1

BasicPhysics of PET andPET/CT

FredericH. FaheyDSc

Children’s Hospital BostonHarvardMedical School

frederic.fahey@childrens.harvard.edu

Outline

• Basicsof PETScannerDesign

• Data Acquisition

• Scintillation Materials

• Reconstruction Methods

• PET/CT

• Time-of-Flight (TOF) PET

• MicroPET

Positron Emission18F

511keV

511keVβ+

e-

DetectorRing

2

Detector Blocks(GE AdvanceNXi) PET Sinograms

PointSource Brain

PET SinogramsSinogram

Imagefor Each Slice

Ang

le

Imagefor Each Angle

Projection View

Slic

e

Note: Sinogramsandprojectionviewsaredifferent waysorshowingthesamedata.

3

True, ScatterandRandomCoincidence Detections

True

Random

Scatter

(R = 2 τ N1 N2)

18 * *17 * * *16 * * *15 * * *14 * * *13 * * *12 * * *11 * * *10 * * *

9 * * *8 * * *7 * * *6 * * *5 * * *4 * * *3 * * *2 * * *1 * *

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Spanof 3 Michelogram

18 * * * *17 * * * * *16 * * * * * *15 * * * * * * *14 * * * * * * *13 * * * * * * *12 * * * * * * *11 * * * * * * *10 * * * * * * *

9 * * * * * * *8 * * * * * * *7 * * * * * * *6 * * * * * * *5 * * * * * * *4 * * * * * * *3 * * * * * *2 * * * * *1 * * * *

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Spanof 7 Michelogram

2D Detector

PMTs

ScintillatorCrys tals

Septa

EndShields

511 kev photon

Axial

Direction

Courtesyof M. Graham,M. Madsen,U Iowa

4

AcquisitionModes

2D

3Dseptaare

removed

16 * * * * * * * * * * * * * * * *15 * * * * * * * * * * * * * * * *14 * * * * * * * * * * * * * * * *13 * * * * * * * * * * * * * * * *12 * * * * * * * * * * * * * * * *11 * * * * * * * * * * * * * * * *10 * * * * * * * * * * * * * * * *

9 * * * * * * * * * * * * * * * *8 * * * * * * * * * * * * * * * *7 * * * * * * * * * * * * * * * *6 * * * * * * * * * * * * * * * *5 * * * * * * * * * * * * * * * *4 * * * * * * * * * * * * * * * *3 * * * * * * * * * * * * * * * *2 * * * * * * * * * * * * * * * *1 * * * * * * * * * * * * * * * *

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Segment1

Segment 2

Segment 3

18 * * * * * * * * * * * *17 * * * * * * * * * * * * *16 * * * * * * * * * * * * * *15 * * * * * * * * * * * * * * *14 * * * * * * * * * * * * * * * *13 * * * * * * * * * * * * * * * * *12 * * * * * * * * * * * * * * * * * *11 * * * * * * * * * * * * * * * * * *10 * * * * * * * * * * * * * * * * * *

9 * * * * * * * * * * * * * * * * * *8 * * * * * * * * * * * * * * * * * *7 * * * * * * * * * * * * * * * * * *6 * * * * * * * * * * * * * * * * *5 * * * * * * * * * * * * * * * *4 * * * * * * * * * * * * * * *3 * * * * * * * * * * * * * *2 * * * * * * * * * * * * *1 * * * * * * * * * * * *

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GE 3D Projection view and Michelogram3D PET

• Sensitivi ty dropsoff towardsedges

• 4-5X increased sensitivityoverall

• Increasedscatter (15%to 40%)

