joint estimation of activity and attenuation in tof-pet...– siemens biograph mct pet/ct • mlaa...

Joint estimation of

activity and attenuation in

TOF-PET

Ahmadreza Rezaei

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• Attenuation Correction in PET

• Time of Flight (TOF) PET

• Data collection

• Statistical Methods for Attenuation Correction in TOF-PET

– MLAA

– MLACF

– MLRR

• Extension to Listmode

• Conclusion

Overview

3 / 29

• Transmission scans

– Problem: cumbersome, and very time consuming

• High quality CT scans,

– Facilitated by hybrid PET/CT scanners

– Attenuation correction: projections of the “adjusted CT” (511 keV photon

energy).

– Problem: between-scan and in-scan motion.• PET and CT data are acquired sequentially

• Long acquisition time for the PET compared to the CT

• Emission data (?!)

– Useful: anatomical information not available, acquisition not possible

– Joint activity and attenuation estimation

Attenuation Correction in PET

– Background

V. Panin, et al. 2011 NSSMIC.

4 / 29

• Consistency Conditions

– Analytical Consistency Conditions• Natterer, Inverse Problems 1993

• Welch et al, IEEE TMI 1997

– Discrete Consistency Conditions• Bronnikov, Inverse Problems 1999, IEEE TMI 2000

• Kudo et al, IEEE NSS-MIC 2000

• Iterative Schemes

– Maximum Likelihood• Krol et al, IEEE TMI 2001, SNM 1995

• Nuyts et al, IEEE TMI 1999

• Laymon et al, IEEE NSS-MIC 2004

• De Pierro et al, IEEE TNS 2007

• Salomon et al, SNM 2009

– POCS, Least Squares• Censor et al, IEEE TNS 1979

• Panin et al, IEEE TNS 2001



Non-TOFNon-TOF

True ImagesTrue Images

Activity (�)

Attenuation (�)

Cross-talk!- Structures not preserved

- NOT quantitative

Can Time of Flight (TOF) improve the joint activity and attenuation reconstructions?!

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Positron Emission Tomography (PET)

– Time of Flight (TOF)

• Difference in photon arrival (t2 - t1)

• Time uncertainty (∆t)– Mainly due to detector properties

• Spatial uncertainty (∆l = c * ∆t / 2)

• Modeled by a Gaussian distribution– FWHM equal to spatial uncertainty

• Commercial TOF-PET systems• Biograph mCT: ∆t ≈ 550 ps ↔ ∆l ≈ 8.25 cm

• Signa: ∆t ≈ 400 ps ↔ ∆l ≈ 6.00 cm

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Tracer distribution

Activity

�


– Data Collection with TOF

radial-dim.

angular-dim.TOF-dim.

��

TOF index

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– Data Collection with TOF

��()Attenuation

�

�� , � = �� ()

TOF Emission Data

��

angular-dim.

radial-dim.

TOF-dim.

TOF indexReconstruction problem: Find �

ACFs

!

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• Consistency Conditions

– Analytical Consistency Conditions• Natterer, Inverse Problems 1993

• Welch et al, IEEE TMI 1997

– Discrete Consistency Conditions• Bronnikov, Inverse Problems 1999, IEEE TMI 2000

• Kudo et al, IEEE NSS-MIC 2000

• Iterative Schemes

– Maximum Likelihood• Krol et al, IEEE TMI 2001, SNM 1995

• Nuyts et al, IEEE TMI 1999

• Laymon et al, IEEE NSS-MIC 2004

• De Pierro et al, IEEE TNS 2007

• Salomon et al, SNM 2009

– POCS, Least Squares• Censor et al, IEEE TNS 1979

• Panin et al, IEEE TNS 2001



TOFTOF

Non-TOFNon-TOF

True ImagesTrue Images

Activity (�)

Attenuation (�)

Cross-talk!- Structures not preserved

- NOT quantitative


• Yes, very significantly! ☺

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( +�, ��) �� , � →

TOF Emission Data

Joint Activity and Attenuation Estimation

– Analytic Solution

!


• Yes, very significantly! ☺

• But the reconstructions are NOT quantitative! �

10 / 29


– Statistical methods, MLAA

ML

AA

ML

AC

FM

LR

R

�� , � = �� ()

��, �� = argmax�,

( �, � , �)

MLEM (Maximum Likelihood

Expectation Maximization)

MLTR (Maximum Likelihood algorithm

for Transmission Tomography)

1:�#, �#$% = arginc�

( �, �# , �)

2: �#$%, �#$% = arginc

( �#$%, � , �)

CTMLEM

A. Rezaei, M. Defrise, G. Bal, C. Michel, M. Conti, C. Watson, and J. Nuyts, “Simultaneous Reconstruction of Activity and Attenuation in Time-of-Flight PET”, In: IEEE Trans. Med. Imaging 31.12 (Dec. 2012), pp. 2224-33.

