Nuclear Medicine (Phys)


spontaneous decomposition of parent nucleus into less energetic/lighter daughter products

α-decay: (Z,A)  (Z-2,A-4) + α (helium nucleus, absorbed by skin layer); in heavy nuclei eg 226Ra222Rn, 235U, 238U)

βdecay: (Z,A)  (Z+1,A) + β(negatron/electron penetrating a few mm) + (antineutrinos); eg 131I131Xe, 90Y, 89Sr, 32P, 153Sm, 165Dy

β+ decay: (Z,A) (Z-1,A) + β+(positron penetrating a few mm) + ν (neutrinos); eg 18F18O, 11C, 13N, 15O, positron annihilates with electron with combined mass (1.022MeV) converted to 2 γ rays of 511keV 180  to each other

electron capture: (Z,A) + e  (Z-1,A)*  (Z-1,A) + characteristic XRs; e usually from K-shell due to greatest probability of passing through nucleus, usually when daughter nucleus < 1.022MeV less than parent

γ-decay: (Z,A)m  (Z,A) + γ (massless, penetrating); eg 99mTc, 201Tl, 131I, 111In, 67Ga

α and β decay frequently leaves nucleus in excited state with subsequent γ-decay

isomer = prohibition/impedance of γ-decay leaving nucleus in meta-stable state

internal conversion = instead of γ-ray emission, kinetic energy given to bound electron; for small excitation energies

Auger electron = photon was to be emitted (from PE) is instead absorbed by an electron which undergoes ionization

maximum energy of emitted radioactivity is ~ 3x average energy

Radioactive Decay Law

radioactive decay law = dN = -λNdt; λ = decay constant

exponential law (integration of decay law) = N = N0e-λt; N0 = number of atoms at t=0; lnN = lnN0 – λt with gradient -λ

λ = ln2/T½; T½ = half-life

mean lifetime = tm = 1/λ = 1/ln2.T½ = 1.44T½

activity (disintegrations/s = Bq = Becquerel; curie = Ci = 3.7 x 1010Bq) = A = dN/dt = λN = A0e-λt

specific activity = A / (elemental mass in mixture of radioactive and stable atoms)

with competing decay modes: dN/dt = -(λ 1 + λ2)N; 1/T½ = 1/T1 + 1/T2

with competing physical decay and biological clearance: 1/Te = 1/Tb+ 1/T½; Te = effective half-live, Tb = biological half life (assuming simple exponential decay); T½ = physical half-life

secular equilibrium – chain of radioactive decays when 1st species has long comparative half-life, hence all daughters decay with the same activity

Detection of Radiation

energetic charged particles cause production of ion pairs (ionization) that is detected

photon energy transferred to orbital electrons (via PE or Compton scattering) and thus dissipated as they move through the medium causing ionization and excitation of atoms

charged particles directly responsible of ionisation

neutrons interact via chance collision with nuclei, transferring energy to recoiling proton

Detector Types

gas-filled ionization chambers

ionized gas in enclosure alters applied V between electrodes, magnitude proportional to number of ions collected (which is dependent on magnitude of V)

ionization = saturation region = increased V increases drift velocity, reducing time and thus chance for recombination until further ↑V has no further effect; insensitive to individual ionizing events, signal proportional to energy deposited in chamber; 200-350V

proportional region = ↑V >400V which accelerates ions to produce secondary ionization by collision; individual particle/photon interactions can be observed

Geiger-Muller region = controlled avalanche of nearly fixed size independent of type of event that triggered it (no energy discrimination) with gains 105-106 (hence extremely sensitive); Geiger counters filled with inert gas (Ar) mixed with alcohol at 100mmHg and ~800V

uncontrolled avalanche region – continuous discharge

scintillation detectors

capable of higher counting rates, elevated photon detection efficiency, proportionality betw energy deposited and signal

crystal coupled to PMT: NaI:Tl, CsI, CsF, CsF2, CdWO4, BaF2, BGO (bismuth germinate), LSO (lutetium oxyorthoscilicate)

scintillation = recoil electrons from ionization de-excites with emission light (UV or blue for NaI:Tl)

