • PET = Positron Emission Tomography • Planar scintigraphy Page 5/55 Nuclide notation Nucleus Notation • Formed of nucleons Element X neutron A proton Z X • Nucleons: A = mass number = number of – proton = particle with positive protons + neutrons charge Z = atomic number = number – neutron = particle with zero of protons charge Isotopes of an element = nuclides with same number of protons (same 푍) but different number of neutrons (different 퐴) Page 6/55 Forces within the nucleus coulomb strong neutron proton strong strong • In stable nuclei forces are well balanced • In unstable nuclei there are too many neutrons or protons → forces are not balanced → nucleus is prone to undergo nuclear rearrangement and decay • Line of stability – For low 푍: 푁 ≈ 푍 – For high 푍: 푁 ≈ 1.5 × 푍 – No stable nuclei for Z > 82 (Lead) Page 7/55 Radioactivity • Intrinsic property of unstable nuclei that have too many neutrons or protons → unstable nuclei emit particles or 훾-rays to become more stable • Definitions: 1. Radionuclide = nuclide that is unstable and undergoes radioactive decay 2. Radioisotope = radioactive isotope 3. Radioactive disintegration or decay = spontaneous change in nucleus composition with associated emission of energy to reach a more stable state 4. Radiotracer = radiopharmaceutical Page 8/55 Radioactive decay law • Number of radioactive atoms in a sample decreases with time: 푑푁 = −휆푡 푑푡 • 푁 푡 = number of atoms left at given time 푡 decreases exponentially: 푁 푡 = 푁0exp −휆푡 푁0 = number of atoms at 푡 = 0 휆 s−1 = decay constant exp −휆푡 = decay factor Page 9/55 Decay constant • Probability that any individual radioactive atom will undergo decay per unit time • Statistical definition → average rate of decay • Exercise: Q: If 휆 = 0.01 s−1 on average how many atoms undergo radioactive decay per unit time? Page 10/55 (Radio)activity 푸 Ref. 1 – Chapter 3.2 and Ref. 2 – Chapter 5.4.1 • (Radio)activity 푄 = number of disintegrations per s = rate of change of number 푁 of radioactive nuclei 푑푁 푄 = − = 휆푁 푑푡 • Units for 푄: 1. SI unit = Bequerel (Bq) 1 Bq = 1 disintegration per second 2. Curies (Ci) = named after Pierre Curie and defined as number of disintegrations per second from 1 gramme of 226푅푎 1 Ci = 3.7 × 1010 disintegrations per second = 3.7 × 1010 Bq Page 11/55 (Radio)activity 푸 decay law • (Radio)activity 푄 decreases with time too • Exercise: Q: Determine the (radio)activity 푄 decay law Page 12/55 Half-life • Half-life 휏1/2 = time required for 푄 to drop to half (50%) of its initial value → 휏1/2 is independent of 푁 • Exercise: Calculate relation between 휏1/2 and 휆 and express 푄 as function of 휏1/2 Page 13/55 Atomic half-lives 푍 (protons) 푍 = 푁 Half-life (seconds) > 1e+15 1e-01 1e+10 1e-02 1e+07 1e-03 1e+05 1e-04 1e+04 1e-05 1e+03 1e-06 1e+02 1e-07 1e+01 1e-15 1e+00 < 1e-15 unknown Courtesy Piero Posocco (Imperial College) 푁 (neutrons) Page 14/55 Biological and effective half-life • In many cases excretion of radiotracer from tissue follows an exponential decay law → biological half-life 휏1/2,푏표 used to characterise the decay → 휏1/2,푏표 gives a measure of how long radiotracer remains in the body • Effective half-life 휏1/2,푒푓푓 given by: 휏1/2 ∙ 휏1/2,푏표 휏1/2,푒푓푓 = 휏1/2 + 휏1/2,푏표 → 휏1/2,푒푓푓 always less than the shorter between 휏1/2 and 휏1/2,푏표 Page 15/55 Exercise • Q: Two patients undergo nuclear medicine scans. One receives a dose of radiotracer A with 휏1/2 = 6 h and the other a dose of radiotracer B with 휏1/2 = 24 h. If dose of radiotracer A is 3 × dose of radiotracer B and 휏1/2,푏표 of A is 6 h and of B 12 h, at what time the radioactivity in the body of the two patients is the same? Page 16/55 Radioactive decay modes Ref. 2 – Chapter 5.4.3 • 훼+2 decay • 훽− decay • 훽+ decay • Electron Capture (EC) • Isomeric transitions – Radiative 훼+2, 훽− and 훽+ decays – Radiative EC • Internal conversion (IC) Page 17/55 휶+ퟐ decay • High A radionuclide emits 훼-particle = helium nucleus = +2 charge • Most energy distributed between: 1. Daughter nucleus = recoil energy 2. 