Transcript PET Imaging (I): Physical Principles Technical Proceedings

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)
Reconstruction
Projections
Slices
SPECT
Single Photon Emission Computed Tomography
only one gamma photon
is detected per decay
collimator
NaI(Tl) crystal
Rotating scintillator
camera
PET
Positron 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
detector

TRUE
coincidence
ee+

unstable nucleus
emits positron
positron annihilates
with electron
detector
two 511 photons
are emitted
simultaneously in
opposite directions
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)
PET CT
Other configurations for
special-purpose applications:
- brain imaging
- animal PET
- mammography, other
True
True
PET/CT
CT
PET
General Electric Medical Systems
CT+PET
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
2D mode
3D mode
(= with septa)
(= no septa)
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
3D mode
(= with septa)
(= no septa)
True
True
not detected
(septa block
photons)
detected
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 resolution
Human brain
Monkey brain
Animal PET
~1998
Image credits:
CTI PET Systems
Image credits:
Crump Institute, UCLA
“Part of the goal is to bring order to this alphabet soup.”
J. Fessler, 2002
PET image reconstruction
Projection
r
Radon Transform
P( , r )  
line( , r )
f(x,y)
2
1
Object
f ( x, y)dl
PET image reconstruction
Sinogram
Object

Projection
angle
r
Projection bin
PET image reconstruction
Sinogram
Object

r
PET image reconstruction
Sinogram
Object

r
PET image reconstruction
Sinogram
Object

r
PET image reconstruction
Sinogram
Object

r
PET image reconstruction
Sinogram
Object

r
Sinogram
PET: 180º
(2 opposite photons)
SPECT: 360º (1 photon)

Other representations can be used instead of the sinogram (linogram,
planogram)
2D Reconstruction
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)
etc
Slice 5
Slice 4
Slice 3
etc
Plane 5
Plane 4
Plane 3
Plane 2
Slice 2
Slice 1
Plane 1
2D reconstruction
2D reconstruction
2D reconstruction
2D reconstruction
2D reconstruction
2D Reconstruction
PET image reconstruction
 Projection and Backprojection
Projection
Backprojection
2D Reconstruction
PET image reconstruction
4 projections
Object
Backprojection
Filtered
Backprojection
16 projections
128 projections
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
PET image reconstruction
 Data corrections are necessary
– the measured projections are not the same as the
projections assumed during image reconstruction
integral of the activity
along the line or tube of
response
Scattered
coincidences
component
assumed
Attenuation
Detector
efficiency
effects
True
coincidences
component
measured
projection
Random
coincidences
component
Object
(uniform
cylinder)
projection
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 (nonnegativity, boundaries)
– Corrections can be included in the reconstruction process
(attenuation, scatter, etc)
 Disadvantages
– Slow
– Less predictive behaviour (noise? convergence?)
PET Image reconstruction
 Iterative methods
image space
Iteration 1
projection space
projection
Estimated
projection
Measured
projection
Current
estimate
Update
Error
image
backprojection
Error
projection
Compare
(e.g. – or / )
PET Image reconstruction
 Iterative methods
image space
Iteration 2
projection space
projection
Current
estimate
Estimated
Estimated
projection
projection
Measured
projection
Update
Error
image
backprojection
Error
projection
Compare
(e.g. - or / )
PET Image reconstruction
 Iterative methods
image space
Iteration N
projection space
projection
Current
estimate
Estimated
Estimated
projection
projection
Measured
projection
Update
Error
image
backprojection
Error
projection
Compare
(e.g. - or / )
Algorithm comparison

600 000 counts (including scatter)
original
3DRP
Hanning
FORE +
OSEM
6 subsets
2 iter.
3D
OSEM
6 subsets
2 iter.
6 subsets
5 iter.
Gauss .5cm
3D OSEM + filt.
Image credits:
Kris Thielemans
MRC CU, London (now IRSL – www.irsl.org)
Reconstruction of a slice from projections
example = myocardial perfusion, left ventricle, long axis
courtesy of Dr. K. Kouris
Iterative reconstruction methods
conventional 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. SpringerVerlag, New York, 1993, ISBN 3-540-94036-7.