Fisher information-based evaluation of image quality for time-of-flight PETKathleen Vunckx1, Lin Zhou1, Samuel Matej2,Michel Defrise3, Johan Nuyts1

1 Dept. of Nuclear Medicine, Katholieke Universiteit Leuven, Leuven, Belgium.2 Dept. of Radiology, University of Pennsylvania, Philadelphia, USA. 3 Dept. of Nuclear Medicine, Vrije Universiteit Brussel, Brussels, Belgium.

Outline

Introduction: TOF PET Aim & motivation Image quality evaluation methods Simulations & results Conclusions & future work

Introduction: TOF PET

1x2x

Conventional PET

Time-of-flight PETc

xt

c

xt 2

21

1 and

x

2

12 ttcx

2

tcx

Annihilation location:

Localization uncertainty:

Time annihilation detection:

Time resolution

2t1t

x

Introduction: TOF PET

Philips Gemini TF PET/CT

non-TOFnon-TOF

TOFTOF

CTCTSlice A Slice B

Courtesy of S. Matej et al.

Outline

Introduction: TOF PET Aim & motivation Image quality evaluation methods Simulations & results Conclusions & future work

Aim & motivation

Effect TOF information on image quality?

Influence TOF kernel accuracy on image quality?

2

tcx

Conventional PET

Time-of-flight PET

Time difference=

Extra information

x

Outline

Introduction: TOF PET Aim & motivation Image quality evaluation methods

– Tomitani’s analytical TOF gain calculation– Fisher information-based evaluation method for

TOF PET Simulations & results Conclusions & future work

Tomitani’sanalytical TOF gain calculation

Restrictions:– Only for central point(s) of a large uniform

non-attenuating disk source– For FBP-like reconstructions

3

2

min, 8 r

xabVarTOF

* Tomitani, IEEE TNS 28(6), 1981.

3

3

min,16 r

DabVar TOFnon

x

D

x

Db

Var

Var

TOF

TOFnon

66.0

2min,

min,

TOF PET* non-TOF PET**

Gain*

** Tanaka et al., Comp. Biol. Med., 1976.

2ln22

r

a

b (standard deviation FWHM)

amount of detected coincidences per cm²

resolution in reconstructed image (FWHM)

D

x

Fisher information-basedevaluation method for TOF-PET

Fisher information ACAF YT 1

projectioncovariance matrix of measurement

backprojection

Fessler et al., IEEE TIP 1996.Qi et al., IEEE TMI 2000.Vunckx et al., IEEE TMI 2008.

Efficient approximations for image quality of

post-filtered MLEM:– Linearized local impulse response (LLIR)– (Co)variance

in 1 pixel or small ROI

MLEM post-filter

Fixed target resolution

Fisher information-basedevaluation method for TOF-PET

0

1

0

Ij QLLIR

0

1

0

010

V

j QVar

0

/1

/1

/1

0

r

r

r

QLLIR IROI

0

/1

/1

/1

0

0111

0

r

r

r

Qrrr

Var VROI

pixels in ROIpixel j

Approximations for individual pixels

Approximations for ROI

with r = # pixels in ROI

due to local shift invariance

Also possible to insert TOF kernel mismatch in model

Outline

Introduction: TOF PET Aim & motivation Image quality evaluation methods Simulations & results

– Sim. 1: Tomitani versus Fisher information– Sim. 2: Attenuating ellipse– Sim. 3: Realistic thorax phantom– Sim. 4: Effect accuracy TOF kernel

Conclusions & future work

Simulation 1:Tomitani versus Fisher information

Homogeneous diskD = 35 cm

No attenuation, no scatter, no randoms, no detector resolution

Pixel size 0.2 cm FOV of 67.2 cm Target resolution 0.6 cm

FWHM x

D

Var

Var

TOF

TOFnon

66.0

D = 35.0cm

Nice agreement!

Simulation 2:Attenuating ellipse

Db

= 2

8.0

cm

Da = 43.8cm

0.4 Da

0.4

Db

Homogeneous ellipseDa= 43.8 cm, Db = 28.0 cm

No scatter, no randoms, no detector resolution

Attenuation (water) Pixel size 0.2 cm FOV of 67.2 cm Target resolution 0.6 cm

FWHM

Gain increases faster in the center!

