positron emission tomography (pet) and pet/ct...positron emission tomography (pet) and pet/ct...
TRANSCRIPT
PositronEmissionTomography(PET)andPET/CT
Positron(β+)Emission
Z
20 40 60 80 100 120 140 160N
Z
20
40
60
80
100
Neutron-poorregiondecayto‘lineofstability’isbypositronemission(orEC)
p+ → n + β + +ν
Z=N
lineofstability
PositronEmission
RadioacIvedecay• startwithneutron-deficientisotope• decaystostableformbyconverIngaprotontoaneutronandejectsa'positron'toconserveelectriccharge
• positronannihilateswithanelectron,releasingtwoanI-colinearhigh-energyannihilaIonphotons
np
np
n
pnp n
pn
p
np
p
pn
p n
pn
p
n
p n np
np
n
pnp n
pn
p
np
n
pn
p n
pn
p
n
p n
~2mm
18F 18O
~180deg
E=mc2=511keV
β+
e-
annihilaIonphoton
Energy Spectrum of Emitted Positrons
LevinPMB1999
MedicallyUsefulPositronEmiYngIsotopes
Isotope Half life (min)
Most probable energy (keV)
FWHM of positron range* in water (mm)
109.7 203 0.102
1.3 1384 0.169
20.3 326 0.111
10.0 432 0.142
2.0 696 0.149
918F
3782Rb
611C
713N
815O
*verylongtails90%ofallclinicalstudies
ScinIllaIonDetectors
high energy511 keV photon
optical photons (~ 1eV)
scintillator(e.g. BGO Dense yet transparent)
current pulse for each UV photon
detected
photomultipliertubes (PMTs)gain of ~ 106
ScinIllatorstriedinPET
Usedincommercialscanners
PETDetectorBlock
ReflecIvelightsealingtape
Two dual photocathode PMTs
Annihilationphoton
scintillationlight
signalouttoprocessing
• PETscannersareassembledinblockmodules
• EachblockusesalimitednumberofPMTstoencodeanarrayofscintillationcrystals
PETScannerDetectorRing
PaulKinahan
Block matrix6 x 8 crystals (axial by transaxial)Each crystal:
6.3 mm axial4.7 mm transaxial
Scanner constructionAxial:
4 blocks axially = 24 rings15.7 cm axial extent
Transaxial:70 blocks around = 560 crystals88 cm BGO ring diameter70 cm patient port
13,440 individual crystals
BlockformaIonforacurrentPETscanner
KeyfeatureofPET:LineofresponsecollimaIonbycoincidenceIming
Dt < 10 ns?
detector A signal
detector B
record coincident event for this line
of response (LOR)
scannerFOV
β+ + e- annihilation
• InSPECTthisisachievedthoughuseofacollimator• InCTtheknowngeometryfromsourcetodetectorisused
scinIllaIoneventdetecIon
Time of Flight (TOF) PET/CT c = 3x1010cm/s with ∆t = 600 ps in timing resolution yields ∆d = 10 cm spatial resolution
∆d = c ∆t/2
timing resolution uncertainty∆d
best guess for location (d)
β+ + e- annihilation
PETImagingEquaIonWithenoughcoincidenteventsforeachlineofresponse,wecanapproximatemeasuresasline-integraldataoftheradioisotopeconcentraIon
φ(l,θ ) = A(x(s), y(s))ds−∞
∞
∫Theintegralisalongaline
L(l,θ ) = (x, y) x cosθ + ysinθ = l{ }
s
A(x, y)
SolvingthePETImagingEquaIon
Wehaveasimple2Dx-ray(Radon)transform,i.e.lineintegral,thatcanbeexactlysolvedbyfilteredbackprojecIon(FBP)
′φ (l,θ ) = A(x(s), y(s))ds−∞
∞
∫
A(x, y) = ρ Φ(ρ,θ )e j2πρl dρ−∞
∞
∫()*+,-dθ
0
π
∫
Φ(ρ,θ ) = F1D ′φ (l,θ ){ }where
PET Imaging equation
FBP solution
Typicalusecase:Glucosemetabolismimaging
FDG-6-PO4is‘trapped’andisamarkerforglucosemetabolicrates*
glucose
glucose 6-phosphate
pyruvate lactate
gylcolysis (anaerobic, inefficient)
TCA (oxidative, efficient)
HOCH2
H 18F
H
OH HHO
H
OH
H
radioactive fluorine
O
