ECT Supplement

Supplementary Material Emission Computed

Tomography

Thanks to those that post interesting material on the

internet. This supplement is a collection from several.

Emission Tomography

f(x,y,z)f(x,y,z)

ProjectionsProjections

ReconstructiReconstructionon

f(x,y,z)f(x,y,z)

SlicesSlices

projection

projection

SPECTSingle Photon Emission Computed Tomography

collimator

only one gamma photon is detected per decay

NaI(Tl) crystal

Rotating scintillator camera

detector

detector

PETPositron Emission Tomography

What do we want to detect in PET?– 2 photons of 511 keV in coincidence, coming in a

straight line from the same annihilation

e-

e+

unstable nucleus emits positron positron annihilates with electron

two 511 photons are emitted

simultaneously in opposite directions

TRUE coincidence

Types of Coincidence True coincidence is the simultaneous detection of the

two emissions resulting from a single decay event. Scatter coincidence is when one or both photons from

a single event are scattered and both are detected. Random coincidence is the simultaneous detection of

emission from more than one decay event.

Coincidences: True Scatter Random

PET radiation detection PET scanner

– Typical configuration: whole-body (patient port ~60 cm; axial FOV~15 cm) scintillator crystals coupled to photomultiplier tubes (PMTs) cylindrical geometry ~24-32 rings of detector crystals hundreds of crystals/ring several millions of Lines Of Response (LORs)

(only a few are shown)

True True

Other configurations for special-purpose applications:

- brain imaging

- animal PET

- mammography, other

PET CT

PET/CT

CT PET CT+PET

General Electric Medical Systems

PET data acquisition Organization of data

– True counts in LORs are accumulated– In some cases, groups of nearby LORs are

grouped into one average LOR (“mashing”)– LORs are organized into projections

etc…

PET data acquisition 2D and 3D acquisition modes

septa

2D mode (= with septa)

3D mode(= no septa)

In the 3D mode there are no septa: photons from a larger number of incident angles are accepted, increasing the sensitivity.

Note that despite the name, the 2D mode provides three-dimensional reconstructed images (a collection of transaxial, sagittal and transaxial slices), just like the 3D mode!

PET data acquisition 2D mode vs. 3D mode

2D mode (= with septa)

3D mode(= no septa)

True

detected

True

not detected (septa block

photons)

PET data acquisition Organization of data

– In 3D, there are extra LORs relative to 2D

3D mode same planes as 2D oblique planes

...

...

+

+

PET evolution: spatial resolutionHuman brain

Animal PET~1998

Monkey brain

Image credits: CTI PET Systems

Image credits: Crump Institute, UCLA

J. Fessler, 2002

“Part of the goal is to bring order to this alphabet soup.”

PET image reconstruction

Projection

Object

P( 2 ,r)

∫=),(

),(),(rline

dlyxfrPφ

φ

Radon Transform

1

2

P(1 ,r)

f(x,y)

r

r


Sinogram

r

Projection

angle

Projection bin

Object


SinogramObject

r


r

SinogramObject

Sinogram

Other representations can be used instead of the sinogram (linogram, planogram)

SPECT: 360º (1 photon)

PET: 180º (2 opposite photons)

PET image reconstruction 2D Reconstruction

– Each parallel slice is reconstructed independently (a 2D sinogram originates a 2D slice)

– Slices are stacked to form a 3D volume f(x,y,z)

2D reconstruction

Plane 5

Slice 5etc

etc

2D reconstruction

Plane 4

Slice 4

2D reconstruction

Plane 3

Slice 3

2D reconstruction

Plane 2

Slice 2

2D reconstruction

Plane 1

Slice 1

2D Reconstruction2D Reconstruction

PET image reconstruction Projection and Backprojection

Projection Backprojection

2D Reconstruction2D Reconstruction

4 projections 16 projections 128 projections

Backprojection

FilteredBackprojection

Object

PET image reconstruction2D Reconstruction2D Reconstruction

Noise In PET Images Noise in PET images is dominated by the counting

statistics of the coincidence events detected. Noise can be reduced at the cost of image resolution

by using an apodizing window on ramp filter in image reconstruction (FBP algorithm).

105 106 107 counts

Unapodized ramp filter

Hanning window, 4mm

Hanning window, 8mm

Scatteredcoincidences component

Attenuation

Random coincidencescomponent

Detector efficiency

effects Truecoincidencescomponent

PET image reconstruction Data corrections are necessary

– the measured projections are not the same as the projections assumed during image reconstruction

Object(uniformcylinder)

projectionmeasured

projectionassumed

integral of the activity along the line or tube

of response

Analytical methods Advantages

– Fast– Simple– Predictable, linear behaviour

Disadvantages– Not very flexible– Image formation process is not modelled image

properties are sub-optimal (noise, resolution)

Iterative methods

Advantages– Can accurately model the image formation process (use

with non-standard geometries, e.g. not all angles measured, gaps)

– Allow use of constraints and a priori information (non-negativity, boundaries)

– Corrections can be included in the reconstruction process (attenuation, scatter, etc)

Disadvantages– Slow– Less predictive behaviour (noise? convergence?)