17.85

1.45 1.75

1.25

13.9013.73

non-TOF

non-TOF

3.37

2.523.31

Simulation 3:Realistic thorax phantom

2D realistic thorax phantom No scatter, no randoms Attenuation modeled Intrinsic resolution 0.5 cm Pixel size 0.3375 cm FOV of 64.8 cm Target resolution 1.2 cm

FWHM

True activity

TOF PET variance t = 500 ps

Non-TOF PET variance

Variance improvement due to TOF information

> 5

4

012

3

> 5

4

0123

TOF PET variance t = 500 ps

Non-TOF PET variance

Variance improvement due to TOF information

Fisher information-based method

Based on recon. of 300 noisy proj. data setsTrue activity

Simulation 3:Realistic thorax phantom

Simulation 4:Effect accuracy TOF kernel

TOF kernel might not be known accuratelyEffect on image quality?

Narrower contrastWider contrast

Daube-Witherspoon, Matej et al., 2006 IEEE NSS Conf. Rec.

FWHM?

t = 300 ps

D = 27.0cm

ROI diam 1.3cm7cm

Simulation 4:Effect accuracy TOF kernel

mea

n R

OI

vari

ance

RO

I

CN

R R

OI

recon TOF kernel FWHM (ps) recon TOF kernel FWHM (ps) recon TOF kernel FWHM (ps)

Too narrowt = 150 ps

Too widet = 600 ps

Real TOF kernel t = 300 ps

pixels

po

st-

sm

oo

the

d

imp

uls

e r

es

po

ns

e

po

st-

sm

oo

the

d

imp

uls

e r

es

po

ns

e

pixels

D = 27.0cm

7cm

ROI diam 1.3cm

Target resolution 6 mm

Simulation 4:Effect accuracy TOF kernel

mea

n R

OI

vari

ance

RO

I

CN

R R

OI

recon TOF kernel FWHM (ps) recon TOF kernel FWHM (ps) recon TOF kernel FWHM (ps)

pixels

po

st-

sm

oo

the

d

imp

uls

e r

es

po

ns

e

po

st-

sm

oo

the

d

imp

uls

e r

es

po

ns

e

pixels

Too narrowt = 150 ps

Too widet = 600 ps

Real TOF kernel t = 300 ps Target resolution 6 mm

D = 27.0cm

7cm

ROI diam 1.3cm

Simulation 4:Effect accuracy TOF kernel

pixels (column coordinates)

activ

ity

Reconstructions homogeneous sphere 27 cm Real TOF kernel t = 300 ps

Recon TOF kernel FWHM t = 150 ps

Recon TOF kernel FWHM t = 300 ps

Recon TOF kernel FWHM t = 600 ps

CORRECTTOO NARROW TOO WIDE

Simulation 4:Effect accuracy TOF kernel

mea

n R

OI

recon TOF kernel FWHM (ps) recon TOF kernel FWHM (ps) recon TOF kernel FWHM (ps)

mea

n R

OI

vari

ance

RO

Iva

rian

ce R

OI

CN

R R

OI

CN

R R

OI

recon TOF kernel FWHM (ps) recon TOF kernel FWHM (ps) recon TOF kernel FWHM (ps)

Gaussian post-filter

Optimal post-filter (imposed Gaussian shape and FWHM)

(imposed target FWHM)

Outline

Introduction: TOF PET Aim & motivation Image quality evaluation methods Simulations & results Conclusions & future work

Conclusions

Gain in center increases with diameter and TOF resolution:

Gain in all pixels Slower increase in eccentric and high-

count regions

x

D

Var

Var

TOF

TOFnon

66.0

Kernel too wide:contrast contrast =

variance variance

Kernel too narrow:contrast contrast =

variance variance

Conclusions

Accurate kernel:best contrast vs.variance trade-off, best CNR

Gaussian post-filterGaussian post-filter Optimal post-filterOptimal post-filter

Flat optimum!Flat optimum!

CNR

CNR

artifacts

Future work

So far: – Design evaluation for multipinhole SPECT– Effect of overlapping projections in multipinhole

SPECT– Image quality improvement due to TOF

Also interesting:– Effect of randoms, scatter, … for TOF PET– 3D TOF PET– Rotating slat hole SPECT (Lin Zhou)