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Modeling a flexible Detector Response Function in small animal SPECT

using Geant4Z. El Bitar1, R. H. Huesman2, R. Buchko2, D. Brasse1, G. T. Gullberg2

1. Université de Strasbourg, IPHC, 23 rue du loess, 67037 Strasbourg, France2. Lawrence Berkeley National Laboratory, Berkeley California 94720, USA

Droite Workshop, Lyon, October 25, 2012

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Outline

1. Context

2. Fully 3D image reconstruction

3. Monte Carlo modelling of the system matrix

4. Including geometrical misalignment

5. Correcting for penetration

6. Phantom and preclinical results

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1- Injection of a radiotracer2- Isotropic emission of gamma rays3- Collimation: Filtering the directions of the photons Parallel

Single Photon Emission Computed Tomography

Pinhole

Parallel Pinhole

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j

Projection p

1.1. Simultaneous reconstruction of the whole volumeSimultaneous reconstruction of the whole volume2.2. Taken into account of 3D physcial phenomena such as : Taken into account of 3D physcial phenomena such as : scatterscatter

and and detector response detector response

i

Activity distribution

f

Fully 3D image reconstruction

• Solving Solving p p = R = R f f using an iterative method like MLEM, OSEM, ART, GC.using an iterative method like MLEM, OSEM, ART, GC.

R(i,j) : Probability that a photon emitted in a voxel i to ba detected in a pixel j

Discrete formulation of the image reconstruction problemp = R x f

detector

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4 Estimation de R

1 • densité• composition atomique

Coupe voxellisée (obtenue par TDM)

Modélisation Monte Carlo de RModèle du TEMP

2

mesuresTEMP

P

5Résolution du problème inverse P = Rx f dans un algorithme itératif (ML-EM, OSEM, ART, CG …)

Données fonctionnelles TEMP (fusion avec TDM)

j

Modélisation Monte-Carlo des probabilités qu’un photon émis en voxel i soit détecté en pixel j

idétecteur

3

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What’s the problem in small animal SPECT ?

1. Monte Carlo simulations are time consuming.

2. Detection efficiency is very low in small animal SPECT due to pinhole collimation.

3. Pinhole SPECT modality is very sensitive to geometrical misalignments => a system matrix should be computed for each set up.

4. We must find a solution to avoid resimulation by Monte Carlo methods for each exam => need to have a detector model independent of the acquisition set up.

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Decomposition of the system matrix

R = Rsubject + Rdetector

Computed once-for-allTo be computed for each subject/exam

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pixel j

collimator

crystal

bin ibin i

Definition of a family of lines (or directions)

The family of lines Lij is defined by all photons’ directions entering the collimator at bin i and aiming the crystal’s pixel j => Calculation of the Detector Responsefunction table (DRFT).

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SPECT Components

Rectangular knife edge collimatorAperture : 2 x 1.5 mm2

Rectangular knife edge collimatorAperture : 0.6 x 0.4 mm2 Both collimators

Shielding

SPECT : General Electric – Hawkeye 3

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SPECT model in Geant4

Collimator + shieldingCollimator

Collimator + Shielding + Crystal

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Validation of the DRFT

Profiles drawn on the projections of three point sources located at :(-20 mm, 0, 0), (0, 0, 0) and (20 mm, 0, 0).

Speed up by a factor of 74

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Pinhole acquisition geometry

7 parameters to estimate: • m : mechanical shift • electronic shift : eu , ev

• distance collimator to centre of rotation : r• distance collimator to crystal : f• Tilt and Twist angle: Ф, Ψ

Calibration parameters are estimated by minimizing the following functions :

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Calibration phantom

1

2 3

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Geometrical Parameters Estimation

u (head1) v (head1)

u (head2) v (head2)u

v1

2 3

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Head1 Head2

Trajectories' fit

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collimator

crystal

x

y

z

Mechanical shift

shift m

s

shift m

Reconstructed Images of a sphere (Ø = 2 mm).

Original m = 2 mm Corrected

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What’s the point ?1. After performing Monte Carlo simulations and

calculating a Detector Response Function Table, one is home-free to used the DRFT(~500 Mbytes).

2. The DRFT can incorporate with ease for any geometrical misalignments (translation, rotation): all what is required is the equation of the entry plan (collimator) and the detection plan (crystal).

