Physics of nuclear medicine
Physics of nuclear medicine
introduction
historic and current NM technologies
„ principle of gamma camera
„ image quality and gamma camera
performance characteristics
„ gamma camera QC
„ data acquisition and processing methods
„ SPECT and SPECT/CT
„ other devices
„
„
Cherry SR, Sorenson JA, Phelps ME, “Physics
in Nuclear Medicine” 3rd ed (2003)
Chapters 12, 13, 14, 15, and 17
Introduction of nuclear medicine
„
radiopharmaceutical (a radionuclide attached
to a chemical compound) administered to
patient, then (hopefully) concentrated to the
abnormal sites through interaction between
the pharmaceutical and cells or molecules
„
decay of the radionuclide in the sites: emitting
of single or annihilation photons
„
detection of the emitted photons using gamma
camera, PET scanner or other devices
Introduction of nuclear medicine
„
sensitive to functional changes Æ earlier
detection of diseases and exclusive diagnostic
capability, e.g. perfusion for heart, brain,
kidney and lungs, and metabolism for cancers
„
interaction at cellular or molecular levels
bound directly to a target molecule (111Inmonoclonal antibody), low sensitivity
„ accumulated by molecular or cellular activities of
the target (18F-FDG, 99mTc-sestamibi, 131I−), high
sensitivity
„
Introduction of nuclear medicine
„
emitted photon energy: 70 to 511 keV
most low-energy photons absorbed by tissues
„ most high-energy photons penetrating the detector
„ charged particles penetrating only mm of tissue
„
pixel value of the image: concentration of
radioactivity
„ may need post-acquisition data processing
„ poorer image quality due to limited photon
number and poor spatial resolution
„
History of nuclear medicine
ƒ 1895 discovery of x-ray by Roentgen
ƒ 1896 discovery of radioactivity by Bequerel
ƒ 1898 production of radium by Curie
ƒ 1927 use of radon to measure the blood
transit time
ƒ 1930s invention of cyclotron by Lawrence
ƒ 1945 invention of nuclear reactor
ƒ 1951 rectilinear scanner to acquire images
History of nuclear medicine
ƒ 1958 invention of Anger camera
ƒ 1964 use of Tc-99m (I-131 only prior to 1964)
ƒ Tc-99m: metastable (T1/2 = 6.01 hr) pure γ decay
(E = 140 keV), flexible for labeling
ƒ I-131: electrons and 364 keV photons, thyroid
disorders only
ƒ 1970 derivation of image reconstruction
algorithm for tomography (CT, SPECT, PET)
ƒ 1998 rapid spread of PET and PET/CT
The most often used radionuclide: Tc-99m
metastable state of 99Tc43: T1/2 = 6.01 hr
Æ long enough for imaging but short for
reduced radiation dose to patient
„ pure γ decay: less radiation dose
„ E = 140 keV: enough photons to escape
from the patient body but most stopped by
the detector
„ flexible for labeling (attached to a
pharmaceutical): wide clinical applications
„
The most often used radionuclide: Tc-99m
The first rectilinear scanner (1951)
The first Anger camera (1958)
Dual-head gamma camera
SPECT gamma camera
Two detectors mounted on a rotation gantry
with different angles (180°, 90°) for tomography
Mobile semiconductor gamma camera
15×20×10 cm CZT detector
„ breast imaging
„ sports medicine
„ ER and OR imaging
3000 0.3×0.3 cm discrete crystals
48 PSPMT
Planar imaging
Dynamical imaging
Tc-99m MDP
Tc-99m sestamibi
3 mm lesion detectable
a series of images with time
SPECT imaging
SPECT imaging
short-axis
vertical
long-axis
transaxial
coronal
sagittal
horizontal
long-axis
Pros and cons of nuclear medicine
ƒ inherent molecular imaging
ƒ high sensitivity Æ low concentration of
radionuclide ~ pmol/liter
ƒ biodistribution depends not only on the
specificity of the carrier but also on the
route of administration.
noisy and suboptimal resolution
ƒ
Molecular imaging
ACR definition: Spatially localized and/or
temporally resolved sensing of molecular and
cellular processes in vivo.