PMT (photomultiplier tube)

  • photocathode (bi-alkali alloy of Sb, K, Cs with spectral response matched to UV/blue light
  • up to a dozen dynodes (1st at 100V +ve to photocathode, accelerated electron causes ejection of several secondary electrons to pass to next dynode; multiplication factor of ~1 million)
  • anode
  • evacuated glass tube

some loss of incident energy from Compton scattering in crystal with the 2nd lower energy photon may/may not be stopped

spectrum of pulse heights (Gaussian distribution around photopeak energy) from statistical variations in number of light photons created and photo-electrons produced and amplified; low energy tail from incomplete energy absorption due to backscattered photons, escape of characteristic XRs, Compton scattering

liquid scintillation counter (scintillating fluid betw 2 photomultipliers) extremely sensitive (eg β), producing ionizing track

linear attenuation coefficient for NaI:Tl at 140keV (99mTc decay) for PE is 5x Compton scattering

when crystal becomes hydrated, it is cloudy causing them to be inefficient and not able to transmit low energetic photons

semiconductor detectors

ionization produces electron-hole pairs that move under influence of V

high purity Si or Ge (germanium Ge:Li) or CdTe

only require 3eV of energy to produce ion pair (35eV in gas, 1keV for PMT), hence spread around photopeak is reduced (increased number of ions); ie energy resolution 20 times better than NaI:Tl)

extremely short response time (no lag) and compact

suffer thermal noise (require cooling of detector and preamplifier with liquid nitrogen) and high cost

Counting and Data Handling Systems

preamplifier (PA) transforms charge pulse to voltage pulse (height conveying energy info), with short rise time (<100ns) and long decay times (several μs)

main/linear amplifier (LA) converts to longer rise times but shorter decay times in a Gaussian-shaped pulse, with gain to give pulses in range of 0-10V

pileup = pulses overlapping, causing errors in amplitude interpretation

pulse height analysis

discriminator – gives output only when certain present V level exceeded

single-channel analyser (SCA) – output when V in a user selected energy window between lower-level discriminator (LLD) and upper-level discriminator (ULD)

ratemeter determines average number of counts per second, scaler (counter) counts number of pulses in a preset time interval (usually displaying digitally)

multichannel analyser (MCA) – can sort and display number of pulses vs pulse heights (energy)

Counting Statistics

Poisson distribution from statistical variation in disintegration, hence statistical uncertainty/error in measurement of radioactivity

  • standard deviation = σ = √N; probable error = P = 0.67√N; N = number of counts recorded
  • probability of observing count N is μ ±P = 0.5; μ ±σ = 0.69, μ ±2σ = 0.96; μ = expected/mean count
  • as μ approaches 10,000 it is equivalent to the normal/Gaussian distribution

standard deviation of measurement = uncertainty = coefficient of variation = √N/N

A = N/t and σ = √N/t for counts Ns over time ts in sample and background Nb, tb

net activity = A = As – Ab, with of their sum/difference added in quadrature, σ2 = σs2 + σb2

σ2 = Ns/ts2 + Nb/tb2, hence for identical acquisitions if two images are added or time doubled, the signal (N or t) doubles, but σ (noise) only improves by √2; hence SNR improves by 2/√2 = √2

Planar Nuclear Imaging with Gamma/Anger camera

collimator so γ-rays detected reflect 2D distribution (several thousand parallel or oblique circular/hexagonal holes in lead); hole area, length, septal thickness affect cone-sized FOV (field of view) or each hole, hence resolution which deteriorates with distance from collimator

collimator may be parallel hole, converging (magnifies), diverging (minifies) or pin-hole (magnifies; for small objects)

sensitivity determined by ratio of total area of holes to detector, and is essentially independent of distance

large circular or rectangular 600 x 400 x 10mm NaI:Tl crystal

thin light guide pipe coupled to PMT and encapsulates the deliquescent crystal

array of ≥ 70 PMTs with largest proportion of light collected by the nearest tubes

preamplifiers, high V supplies for PMTs and logic circuitry included in lead-shielded detector housing

analogue and early hybrid digital cameras produced x and y co-ordinate and z (energy) signals

fully digital camera PMT output are digitized by ADC before further signal processing to reduce noise, increases resolution, linearity and count rate performance

spatial encoding signals (x,y) determined by centroid calculation (analogue or hybrid cameras) or via look-up table (digital cameras)

energy signal (z or E) obtained by adding signals from all PMTs

MCA window adjusted for photopeak energy ± 10% to reject unwanted events (Compton scattering in crystal or patient)

asymmetric/off-peak images set energy window slightly higher than photopeak to reduce scatter

