Physics of nuclear medicine
introductionhistoric and current NM technologies principle of gamma cameraimage quality and gamma camera performance characteristicsgamma camera QCdata acquisition and processing methodsSPECT and SPECT/CTother devices
Physics of nuclear medicine
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 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 (111In-monoclonal antibody), low sensitivityaccumulated 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 keVmost 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 radioactivitymay need post-acquisition data processingpoorer image quality due to limited photon number and poor spatial resolution
History of nuclear medicine
1895 discovery of x-ray by Roentgen1896 discovery of radioactivity by Bequerel1898 production of radium by Curie1927 use of radon to measure the blood
transit time 1930s invention of cyclotron by Lawrence1945 invention of nuclear reactor1951 rectilinear scanner to acquire images
History of nuclear medicine
1958 invention of Anger camera1964 use of Tc-99m (I-131 only prior to 1964)
Tc-99m: metastable (T1/2 = 6.01 hr) pure γ decay (E = 140 keV), flexible for labeling
I-131: electrons and 364 keV photons, thyroid disorders only
1970 derivation of image reconstruction algorithm for tomography (CT, SPECT, PET)1998 rapid spread of PET and PET/CT
The most often used radionuclide: Tc-99m
metastable state of 99Tc43: T1/2 = 6.01 hr long enough for imaging but short for
reduced radiation dose to patient
pure γ decay: less radiation doseE = 140 keV: enough photons to escape from the patient body but most stopped by the detectorflexible 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 detectorbreast imaging sports medicine ER and OR imaging
3000 0.3×0.3 cm discrete crystals48 PSPMT
Planar imaging
Tc-99m sestamibi3 mm lesion detectable
Tc-99m MDP
Dynamical imaging
a series of images with time
SPECT imaging
transaxial coronal sagittal
SPECT imaging
short-axis
verticallong-axis
horizontallong-axis
Pros and cons of nuclear medicine
inherent molecular imaginghigh sensitivity low concentration of
radionuclide ~ pmol/liter
biodistribution depends not only on the specificity of the carrier but also on the route of administration.
noisy and suboptimal resolution
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
resolution ____modality sensitivity spatial temporal contrast
MRI + 10-100µm msec +++MRS + 1 cm min-h +PET +++ 3-4 mm min ++SPECT ++ 8-12 mm min +optical +++ 1-2 mm msec +++US +++ 1 mm msec ++
+++: high, ++: medium, +: low
Probes for molecular imaging
bound directly to a target molecule
accumulated by molecular or cellular activities of the target
activated by the target enzyme in vivo
Smart NIR agents
With specific enzyme cleavage, fluorophores are separated from the backbone and each other so as to markedly increase their fluorescence.
Gamma camera
pat ient
collimat ordet ect or
PMT
pre- amp
amp & sum
posit ionPHA
comput er
display
X Y Z
Major components
collimatorto establish position relationship between γ photon source and detector (projection imaging)
scintillation detector (NaI(Tl))to convert x or γ photons to blue light photons
photomultiplier tube (PMT)to convert blue photons to electrons and to increase the number of electrons
electronicsto amplify and discriminate electrical signals
displayto display the image acquired by gamma camera
Collimator
to establish position relationship between the source and detectorpoor spatial resolution (abilityto see details) and low detection efficiency (ability to count photons)The weak link of a gammacamera: The collimatordetermines the resolutionand sensitivity of a gammacamera.