„ SNM definition: Visualization, characterization,
and measurement of biological processes at the
molecular and cellular levels in human and
other living systems.
„
„
„
2-D or 3-D imaging and variation over time
Including NM, PET, MRI, MRS, optical, US and CT
with contrast
Molecular imaging modalities
modality
MRI
MRS
PET
SPECT
optical
US
sensitivity spatial
+
+
+++
++
+++
+++
Probes for molecular imaging
resolution
____
temporal contrast
10-100µm
1 cm
3-4 mm
8-12 mm
1-2 mm
1 mm
msec
min-h
min
min
msec
msec
+++
+
++
+
+++
++
ƒ bound directly to a target molecule
ƒ accumulated by molecular or cellular
activities of the target
ƒ activated by the target enzyme in vivo
+++: high, ++: medium, +: low
Smart NIR agents
Gamma camera
With specific enzyme cleavage, fluorophores are
separated from the backbone and each other so as
to markedly increase their fluorescence.
PH A
posit ion
amp & sum
X Y
Z
comput er
pr e - am p
PMT
det e ct or
co llim at or
display
pat ient
Major components
„
collimator
„
scintillation detector (NaI(Tl))
„
photomultiplier tube (PMT)
Collimator
to establish position relationship between γ photon
source and detector (projection imaging)
to convert x or γ photons to blue light photons
to convert blue photons to electrons and to
increase the number of electrons
„
electronics
„
display
to amplify and discriminate electrical signals
to display the image acquired by gamma camera
Collimator
to establish position relationship between the
source and detector
„ poor spatial resolution (ability
to see details) and low detection
efficiency (ability to count
photons)
„
The weak link of a gamma
camera: The collimator
determines the resolution
and sensitivity of a gamma
camera.
Parallel-hole collimator
design principle:
to optimize the trade-off between resolution
R and sensitivity η
„ hole size d and hole length l
„
t
smaller (or longer) holes
Æ higher R but lower η
„
septal thickness t
penetration < 5%
„
hole orientation:
parallel-hole, converging, diverging
pinhole: single hole
d
increasing source-to-detector
distance leads to
„ same sensitivity
„ same FOV
„ same image size
„ lower R
Converging beam collimator
increasing source-to-detector
distance leads to
„ decreasing FOV
„ increasing image size
„ lower R
„ higher sensitivity
fan
cone
Pinhole collimator
FOV
increasing source-to-detector
distance leads to
„ increasing FOV
„ decreasing image size
„ lower R
„ lower sensitivity
F
FOV
NaI (Tl) detector energy spectrum
NaI (Tl) detector energy spectrum
ƒ scintillation process to convert γ photons to blue
photons (E ≈ 3 ev or λ ≈ 415 nm)
ƒ theoretical deposited energy spectrum in detector
ƒ photopeak:
completely absorbed
ƒ compton edge:
Ee = E0 – Es (at 180º)
ƒ above the edge:
multiple scatter
ƒ below the edge:
single + multiple
photopeak
single scatter
double scatter
Compton edge
p.e
p.e
c.s
c.s
c.s
c.s
c.s
c.s
NaI (Tl) detector energy spectrum
NaI (Tl) detector energy spectrum
ƒ actual deposited energy spectrum in detector
ƒ spread photopeak caused by imperfect energy
resolution (random fluctuation of blue photon
number in detector)