γ rays (up to 1 million) detected individually and built up over 5-10min to produce the image

in hybrid and fully digital cameras position signals digitised and if MCA satisfied adds one to that pixel in the image matrix (1282 or 2562 matrices)

digitization also allows for image manipulation and processing (smoothing, addition, subtraction, cardiac gating)

dual energy/radioisotope studies eg 201Tl in cardiac imaging with 3 useful γ emissions and 67Ga GIT studies to improve noise

  • cross-talk when higher γ contributes Compton events to lower energy γ)

computer corrects for uniformity variations from imperfections in crystal or different PMT efficiencies after calculating correction factors from a flood field (high-uniformity 99mTc or 57Co flat source)

whole body scanners detect radiation naturally produced from body or contaminated person without any additional radioisotope administered

Resolution and Efficiency

intrinsic spatial resolution – from detector and electronics alone (disregarding degradation from collimator), dictated by number/size of PMTs, crystal thickness (thinner 6-9mm capable of 3.5mm FWHM), count rates, matrix size; measured with source touching crystal

system spatial resolution – also incorporates collimator design (main limiting factor at given depth; scatter, energetic γ penetrating septa), distance from collimator (best 8-15mm at 10-15cm depth); resolution ; D = collimator hole diameter, L = length of hole, H = distance from source

efficiency of light collection increased by entire crystal surface covered by hexagonal/square PMTs, crystal thickness (but reduced by Compton scattering), and mostly collimator efficiency

sensitivity ; C = hole shape constant (hexagonal 0.069, round 0.063, square 0.080), T = septal thickness, D = collimator hole diameter

dead time = finite time of spatial encoding logic circuitry to determine position and acceptability of event when system paralyzed (unable to accept further events); with high count rates substantial number are lost

pulse pile-up – two events appearing as one with energy added together (usually rejected by ULD of MCA)

Two-Three Crystal Gamma Camera

detector heads similar to above digital detectors, but have improved speed of data acquisition

allow whole body studies to be performed more quickly and both PA and AP views to be obtained simultaneously

Multiple Crystal Gamma Camera

single large detector replaced by multiple small ones or multiwire proportional chambers or semiconductor detectors

able to handle very high count rates, sensitivity esp at higher energy γ (due to deeper detectors), but have poor spatial resolution

Emission Computed Tomography (ECT)

reconstruction 2D FT or convoluted back projection

Single Photon Emission Computed Tomography (SPECT)

2-3 large detectors rotate 180-360° around patient with parallel hole collimators pointing towards axis of rotation

moves in elliptical/circular or complicated orbit so detectors placed close to patients skin with improved spatial resolution

~64 images obtained with 64 x 64 pixel resolution

width of collimated bands/rays determined by how finely image is digitised and ≈4mm

profile = single projection = built up from rays along detector, these 1D projections reconstructed to form image

acquisition time (~5-20min) depends on amount of activity, number of detector heads, counting efficiency

attenuation and scattering within the body

highest pixel number = white; zero = black on a linear scale

images quantum limited with noise in high spatial frequency

prefiltering with ramp (rarely used as it amplifies high f), cosine, Gaussian or Hanning (lower at low and high f)

convolution filter then post-reconstruction filter

image quality

spatial resolution determined by intrinsic detector resolution, collimator, proximity to patient (also determines FOV), number of profiles and angular range, field/pixel size, filtering, activity and time per view, radius and centre of rotation correction, slice thickness (partial volume effect), attenuation correction, width and level of MCA

system resolution = intrinsic resolution (when object touching collimator) + collimator/geometric resolution

resolution measured with FWHM or MTF

reduced patient-detector distance with special head support at end of couch (hence proximity limited by pt shoulders and not couch), departure from purely elliptical orbit, slant hole collimators with angled camera heads (for cardiac imaging)

noise (quantum limited) determined by detector efficiency, multiple cameras, collimator, N profiles, pixel size, slice thickness, filtering, object size (attenuation), activity and time per view, attenuation and uniformity correction