11 / 29


– Statistical methods, MLAA

Scale?

– Enforcing expected tissue attenuation during reconstruction!

• Tissue: 0.096 cm-1

• Bone: 0.170 cm-1

CTMLEMM

LA

AM

LA

CF

ML

RR

A. Rezaei, M. Defrise, G. Bal, C. Michel, M. Conti, C. Watson, and J. Nuyts, “Simultaneous Reconstruction of Activity and Attenuation in Time-of-Flight PET”, In: IEEE Trans. Med. Imaging 31.12 (Dec. 2012), pp. 2224-33.

12 / 29

• Thorax scan

– Duration: 5 minute scan

– Tracer: 570 MBq 18F-FDG

– Siemens Biograph mCT PET/CT

• MLAA

– Scaled to have expected tissue

attenuation

PET-MLEM PET-MLAA-Activity

CT-FBP PET-MLAA-Attenuation

MLAA

– Patient data

* Data courtesy of M.Conti from Siemens

Medical Solutions, Molecular Imaging,

Knoxville, TN 37932 US

13 / 29


– Statistical methods, MLACF

�� , A = �� A

��, +�� = argmax�,,

( �, + , �)

1:+# , �#$% = arginc�

( �, +# , �)

2: �#$%, +#$% = arginc,

( �#$%, + , �)

ACF update

CTMLEMM

LA

AM

LA

CF

ML

RR



M. Defrise, A. Rezaei, and J. Nuyts, “Transmission-less attenuation correction in time-of-flight PET: Analysis of a discrete iterative algorithm”, In: Phys. Med. Biol. 59.4 (Feb. 2014), pp. 1073-95. A. Rezaei, M. Defrise, and J. Nuyts, “ML-Reconstruction for TOF-PET With Simultaneous Estimation of the

Attenuation Factors”, In: IEEE Trans. Med. Imaging 33.7 (July 2014), pp. 1563-72.

14 / 29


– Statistical methods, MLACF

Scale?

– More complex!

– Post-reconstruction of ACFs

– Addition of a vial of known activity?

CTMLEMM

LA

AM

LA

CF

ML

RR

M. Defrise, A. Rezaei, and J. Nuyts, “Transmission-less attenuation correction in time-of-flight PET: Analysis of a discrete iterative algorithm”, In: Phys. Med. Biol. 59.4 (Feb. 2014), pp. 1073-95. A. Rezaei, M. Defrise, and J. Nuyts, “ML-Reconstruction for TOF-PET With Simultaneous Estimation of the

Attenuation Factors”, In: IEEE Trans. Med. Imaging 33.7 (July 2014), pp. 1563-72.

15 / 29

MLACF

– Patient data

CT

• Thorax scan




• MLAA

– Scaled by total amount of activity

• MLACF


* Data courtesy of S.Stroobants,

S.Staelens and M.Lambrechts from

Universiteit Antwerpen.

16 / 29

MLACF

– Brain scan data

MLEM

MLAA activity

MLACF

• Brain scan




• MLAA

– Scaled by expected tissue

attenuation

• MLACF


– Attenuation estimate regularized




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MLAA attenuationCT

MLEM

MLAA activity

MLACF

MLACF

– Brain scan data

18 / 29


– Statistical methods, MLRR

�� ,M = �� (.∘)

��, 01�� = argmax�,2

( �,0 , �)

1:0#, �#$% = arginc�

( �,0# , �)

2: �#$%, 0#$% = arginc2

( �#$%, 0 , �)

MLTR + demons

CTMLEMM

LA

AM

LA

CF

ML

RR

A. Rezaei, C. Michel, M. E. Casey, and J. Nuyts. “Simultaneous reconstruction of the activity image and registration of the CT image in TOF-PET.” In: Phys. Med. Biol. 61.4 (Feb. 2016), pp. 1852-1874.



19 / 29


– Statistical methods, MLRR

Scale?

– Automatically fixed!

CTMLEMM

LA

AM

LA

CF

ML

RR

A. Rezaei, C. Michel, M. E. Casey, and J. Nuyts. “Simultaneous reconstruction of the activity image and registration of the CT image in TOF-PET.” In: Phys. Med. Biol. 61.4 (Feb. 2016), pp. 1852-1874.

20 / 29

MLRR

– Patient data

• Thorax scan




• MLAA

– scaled to have expected tissue

attenuation

• MLACF

– scaled by total amount of activity

• MLRR

– No scaling required

CTMLRR

attenuation

MLAA

attenuation

MLEM MLRR activityMLAA activity




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MLEM MLRR MLAA

CT Deformed CT MLAA

MLRR

– Patient data

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Extension to Listmode - MLAA

– Hoffman brain scan

TOF-MLEM MLAA – ACT.