ƒ backscatter peak due to photon penetrating the
detector, backscattered by surrounding material,
reentering detector, and absorbed by the detector:
Eb + Ee = E0
ƒ iodine escape peak 30 keV K-shell x-rays following
p.e. absorption of iodine: Ee ≅ E0 – 30 keV
ƒ lead K-shell x-ray (80 – 90 keV) following p.e. in lead
NaI (Tl) detector energy spectrum
Hg-197 w.o. scatter
I-131 w/w.o. scatter
backscatter
iodine escape
lead x-rays
e
c.s
x-ray
γ
NaI
p.e
p.e
x
x-ray
p.e
p.e
Advantages of NaI (Tl) detector
ƒ good stopping power for low-energy γ
(ρ = 3.67 g/cm3, Zeff = 50, PE dominant)
ƒ µ = 16.58 cm-1 @ 69 keV, t = 0.95 cm, T ≅ 0%
ƒ µ = 2.57 cm-1 @ 140 keV, t = 0.95 cm, T = 7.7%
ƒ µ = 0.72 cm-1 @ 247 keV, t = 0.95 cm, T = 48.5%
ƒ good detector linearity over 20 - 2000 keV
ƒ good conversion efficiency: ~ 26 eV/blue photon
ƒ good transparent to blue photons
ƒ blue photons matched with the performance of
PM tube
ƒ easy to manufacture
Disadvantages of NaI (Tl) detector
ƒ poor stopping power at Eγ > 200 keV
ƒ slow scintillation decay (230 ns)
Æ low counting rate
ƒ Compton scatter dominated at Eγ > 250
keV Æ poor spatial resolution
ƒ fragile
ƒ must keep dry
Photomultiplier tube
ƒ stable high voltage
ƒ 1200 V needed for 10 dynodes
ƒ 1% increase of high voltage Æ 10 % increase of
current at anode
ƒ sealed in glass and evacuated
ƒ wrapped in ‘Mu-metal’
(alloy of Fe, Ni, Cu)
to shield magnetic field
magnetic field affecting
focusing of electron beam
Photomultiplier tube
to create and amplify e-pulse
To preamplifier
photocathode (CsSb):
blue light to electrons
dynode
„ 9 - 12 dynodes:
+600v
each increasing electrons
3 – 6 times
+400v
cathod
„ anode:
collect electrons: 610 ≅ 6 × 107
„
anode
+700v
+500v
+300v
NaI(Tl)
0
Photomultiplier tube
ƒ 40 to 100 PM tubes (d = 5 cm) in a modern
gamma camera
ƒ photocathod directly coupled to detector
or connected using plastic light guides
ƒ anode connected
to electronics in
the tube base
ƒ ultrasensitive to
magnetic field
Electronics
„
Electronics
preamplifier
„
to amplify pulses from the PM tube
to match impedances between the detector
and subsequent components
„ to shape pulses for subsequent processing
„ voltage- and charge-sensitive circuits
„
„
„
pulse height analyzer: selecting the pulses of
certain voltage amplitudes (channel) Æ to
discriminate against unwanted γ photon
lower-level discriminator
upper-level discriminator
„ anticoincidence circuit
„
V2 (154 keV)
„
amplifier
V1 (126 keV)
to amplify pulses from mV to V
to reshape slow decay pulses to narrow ones
using resistor-capacitor circuit
„ baseline restoration circuit
„
„
Electronics
„
y
x = kx
y = ky
i
∑X − ∑X
+
i
i
−
i
i
i
Z
∑Y − ∑Y
+
i
−
i
i
i
Z
cathode ray tube (CRT)
linearity
dynamic range
contrast
brightness
Z = ∑ Xi+ + ∑ Xi− + ∑ Yi+ + ∑ Yi−
i
3
Display
ƒ position circuit
i
2
1
x
anode
y
x
z
e - so ur c e
d e f le c t io n
plat es
„
LCD: thin film transistor (TFT)
„
plasma display
scre e n
Detection of a γ-photon
„
Image quality
1 γ-photon Æ 1 electrical pulse (1 count)
The photon may experience p.e in the detector (A), c.s in the
detector (B), or c.s in the patient (C).
