Nuclear Medicine Physics Nuclear Medicine Physics Review Jerry Allison, Ph.D. Department of Radiology Medical College of Georgia

Nuclear decay must obey the conservation laws (energy-mass, electric charge, momentum, etc) to approach a stable N/Z ratio by 1. emission of charged particles (, , a) 2. capture of orbital electrons 3. fission to release extra energy by 1. g decay (isomeric transition) 2. internal conversion

b- decay A neutron decays to a proton, electron and anti- neutrino: n  p + e- + ~. e- and ~ created inside the nucleus at the moment of decay and ejected right away: e.g. 99Mo42  99mTc43 + e- + ~ 131I53  131Xe54 + e- + ~ e- ~

b+ decay A proton decays to a neutron, positron and neutrino: p  n + e+ + . e+ and  created in the nucleus at the moment of decay and ejected right away e.g. 18F9  18O8 + e+ +  15O8  15N7 + e+ +  e+ 

Annihilation e- + e+ = 2  or e- + b+ = 2  each  has energy: 511 keV due to energy-mass conservation or 2 g’s always traveling in opposite directions due to momentum conversation  PET imaging

Electron capture primary: an orbital electron is absorbed into nucleus and is immediately combined with a proton to form a neutron and neutrino: e- + p  n +  e.g. 7Be4 + e-  7Li3 +  secondary: emission of characteristic x-rays or Auger electrons Auger e-  x-ray

g decay (isomeric transition) emitting a g photon to release extra energy of the nucleus: excited state  ground state 99mTc43  99Tc43 + g g photon ejected out of the nucleus g-ray It often follows other decays that result in an unstable nucleus. A metastable state has a half-life greater than 10^-12 seconds “meta” from the greek means almost --- almost stable

A Review Nuclear decay rules Based on conservation laws -decay: AXZ  AYZ+1 + e- + ~ -decay: AXZ  AYZ-1 + e+ +  e-capture: AXZ + e-  AYZ-1 +  -decay and internal conversion: no changes for A & Z

Radioactivity : decay constant with units of 1/sec or 1/hr A (t): disintegration rate at time t (decays/sec) N(t): number of nuclei at time t : decay constant with units of 1/sec or 1/hr  = ln2/T1/2 = 0.693/T1/2 half life: T1/2 = ln2/ = 0.693/

Radioactivity unit in SI: 1 Bq = 1 disintegrations per second (Becquerel) traditional unit: 1 Ci = 3.7×1010 dps (1g of Ra-226, extracted first by Mme. Curie) 1 mCi = 37 MBq NM imaging: ~ 1 to 30 mCi (30 – 1100 MBq)

Physical Half-life (Tp) Tp = time required for the number of radioactive atoms to reduce by one half Basic equations: Nt = N0e-t or At = A0e-t Tp = 0.693 /   = 0.693 / Tp N0 = Initial number of radioactive atoms Nt = number of radioactive atoms at time t 2015 Nuclear Medicine Physics for Radiology Residents Sameer Tipnis, PhD, DABR

Effective half life Te = Time to reduce radiopharmaceutical in the body by one half due to functional clearance and radioactive decay Te = 𝟏 𝐓𝐩 + 𝟏 𝐓𝒃 Te = 𝐓𝐩𝐓𝐛 𝐓𝐩+𝐓𝐛 if Tp >> Tb, Te ≈ Tb if Tp << Tb, Te ≈ Tp

Transient equilibrium For 99mTc, Max yield ~ 24 hrs ~3 Curies of Mo99 2015 Nuclear Medicine Physics for Radiology Residents Sameer Tipnis, PhD, DABR

Transient equilibrium is the basis of: Mo-99 -> Tc99m generator and Sr-82 -> Rb-82 generator 2015 Nuclear Medicine Physics for Radiology Residents Sameer Tipnis, PhD, DABR

Radionuclides used in nuclear medicine Less than 20 radionuclides but hundreds of labeled compounds © Physics in Nuclear Medicine: Cherry, Sorenson and Phelps, 4th edition, 2012

Radiation Detectors in NM Survey meters (gas-filled detector) Ionization chambers (IC) Geiger Müeller (GM) Dose calibrator (gas-filled detector) Well counter (scintillation detector) Thyroid probe (scintillation detector) Miniature g-probe (scintillation)

Gas-filled detectors Survey meters (IC) Dose calibrators (IC) GM chamber “pancake” (GM) 2015 Nuclear Medicine Physics for Radiology Residents Sameer Tipnis, PhD, DABR