[18F]fluorodeoxyglucose (FDG)
positron emitter, i.e. what we see
FDG
FDG 6-phosphate
X
CTimageshowingsuspiciousnodule PETimageconfirmingcancer
CombinedPET/CTimagingcombinesfuncIonalandanatomicalimaging(likeSPECT/CT)
PETImageofFuncIon FuncIon+Anatomy CTImageofAnatomy
PET/CTscannerarrangement
All3(couch,CTandPET)mustbeinaccuratealignment
Commercial/ClinicalPET/CTScannerPETdetectorblocksthermalbarrierrotaIngCTsystem
Confoundingeffects
Lost (attenuated)event
Scattered coincidenceevent
Random coincidenceevent
incorrectly determined LORs
Compton scatter
no detection (i.e. no LOR)
CorrecIonshavetobeappliedfortheseeffects
scinIllaIoneventdetecIon
AnenuaIoninPETImaging2anI-colinearphotonsalongthelineofresponse(LOR)
annihilation location
detector A: number of events detected = NA
detector B: number of events detected = NB
attenuation distance from annihilation location to detector B
NA = N0 exp − µ(x( "s ), y( "s );E)d "sS0
R
∫{ }NB = N0 exp − µ(x( "s ), y( "s );E)d "s
−R
S0
∫{ }photons detected from a single
annihilation location at s0
AnenuaIoninPETImagingTotalnumberofannihilaIonphotonsarrivingincoincidenceNCisNO(acIvityatsO)reducedbytheproductoftheanenuaIonfactors
WecannowallowforadistributedsourceofpositronsalongLOR
evenbener,wenowhaveanenuaIonasasimplemulIplicaIon
NC = N0 exp − µ(x( ′s ), y( ′s );E)d ′sS0
R
∫{ }exp − µ(x( ′s ), y( ′s );E)d ′s−R
S0∫{ }= N0 exp − µ(x( ′s ), y( ′s );E)d ′s
−R
R
∫{ }
φ(l,θ ) = K A(x(s), y(s))exp − µ(x( $s ), y( $s );E)d $s−R
R
∫{ }ds−R
R
∫
φ(l,θ ) = K A(x(s), y(s))ds−R
R
∫ ⋅exp − µ(x(s), y(s);E)ds−R
R
∫{ }
keystepiscombiningintegrals
notdependentonssocantakeoutofintegral
ComparisonofImagingEquaIons
AnenuaIonCorrec9oninPETImagingWenowhaveanenuaIonasasimplemulIplicaIonSoiswecansomehowmeasureanenuaIonalongtheLOR,i.e.ThenwecanwriteWhichweknowhowtosolveforA(x,y)RecallthatA(x,y)istheradiotracer(positroneminer)concentraIonthatwewanttoknow
φ(l,θ ) = K A(x(s), y(s))ds−R
R
∫ ⋅exp − µ(x(s), y(s);E)ds−R
R
∫{ }
a(l,θ ) = exp − µ(x(s), y(s);E = 511keV)ds−R
R
∫{ }
′φ (l,θ ) = φ(l,θ )Ka(l,θ )
= A(x(s), y(s))ds−∞
∞
∫
HowtomeasureanenuaIon?
1. PETtransmissionsource(68Ge/68Ga):CoincidentannihilaIonphotons(mono-energeIc@511keV),265dayhalflife
2. X-rayCTscan:X-rayswithadistribuIonofenergiesfrom~30to130keV(effecIveenergyof~70keV)
E
I0(E) X-raysourcespectra
PETanenuaIonimaging
• µ(x,y)valuesaremeasuredatdesiredenergyof511keV• Near-sidedetectors,however,sufferfromdeadImeduetohighcountrates• AlsosubjecttobiasfromemissionphotonsfrompaIent
orbiIng68Ge/68Gasource
PETscanner
near-sidedetectors
511keVannihilaIonphoton
paIent
X-rayCTanenuaIonimaging
• µ(x,y,E)ismeasuredasaweightedaveragefrom~30-130keV,soweneedtoconverttotµ(x,y,E=511keV),potenIallyintroducingbias
• Photonfluxisveryhigh,soverylownoiseandfasterthanPETtransmissionimaging
orbiIngX-raytube
X-raydetectors
30-130keVX-rayphoton
paIent
PETTX:3min,E=511keVunbiasedesImate,highnoise
X-rayCTTX:20s,E=30-120keVbiasedesImate,lownoise
ComparisonofanenuaIonimagingmethods
DuetodiagnosIcsuperiorityofPET/CT,allPETscannersarereallyPET/CTscannerssowecanuseCTforanenuaIoncorrecIon
CT-basedAnenuaIonCorrecIon
0
25,000
50,000
75,000
100,000
0 100 200 300 400 500 600
keV
ITransform?