Collimator
design principle:to optimize the trade-off between resolutionR and sensitivity ηhole size d and hole length l
smaller (or longer) holeshigher R but lower η
septal thickness tpenetration < 5%hole orientation:parallel-hole, converging, divergingpinhole: single hole
d
t
Parallel-hole collimator
increasing source-to-detectordistance leads to
same sensitivitysame FOVsame image sizelower R
Converging beam collimator
increasing source-to-detectordistance leads to
decreasing FOVincreasing image sizelower Rhigher sensitivity
FOV
Ffan cone
Pinhole collimator
increasing source-to-detectordistance leads to
increasing FOVdecreasing image sizelower Rlower sensitivity
FOV
NaI (Tl) detector energy spectrum
scintillation process to convert γ photons to blue photons (E ≈ 3 ev or λ ≈ 415 nm)theoretical deposited energy spectrum in detector
photopeak:completely absorbedcompton edge:Ee = E0 – Es (at 180º)above the edge: multiple scatterbelow the edge:single + multiple
NaI (Tl) detector energy spectrum
photopeak single scatter double scatter
p.e p.e c.sc.s
Compton edge
c.s c.sc.s
c.s
NaI (Tl) detector energy spectrum
actual deposited energy spectrum in detectorspread photopeak caused by imperfect energy resolution (random fluctuation of blue photon number in detector)backscatter peak due to photon penetrating the detector, backscattered by surrounding material, reentering detector, and absorbed by the detector:Eb + Ee = E0
iodine escape peak 30 keV K-shell x-rays following p.e. absorption of iodine: Ee ≅ E0 – 30 keVlead K-shell x-ray (80 – 90 keV) following p.e. in lead
NaI (Tl) detector energy spectrum
backscatter iodine escape lead x-rays
p.e
c.s
p.e
p.e
NaIx-ray
x-rayp.e
e
x
γ
NaI (Tl) detector energy spectrum
Hg-197 w.o. scatter I-131 w/w.o. scatter
Advantages of NaI (Tl) detector
good stopping power for low-energy γ(ρ = 3.67 g/cm3, Zeff = 50, PE dominant)
µ = 16.58 cm-1 @ 69 keV, t = 0.95 cm, T ≅ 0%µ = 2.57 cm-1 @ 140 keV, t = 0.95 cm, T = 7.7%µ = 0.72 cm-1 @ 247 keV, t = 0.95 cm, T = 48.5%
good detector linearity over 20 - 2000 keV good conversion efficiency: ~ 26 eV/blue photongood transparent to blue photonsblue photons matched with the performance of PM tubeeasy to manufacture
Disadvantages of NaI (Tl) detector
poor stopping power at Eγ > 200 keV
slow scintillation decay (230 ns)low counting rate
Compton scatter dominated at Eγ > 250 keV poor spatial resolutionfragilemust keep dry
Photomultiplier tube
to create and amplify e-pulse
photocathode (CsSb): blue light to electrons
9 - 12 dynodes: each increasing electrons3 – 6 times
anode: collect electrons: 610 ≅ 6 × 107 NaI(Tl) 0
+ 3 0 0 v+ 4 0 0 v
+ 5 0 0 v+ 6 0 0 v
+ 7 0 0 v
cathod
anode
dynode
To preamplifier
Photomultiplier tube
stable high voltage1200 V needed for 10 dynodes1% increase of high voltage 10 % increase of current at anode
sealed in glass and evacuatedwrapped in ‘Mu-metal’(alloy of Fe, Ni, Cu) to shield magnetic fieldmagnetic field affecting focusing of electron beam
Photomultiplier tube
40 to 100 PM tubes (d = 5 cm) in a modern gamma cameraphotocathod directly coupled to detector or connected using plastic light guidesanode connectedto electronics inthe tube baseultrasensitive to magnetic field
Electronics
preamplifierto amplify pulses from the PM tubeto match impedances between the detector and subsequent componentsto shape pulses for subsequent processingvoltage- and charge-sensitive circuits
amplifier to amplify pulses from mV to Vto reshape slow decay pulses to narrow ones using resistor-capacitor circuitbaseline restoration circuit
Electronics
pulse height analyzer: selecting the pulses of certain voltage amplitudes (channel) to discriminate against unwanted γ photon
lower-level discriminatorupper-level discriminatoranticoincidence circuit
1 2 3
V2 (154 keV)
V1 (126 keV)
Electronics
position circuit
x
y
Z
YYky
Z
XXkx
YYXXZ
ii
ii
y
ii
ii
x
ii
ii
ii
ii
∑∑
∑∑
∑∑∑∑
−+
−+
−+−+
−=
−=
+++=
Display
cathode ray tube (CRT)
linearity
dynamic range contrastbrightness
LCD: thin film transistor (TFT)
plasma display
e- source
anode
def lect ion plates
screen
z
y x
Detection of a γ-photon
1 γ-photon 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 # blue photons pulse height