Ionization Chamber Region IC region Current pulse (signal) produced by radiation Signal strength is proportional to energy deposited Used for measuring “amount” of radiation (i.e., exposure, air kerma) S2 S1 2015 Nuclear Medicine Physics for Radiology Residents Sameer Tipnis, PhD, DABR

Dose calibrator Measure activity only Select correct isotope button Drop a sample to the bottom to avoid position effect Quality control is regulated by NRC or Agreement State Every patient dose must be assayed before administration

Dose calibrator quality control Constancy: daily, using Cs-137 (660 keV, 30 y) and Co-57 (122 keV, 9 mo) for all nuclide settings, error < 10% Linearity: quarterly, using 300mCi Tc-99m, down to 10 Ci or lineators, error < 10% Accuracy: yearly, using Cs-137 and Co-57, error < 5% Geometry: upon installation, using 1 mCi Tc-99m with different volumes, error < 10% Syringes (1ml, 3ml, 5ml, 10ml) Vial (10ml)

Geiger-Müller Region GM region High voltage applied to anode Iniitial ionizations produced by radiation and secondary ionizations produced by accelerating electrons Signal strength is independent of energy deposited Used for measuring “presence” of radiation S 2015 Nuclear Medicine Physics for Radiology Residents Sameer Tipnis, PhD, DABR

Scintillation Detectors Two main components - Scintillator Radiation deposits energy in scintillator causing light flashes (fluorescence) Photomultiplier tube (PMT) Used to detect fluorescence from scintillator and amplify the signal NM – Inorganic solid scintillator (e.g. NaI(Tl)) and PMT 2015 Nuclear Medicine Physics for Radiology Residents Sameer Tipnis, PhD, DABR

Scintillation Detectors Thyroid probe (NaI(Tl)) 2015 Nuclear Medicine Physics for Radiology Residents Sameer Tipnis, PhD, DABR

Major components of gamma camera i e n c o l m r NaI(Tl) crystal P M T - amplify & sum position analysis Pulse Height Analysis u d s y X Y Z

Why collimator? – image formation to establish geometric relationship between the source and image The collimator has a major affect on gamma camera count rate and spatial resolution parallel-hole collimator

Detection of g photons in detector An incident g photon may be stopped (absorbed) by or penetrate the detector more penetration with higher photon energy g photons recorded as counts (electrical pulses) Counts represent concentration and distribution of radioactivity in the patient A: absorption B A B: penetration p.e c.s A: absorption p.e

Event Location X+ = x+ - x- Z Y+ = y+ - y- Z The X, Y outputs from all the PMT’s are summed to estimate the center of scintillation

Energy Signal Z = x+ + x- + y+ - y- The outputs from all the PMT’s are summed to estimate energy deposited

© Physics in Nuclear Medicine: Cherry, Sorenson and Phelps

Filtered Back Projection (of noiseless data) © Physics in Nuclear Medicine: Cherry, Sorenson and Phelps © Physics in Nuclear Medicine: Cherry, Sorenson and Phelps

Image recon - Iterative Common IR recon is the OSEM For OSEM, # iterations (I) and # subsets (S) affect image quality  # (I/S)   noise, but sharper images 2015 Nuclear Medicine Physics for Radiology Residents Sameer Tipnis, PhD, DABR

Attenuation Correction Like all radionuclide imaging there is a problem due to attenuation. Correction can be important for judging the activity of lesions

Lines of response (LOR) PET image formation t1   t = t1 – t2  t < 5 (to 12) ns ? Yes Register as a “coincident” event  t2 Why 5 & 12ns? Lines of response (LOR) Positional information is gained LOR is assigned by electronic coincidence circuitry 2015 Nuclear Medicine Physics for Radiology Residents Sameer Tipnis, PhD, DABR

+ emitters used in PET p  n + e+ +  Proton-rich nuclei: positron emission p  n + e+ +  18F9  18O8 + e+ +  T1/2 = 110 min 15O8  15N7 + e+ +  T1/2 = 2 min 13N7  13C6 + e+ +  T1/2 = 10 min 11C6  11B5 + e+ +  T1/2 = 20 min 82Rb37  82Kr36 + e+ +  T1/2 = 73 sec