3. Resimulation of all photons’ trajectories inside the detector is not required for each study.

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Target emission window:

{x > -1; x < 1}{z > -1; z < 1}

{x > -3; x < 3}{z > -3; z < 3}

{x > -3; x < -1} U { x > 1; x < 3 } {z > -3; z < -1} U { z > 1; z < 3 }

Target window = 2 mm Target window = 6 mm Penetration window

x

z

y

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Penetration validation

2

tgxd

16.3)140( mmkeVtung

Penetration ratio

0

0,1

0,2

0,3

0,4

0,5

0,6

0,1 0,2 0,3 0,4 0,5

Distance from the knife edge border (mm)

Pen

etra

tio

n r

atio

Theory

Geant4

x

dα

)2

(22

2))

2(

2(

tgtggeodgeodeffectived

*Roberto Accorsi and Scott Metzler : Analytic Determination of the Resolution-equivalent effective diameter of a Pinhole Collimator (IEEE, TMI, vol 23, June 2004)

mmmmgeodmmkeVweffectived 29.2deg)90,2:,16.3:)140((

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Penetration effect : simulation studyProjection of Cylindre : Diameter = 40 mm, Height = 40mm

Target window = 2 mm Target window = 6 mm Penetration window

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Tomography• Spatial resolution:

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2int

geoRM

RsystemR

Where:• Rint is the intrinsic spatial resolution of the crystal• Rgeo is the spatial resolution due to the geometry of the pinhole• M is the magnification factor (distante detector-pinhole)/(distance pinhole-centerFOV)

)1

1(M

dgeometryR

Where:• d is the diameter of the aperture of the pinhole

Expected radial spatial resolution with:

Wide collimator (2 x1.5 mm2) : 2.55 mm Narrow collimator (0.6 x 0.4 mm2) : 1.14 mm

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Effect on reconstruction

Window projection : 2 mmWindow system matrix : 2 mm

Window projection : 2 mmWindow system matrix : 6 mm

Window projection : 6 mmWindow system matrix : 2 mm

Window projection : 6 mmWindow system matrix : 6 mm

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Real data: micro Jaszczack phantom (1)

4.8 mm4.0 mm

3.2 mm

2.4 mm1.2 mm

1.6 mm

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Real data: micro Jaszczack phantom (2)

Window system matrix : 2 mm Window system matrix : 6 mm

Correction for the penetration effect2 mm

1.5 mm

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Real data: micro Jaszczack phantom (3)

Before correction After correction

Misalignment correction

0.6 mm

0.4 mm

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Computation time : parallelization of the system matrix calculation

Field of view

Each processor calculate the system matrix corresponding to a slice

Computation time for an object of 152x152x152 voxels ~= 20 minutes

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Slaves tasks:Slaves tasks:

1.1. Forward-projectionForward-projection

Master TasksMaster Tasks

2/3 2/3 2/3

2.2. Send projections Send projections

3.3. Receive projectionsReceive projections

4.4. Sum the projectionsSum the projections

5.5. Compute the correction coefficientsCompute the correction coefficients (CC = P(CC = Pmeasuredmeasured/ P/ Pestimatedestimated))

8.8. Back-projectionBack-projection

MasterMaster

PC 1 PC 2 PC 10

SlaveSlave

7.7. Receive CCReceive CC

6.6. Send the CC to the slavesSend the CC to the slaves

6/7 6/7 6/7

Volume’s slicesVolume’s slicesto be reconstructedto be reconstructed

Reconstruction TomographiqueParallelization of the iterative reconstruction

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Most recent result150x150x150 voxels (0.4x0.4x0.4 mm3),

90 projections (128x88 pixels)Size of system matrix ~= 40 GBytes

MLEM (50 iterations) < 3 minutes

0.6 x 0.4 mm2

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Small animal result

Reconstruction slice of a rat heart using MIBG

(ML-EM, 50 iterations)Profile drawn through the heart

El Bitar et al, submitted to Phys Med Biol

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Acknowledgment Grant T Gullberg (discussion)

Ronald H Huesman (discussion)

Rostystalv Boutchko (calibration)

Archontis Giannakdis (discussion)

Martin Boswell (computing)

Nichlas Vandeheye (experiments)

Steven Hanrahan (experiments)

Bill Moses (experiments)

Special thanks to the Franco-American Fulbright-commission !