entire energy maximum pulse height (A)partial energy reduced pulse height (B, C)
A B C BA C
Image quality
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
image sharpness and details3. artifacts
Factors determining image quality
camera performance characteristics
detection efficiency count rate image noise contrast, resolution
collimator performance resolutionpatient-to-detector distance resolution
energy resolution width of energy window scatter counts contrast
non-uniform FOV artifactsdead time artifacts or count loss at high count rates
Factors determining image quality
patient motion contrast, resolution, artifacts photon attenuation and scatter contrastlow-pass filter in the reconstructionresolutionwrong energy window contrast, artifacts
Non-uniform FOV
collimator defect defected PMTs
Image noise and off-peak effects
50,000 500,000
1,000,000 2,000,000
Collimator performance
low-energy all purpose (LEAP) collimator better efficiency but worse resolution
low-energy high resolution (LEHR) better resolution but worse efficiency
low-energy fan-beam (LEFB) collimatorlow-energy cone-beam (LECB) collimatormedium-energy all purpose (MEAP) high-energy all purpose (HEAP) collimator
Patient-to-detector distance
system resolution Rsys
intrinsic resolution Rint
collimator resolution Rcol
at d > 5 cm, Rcol >> Rint
larger d poorer Rcol
poorer Rsys
R R R 2col
2intsys +=
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 electronicsenergy resolution: 8 – 10% for NaI
~ 20% for BGOenergy window: ±10% for NaI
±30% for BGObetter energy resolution smaller energy window 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 studye.g. cardiac perfusion: Tc-99m and Tl-201140±10% keV and 70 keV + 167 keV
Down scatter contamination must be corrected.
Performance at high count rates
pulse pile-up effectsTwo events acquired at different locations but same time are recorded as a single event with summed energy at a location between them.
2 scatter counts possibly accepted as 1 event image quality degradation
rejected if both events in photopeak
count loss
Performance at high count rates
typical dead time in clinic: 4 – 8 µs5 µs dead time 20% count loss at 40,000 cpse.g. first-pass cardiac study: 100,000 cps
very high count rate may paralyze camera.
Camera quality control
uniformity: daily, 256×256, > 4M counts
resolution: weekly, 512×512, > 4M counts
energy and COR: monthly
acquisition of new uniformity maps and possible energy map: quarterly, > 30Mcounts
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.
Bar phantoms
Data acquisition
collimator: LEAP, LEHR, LEFB, LECB, MEAP, HEAPenergy window: match the radioisotope and energy resolutionpixel size: 1/3 ~ 1/2 of spatial resolution
64×64, 128×128 or 256×256, 2 bytes in pixel depthpatient close to the detector, steady, in FOV
size pixelsizedetector size matrix =
Matrix size
64×64 128×128
Data acquisition
static acquisition: recording x and y in a matrixdynamic acquisition: recording a sequence of static images at different time, each image corresponding a certain time periodlist mode acquisition: recording x, y, t (and R-wave trigger for gated list mode), no frames during acquisition and later reframing needed
Data processing
windowing in display: 2 byte image displayed on a 256 gray color monitor 2-D filtering the image: reducing noisetemporal filtering for dynamic images: reducing noiseROI: 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 contrastmore accurate lesion localization more demanding technically and longer data acquisitionmore severe image noise
Data acquisition
a sequence of 2-D static images at different angular positions (views)detector rotation range
180º with 2 perpendicular detectors or 360º with 2 opposite detectors
45º RAO
45º LPO
Data acquisition
circular or elliptical orbitcloser to the patient better spatial resolution
step-shoot or continuous acquisition
Data acquisition
energy windowacquisition time or counts per viewmatrix 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
mechanical center coinciding with COR using software, calibration and testing
all detectors aligned accurately in axial direction to acquire same slice data
uniformity < 1% ~ 41 M for 64×64 image
SPECT reconstruction
