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Nuclear Medicine Basic Science Lectures Stephen Bowen
October 18, 2011 Email: [email protected]
1
Stephen Bowen, Ph.D.
Nuclear Medicine Basic Science Lectures October 18, 2011
Introduction to Positron Emission Tomography
Planar and SPECT Cameras Summary
System components: – Collimator Detector Electronics
Collimator – Types: Parallel, Converging, Diverging, Pinhole, Multi-pinhole – Performance: Penetration, Resolution, Efficiency
Detector: – Components: Scintillator crystal, Optical spacer, PMTs – Performance: Efficiency, Intrinsic (spatial) resolution, Energy resolution
Acquisition modes: – Frame vs List mode – Static (time-averaged), Dynamic (TAC), Gated (cardiac / respiration)
Camera QA corrections: – Uniformity, Linearity, Photo-peak window, Multi-energy registration
SPECT QA/QC: – Center-of-rotation, Head tilt, uniformity
PET Definition
Positron – Uses positron (+) emitting radio-isotopes to label physiologic
tracers (e.g. glucose metabolism, cell proliferation, hypoxia) – Positrons are unstable in that they annihilate with electrons,
resulting in two anti-parallel photons each with energy 511 keV – PET scanners measure coincident annihilation photons and
collimate the source of the decay via coincidence detection
Emission – The source of the signal is emission of annihilation photons from
within the patient, as opposed to photons transmitted through the patient in x-ray imaging
Tomography – Three-dimensional volume image reconstruction through collection
of projection data from all angles around the patient
Positron Annihilation
~ 1 mm
N N
N P
P P P
P P N N
Parent nucleus: unstable due to excessive P/N ratio (18F, 11C, 13N, 15O, 124I)
positron emission
two anti-parallel annihilation
photons
positron annihilates with an electron: mass energy is converted to electromagnetic energy resulting in
positron may scatter
e- e+
N N
N P
P P P
P N N N
proton decays to neutron
(18O, 11B, 13C, 15N, 124Te) + + +
neutrino also emitted
(inconsequential to PET)
e+
Nuclear Medicine Basic Science Lectures Stephen Bowen
October 18, 2011 Email: [email protected]
2
detector i
detector j
detector i-j coincidence
coincidence events
Emission Coincidence Detection
time
i
j
Random rate determined from i, j singles rates
Tomographic Data Acquisition
All coincidence events acquired over time allows dynamic imaging
Sort LOR into sinograms and/or save list-mode data
Group coincidence data into parallel projections (LOR) for tomographic reconstruction
LOR
Projection Angle
Coincidence Events: Signal and Noise
True coincidence:
anti-parallel photons travel directly to and are absorbed
by detectors
PET detectors seek simultaneous gamma ray absorptions (“simultaneous” → within ~ 5-10 ns)
Random coincidence:
photons from different nuclear decays are detected
simultaneously
NOTE: scattered and random coincidence lines-of-response need not pass through object!
Scattered coincidence:
one or both photons change direction from a scatter before
detection
PET signal components
S and R has to be estimated and removed
Estimation challenges – R estimation accurate and efficient (singles method) – S estimation can have significant errors (e.g. lung)
P = T + S + RMeasured Projections
True Signal
Noise from Scatter
Noise from Random
T !"t # rij ! activity
R!"t # ri # rj ! activity2 ri = single photon
detection rate in pixel i
rij = photon pair detection rate in detector pixels i,j
Nuclear Medicine Basic Science Lectures Stephen Bowen
October 18, 2011 Email: [email protected]
3
PET Acquisition: 2D vs. 3D Mode Form of collimation (septa) that separate axial slices in 2D PET
- reduces scattered and random events (also reduces trues!)
2D PET uses axial septa 3D PET uses no septa
detector crystals
septa & end shielding
blocked
scatter & randoms
PET Contrast and Quantitation Noise from Scattered Coincidence
– Predominantly Compton scatter. Gamma rays scatter off of electrons, change direction and lose energy.
