Implementation and evaluation of a fully 3D OS-MLEM reconstruction algorithm accounting for the PSF of the PET imaging system

Transcription

1 Implementation and evaluation of a fully 3D OS-MLEM reconstruction algorithm accounting for the PSF of the PET imaging system 3 rd October th Topical Seminar on Innovative Particle and Radiation Detectors 1-4 October 2008 Siena, Italy

2 2 Positron Emission Tomography PET is a diagnostic exam relying on the annihilation of positrons with electrons in the medium Radiopharmaceutical marked with a β+-emitter administered to the patient CT Functional studies Oncology 93% Neurology 5% Cardiology 2% PET

3 Physical effects at emission level 3 Poisson statistics e P( n) = λ n λ n! λ is the required quantity n is the emitted quantity Non collinearity Positron residual energy Random coincidences Two uncorrelated photons on the crystals inside the coincidence time τ R rand = 2τR R 1 fake LOR 2 Source decay A( t) = A t e Measured: Required: T t 0 A t0 Photons not exactly back-to-back 0 ( t t ) t 0 1/ 2 ln 2 0 ( T ) A( t) dt A t Scattered coincidences One of the two photons scattered by the tissues in the body E E = E 1+ 2 m c e ( 1 cosθ ) wrong LOR t θ = ( 180 ± 0. 5) 0 Positron range The positron travels before annihilating Image reconstruction Annihilation point Emission point Attenuation The detected photon pairs are less than the emitted ones due to absorption along the flight ( x) = N e x N 0 0 μ ( t) ρ ( t) dt Internal parts appear less active

4 Physical effects at acquisition level 4 Energy resolution Small crystals Incident radiation not monoenergetic Multicrystal response Two uncorrelated photons are contemporarily detected in two crystals Crystal efficiency Scintillation efficiency dependent on the single crystal and on the ambience PMTs response may change Radial geometry Widths of sinogram bins dependent on radial position Scatter inside crystals The incoming photon is scattered in neighbouring scintillators Crystal dimensions and depth of interaction Crystal response: triangular function A photon may not be confined and lose its energy also in neighbouring crystals Dead time Pile-up due to crystal scintillation Elaboration time of the electronics paralyzable non paralyzable

5 The Point Spread Function 5 Various effects are not corrected A point source (impulse) is rendered with finite dimensions Gaussian (thanks to CLT) Point Spread Function (PSF) r v v R( x) = A( x) PSF( x) Recorded activity distribution Real activity distribution Four main components: Multicrystal response Depth of interaction Scatter inside crystals Finite dimensions of crystals Non collinearity of photons Positron range Block effects FWHM D FWHM N FWHM P FWHM B = 2 4 mm = 1 2 mm = mm = 2 3 mm tot R 2 D FWHM = k FWHM + FWHM + FWHM + FWHM 2 N 2 P 2 B Constant due to the reconstruction algorithm k R 1.25 FWHM tot 5 6 mm

6 The Point Spread Function 6 Cylindric scanner Cylindric symmetry In the radial direction, the PSF is asymmetric due to the circular disposition of the crystals Nearly symmetric Larger sigma towards the scanner center Acquired point source Bidimensional (radially asymmetric) gaussian

7 Image reconstruction 7

8 Image reconstruction 8 LOR

9 Image reconstruction 9 LOR LOR

10 Image reconstruction 10 LOR LOR Radial position Projection angles

11 Image reconstruction 11 LOR Sinogram LOR Radial position Image matrix Projection angles

12 Iterative reconstruction: OSEM Statistical approach: iterative maximization of the log-likelihood ( Data Img) log P 12 Ordered Subsets (Maximum Likelihood with) Expectation Maximization The voxel b in image λ at iteration k -1 is updated using the rule λ [ k ] b λ [ k 1] BP b = BP Add Add A [ ] dd yd k 1 P λb + Rd + Sd y d events detected in LOR d R d estimation of randoms in LOR d S d estimation of scatter in LOR d A dd attenuation correction factor relative to LOR d Key concept: probability p(b,d) of detecting in LOR d an event coming from voxel b P B () = () p BP() = () b = 1 Converts image into sinogram b d d S m Converts sinogram into image p bd

13 PSF measurements 13 Work performed at San Raffaele Hospital (in Milano) Collaboration with GE for the implementation of the reconstruction algorithm Scanner used: Discovery STE (GE Medical Systems) Integrated PET-CT system BGO crystals (4.7 x 6.3 x 30 mm 3 ) Point source: encapsulated 22 Na non collimated source 1.5 mm x 1.5 mm cylinder surrounded by Lucite capsule PSF modelled as a radially-asymmetric tridimensional Gaussian Function in image space (with position-dependent sigmas) referred to a space variant axes system (r,θ, z)

14 PSF measurements on OSEM reconstructed images 14 Transaxial measurements: in the center of axial FOV the source was acquired at different radial distances Axial measurements: the source was acquired at different axial positions on a line parallel to the scanner axis and located at 5 cm from it Each acquisition was reconstructed with 3D-OSEM (FOV=128 mm, image matrix 256x256, 7 subsets, 10 iterations) and post-filtered (transaxial planes) with a Gaussian (FWHM=2 mm) Without post filter With post filter