„
energy deposited on the detector Æ # blue photons Æ
pulse height
„
„
entire energy Æ maximum pulse height (A)
partial energy Æ reduced pulse height (B, C)
A
B
C
A
B
C
main factors of image quality:
1. contrast: the difference in count density
between two objects (or background)
C = (Imax-Imin)/(Imax+Imin), MTF (k) = Cout(k)/Cin(k)
2. resolution: ability to distinguish between
two objects in close distance, measured by
full width at half maximum (FWHM) of PSF
Æ image sharpness and details
3. artifacts
Factors determining image quality
„
camera performance characteristics
detection efficiency Æ count rate Æ image noise
Æ contrast, resolution
„ collimator performance Æ resolution
„ patient-to-detector distance Æ resolution
„ energy resolution Æ width of energy window Æ
scatter counts Æ contrast
„ non-uniform FOV Æ artifacts
„ dead time Æ artifacts or count loss at high count
rates
„
Factors determining image quality
patient motion Æ contrast, resolution,
artifacts
„ photon attenuation and scatter Æ contrast
„ low-pass filter in the reconstruction Æ
resolution
„ wrong energy window Æ contrast, artifacts
„
Non-uniform FOV
Image noise and off-peak effects
50,000
collimator defect
500,000
defected PMTs
1,000,000
Collimator performance
„ low-energy all purpose (LEAP) collimator
Æ better efficiency but worse resolution
„ low-energy high resolution (LEHR)
Æ better resolution but worse efficiency
„ low-energy fan-beam (LEFB) collimator
„ low-energy cone-beam (LECB) collimator
„ medium-energy all purpose (MEAP)
„ high-energy all purpose (HEAP) collimator
2,000,000
Patient-to-detector distance
2
2
R sys = R int
+ R col
system resolution Rsys
intrinsic resolution Rint
collimator resolution Rcol
ƒ at d > 5 cm, Rcol >> Rint
ƒ larger d Æ poorer Rcol
Æ poorer Rsys
Detection efficiency
Energy resolution and energy window
energy spread due mainly to fluctuation of the
blue photon number in the detector and of
electric signal in the subsequent electronics
„ energy resolution: 8 – 10% for NaI
~ 20% for BGO
„ energy window: ±10% for NaI
±30% for BGO
„ better energy resolution Æ smaller energy
window Æ fewer scatter counts
„
Multiple energy window
„
summing images to increase count rate
Tl-201: 70±10% keV + 167±10% keV
In-111: 171 keV + 245 keV
Ga-67: 93 keV + 185 keV + 300 keV
„
dual energy window simultaneous
acquisition to accelerate study
e.g. cardiac perfusion: Tc-99m and Tl-201
140±10% keV and 70 keV + 167 keV
Æ Down scatter contamination must be
corrected.
Performance at high count rates
ƒ pulse pile-up effects
Two events acquired at different locations but
same time are recorded as a single event with
summed energy at a location between them.
ƒ 2 scatter counts possibly accepted as 1 event
Æ image quality degradation
ƒ rejected if both events in
photopeak
Æ count loss
Performance at high count rates
Camera quality control
ƒ typical dead time in clinic: 4 – 8 µs
5 µs dead time Æ 20% count loss at 40,000 cps
e.g. first-pass cardiac study: 100,000 cps
ƒ very high count rate may paralyze camera.
„
uniformity: daily, 256×256, > 4M counts
„
resolution: weekly, 512×512, > 4M counts
„
energy and COR: monthly
„
Uniformity of detector
integral unif = max. count – min. count
< 5%
max. count + min. count
differential unif = max. count diff. – min. count diff.
