Professor Brian F HuttonInstitute of Nuclear MedicineUniversity College London

brian.hutton@uclh.nhs.uk

Emission Tomography Principles and Reconstruction

Outline

• imaging in nuclear medicine

• basic principles of SPECT

• basic principles of PET

• factors affecting emission tomography

SPECT

History• Anger camera 1958• Positron counting, Brownell 1966• Tomo reconstruction; Kuhl & Edwards 1968• First rotating SPECT camera 1976• PET: Ter-Pogossian, Phelps 1975

Gamma Ray

Light

Position/Energy CircuitsX Y Z

Collimator

NaI (Tl)Crystal

Photo Multiplier Tubes

Detector

To Display &Computer

D1

D3

D5

D7D8

D6

D4

D2

Anode

Cathode

Anode

D8

D7

D6

D5

D4

D3

D2

D1

Cathode

HV Supply

Capacitor

OutputPulse

Light fromcrystal

(D - Dynode)

e-

e-

e-

Anger gamma camera Detector: 400x500mm ~9mm thickEnergy resn ~10%Intrinsic resn 3-4mm

Radionuclides: Tc-99m 140keV, 6hr I -123 159keV, 13hr Ga-68 93-296keV, 3.3dy I-131 360keV, 8dy

CollimatorDesigned to suit energy HR: hole size 1.4mm

length 33mmsepta 0.15mm

parallel fanbeam conebeam

pinhole slit-slat crossed slit

Organ-specific options specialized collimators for standard cameras

Single Photon Emission Computed Tomography (SPECT)

Single Photon Emission Computed Tomography (SPECT)

• relatively low resolution; long acquisition time (movement)• noisy images due to random nature of radioactive decay• tracer remains in body for ~24hrs: radiation dose ~ standard x-ray• function rather than anatomy

SPECT Reconstruction

1 angle 2 angles 4 angles 16 angles 128 angles

Filtered back projection

sinogram for each transaxial slice

Organ-specific systemsspecialised system designs, with use limited to a specific application

Positron Annihilation

Isotope Emax

(keV)Max range

(mm)FWHM(mm)

18F11C13N15O

82Rb

663 2.6 0.22

960 4.2 0.28

1200 5.4 0.35

1740 8.4 1.22

3200 17.1 2.6

Coincidence Detection

detector 1

detector 2

coincidence window

time (ns)

PET "Block" Detector

Scintillatorarray

PMTs

Histogram

A B

C

Images courtesy of CTI

BGO(bismuth

germanate)

Nox

µ

D

e-µx e-µ(D-x)

No

µ

D

e-µ0 e-µD

Attenuation Correction in PET

attenuation foractivity in bodyN = N0 e -x. e - (D-x)

= N0 e -D

attenuation for external sourceN = N0 e -D

(D=body thickness)

(for 511 keV ~ 0.096/cmattenuation factors: 25-50)

Coincidence Lines of Response (LoR)

parallelfanbeamsinogram

PET Reconstruction

1 angle 2 angles 4 angles 16 angles 128 angles

• conventional filtered back projection• iterative reconstruction

sinogram

Understanding iterative reconstruction

ObjectiveFind the activity distribution whose estimated projections match the measurements.

Modelling the system (system matrix)What is the probability that a photon emitted from location X will be detected at detector location Y.

- detector geometry, collimators- attenuation- scatter, randoms

detector(measurement)

object

estimated projection

X

Y

X

Y1

Y2

0

0

0

0

0

0

1

0

0

0

0 0 0 0 0 0 0 1 0 0

0 0 0 0 0 1 0 0 0 0

System matrix

voxelj

pixeli

ML-EM reconstruction

originalprojections

estimatedprojections

currentestimate

original estimate

update(x ratio)

FP

BP NOCHANGE

patient

Image courtesy of Bettinardi et al, Milan

• stop at an early iteration• use of smoothing between iterations• post-reconstruction smoothing• penalise ‘rough’ solutions (MAP)• use correct and complete system model

Noise control

Factors affecting quantification

courtesy Ben Tsui, John Hopkins

+ -

transmission

withoutattenuationcorrection

withattenuationcorrection

detector

0

0

0

0

0

0

0.9

0

0

0

0 0 0 0 0 0 0 0.2 0 0

0 0 0 0 0 0.5 0 0 0 0

System matrix: with attenuation

Partial volume effects

• effect of resolution and/or motion

• problems for both PET and SPECT

• similar approaches to correction

• scale of problem different due to resolution

• some different motion effects due to timing:

ring versus rotating planar detector

Modelling resolution

Gamma camera resolution• depends on distance

SPECT resolution• need radius of rotation

PET resolution • position dependent

0

0

0

0

0

0.3

0.9

0.3

0

0

0 0 0 0 0 0 0.1 0.2 0.1 0

0 0 0 0 0.2 0.5 0.2 0 0 0

System matrix: including resolution model

FWHMtotal2 = FWHMdet

2 + FWHMrange2 + FWHM180

2

positron range colinearity

detector

PET resolution

depth of interaction results in asymmetric point spread function

tangential

radial int radial ext

detector(projection)

object

Courtesy: Panin et al IEEE Trans Med Imaging 2006; 25:907-921

• potentially improves resolution• requires many iterations• slow to compute

Modelling resolution

w/o resn model

with resn model

• stabilises solution• better noise properties

detector

object

Scatter correction

• multiple energy windows for SPECT; PETCT standard models

• SPECT local effects; PET more distributed

Can we consider measurements to be quantitative?

Scatter fraction

• SPECT ~35% PET 2D ~15%; 3D ~40%

• scatter modelsanalytical, Monte Carlo, approximate models

• measurement triple energy window (TEW), multi-energy

subtract from projections:measured proj – TEW

or combine with projector in reconstruction:compare (forward proj + TEW) with measured proj

Scatter• influenced by photon energy, source location, scatter medium• reduces contrast

measured

Monte Carlo

3D reconstructionApproaches• rebin data followed by 2D reconstruction

single slice rebinning (SSRB)multi-slice rebinning (MSRB)Fourier rebinning (FORE)

• full 3D reconstruction3D OSEM3D RAMLA

limits for FORE

Courtesy V Bettinardi, M Gilardi, Milan

2D 4min 3D 4min 2D 2min 3D 2min

FORE 2D-OSEM 28subsets 5 iter

VUE Point 3D-OSEM28subsets 2iter

FORE 2D-OSEM 28subsets 2 iter

Summary

Emission tomography• functional rather than anatomical• single photon versus dual photon (PET)• main difference is ‘collimation’

Iterative reconstruction• very similar approach for SPECT and PET• currently most popular is OSEM (or similar)• the better the system model the better the reconstruction