• Increasedrandomsfrom out-of-field activity

• Rebinning algorithmsto apply2Dreconstruction

• Somedevices canacquirein 2D or 3D whereassomecanonly acquirein 3D

• 3D in Brain, 2D (or 3D) in WholeBody

5

Criteriafor Scintillation Material

• Detection Efficiency (StoppingPower)– High Effective Z– High Density

• Light Output– Goodenergy resolution– Goodcrystal identifi cation

• Decay Time– Reductionof randomcoincidences– Time-of-Flight PET

CrystalIdentification

SCINTILLATOR NaI(Tl) BGO LSO GSO

Rel. Light Output 100 15-20 75 20-25

PeakWavelength (nm) 410 480 420 440

DecayConstant(ns) 230 300 12,42 30-60

Density(g/mL) 3.67 7.13 7.40 6.71

Effective Z 51 75 66 59

Indexof Refraction 1.85 2.15 1.82 1.85

Hygroscopic? Yes No No No

New Detector Materials Feedback Loop

Backprojection

SimulatedProjections

ActualProjections

Compare

Usetoimprovecurrentestimate

Current Estimate

Err or

Courtesy of JeroldW. Wallis, M.D.

6

Maximum LikelihoodReconstruct ion (ML -EM)

• Maximizethelikelihoodthattheestimatedactivity distribution in thebody(thereconstructed transaxialslices)would leadto themeasured projections

• Usetheexpectation maximization(EM)algorithm to iteratively estimate theactivitydistribution

pixelj

projection bini

aij is theprobabilitythat a photonemittedfrom pixelj isdetectedatprojectionbini.

EM-ML Reconstruction

• aij can contain physical information(effectsof spatialresolution,scatter, attenuation…)

• EM-ML algorithm takesinto accountthenatureof thenoise(quantummottle)in theprojectiondata

• Canyield a moreaccuratereconstruction

λ’ (k)j = λ’ (k -1)j Σ [aij { d/ Σ [aij] λ’ (k -1)j } ]Σ [aij]

λ’ (k)j is thenewestestimateof theobjectpixel value

λ’ (k -1)j is estimateof theobject at last iteration

d is theprojection data

d’ = Σ [aij] λ’ (k -1)j is thecalculated projection data

ML-EM Algorithm

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λ’ (k)j = λ’ (k -1)j Σ [aij {d/ (Σ [aij] λ’ (k -1)j+acj(rj nj + cj) } ]Σ [aij/nj acj]

acis photonattenuation data

r is randomdata

n is normalization data

c is scatter data

ML-EM Algorithm (addedcorrections)Advantagesof Iterative Reconstruction

• Correct physicscanbeincluded in thereconstruction andPoissionstatistics

• Attenuationcorrection

• Reduction of streak artifact

• Overall quality

Courtesyof SiemensMedical Solutions

Accuratecharacterizationofthepoint spreadfunctions(PSFs) throughout thefilesofview allowsfor anaccurateestimationof the“aij” matrixleading to improvementinspatial resolution andsignal-to-noise.

Courtesyof SiemensMedical Solutions

FBP HD

ImprovedImageQuality with AccurateSpecificationOf thePSFThroughouttheField of View

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Disadvantagesof IterativeReconstruction

• Slow convergenceto thedesired solution(e.g. tens- hundredsof iterations)

• Computationally demanding- numberofiterationsand inclusionof thephysics

Waysto Increase theRateof Convergence

• Stoppingrules

• Regularization

• OS-EM

OS-EM Algorithm• Ordered-subsetexpectation maximization• At eachstep,project andbackprojectat only some

angles(i.e. a subset)• Performthestepsin anordered way to includeall

angles• Datastart to convergeevenbefore the1st iteration

is complete• Convergenceachievedin 3 - 10 iterations• Computationtime of a few minutes

OSEM IterativeReconstruction

Ang

le

Assume80 angles(rows)Divided into 8 subsetsThus,10 rows/subset.

First Subset

OSEM IterativeReconstruction

Ang

le

Assume80 angles(rows)Divided into 8 subsetsThus, 10 rows/subset.

SecondSubset

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OSEM IterativeReconstruction

Ang

le

Assume80 angles(rows)Divided into 8 subsetsThus,10 rows/subset.

Third Subset

By thetimeone hasprocessedall of the

projections(rows)once,theestimateof theobjecthasbeenupdated8 times.

