Modeling a flexible Detector Response Function in small animal SPECT using Geant4 Z. El Bitar1, R. H. Huesman2, R. Buchko2, D. Brasse1, G. T. Gullberg2 Université de Strasbourg, IPHC, 23 rue du loess, 67037 Strasbourg, France Lawrence Berkeley National Laboratory, Berkeley California 94720, USA Droite Workshop, Lyon, October 25, 2012

Outline Context Fully 3D image reconstruction Monte Carlo modelling of the system matrix Including geometrical misalignment Correcting for penetration Phantom and preclinical results

Single Photon Emission Computed Tomography 1- Injection of a radiotracer 2- Isotropic emission of gamma rays 3- Collimation: Filtering the directions of the photons Parallel Pinhole Parallel Pinhole

Fully 3D image reconstruction j Projection p Activity distribution f detector i Discrete formulation of the image reconstruction problem p = R x f R(i,j) : Probability that a photon emitted in a voxel i to ba detected in a pixel j Simultaneous reconstruction of the whole volume Taken into account of 3D physcial phenomena such as : scatter and detector response Solving p = R f using an iterative method like MLEM, OSEM, ART, GC.

Données fonctionnelles TEMP (fusion avec TDM) Modélisation Monte Carlo de R Modèle du TEMP 2 1 densité composition atomique Coupe voxellisée (obtenue par TDM) j Modélisation Monte-Carlo des probabilités qu’un photon émis en voxel i soit détecté en pixel j i détecteur 3 mesuresTEMP P 4 Estimation de R 11’ Revoir le discours sur le transparent – fonte de R dans la case 3 Mettre des animations adaptées pour faire arriver les différentes étapes. 5 Résolution du problème inverse P = Rx f dans un algorithme itératif (ML-EM, OSEM, ART, CG …) Données fonctionnelles TEMP (fusion avec TDM)

What’s the problem in small animal SPECT ? Monte Carlo simulations are time consuming. Detection efficiency is very low in small animal SPECT due to pinhole collimation. Pinhole SPECT modality is very sensitive to geometrical misalignments => a system matrix should be computed for each set up. 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.

Decomposition of the system matrix R = Rsubject + Rdetector To be computed for each subject/exam Computed once-for-all

Definition of a family of lines (or directions) pixel j collimator crystal bin i 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 Response function table (DRFT).

SPECT Components Rectangular knife edge collimator Aperture : 2 x 1.5 mm2 Rectangular knife edge collimator Aperture : 0.6 x 0.4 mm2 Both collimators Shielding SPECT : General Electric – Hawkeye 3

Collimator + shielding Collimator + Shielding + Crystal SPECT model in Geant4 Collimator + shielding Collimator Collimator + Shielding + Crystal

Profiles drawn on the projections of three point sources located at : 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

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 :

Calibration phantom 1 2 3

Geometrical Parameters Estimation u (head1) v (head1) u (head2) v (head2) 1 v 2 3 u

Trajectories' fit Head1 Head2

Reconstructed Images of a sphere (Ø = 2 mm). Mechanical shift y crystal s shift m shift m collimator x Reconstructed Images of a sphere (Ø = 2 mm). Original m = 2 mm Corrected z

What’s the point ? After performing Monte Carlo simulations and calculating a Detector Response Function Table, one is home-free to used the DRFT(~500 Mbytes). 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). Resimulation of all photons’ trajectories inside the detector is not required for each study.

Target emission window: x z y 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

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

Penetration effect : simulation study Projection of Cylindre : Diameter = 40 mm, Height = 40mm Penetration window Target window = 2 mm Target window = 6 mm

Tomography Spatial resolution: 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) 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

Effect on reconstruction Window projection : 2 mm Window system matrix : 2 mm Window projection : 2 mm Window system matrix : 6 mm Window projection : 6 mm Window system matrix : 2 mm Window projection : 6 mm Window system matrix : 6 mm

Real data: micro Jaszczack phantom (1) 4.8 mm 4.0 mm 3.2 mm 2.4 mm 1.2 mm 1.6 mm

Real data: micro Jaszczack phantom (2) 2 mm 1.5 mm Correction for the penetration effect Window system matrix : 2 mm Window system matrix : 6 mm

Real data: micro Jaszczack phantom (3) 0.6 mm 0.4 mm Misalignment correction Before correction After correction

Computation time : parallelization of the system matrix calculation Each processor calculate the system matrix corresponding to a slice Computation time for an object of 152x152x152 voxels ~= 20 minutes Field of view

Parallelization of the iterative reconstruction Reconstruction Tomographique Slaves tasks: Master PC 1 PC 2 PC 10 Slave Forward-projection 2/3 Send projections Receive projections Receive CC Send the CC to the slaves 6/7 Volume’s slices to be reconstructed Back-projection Master Tasks Sum the projections Compute the correction coefficients (CC = Pmeasured/ Pestimated)

Most recent result 150x150x150 voxels (0. 4x0. 4x0 Most recent result 150x150x150 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

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

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 !