MLAA – ATT.UMAP

• Siemens Biograph mCT

• ~200 MBq scanned for 10 min

• Reconstruction:

– 5 iterations and 12 subsets

MLACFMLACF 10:12

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Extension to Listmode - MLACF

– Hoffman brain scan

MLACF

TOF-MLEM MLAA – ACT.

MLAA – ATT.UMAP

24 / 29


– Hoffman brain scan & Motion

TOF-MLEM + no ACF cor.

UMAP

• 10 min scan with continuous motion

• M Bickell et al. “Rigid motion correction of PET and CT for a PET/CT scanner”, MIC2015, M5DP-124

25 / 29

• 10 min scan with continuous motion

• M Bickell et al. “Rigid motion correction of PET and CT for a PET/CT scanner”, MIC2015, M5DP-124

• MLACF: no time-averaged sensitivity image needed


– Hoffman brain scan & Motion

MLACF

UMAP MLACF 10:12

TOF-MLEM + motion Cor.

26 / 29

• With Time-of-Flight PET data,

– Simultaneous activity and attenuation

estimation is possible!

– Constant/Scale correction technique needed

• MLAA

– Scale correction: expected tissue

attenuation!

• MLACF

– Fast compared to MLAA/MLRR

– Scale correction: ?!

• MLRR

– Makes use of high CT quality

– Scale correction: automatically solved

Conclusions/Future Work

27 / 29

• Joint Estimation methods in Gated TOF-PET

– Mitigate the longstanding problem of attenuation correction

– Extended MLACF in a Fully4D reconstructions framework

• Future work

– Tracers with more focal activity uptake

– Analysis of different flavors of JE methods

• E.g. MLACF with Poisson or Gaussian ACF model, sMLACF, …

– More quantitative studies on JE methods

• MLAA, MLACF and MLRR

Conclusions/Future Work

28 / 29

• My sincere thanks to:

– Johan Nuyts, Michel Defrise, and my lab members at KU Leuven

– Roger Fulton and J Kim from the University of Sydney

– Mike Casey, Vladimir Panin and Judson Jones from Siemens

Healthcare, Molecular Imaging for data processing and providing the

data-based gating software.

– Sigrid Stroobants, Steven Staelens and Michel Lambrechts from the

Universiteit Antwerpen and Fernando Boada and Thomas Koesters

from NYU.

– Christian Michel, Girish Bal, Frank Kehren, Maurizio Conti, Charles

Watson from Siemens Healthcare, Molecular Imaging,

– Floris Jansen, Michel Tohme, Sangtae Ahn from GE, and

Annemie Ribbens from KU Leuven for the very insightful discussions.

– You! for your attention. ☺

Acknowledgements

29 / 29

• Activity recons. scaled to have “known” total activity

• Monte Carlo simulation

– NEMA-like phantom

– Siemens Biograph mCT specs.

– No scatter in emission data

A Quantitative study

– Monte Carlo Simulation

2.0

0.0 -0.2

+0.2

0.0

0.1MLAA Attenuation

MLEMGT - MLEMGTMLEMGT

MLAAGT

30 / 29

ML Scatter Scaling

• Activity recons. scaled to have “known” total activity

• Monte Carlo simulation

– NEMA-like phantom

– Siemens Biograph mCT specs.

– With scatter in emission data

A Quantitative study

– Monte Carlo Simulation

MLEM - MLEMGT

MLAA - MLEMGT

31 / 29

Listmode MLTR

• MLTR (Maximum Likelihood Transmission Reconstruction)

• ISRA-like algorithm

– Image Space Reconstruction Algorithm

– Back-projection of all events

– subsets on all possible LORS

Sinogram Listmode

Attenuation

image

voxel index

Measured

data

Expected

counts

Activity

projectionattenuationLOR

index

Voxel-LOR

intersection lengthMeasured

LOR index

32 / 29

Listmode MLAA: MLTR + MLEM

• MLAA (Maximum Likelihood Activity and Attenuation reconstruction)

• 2 sets of subsets in MLEM

• 3:1 attenuation-to-activity updates

Sinogram Listmode

Attenuation

image

voxel index

Measured

data

Voxel-LOR

intersection lengthMeasured

LOR index

Expected

counts

Activity


index

Activity image Voxel-LOR

sensitivity

33 / 29

• MLACF (Maximum Likelihood Attenuation Correction Factors)

• Back-projections are matched

• ONLY Sensitivity of measured events needed

• ACFs are not computed explicitly

Listmode MLACF

Expected

counts

Activity


index

Sinogram Listmode

joint estimation of activity and attenuation in tof-pet...– siemens biograph mct pet/ct • mlaa...

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