OSEM IterativeReconstruction

• FilteredBack-Projection– Fast

– Robust

– Subjectto noise& streaks

• OSEM– Almost asfast

– Handlesnoise& streaks

Example: 28 subsets(12projectionsper subset)and2 iterations)

Single Slice Rebinning (SSRB) FourierRebinning

• More accurate approachto rebinning

• Better estimate of determininginto whichparallelplaneobliquedatashouldbeplaced

• Based on thefrequency-distancerelationship(Valueof Fouriertransformofa sinogramreceivescontributionsmainlyfrom sources at a fixed distancet=-k/ω)

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PET/CT

• State-of-the-art PETcombinedwithstate-of-the-art CT (up to 64 slice)

• Anatomical correlation

• CT-basedattenuationcorrection

GE DiscoveryST PET/CT

CT PET

PET AttenuationCorrection

L

X

P1 = e-µx

P2 = e-µ(L-x)

PTOT = P1 x P2= e-µL

PET-CT AttenuationCorrection

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PET-CT Attenuation Correction PET-CT AttenuationCorrection

• Acquire CT Scanandreconstruct

• Apply energy transformation

• Reproject to generatecorrection matrix

• Smoothto resolution of PET

• Apply duringreconstruction

Dosefrom CT of PET-CTCTADIv ol (160 m A, 0.8 s , 1.5:1 pitc h)

0.00

500.00

1000.00

1500.00

2000.00

2500.00

3000.00

70 90 110 130 150

Tube Voltag e (kVp)

CT

AD

Ivo

l(m

rad

) New Born

1 Year Old

5 Year Old

10 Year Old

Med Adult

ED from14 mCi of FDG

1 rad

Quality of CTAC

80 kVp10 mA0.5s/rot

1.5:1

140 kVp160mA0.8 s/rot

1.5:1

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Quality of CTAC

80 kVp10 mA0.5s/rot

1.5:1

140kVp160 mA0.8 s/rot

1.5:1

Effect of PatientSize80 kVp, 10 mA, 0.5s/rotation

Acc ura cy of Atten ua tion Correction w it h Pati ent Siz e

0.0780

0.0800

0.0820

0.0840

0.0860

0.0880

0.0900

0.0920

80/10/.5

Lin

ear

Att

enu

atio

nC

oef

fici

ent

(cm

-1)

New born

1 YO

5 YO

10 YO

15 YO

Small Adult

Med Adult

Large Adult

PET-CT Scanners

• SiemensBiograph

• GE DiscoveryST

• GE DiscoverySTE

• PhilipsGemini

PET-CT ScannersGE Discovery STE GE Dis co very ST Philips Gemin i

Detector Dimension (m m) 4.7 x 6.3 x 30 6.2 x 6.2 x 30 4 x 6 x 20# of PET Detec tors 13,440 10,080 17,864PET Detecto r Material BGO BGO GSOSpatial Resolution 5.0 6.1 4.92D/3D 2D/3D 2D/3D 3DAtten Corr CT CT CT&Cs-137

Siemens Biograph LSO Siemens Hi-Rez LSODetec tor Dimension (m m) 6.5 x 6.5 x 25 4 x 4 x 20# of PET Detectors 9,216 23,336PET Detector Materia l LSO LSOSpatia l Resoluti on 6.3 4.62D/3D 3D 3DAtten Corr CT CT

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Time-of-Flight PET

Speed of Light c = 3 x 1010 cm/s

15030153Distance(cm)

5.01.00.50.1Time (ns)

Time-of-Flight PET

∆x = c ∆t/2

Where∆x is thetime-of-fli ght spatialuncertaintyand∆t is thetiming resolution.