filtered backprojection algorithm (FBP)iterative algorithms (OSEM, MLEM)compensation techniques
attenuationscatterpatient motionspatially variant blurring
Filtered backprojection
ramp filter required even for noise-free data to remove 1/r blurring
low-pass filterto suppress noise
Filtered backprojection
Hann filter: 0.5 k (1 + cos(πk/kc))
Butterworth filter:
0
k1 + k / k c
2n
4.25 4.15 8.15
RampHannBW 4.25BW 4.15BW 8.15
frequency
filte
r
1
Iterative algorithm
to assume an initial image and toupdate the image iterativelySteps of one iteration:
1. to project the image2. to compare to the data3. to backproject P - P0
4. to update the imageI1 = I0 + bpj (P - P0)
I0 P0
P
I1
P-P0
Photon attenuation and scatter
attenuation decreased photon number on AB due to absorption and scatter, half of 140 keV photons absorbed over ~ 5 cm inwaterscatter and downscatter
misplaced source position C instead of A
det ect or
A
B
C
D
pat ient
θ
Photon attenuation effect Attenuation compensation
geometric meanP = (p1× p2)1/2
exact compensation for a pointsource in uniform medium
analytical method: uniform attenuation built in FBP, magnifying image noise
Chang’s method, for uniform µ (brain SPECT)
transmission images attenuation map used in iterative algorithm, most accurate and best noise control
p1
p2
Transmission image
Gd-153 (97-103 keV, 8 mo)moving line source for parallel-hole collimatorsstationary line source for fan-beam collimatorsstationary point source for cone-beam collimators
x-ray source and detector (SPECT/CT)p = p0 exp(-Σµi∆xi): Σµi∆xi= ln(p0/p) µi
Transmission image
scaling µ to the photon energy of emission image downscatter contamination
Photon scatter and compensation
reduced contrast
spill of counts from a hot spotscatter model built in iterative algorithmdeconvolution dual energy window method prior to image
reconstructiondata P acquired from 126 - 154 keVdata S acquired from 91 - 125 keVcompensated data = P - S/W, e.g. W = 2
Photon scatter and compensation
Partial volume effects
occurring for small sources Vs
resolution volume VR = π.FWHMT2.FWHMA
when Vs < VR, pixel value < concentration
Partial volume effects
reducing contrast and error in quantitaion, ‘spillover’recovery coefficient RC = Capparent/Ctrue
RC used to correct PV with known Vsand VR , but not feasible in clinic
Compensation for movement
patient motion1. a Tc point source with Tl patient2. fast, repeated acquisition 3. software correction
physiological organ movementgated cardiac imaging
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
CT: to create attenuation map for SPECT attenuation correction with any radioisotopesImage fusion for SPECT and CT to better localize the diseaseSPECT/CT advantage over PET/CT: possible to label the imaging agent with a therapeutic isotope to highly-specifically treat the disease
SPECT/CT scanner
GE Infinia Hawkeyehelical CT, 140 keV, 2.5 mA, 4 rows × 384Elements, 16 slice/min, in-plane res = 4 lp/cm,sw = 0.5 mm
Siemens Symbia T, T2, T6, T16
Philips Precedence 6, 16 slice
SPECT/CT image fusion
Cardiology
SPECT/CT image fusion
Oncology
Gas-filled detectors
to measure activity onlyionization chamber: dose calibrator and survey meterGeiger-Muller counter(quenching gas): sensitive survey meter,area monitor
γh
e
+
_
.
Dose calibrator
high pressure (12 a.p.) 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
detecting in-vitro x- and γ-raysmain components
single NaI crystal (4.5×5 cm or 1.6×3.8 cm) with a hole for samplea PM tubepreamplifier amplifierSCA or MCAreadout device
Well counter
detection efficiencyintrinsic: 100% for Eγ < 150 keV geometry: for < 1 mL sample at bottom: 93%absolute activity: Asam= Astd× [Csam/Cstd]shieldingenergy calibrationdead time ~ 4 µsA < 10 kBqfor 50 kBq, 18% loss
Thyroid probe
measuring thyroid uptake of I-131 in-vivo
5×5 cm NaI(Tl) with 15 cm long conical collimatorpointing to neck, thigh bkgcalibration phantom with
known activity for calculatinguptake1 – 2 cm diff. in depth
10 – 40% diff. in count rate
Miniature γ probe
used in surgerydetecting sentinel lymph nodes with Tc-colloiddetecting radioactive monoclonal antibodies of In-111, I-131, I-125
5×10 mm, high directional sensitivity, light, easyto use, no hazard