Annihilation location  Ejection location The distance depends on the e+ initial kinetic energy and medium. Isotope Max E Max d FWHM F-18 0.64 MeV 2.3 mm .22 mm C-11 0.96 MeV 3.9 mm .28 mm O-15 1.72 MeV 6.6 mm 1.1 mm Rb-82 3.35 MeV 16.5 mm 2.6 mm Shorter distance in a medium with higher density or higher Z

Residual momentum of e+ and e- Neither positron nor electron are at complete rest when annihilation occurs. The residual momentum causes a small angular deviation from 180. h  0.0022 × ring diameter For D = 80 cm, h ~ 2 mm g LOR

Ultimate spatial resolution in PET The uncertainties in annihilation (location & residual particle momentum) determine the ultimate spatial resolution (~ 2 mm)

Types of coincidences (correct LOR assigned) (incorrect LOR assigned) True Scatter Random True coincidences form a “true” distribution of radioactivity Scatter & random coincidences distort the distribution of radioactivity, add to image noise, degrade image quality 2015 Nuclear Medicine Physics for Radiology Residents Sameer Tipnis, PhD, DABR

No collimators in a PET scanner Photon direction determined by LOR  no collimators Absence of lead improves: detection efficiency (count rate) spatial resolution

Detector materials BGO (Bi4Ge3O12) used by GE LSO (Lu2SiO5) used by Siemens GSO (Gd2SiO5 ) used by Philips LYSO (Lu2YSiO5, 9(L):1(Y)) used by all

Advantages of PET imaging No collimators  higher detection efficiency and better spatial resolution Ring detectors  higher detection efficiency Block detectors  higher detection efficiency and better spatial resolution

Time-of-flight PET Theoretically it is possible to determine the annihilation location from the difference in arrival times of two g photons: d = c∙Dt/2. Because of fast speed of light (c = 30 cm/ns), fast time resolution of detection is required for spatial accuracy. e.g. 0.067 ns  1 cm accuracy No such fast scintillator yet. The currently used LYSO for ToF PET has a time resolution of 0.585 ns which leads to 8.8 cm accuracy. d LOR t1 t2

PET Data Corrections Attenuation Normalization Random coincidences CT based Normalization Correction for variation in performance of ~20,000 individual detectors Random coincidences Delayed coincidence time window (~64 ns) Scattered radiation Modeling from transmission & emmission data Extrapolation from tails of projections Dead time Empirical models

CT number: Hounsield Units CT number (x,y) = 1000 (m(x,y) – mwater) / mwater

Semiquantitative PET: Standard Uptake Value (SUV) Defined as the ratio of activity concentrations SUV = conc. in vol. of tissue / conc. in whole body SUV = (MBq/kg) / (MBq/kg) Usually, SUV ~ 2.5 taken as cut-off between malignant and non-malignant pathology 2015 Nuclear Medicine Physics for Radiology Residents Sameer Tipnis, PhD, DABR

SUV in clinical studies Numerator: highest pixel value (SUVmax) from an ROI Or SUVmean Denominator: Activity administered/ body mass Or lean body mass Or body surface area SUV will depend on – physiologic condition, uptake time, fasting state, etc. Image noise, resolution, ROI definition Small changes in SUV need to be interpreted carefully 2015 Nuclear Medicine Physics for Radiology Residents Sameer Tipnis, PhD, DABR

Photon attenuation within patient Every PET study is compensated for attenuation. Correction of attenuation in PET reconstruction needs attenuation map from CT  values must be extrapolated from CT energies (< 120 keV) to 511 keV w/o compensated

Definitions Absorbed dose D (Gy): energy deposited in a unit mass of absorber 1 Gy = 1 joule/kg (SI unit) 1 rad = 100 erg/g (traditional unit) 1 Gy = 100 rad

Definitions Equivalent dose HT (Sv): quantity that expresses absorbed dose across an organ or tissue with a weighting factor for type and energy of radiation HT = DT . wR DT: absorbed dose in a tissue wR : weighting factor that denotes relative biologic damage for type of radiation For x, , e- , e+ : wR = 1 For n: depends on energy For p (> 2 MeV): wR = 2, For a, fission fragments, heavy ions: wR = 20

Definitions Effective dose E (Sv): measure of absorbed dose to whole body, the product of equivalent dose and organ specific weighting factors Whole body dose equivalent to the nonuniform dose delivered

Effective dose of NM procedures

© Physics in Nuclear Medicine: Cherry, Sorenson and Phelps Dose limits Occupational: ALARA 1 & ALARA 2 Embryo/fetus: 5 mSv total © Physics in Nuclear Medicine: Cherry, Sorenson and Phelps