  • variable attenuation usually corrected by assuming typical body contour with uniform attenuation; μ 0.12-0.13/cm used is less than true μ due to large contribution of scatter (30%) to image
  • partial volume effects
  • ring artefacts from poor detector uniformity
  • mechanical and computer calculated centre of rotation offsets with points appearing as halos; important if misalignment >1/2 pixel
  • motion artefacts

Positron Emission Tomography (PET)

18F, 11C, 15O, 13N with very short half life positron emission used without modifying chemical behaviour

fluorine labelled deoxyglucose (FDG) λ 110min, max positron range 2.6mm for glucose metabolism; gets stuck in cell as unable to undergo metabolism by glucose-6-phosphate

λ vary from 1.5-20min; max positron range 2.6-15mm

β+ + β positronium, then annihilate 2γ of 511keV emerging 180° to each other; very small chance of 3 photons being produced

detection of γ in coincidence (at the same time; within time window of 6-12ns), defining line/ray path

detector elements mounted in circular or hexagonal array

collimation not required hence sensitivity increased; axial collimation used to reject events outside plane of ring

profiles corrected for radionuclide decay, subtraction of random coincidences, attenuation (μ = 0.1/cm), dead time losses and detector inhomogeneities before FT, filtered back projection and iFT

coronal, sagittal and oblique slices not readily obtained

3D scanning and reconstruction performed along a length using 48 discrete detector rings

attenuation correction more accurate in PET (cf SPECT) due to being independent from point of positron annihilation and depends only on total thickness of tissue that both photons pass; but compromised in regions where attenuation coefficients vary substantially (eg chest)

attenuation map from transmission or CT scanning improves correction technique

resolution ~5mm with slice thickness ~6mm deteriorating at edge of FOV

range of positron in tissue and angular variation of photons (180°±0.25° due to conservation of momentum of the moving positron) degrade resolution 1.5-3mm FWHM; positrons emitted have spectrum of energies and very few travel to max range and those travelling along direction of γ do not reduce resolution

time-of-flight imaging measures t between detection of coincident γ rays to localise position along ray path using timing electronics and fast detector responses (BaF2, CsF)

  • electronics temporal resolution is 0.5ns, hence localisation to 75mm but method reduces noise (back projection restricted to only part of ray path)
  • superior random coincidence rejection, better SNR and ability to handle higher count rates

scanning time of single slice 20s to several minutes

8×8 arrays of 4mm detector elements (BGO) with 4 PMTs in multiple rings allowing up to 48 slices being obtained simultaneously

true coincidence = photons 180° to each other detected from the single annihilation

random/accidental coincidence – detection of 2 γ rays that originate from different points with other γ rays not detected; Compton scattering in detector (hence detector threshold energy not reached), rays detected by elements not operated in coincidence with each other, rays pass between adjacent elements or pass outside detection plane

multiple coincidence = detection of 3 or more γ in coincidence from different events

misregistration = scattered coincidence – one photon undergoes scattering, and changes direction of path

poor energy discrimination as energy resolution at 511keV is poor (level set as low as 350keV), hence acceptance of substantial fraction of Compton scattered γ

PET acquisition modes

2D ring system – septa used so detectors only see γ rays from that slice

3D ring system of detectors, or one large NaI detector – no septa, rays can be in coincidence if from different planes; increased efficiency but artefacts introduced from gamma rays originating from eg hot bladder and scattering