15 Fitting method on the OSEM images 15 The tridimensional image can be represented by a matrix N-PIXELS x N-PIXELS x N-SLICES From the image, extracted 3 bidimensional planes fixing row number column number slice number radial-axial tangential-axial radial-tangential and each plane was fitted with a bidimensional function of the sigmas

16 Fitting method on the OSEM images 16 The fit functions have 6 (radial-tangential and radial-axial) or 4 (tangential-axial) parameters and take into account the post-filter Each sigma was estimated twice (in two of the three fits of the planes) The final value was the mean of the two estimations The values for each distance were fitted

17 Results of the fitting 17

18 Fitting method on the OSEM images 18 The fit functions have 6 (radial-tangential and radial-axial) or 4 (tangential-axial) parameters and take into account the post-filter Each sigma was estimated twice (in two of the three fits of the planes) The final value was the mean of the two estimations The values for each distance were fitted

19 Fitting method on the OSEM images 19 The fit functions have 6 (radial-tangential and radial-axial) or 4 (tangential-axial) parameters and take into account the post-filter Each sigma was estimated twice (in two of the three fits of the planes) The final value was the mean of the two estimations The values for each distance were fitted and the dependences on the distance (transaxial for radial and tangential sigma, axial foraxialsigma) weredescribedby σ[ mm ] = f ( d[ cm]) σ σ σ σ i e t a = d 2 = d = d = d d d

20 Implementation of the PSF in the OSEM algorithm 20 Standard OSEM λ [ k ] b λ [ k 1] BP b = BP Add Add A [ ] dd yd k 1 P λb + Rd + Sd P B () = () BP b = 1 () = () d S m p b d p bd PSF-OSEM λ [ k ] b λ [ k 1] BP b = BPAdd Add A [ ] dd yd k 1 Pλb + Rd + Sd P B () = [() PSF] BP b = 1 T () = PSF () p bd d S m PSF T r p r b d ( x) = PSF( x)

21 Validation of the PSF-OSEM algorithm 21 Phantom data Six 22 Na point sources NEMA IEC IQ phantom Tank containing six fillable spheres having different diameters and four additional capillaries Clinical data Neurogical patient Oncological patient Suspect of Parkinson s disease Lesions in the lungs

22 Estimators for quantitative analysis 22 Background mean level Taking ROIs (regions of interest) or VOIs (volumes of interest) in the background regions, let C i be the counts recorded in voxel i μ B = 1 N voxels i R C i Noise standard deviation The reconstructed image of a uniform region should contain constant values in the different voxels STD = N 1 voxels 1 ( Ci μb ) i R 2 Hot contrast recovery μ μ R Let R be the real ratio between signal and background, μ B S B the background mean level and μ the signal mean level CRChot = S 1 1

23 IQ Phantom (reduced statistics): qualitative analysis 23 Reconstruction on FOV=700 mm, 256 pixels x 256 pixels, 28 subsets, 5 iterations, M=13, M-AXIAL=7 OSEM PSF-OSEM

24 IQ Phantom (reduced statistics): quantitative analysis 24 Reconstruction on FOV=700 mm, 256 pixels x 256 pixels, 28 subsets, up to 10 iterations, M=13, M-AXIAL=7 +6.5% +32.7% +5.2% +13.2% Largest sphere (d=37 mm) Smallest sphere (d=10 mm) Noise standard deviation -42.3% Background mean level -45.1%

25 22 Na sources 25 Reconstruction on FOV=500 mm, 256 pixels x 256 pixels, 14 subsets, 10 iterations, M=13, M-AXIAL=7 OSEM PSF-OSEM Scanner center

26 Clinical patients 26 Reconstruction on 256 pixels x 256 pixels, 28 subsets, 5 iterations OSEM PSF-OSEM FOV=512 mm M=15 M-AXIAL=9 FOV=700 mm M=9 M-AXIAL=7

27 Clinical patients 27 Reconstruction on 256 pixels x 256 pixels, 28 subsets, 5 iterations OSEM PSF-OSEM FWHM=4 mm FOV=512 mm M=15 M-AXIAL=9 FWHM=5 mm FOV=700 mm M=9 M-AXIAL=7

28 Conclusions and future perspectives 28 The resolution of PET depends on some effects impossible to be readily corrected In this work the implementation of 3D spatially-variant PSF (radially asymmetric) in a 3D iterative reconstruction algorithm has been proposed Simple acquisition scheme and measurement procedure Higher contrast recovery, lower noise and more defined volumes

29 Conclusions and future perspectives 29 The resolution of PET depends on some effects impossible to be readily corrected In this work the implementation of 3D spatially-variant PSF (radially asymmetric) in a 3D iterative reconstruction algorithm has been proposed Simple acquisition scheme and measurement procedure Higher contrast recovery, lower noise and more defined volumes Thank you for the attention!