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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 (energymass, 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
 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.
99Mo
99mTc
- + ~

+
e
42
43
131I
131Xe
- + ~

+
e
53
54
e-
~
 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.
 18O8 + e+ + 
15O  15N + e+ + 
8
7
18F
9
e+

Annihilation
e- + e+ = 2 g
or
e- +  + = 2 g
 each g 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:
x-ray
 e- + p  n + 
e.g. 7Be4 + e-  7Li3 + 
 secondary: emission of
characteristic x-rays or
Auger electrons
Auger e-

g decay (isomeric transition)
 emitting a g photon to release extra energy of
the nucleus: excited state  ground state
99mTc
99Tc

43
43 + g
 g photon ejected
out of the nucleus
 It often follows other
decays that result in
an unstable
nucleus.
g-ray
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 + 
 g-decay and internal conversion:
no changes for A & Z
Radioactivity

A(t) = l × N(t)
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
𝟏
+
𝐓𝐩 𝐓𝒃
Te =
𝐓𝐩𝐓𝐛
𝐓𝐩+𝐓𝐛
if Tp >> Tb, Te ≈ Tb
if Tp << Tb, Te ≈ Tp
Transient equilibrium
For 99mTc,
Max yield ~ 24 hrs
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
15
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
S2
S1
“amount” of radiation
(i.e., exposure, air
kerma)
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
S
 Used for measuring
“presence” of radiation
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
Pulse Height
Analysis
position
analysis
X
Y
Z
c o m p ut e r
amplify & sum
p r e - a m p
P M T
NaI(Tl) crystal
display
c o lli m a t o r
p a t ie n t
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
p.e
A: absorption
p.e
B: penetration
c.s
c.s
c.s
B
A
26
Event Location
+
X
=
+
x
-
x
-
y
Z
+
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
Common IR recon is the OSEM
Image recon - Iterative
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
PET image formation
t1
g
 t = t1 – t2
 t < 5 (to 12) ns ?
Yes
g
Register as a
“coincident” event
t2
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
Proton-rich nuclei: positron emission
p  n + e+ + 
18F
9
 18O8 + e+ + 
T1/2 = 110 min
15O
8
 15N7 + e+ + 
T1/2 = 2 min
13N
7
 13C6 + e+ + 
T1/2 = 10 min
11C
6
 11B5 + e+ + 
T1/2 = 20 min
82Rb
37
 82Kr36 + e+ + 
T1/2 = 73 sec
34
Annihilation location  Ejection location
 The distance depends on the e+ initial
kinetic energy and medium.
Isotope
Max E
Max d
FWHM
F-18
C-11
0.64 MeV
0.96 MeV
2.3 mm
3.9 mm
.22 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
35
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
36
Ultimate spatial resolution in PET
The uncertainties in annihilation
(location & residual particle momentum)
determine the ultimate spatial resolution
(~ 2 mm)
37
Types of coincidences
(correct LOR assigned)
True
(incorrect LOR assigned)
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
39
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
40
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
41
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∙t/2.
 Because of fast speed of light (c = 30 cm/ns),
fast time resolution of detection is
required for spatial accuracy.
t2
e.g. 0.067 ns  1 cm accuracy
 No such fast scintillator yet.
t1
The currently used LYSO for ToF
PET has a time resolution of 0.585 ns
which leads to 8.8 cm accuracy.
42
PET Data Corrections
 Attenuation
 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
43
CT number: Hounsield Units
CT number (x,y) = 1000 ((x,y) – water) / water
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
2015
carefully
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
48
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, g, e- , e+ : wR = 1
 For n: depends on energy
 For p (> 2 MeV): wR = 2,
 For a, fission fragments, heavy ions: wR = 20
49
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
50
Effective dose of NM procedures
51
Dose limits
Occupational:
ALARA 1 &
ALARA 2
Embryo/fetus:
5 mSv total
52
© Physics in Nuclear Medicine: Cherry, Sorenson and Phelps