BGO, BaF2, CsF, caesium doped gadolinium orthosilicate (GSO), cerium doped lutetium oxyorthoscilicate (LSO) made much smaller than NaI:Tl and except for BGO have superior timing characteristics; however have lower light yields cf NaI:Tl

hybrid PET systems

gamma camera/PET (GCPET) have dual head gamma camera with increased thickness of detectors (9-10mm16-19mm due to increased penetration of 511keV) addition of coincidence circuitry

count rate performance and coincidence counting efficiency remains poor cf dedicated PET

combined PET/CT have low power CT for providing attenuation corrections (CTAC); however modern CT combinations also have diagnostic CT capabilities

artefact from CTAC include dense lesions showing up bright on PET image or motion between CT and PET causing area that was dense on CT being hot on PET (which is now not dense; = malalignment, eg diaphragm)

hybrid MR-PET and SPECT/CT



physical properties: minimal particulate radiation (β, α that would just add to dose), γ with sufficient energy to escape without excessive attenuation but low enough for detection, half-life compromise between low dose (short) and ease of manufacture/transport/administration (long), and capable of being produced in extremely pure form

chemical: pure chemical form, chemically stable and capable of being attached to any of several pharmaceuticals

pharmacology: sterile, pyrogen free, non-toxic, neutral pH

general: easy to produce, ease of transport, not excessively expensive


99Mo (fission product of nuclear reactor or neutron activated 98Mo) decays by β to 99mTc (T½ 67h)

generator = cow consists of alumina columns that 99Mo is adsorbed to, soluble sodium pertechnetate is milked/eluted off with normal saline up to twice daily; generator sufficient activity (40GBq) for a week

99Mo breakthrough can occur, so purity needs to be confirmed, as it is toxic, leads to unnecessary absorbed dose and degrades image quality

99mTc initially decays via internal conversion from isomeric level 143keV to 140keV, before ejecting the 140keV γ-ray used for imaging

T½ 6h, γ 140keV, low energy XR, Auger & internal conversion electrons; used for kidney (MAG3), bone (sodium diphosphonate), brain (HMPAO), spleen (heat damaged RBC), heart wall (MIBI), cardiac (RBC), GIT blood loss (RBC), liver & spleen (sulphur/tin colloid or calcium phytate), liver blood pool (RBC), lung perfusion (MAFT/macroaggregated albumin), lung ventilation (technigas), thyroid (sodium pertechnetate), biliary (DISIDA/E-HIDA)


produced by β decay of 131Te

T½ 8d, γ 364keV, some low energy XR, Auger & internal conversion electrons, β; for thyroid function and therapy (sodium iodide)

other radioisotopes

201Tl T½ 73.1h, γ 80, 135, 167keV; for heart wall (thallous chloride), bone tumour (thallous chloride)

111In T½ 67.2h, γ 171, 245keV; for infection (indium-white cells)

67Ga T½ 78.3h, γ 93,184,300keV; for infection (gallium citrate), tumour (gallium citrate)


nuclear reactor produced radionuclides

produced by neutron capture, with preference for β decay

235U is enriched to produce self-sustained controlled chain fission with release of energetic neutrons to induce new fissions; moderator (hydrogenous material eg water, heavy water, graphite) reduces energy to control the reaction

target to be irradiated is inserted into core by rabbit (pneumatic conduction system), or longer lived isotopes extracted from fixed targets attached to control rods or processed from spent fuel rods

neutron capture/activation: (Z,A) + n  (Z,A+1) + γ

target must be able to withstand elevated temperatures, available, chemical purity and result in only a single isotope of the element desired (isotope separation is difficult)

fission of 235U gives rise to nuclides with masses from 72 to 162 (90Sr, 99Mo, 131I, 133Xe), but are difficult to separate

carrier material = non-radioactive isotope of the same element

cyclotron produced radionuclides

cyclotron is a particle accelerator with electric and magnetic fields accelerating positively or negatively charged ions (usually protons, deuterons; but not electrons) through a helical trajectory through electron stripping foil (carbon foil) and onto a target material (dictated by physical and chemical properties of the target; beam energy, particulate, activity, and chemistry of end product; to be carrier-free target must be different element than end product)

result in proton-rich isotopes that preferentially decay be β+ decay

18O(p,n)18F = p + 18O  n + 18F

12C(d,n)13N, 14N(d,n)15O, 11B(p,n)11C