< 5%
max. count diff. + min. count diff.
acquisition of new uniformity maps and
possible energy map: quarterly, > 30M
counts
Bar phantoms
Data acquisition
„
„
„
„
„
Matrix size
collimator: LEAP, LEHR, LEFB, LECB, MEAP,
HEAP
energy window: match the radioisotope and energy
resolution
pixel size: 1/3 ~ 1/2 of spatial resolution
matrix size =
detector size
pixel size
64×64
64×64, 128×128 or 256×256, 2 bytes in pixel depth
patient close to the detector, steady, in FOV
Data acquisition
static acquisition: recording x and y in a
matrix
„ dynamic acquisition: recording a sequence
of static images at different time, each
image corresponding a certain time period
„ list mode acquisition: recording x, y, t (and
R-wave trigger for gated list mode), no
frames during acquisition and later
reframing needed
„
128×128
Data processing
windowing in display: 2 byte image displayed
on a 256 gray color monitor
„ 2-D filtering the image: reducing noise
„ temporal filtering for dynamic images:
reducing noise
„ ROI: maximum, minimum, mean counts, s.d.
„ time-activity curve from a dynamic image:
renogram, first-pass
„ count profile: often used in camera QC
„
Time-activity curve
SPECT
eliminate overlaying and underlying
activity of a slice
„ better contrast
„ more accurate lesion localization
„ more demanding technically and longer
data acquisition
„ more severe image noise
Data acquisition
Data acquisition
a sequence of 2-D static images at different
angular positions (views)
„ detector rotation range
„
„
circular or elliptical orbit
closer to the patient Æ better spatial resolution
180º with 2 perpendicular detectors or
360º with 2 opposite detectors
45
ºR
AO
45
ºL
PO
„
step-shoot or continuous acquisition
Data acquisition
energy window
„ acquisition time or counts per view
„ matrix size for each view depending on the
spatial resolution (64×64 or 128×128)
„ number of views = matrix size for 360º SPECT
(64 or 128)
„ ECG gated for cardiac SPECT
View number
„
128 views
64 views
43 views
32 views
SPECT camera performance
SPECT reconstruction
ƒ mechanical center coinciding with COR
„
using software, calibration and testing
„
ƒ all detectors aligned accurately in axial
direction to acquire same slice data
ƒ uniformity < 1% Æ ~ 41 M for 64×64
image
„
filtered backprojection algorithm (FBP)
iterative algorithms (OSEM, MLEM)
compensation techniques
attenuation
scatter
patient motion
spatially variant blurring
Filtered backprojection
Filtered backprojection
„ ramp filter required even for noise-free data
„
Hann filter: 0.5 k (1 + cos(πk/kc))
„
Butterworth filter:
filter
to remove 1/r
blurring
„ low-pass filter
k
1+ k /kc
Ramp
Hann
BW 4.25
BW 4.15
BW 8.15
4.25
2n
4.15
8.15
to suppress noise
1
0
frequency
Iterative algorithm
to assume an initial image and to
update the image iteratively
Steps of one iteration:
1. to project the image
2. to compare to the data
3. to backproject P - P0
4. to update the image
I1 = I0 + bpj (P - P0)
Photon attenuation and scatter
„ attenuation decreased photon number on
P
I0
P0
P-P0
I1
AB due to absorption and scatter, half of
140 keV photons absorbed over ~ 5 cm in
water
de t e ct or
„ scatter and downscatter
D
B
misplaced source position
θ
C instead of A
C
A
pa t ie nt
Photon attenuation effect
Attenuation compensation
ƒ geometric mean
P = (p1× p2
p1
)1/2
exact compensation for a point
source in uniform medium
p2
ƒ analytical method: uniform attenuation built in
FBP, magnifying image noise
ƒ Chang’s method, for uniform µ (brain SPECT)
ƒ transmission images Æ attenuation map Æ used