• results in misplaced events due to change in photon direction (loss of contrast)
• energy discrimination can eliminate scatter (but not all) • correction based on scatter equations, scatter object (CT), measured
data
Noise from Random Coincidence – Random events proportional to singles rates squared – Mean random events estimated in two ways:
• measured with delayed coincidence window (direct measure, high noise due to random rate)
• calculated based on system singles rates (low noise singles-based calculation)
Attenuation of Signal – Gamma rays are absorbed in the patient
• Variability due to heterogeneity of attenuating tissue – Correctable with properly aligned attenuation map
Signal and Noise Estimates
NEC = T 2
T + S +!R
depends on randoms estimation method
Noise Equivalent Counts (NEC)
Scatter Fraction (SF)
SF = ST + S
SNR = T! P( )
!T
T + S +!R
Signal to Noise Ratio (SNR)
NEC = T 2
T + S +!R
0
100
200
300
400
0 5 10 15 20
DSTE Count Rates: NEMA Cylinder Phantom
Cou
nt ra
te (k
cps)
Phantom activity (mCi)
3D R
3D T
2D S
3D S 2D T
2D R
0
20
40
60
80
100
0 5 10 15 20
DSTE Measured NEC
NE
C ra
te (k
cps)
Phantom activity (mCi)
3D NEC
2D NEC
2D = 20% 3D = 34%
FDG oncology patient activity:
PET Contrast: 2D vs. 3D mode
SF = ST + S
Ascan = Ainj !e"! tscan"tinj( )
Ascan = 10"15mCi( ) ! 12
60min110min
# 7"10mCi
Nuclear Medicine Basic Science Lectures Stephen Bowen
October 18, 2011 Email: [email protected]
4
Annihilation Photon Attenuation Anti-parallel gamma ray coincidence detection means that attenuation is
independent of position along any line of response.
P1 = e− µ x( )dx0
′x
∫P2 = e
− µ x( )dx′x
a
∫
PC = P1P2 = e− µ x( )dx0
a
∫
detector 1 detector 2
x x’ a 0
Attn. of photon 1: Attn. of photon 2:
Total attn. of coincidence pair:
Pc is independent of annihilation position x’
PET/CT Scanners" CT scan used for PET AC" CT image is downsampled to PET resolution"
– Advantages"• Fast acquisition"• Low image noise"
– Disadvantages"• Higher dose"• Attn. coeff. measured with poly-energetic
photons < 140 keV"
Consequences of CTAC! More accurate quantitation"
PET/CT Attenuation Correction (AC)
CT (diagnostic)
same CT, re-‐sampled to PET resolution
PET/CT Scanners
Micro PET/CT Clinical PET/CT
PET Detector Block
Reflective light sealing tape
Two dual photocathode PMTs
• PET scanners are assembled in block modules
• Each block uses a limited number of PMTs to decode an array of scintillation crystals
gamma rays scintillation light
signal out to processing
Nuclear Medicine Basic Science Lectures Stephen Bowen
October 18, 2011 Email: [email protected]
5
Block matrix: BGO crystals""6 x 8 crystals (axial by transaxial)""Each crystal:"" "6.3 mm axial"" "4.7 mm transaxial"
"Scanner construction""Axial:"" "4 blocks axially = 24 rings"" "15.7 cm axial extent""Transaxial:"" "70 blocks around = 560 xtals"" "88 cm BGO ring diameter"" "70 cm patient port"
13,440 individual crystals"
Inside GE Discovery STE PET/CT Positron Physics
– Positron Range – Photon Non-colinearity
Detectors – Response function
Ring Geometry – Non-uniform LOR sampling – Depth-of-interaction
Reconstruction Filters
PET Spatial Resolution
Rsystem = Rpos. phys.2 + Rdet
2 + Rsampl2 + Rrecon
2
Resolution components add in quadrature
Positron Physics Resolution
Positron range • maximum energy of isotope • scatter medium
Photon non-colinearity – Non-colinearity: Rnon-colin = 0.0022 x Ring Diameter – Clinical scanner: Diam. ~ 80 - 90 cm; Rnon-col. ~ 2 mm – Small animal scanner ~ 15 - 20 cm; Rnon-col. ~ 0.4 mm
data from Derenzo, et al. IEEE TNS 33:565-569, 1986
0
0.5
1
1.5
2
2.5
3
0 0.5 1 1.5 2 2.5 3 3.5
Pos
itron
rms
rang
e (m
m)
Maximum positron kinetic energy (MeV)
82Rb
18F 11C
68Ga
13N 15O
Tran
sver
se Axial
A
B
C
D
Signal Decoding Energy, E = A + B + C + D
Axial position, Z = (C +D) / E Transverse position, X = (B + D) / E
Radial position: not determined (no DOI)
Light Sharing Relative PMTs signal heights
depend on crystal of interaction
PMTs
A C
Rad
ial
Axial
Detector Signal Decoding
Nuclear Medicine Basic Science Lectures Stephen Bowen
October 18, 2011 Email: [email protected]
6
Detector Resolution
• Peaks for different crystals at different positions"• Window center and width adjusted for each crystal"
PET Ring Geometry Effect on Resolution
center
edge
entrance position and true line-of-response
detection position and assigned line-of-response
photon penetration
Depth-of-Interaction error:
w/2
w
Data Sampling Error: Coincidence lines-of-response are not uniformly spaced across a ring detector
Interpolate to uniform spacing, or account for non-uniformity in reconstruction
Resolution Effect of Smoothing vs. Noise with FBP Human abdomen simulation with 2cm diam. lesion 2:1 contrast
