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

2. 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

3. 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- ~

4. 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+ 

5. 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

6. 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

7. 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

8. 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

9. 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/

10. 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)

11. 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 = / 
 = / Tp
N0 = Initial number of radioactive atoms
Nt = number of radioactive atoms at time t
Nuclear Medicine Physics for Radiology Residents Sameer Tipnis, PhD, DABR

12. 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

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

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

15. 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

16. 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)

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

18. 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
Nuclear Medicine Physics for Radiology Residents Sameer Tipnis, PhD, DABR

19. 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

20. 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)

21. 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
Nuclear Medicine Physics for Radiology Residents Sameer Tipnis, PhD, DABR

22. 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
Nuclear Medicine Physics for Radiology Residents Sameer Tipnis, PhD, DABR

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

24. Major components of gamma camerai 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

25. 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

26. 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

27. 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

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

29. © Physics in Nuclear Medicine: Cherry, Sorenson and Phelps

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

31. 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
Nuclear Medicine Physics for Radiology Residents Sameer Tipnis, PhD, DABR

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

33. 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
Nuclear Medicine Physics for Radiology Residents Sameer Tipnis, PhD, DABR

34. + 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

35. Annihilation location  Ejection location
The distance depends on the e+ initial kinetic energy and medium.
Isotope Max E Max d FWHM F MeV 2.3 mm mm C MeV 3.9 mm mm
O MeV 6.6 mm mm
Rb MeV 16.5 mm 2.6 mm
Shorter distance in a medium with higher density or higher Z

36. 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  × ring diameter
For D = 80 cm,
h ~ 2 mm g
LOR

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

38. 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
Nuclear Medicine Physics for Radiology Residents Sameer Tipnis, PhD, DABR

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

40. 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

41. 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

42. 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 ns  1 cm accuracy
No such fast scintillator yet.
The currently used LYSO for ToF
PET has a time resolution of ns
which leads to 8.8 cm accuracy. d
LOR t1 t2

43. 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

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

45. 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
Nuclear Medicine Physics for Radiology Residents Sameer Tipnis, PhD, DABR

46. 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
Nuclear Medicine Physics for Radiology Residents Sameer Tipnis, PhD, DABR

47. 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

48. 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

49. 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

50. 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

51. Effective dose of NM procedures

52. © 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