15.07.54.51.5∆x (cm)

1.00.50.30.1∆t (ns)

Time-of-Flight PET Time-of-Flight PET

Assume∆t of 0.5ns=> ∆x of 7.5cm

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Time-of-Flight PET

SNR Gainfrom Time-of-Flight PET

D/1.6∆x ≈ 2 D/ 1.6c ∆t

whereD is thediameter of theobject

3.32.51.6SNRGain

403020D (cm)

PET/CT scanner

PET scanner70-cm bore18-cm axial FOV

LYSO crystals

CT scannerBrilliance 16-slice

Philips Gemini TF

NEMA NU-2Spatial resolution: 4.8 mm at 1 cm, 5.2 mm at 10 cmSensitivity: 6.6 cps/kBqScatter fraction (at 440 keV): 27% for 20-cm x 70-cmPeak NEC: 125 kcps @ 0.42µCi/ml

Energy resolution: 11.5% fwhm, Timing resolution: 585 psIntrinsic

Courtesyof Joel Karp, PhD, Univ of Penn

Measurements: 35-cm lesion phantom

60s

TOF non TOF

180s

6-to-1 contrast

300ssimilar noiseand scan time

TOFhigherCRC

CourtesyofJoel Karp, PhD,Univ of Penn

Heavy-weight patient study13 mCi2 hr post-inj3 min/bed

MIP

Colon cancer

119 kgBMI = 46.5

non-TOF

Gemini TF

TOFLDCT

Courtesyof Joel Karp, PhD, Univ of Penn

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non-Hodgkin’s lymphoma 136 kg (45 BMI)

TOF tumor contrast (SUV) higher than non-TOF by 1.5

nonTOF 30 min TOF 30 min TOF 10 min

TOF tumor contrast superior to non-TOF for 10 min as well as 30 min scan

Courtesyof JoelKarp, PhD,Univ of Penn

CHB MicroPET

• Installed 8/16/06• SiemensFocus 120• 1.5 mm spatialresolution• 7 % Sensitivity

Summary• Modern scannersdesignedfor oncologic imaging• Practically all PET sales arePET/CT scanners• New scintillation crystals combine excellent

detection efficiencywith shortdecaytimes• Appropriatechoiceof reconstruction algorithm

canleadto betterimagequality• Shorter decaytimes leadsto possibility of time-of-

flight PET.• MicroPETscannerscanprovidevery high spatial

resolutionwith high sensitivi ty in a small footprint and easyaccess to theresearch animals.

Now for theSAM questions!!

Acquiring a PETscanin 3D modeleadsto

0%

0%

0%

0%

10

1. Shorterreconstructiontimes

2. Lessscatter andrandomcoincidences

3. Improved spatial resolution

4. Improved sensitivity

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Answer

4. Improvedsensitiv ity

Reference: CherrySR,SorensonJA, PhelpsME,“Physicsin NuclearMedicine,Saunders,

PhiladelphiaPA. page351-352.

Explanation: 3D PEThasapproximatelythe samespatialresolutionas2D PETwith increasedscatterandrandom coincidences. It isalsomorecomplicatedto reconstruct.However, theremovalof theinter-planesepta leadsto a largeincreasein thelines-of-response(LORs) andthusa 4 to 5 fold increasein sensitivity.

Time-of-flight PETimprovesimagequality, particularly in

0%

0%

0%

0%

10

1. Fast scans

2. Largerpatients

3. Smallanimals

4. Time sequencesof scans

Answer

2. Larger Patients

Reference: SulemanSurti, Austin Kuhn,MatthewE. Werner,Amy E. Perkins,Jeffrey KolthammerandJoel S.Karp,“Performanceof PhilipsGeminiTF PET/CT Scannerwith SpecialConsiderationfor Its Time-of-Flight ImagingCapabilities” ,J Nucl Med 48: 471-480,2007.

Explanation: Time-of-flight PETinvolvesbothdataacquisitionandreconstruction. It allowsoneto locatetheannihilationeventalongthe line-of-responsewhich leadsto reducednoiseandhighercontrastin the imagedata. With currenttechnology,theevent canbelocalizedto within about7-8 cm which leadsto betterimageimprovement in largerpatientsbut not for small patientsor smallanimals. It is not atall relatedto thedurationof thescan or whetherthe study is acquired as a time sequence.