more counts (less noise)
less smoothing (more noise)
1. Absorption efficiency of detectors – scintillation crystal attenuation coefficient – scintillation crystal thickness – detector response uniformity
2. Solid angle coverage of object by detectors – PET ring diameter – smaller diameter
• pro: increases solid angle and sensitivity, reduces system cost
• con: leads to DOI resolution degradation • con: limits patient size
– PET ring axial length larger axial extent • pro: increases solid angle and sensitivity • con: increases system cost
PET Sensitivity
Nuclear Medicine Basic Science Lectures Stephen Bowen
October 18, 2011 Email: [email protected]
7
Detector Sensitivity vs. Resolution Tradeoff
sensitivity
energy & spatial resolution
counting speed (randoms rate, dead-‐time
photo-‐sensor matching, manufacturing cost
relevant PET scanner property
Inorganic scintillation crystals
*crystal thickness, t: typically BGO scanners use t = 3cm, LSO scanners use t = 2cm for cost reasons. PET scanners are not made from NaI(Tl) or BaF2 due to low sensitivity, despite other advantages
Geometric Efficiency vs. Sensitivity
sensitivity qmax
Graph from “Emission Tomography”, Eds. Wernick, Aarsvold, pg.186
Limited q
PET scanner axis
Full q
max
max
axial center plane
axial end plane
PET scanner sensitivity scales with the number of detectable coincidence events, which in turn scales as max.
This results in lower sensitivity at the end of any PET scanner
scanner axis
edge = 0o
edge
source
QA for PET Scanners: Evaluation of Performance Metrics
• Sensitivity - both system and per transaxial slice (measured with a line source)
• Spatial resolution - measured with a point source and an analytical image reconstruction algorithm at several positions in the scanner FOV (x,y,z resolution)
• Uniformity - measured with a uniform cylinder of activity
• Count rate - measured with a decaying line source in a solid, cold cylinder
• Dead time correction accuracy - measured from the count rate data
• Scatter fraction - measured from the count rate data
• Attenuation correction accuracy, contrast performance - from a non-cylindrical phantom with hot and cold spheres.
Current specifications based on National Electrical Manufacturers Association (NEMA) Standard
PET Image Formation Workflow
Primary Detection Decoding Detector
corrections
Coincidence Processing
Data Binning
Data Corrections
Image Reconstruction
Nuclear Medicine Basic Science Lectures Stephen Bowen
October 18, 2011 Email: [email protected]
8
Analytic Reconstruction
FBP assumes linear projections and does not account for many sources of variability in LOR
Backprojection leads to streak artifacts in PET images
Backprojection Filtered Backprojection
From WikiBooks Basic Physics of Digital Radiography • There are many ways to: – model the system (and the noise) – compare measured and estimated projection data – update the image estimate based on the differences between measured
and estimated projection data – decide when to stop iterating
Iterative Reconstruction
measured data
p(k) =Hf (k) + n
compute estimated projection data
f (k )
compare measured and
estimated projection data
initial image estimate
p
pp(k )
f (k) → f (k+1)
update image estimate based
on ratio or difference
f (0 )
Reconstructed PET/CT images
No AC
OS-EM
kVCT AC-CT
FBP fused
AC: Attenuation Correction OS-EM: Ordered Subsets Expectation Maximization FBP: Filtered Back-Projection
Modern Times: Time-of-Flight Time-of-flight capability is now offered in many new PET scanners"
– Measure time difference of detection of coincidence gammas"– Defines a line segment in space, shorter than distance between detectors"
– Improves image signal to noise that is a function of the object size."
TOF Gaussian SOR Conventional LOR
segment length x = cDt/2 c = speed of light
Dt = timing resolution
x = 7.5 cm for the Dt ~ 0.5 ns typical of TOF PET scanners
x
Nuclear Medicine Basic Science Lectures Stephen Bowen
October 18, 2011 Email: [email protected]
9
PET Introduction Summary PET concept
– Physics of positron emission, photon annihilation, coincidence detection
PET components – 2D collimated vs. 3D acquisition mode, detector block
PET resolution – Positron range, detector response, line-of-response sampling, depth-of-interaction – Take home 1: clinical PET resolution ~ 5 mm, small animal PET ~ 1 mm
PET quantitation – CT attenuation correction – Take home 2: separable attenuation correction makes PET more quantitative
than SPECT or MRI
PET sensitivity – Absorption efficiency, geometric efficiency – Take home 3: PET sensitivity 103 greater than SPECT, 106 greater than MRI
PET image formation – Acquisition – Reconstruction