in iterative algorithm, most accurate and best noise
control
Transmission image
ƒ Gd-153 (97-103 keV, 8 mo)
moving line source for parallel-hole collimators
stationary line source for fan-beam collimators
stationary point source for cone-beam collimators
ƒ x-ray source and detector (SPECT/CT)
ƒ p = p0 exp(-Σµi∆xi): Σµi∆xi= ln(p0/p) Æ µi
Transmission image
ƒ scaling µ to the photon energy of emission image
ƒ downscatter contamination
Photon scatter and compensation
Photon scatter and compensation
reduced contrast
„ spill of counts from a hot spot
„ scatter model built in iterative algorithm
„ deconvolution
„ dual energy window method prior to image
reconstruction
„
data P acquired from 126 - 154 keV
data S acquired from 91 - 125 keV
compensated data = P - S/W, e.g. W = 2
Partial volume effects
ƒ occurring for small sources Vs
ƒ resolution volume VR = π.FWHMT2.FWHMA
ƒ when Vs < VR, pixel value < concentration
Partial volume effects
ƒ reducing contrast and error in quantitaion,
‘spillover’
ƒ recovery coefficient RC = Capparent/Ctrue
ƒ RC used to correct
PV with known Vs
and VR , but not
feasible in clinic
Compensation for movement
„
patient motion
1. a Tc point source with Tl patient
2. fast, repeated acquisition
3. software correction
„
physiological organ movement
gated cardiac imaging
SPECT/CT scanner
ƒ CT: to create attenuation map for SPECT
attenuation correction with any radioisotopes
ƒ Image fusion for SPECT and CT to better
localize the disease
ƒ SPECT/CT advantage over PET/CT: possible
to label the imaging agent with a therapeutic
isotope to highly-specifically treat the disease
SPECT/CT scanner
A gamma camera and a
multi-slice spiral CT
scanner on the same
gantry with a single
patient table
SPECT/CT scanner
ƒ GE Infinia Hawkeye
helical CT, 140 keV, 2.5 mA, 4 rows × 384
Elements, 16 slice/min, in-plane res = 4 lp/cm,
sw = 0.5 mm
ƒ Siemens Symbia T, T2, T6, T16
ƒ Philips Precedence 6, 16 slice
SPECT/CT image fusion
Cardiology
SPECT/CT image fusion
Oncology
Gas-filled detectors
to measure activity only
„ ionization chamber: dose calibrator and survey meter
„ Geiger-Muller counter
(quenching gas):
sensitive survey meter,
area monitor
.
+
e
h
γ
_
Dose calibrator
ƒ high pressure (12 a.p.)
ƒ
ƒ
ƒ
Ar-filled ion chamber
to assay activity only
sample volume effect
linearity of response
versus sample activity
Dose calibrator quality control
constancy: daily, Cs-137 (660 keV, 30 y) and
Co-57 (122 keV, 9 mo): ±10%
„ linearity: quarterly, 10 µCi - 300 mCi
Tc-99m, long-term decay or lineator: ±10%
„ accuracy: yearly, Cs-137 and Co-57: ±5%
„ geometry: upon installation, Tc-99m: ±10%
„
Well counter
ƒ detection efficiency
intrinsic: 100% for Eγ < 150 keV
geometry: for < 1 mL sample at bottom: 93%
ƒ absolute activity: Asam= Astd× [Csam/Cstd]
ƒ shielding
ƒ energy calibration
ƒ dead time ~ 4 µs
A < 10 kBq
for 50 kBq, 18% loss
Well counter
detecting in-vitro x- and γ-rays
main components
ƒ single NaI crystal (4.5×5 cm or 1.6×3.8
cm) with a hole for sample
ƒ a PM tube
ƒ preamplifier
ƒ amplifier
ƒ SCA or MCA
ƒ readout device
Thyroid probe
measuring thyroid uptake of
I-131 in-vivo
ƒ 5×5 cm NaI(Tl) with 15 cm
long conical collimator
ƒ pointing to neck, thigh bkg
ƒ calibration phantom with
known activity for calculating
uptake
ƒ 1 – 2 cm diff. in depth Æ
10 – 40% diff. in count rate
Miniature γ probe
ƒ used in surgery
ƒ detecting sentinel lymph nodes with Tc-colloid
ƒ detecting radioactive monoclonal antibodies of
In-111, I-131, I-125
ƒ 5×10 mm, high directional
sensitivity,
light, easy
to use, no
hazard