• Weusethefactthatthemass-anenuaIoncoefficient(µ/ρ)issimilarforallnon-bonematerialssinceComptonscanerdominatesforthesematerials
• Bonehasahigherphotoelectriccross-secIonduetocalcium• Canusetwodifferentscalingfactors:oneforboneandonefor
everythingelse
0.01
0.10
1.00
10.00
100.00
10 100 1000keV
µ/ρ
Bone, Cortical
Muscle,SkeletalAir
bone
everythingelse
70 511
CT-basedAnenuaIonCorrecIon
0.00
0.05
0.10
0.15
0.20
-1000 -500 0 500 1000 1500
CT Hounsfield Units
linea
r at
tenu
atio
n co
effc
ient
(µ)
CT-basedAnenuaIonCorrecIon• Bi-linearscalingmethodsapplydifferentscalefactorsforboneandnon-bonematerials
• ShouldbecalibratedforeverykVpand/orcontrastagent
air-water mixture
water-bone mixture
air soft tissue dense bone
• CTimagesarealsousedforcalibraIon(anenuaIoncorrecIon)ofthePETdata
• Notethatimagesarenotreallyfused,butaredisplayedasfusedorside-by-sidewithlinkedcursors
• NotealsothattheCTisusedforanenuaIoncorrecIon,thusasignificantpotenIalforerrorifthereisamis-alignmentorinaccuratescaling
DataFlowandProcessing
X-rayacquisi0on Anatomical(CT)Reconstruc0on
PETEmissionAcquisiIon
CTImage
TranslateCTtoPETEnergy(511keV)
SmoothtoPETResoluIon
AnenuaIonCorrectPETEmissionData
FuncIonal(PET)ReconstrucIon
PETImage
DisplayofPETandCTimagevolumes
MaterialarIfact:MetalClip
Artifact
CT PET with CTAC
Courtesy O Mawlawi MDACC
PosiIonalarIfact:PaIentand/orbedshiuing
LargechangeinanenuaIonatlungboundaries,soverysuscepIbletoerrors
PETimagewithoutanenuaIoncorrecIon
PETimagewithCT-basedanenuaIoncorrecIon
PETimagefusedwithCT
RespiratoryMoIonArIfacts
Attenuation artifacts can dominate true tracer uptake values
PET Signal, Bias, and Noise
True coincidence (T): line integral signal we want but effected by photon counting noise
Random coincidence (R): different type of bias added to data, also noise
Scattered coincidence (S): bias and noise added to data
Components of measured PET data
! IfwecanesImateSandRasS’andR’(howisbeyondscopeofthislecture)then:
! WecansolvethiswithFBP
P =℘ aT{ }+℘ S{ }+℘ R{ }MeasuredProjections
attenuatedTrueSignal
biasfromScatter
biasfromRandomevents
T = ′φ (l,θ ) = A(x(s), y(s))ds−∞
∞
∫℘ x{ },Poisson random process with mean x
A(x(s), y(s))ds
−∞
∞
∫ !1aP − ′S − ′R( )
Signal to Noise Ratio (SNR)• SignalisthetruecountsT• ThenoiseisthetotalnoiseinthedataP• WecanesImatenoisebyrealizingthatphotoncounIngisaPoissonprocess,sothevarianceisequaltothemean
NEC = T 2
T + S +αR< T
αdependsonrandomsesImaIonmethod
SNR = Tσ P( ) ≈
TT + S +αR
= NEC
σ (P) = T + S +αR
NECiscalledthe‘noiseequivalentcount’rate,i.e.theusefulcountrate
TheNECisalwayslessthanT
PET Acquisition: 2D vs. 3D Mode 3D mode typically has higher NEC than 2D mode for activity levels of interest
2D PET uses axial ‘septa’ 3D PET uses no septa
detector crystals
septa & end shielding
blocked
scatter & randoms
Impactof3Dand2DmodeonNECrates
TypicalclinicalacIvityrange
idealcountrate
• Positron Physics – Positron Range – Photon Non-colinearity
• Detectors – Response function
• Ring Geometry – Non-uniform LOR sampling – Depth-of-interaction
• Reconstruction Filters
SpaIalResoluIoncomponentofSNR
Rsystem = Rpos. phys.2 + Rdet
2 + Rsampl2 + Rrecon
2
Resolution components add in quadrature
Size-DependentResoluIonLosses
• Spherediamof10,13,17,22,28,and37mm
• Target/backgroundraIo4:1