훼-particle = kinetic energy = 4÷8 MeV → travels few mm in tissue • If nucleus left in excited state → de-excitation is through emission of g-rays • Not use in medical imaging (shallow penetration in tissue) but as sealed X- or g-rays sources in therapy Page 18/55 휷− decay • Neutron-rich radionuclide ejects Example 훽− particle = e− = −1 charge in 훽− 14 decay 14 − the process: 6퐶 7푁 + 훽 + 휈 + 퐸 푛 → 푝 + e− + n 퐸 = shared randomly between n and • Three-body decay → energy kinetic energy of 훽− spectrum of e− = continuum up to a maximum 14 퐶 − • 푍 → 푍 + 1, 퐴 and atomic weight 6 훽 decay remain the same • e− penetration in tissue < 2 mm 14 → not used in medical imaging 7푁 Page 19/55 Radiative 휷− decay (휷−, 휸) • If following 훽− decay daughter nuclide Example ∗ is produced in excited state 푋 → 훽− 133 133 ∗ γ 133 prompt de-excitation to more stable 54푋푒 55퐶푠 55퐶푠 state through emission of g rays 133 g decays • 푍 → 푍 + 1, 퐴 and atomic weight 54푋푒 remain the same 133 54푋푒 • Typical energy of g rays = 50÷500 keV 0.38 MeV → useful for imaging • Disadvantage: patient still exposed to 0.16 MeV − 훽− decays 훽 particle → dose 0.08 MeV 0 MeV 133 55퐶푠 Page 20/55 휷+ decay • Proton-rich or neutron deficient Example radionuclide ejects 훽+-particle = e+ = 훽+ 15 decay 15 + +1 charge in the process: 6푂 7푁 + 훽 + 휈 + 퐸 푝 → 푛 + e+ + 휈 퐸 = shared randomly between 푣 and • Three-body decay → energy spectrum kinetic energy of 훽+ + of e = continuum up to a maximum 푚푎푥 Average kinetic energy 퐸 + ≅ 퐸 + /3 • 푍 → 푍 − 1, 퐴 and atomic weight 훽 훽 15 remain the same 8푂 + 1.022 MeV • e travels ~1 mm in tissue → comes + to rest → combines with atomic e− → 훽 decay 2 back-to-back 511 keV g-rays 푚푎푥 퐸 + = 1.7 MeV • If daughter nuclide is produced in 훽 15 excited state → de-excitation is 7푁 through emission of g-rays Page 21/55 Electron Capture (EC) and radiative Electron Capture (EC, 휸) • In proton-rich radionuclide inner Example − orbital (K-shell) e = closer to 퐸퐶 125 − 125 ∗ γ 125 nucleus, captured within nucleus: 53퐼 + 푒 52푇푒 + 휈 + 퐸 52푇푒 푝 + e− → 푛 + 휈 + 퐸 125 • 푍 → 푍 − 1 53퐼 • e− from outer orbital fills vacancy → emission of X-ray characteristic EC of daughter nuclide = can be useful for imaging if high enough 퐸 0.035 MeV 125푇푒∗ • The higher 푍 the closer to the 52 훾 nucleus are the e− shells → probability of EC increases with 푍 125 52푇푒 • If daughter nuclide is produced in excited state 푋∗ → de-excitation is through emission of g-rays Page 22/55 Feynman diagrams for 휷−, 휷+ decays and EC 훽− 퐴 퐴 − 푍푋 푍+1푌 + e + 푣푒 훽+ 퐴 퐴 + 푍푋 푍−1푌 + e + 푣푒 퐸퐶 퐴 − 퐴 푍푋 + e 푍−1푌 + 푣푒 Page 23/55 Courtesy Piero Posocco (Imperial College) 휷 emitters (휷−, 휸) emitters1 Nuclide Half-life 퐸훽 (MeV) 퐸훾 (keV) 60퐶표 5.27 yrs 0.096 1173, 1332 131퐼 8.04 days 0.192 364 133푋푒 5.24 days 0.101 81 137퐶푠 30.00 yrs 0.173 662 휷+ emitters 푚푎푥 + Nuclide Half-life (min) 퐸훽+ (MeV) 훽 푟푎푛푔푒 in water (cm) 11퐶 20.30 0.961 0.103 13푁 10.00 1.190 0.132 15푂 2.07 1.720 0.201 18퐹 110.00 0.635 0.064 1Only dominant 훽− and 훾 emissions shown Page 24/55 EC and (EC, 휸) radionuclides EC radionuclides Nuclide Half-life 푬푿−풓풂풚 (keV) 125퐼 60.1 days ~30 201푇푙 3.04 days ~70 (EC, 휸) radionuclides Nuclide Half-life 푬휸 (keV) 57퐶표 270 days 122, 136 67퐺푎 78.3 h 93, 185 111퐼푛 2.83 days 171, 245 123퐼 13.2 h 159 Page 25/55 Isomeric transitions (IT) and metastable states • Excited state in which daughter Example nuclide can be produced called 99 푚 isomeric state • 푇푐 most common example of metastable isotope used in nuclear • Sometimes radiative decays from medicine isomeric state to ground state are called isomeric transition • Decay chain: • Isomeric transitions can take from 훽− γ 99푀표 99푇푐푚 99푇푐 fractions of seconds (short-lived states) to many years (long-lived Half-life for 훽− decay = 66 h states) Half-life for isomeric transition = 6 h • Long-lived isomeric states are 퐴 푚 called metastable states 푍푋 Page 26/55 Internal Conversion (IC) • 훾-ray emitted in isomeric transition interacts with atomic e− → e− is ejected = conversion electron • Interaction is usually with K-shell e− as they are closest to nucleus • Conversion e− has kinetic energy 퐸: 퐸 = 퐸훾 − 퐸푏푛푑푛푔 • e− from outer shell fills vacancy → characteristic X-ray emitted • X-ray emitted can interact with other outer shell e− − − → e get ejected if 퐸푋−푟푎푦 > 퐸푏푛푑푛푔 = Auger e Page 27/55 Radioactive decay table 푍 (protons) Stable EC, 훽+ 훽− 훼 P N Unknown Courtesy Piero Posocco (Imperial College) 푁 (neutrons) Page 28/55 Production of radionuclides Ref.
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