PET Image reconstruction Iterative methods

Current Current estimateestimate

Measured Measured projectionprojection

CompareCompare

(e.g. (e.g. –– or or // ) )

Error Error projectionprojection

projectionprojectionEstimated Estimated projectionprojection

image spaceimage space projection spaceprojection space

backprojectionbackprojectionErrorErrorimageimage

UpdateUpdate

Iteration 1




CompareCompare

(e.g. (e.g. -- or or // ) )


projectionprojectionEstimated Estimated projectionprojection



UpdateUpdate

Estimated Estimated projectionprojectionEstimated Estimated projectionprojection

Iteration 2




CompareCompare

(e.g. (e.g. -- or or // ) )


projectionprojection



UpdateUpdate

Estimated Estimated projectionprojectionEstimated Estimated projectionprojectionEstimated Estimated projectionprojectionEstimated Estimated projectionprojection

Iteration N

Algorithm comparison 600 000 counts (including scatter)

original

3DRP Hanning

3D OSEM + filt.6 subsets5 iter.Gauss .5cm

FORE + OSEM

6 subsets2 iter.

3D OSEM

6 subsets2 iter.

Image credits: Kris ThielemansMRC CU, London (now IRSL – www.irsl.org)

Reconstruction of a slice from projectionsexample = myocardial perfusion, left ventricle, long axis

courtesy of Dr. K. Kouris

Iterative reconstruction methodsconventional iterative algebraic methods

algebraic reconstruction technique (ART) simultaneous iterative reconstruction technique (SIRT)

iterative least-squares technique (ILST)

iterative statistical reconstruction methods (with and without using a priori information)

gradient and conjugate gradient (CG) algorithms maximum likelihood expectation maximization (MLEM)

ordered-subsets expectation maximization (OSEM) maximum a posteriori (MAP) algorithms

algorithm (a recipe)

(1) make the first arbitrary estimate of the slice (homogeneous image),

(2) project the estimated slice into projections analogous to those measured by the camera (important: in this step, physical corrections can be introduced - for attenuation, scatter, and depth-dependent collimator resolution),

(3) compare the projections of the estimate with measured projections (subtract or divide the corresponding projections in order to obtain correction factors - in the form of differences or quotients),

(4) stop or continue: if the correction factors are approaching zero, if they do not change in subsequent iterations, or if the maximum number of iterations was achieved, then finish; otherwise

(5) apply corrections to the estimate (add the differences to individual pixels or multiply pixel values by correction quotients) - thus make the new estimate of the slice,

(6) go to step (2).

Iterative reconstruction - multiplicative corrections

Iterative reconstruction - differences between individual iterations

Iterative reconstruction - multiplicative corrections

Filtered back-projection very fast direct inversion of the

projection formula

corrections for scatter, non-uniform attenuation and other physical factors are difficult

it needs a lot of filtering - trade-off between blurring and noise

quantitative imaging difficult

Iterative reconstruction

discreteness of data included in the model

it is easy to model and handle projection noise, especially when the counts are low

it is easy to model the imaging physics such as geometry, non-uniform attenuation, scatter, etc.

quantitative imaging possible

amplification of noise long calculation time

References:Groch MW, Erwin WD. SPECT in the year 2000: basic principles. J Nucl Med Techol 2000; 28:233-244, http://www.snm.org.

Groch MW, Erwin WD. Single-photon emission computed tomography in the year 2001: instrumentation and quality control. J Nucl Med Technol 2001; 20:9-15, http://www.snm.org.

Bruyant PP. Analytic and iterative reconstruction algorithms in SPECT. J Nucl Med 2002; 43:1343-1358, http://www.snm.org.

Zeng GL. Image reconstruction - a tutorial. Computerized Med Imaging and Graphics 2001; 25(2):97-103, http://www.elsevier.com/locate/compmedimag.

Vandenberghe S et al. Iterative reconstruction algorithms in nuclear medicine. Computerized Med Imaging and Graphics 2001; 25(2):105-111, http://www.elsevier.com/locate/compmedimag.

References:Patterson HE, Hutton BF (eds.). Distance Assisted Training Programme for Nuclear Medicine Technologists. IAEA, Vienna, 2003, http://www.iaea.org.

Busemann-Sokole E. IAEA Quality Control Atlas for Scintillation Camera Systems. IAEA, Vienna, 2003, ISBN 92-0-101303-5, http://www.iaea.org/worldatom/books, http://www.iaea.org/Publications.

Steves AM. Review of nuclear medicine technology. Society of Nuclear Medicine Inc., Reston, 1996, ISBN 0-032004-45-8, http://www.snm.org.

Steves AM. Preparation for examinations in nuclear medicine technology. Society of Nuclear Medicine Inc., Reston, 1997, ISBN 0-932004-49-0, http://www.snm.org.

Graham LS (ed.). Nuclear medicine self study program II: Instrumentation. Society of Nuclear Medicine Inc., Reston, 1996, ISBN 0-932004-44-X, http://www.snm.org.

Saha GB. Physics and radiobiology of nuclear medicine. Springer-Verlag, New York, 1993, ISBN 3-540-94036-7.

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