• MaxandmeanacIvityconcentraIonsmeasuredvia10mmdiameterregions
20x30cm,similartoabdominalx-secIon
ModifiedNEMANU-2IQPhantom
CT
PET
Recoverycoefficient(RC)=measured/true(ideally100%)
size-dependentbias
SNMTorsophantomwith1cmspheres
10mmsmoothing4mmsmoothing 7mmsmoothing
0.85
0.92
0.52
0.80
0.40
0.72
Increasingsmoothingreducesbothsignalandnoise
Clinicalexamples
PaulKinahan
1. Scout scan (5-10 sec)
CT PET
4. Whole-body PET (15-30 min)
CT PET
TypicalPET/CTScanProtocol
3. Helical CT (10 - 20 sec)
CT PET
2. Selection of scan region
Scout scan image
• CTimagesarealsousedforcalibraIon(anenuaIoncorrecIon)ofthePETdata
• Notethatimagesarenotreallyfused,butaredisplayedasfusedorside-by-sidewithlinkedcursors
Reminder:DataFlowandProcessing
X-rayacquisi0on Anatomical(CT)Reconstruc0on
PETEmissionAcquisiIon
CTImage
TranslateCTtoPETEnergy(511keV)
SmoothtoPETResoluIon
AnenuaIonCorrectPETEmissionData
FuncIonal(PET)ReconstrucIon
PETImage
DisplayofPETandCTimagevolumes
PET/CT for precise localization
• 68-y-old man, 3 y after partial gastrectomy for adenocarcinoma of stomach
• Referred for 18F-FDG PET/CT for evaluation of mass detected on routine follow-up gastroscopy and equivocal biopsy results
• (A) 18F-FDG PET show increased 18F-FDG uptake in region of stomach (arrow)
• (B) Hybrid PET/CT axial image (top) precisely localizes and defines uptake as physiologic activity at gastric stump (arrowhead). Suspicious mass in anastomotic region (arrow), seen on corresponding hybrid and CT slices (bottom) obtained during same acquisition, shows no uptake of 18F-FDG.
• Findings on PET/CT were interpreted as physiologic 18F-FDG uptake in stomach and nonviable residual mass.
• Patient showed no evidence of disease for follow-up of 7 mo.
PET/CT for precise characterization
• A 35-y-old man, 22 mo after treatment for colon cancer
• Negative high-resolution contrast-enhanced CT and normal levels of serum tumor markers, was referred for 18F-FDG PET for further assessment of pelvic pain
• (A) Coronal PET images show area of increased 18F-FDG uptake in left pelvic region (arrow), interpreted as equivocal for malignancy, possibly related to inflammatory changes associated with ureteral stent or to physiologic bowel uptake
• (B) Hybrid PET/CT axial image (top) precisely localizes uptake to soft-tissue mass adjacent to left ureter, anterior to left iliac vessels. Mass (arrow) was detected only retrospectively on both diagnostic CT and CT component of hybrid imaging study
• Patient received chemotherapy, resulting in pain relief and decrease in size of pelvic mass on follow-up CT.
PET/CT for precise localization
• A 33-y-old man with Hodgkin’s disease in left cervical region was referred for 18F-FDG PET for staging
• No other sites of disease were reported on CT
• (A) PET images show infradiaphragmatic focus of abnormal 18F-FDG uptake in medial border of liver, consistent with either liver involvement (stage IV disease?) or nodal disease in porta hepatis (stage III disease?)
• (B) Hybrid PET/CT axial image precisely localizes 18F-FDG uptake to adenopathy (abnormally large lymph node) at porta hepatis, only retrospectively detected on corresponding CT image (arrow)
• Patient was treated as having stage III disease and achieved complete response, showing no evidence of disease for follow-up of 12 mo.