Professor Brian F Hutton Institute of Nuclear Medicine University College London An overview of iterative reconstruction applied to PET (and SPECT)? 

Outline Understanding iterative reconstruction (ML-EM + OS-EM) the flexibility in system modelling modelling resolution time-of-flight 

Single Photon Emission Computed Tomography (SPECT) Single Photon Emission Computed Tomography (SPECT) relatively low resolution; long acquisition time (movement) noisy images due to random nature of radioactive decay tracer remains in body for ~24hrs: radiation dose ~ standard x-ray function rather than anatomy

Coincidence Detection: Positron Emission Tomography (PET) detector 1 detector 2 coincidence window time (ns) valid coincidence event if two gammas detected within short time (8-12ns)

Coincidence Lines of Response (LoR) parallel fanbeam distance sinogram angle data acquired direct to sinogram: set of projections versus angle

PET / SPECT Reconstruction 1 angle2 angles 4 angles 16 angles 128 angles conventional filtered back projection iterative reconstruction

Understanding iterative reconstruction Objective Find the activity distribution whose estimated projections match the measurements. Modelling the system (system matrix) What is the probability that a photon emitted from location X will be detected at detector location Y. - detector geometry, collimators - attenuation - scatter, randoms detector (measurement) object  estimated projection  X Y X Y1Y1 Y2Y2

ML-EM reconstruction original projections estimated projections current estimate original estimate update (x ratio) FP BP NO CHANGE patient

EM reconstruction comparison with projections comparison with actual object

forward projection back projection ML-EM algorithm new estimate old estimate system matrix

System matrix voxel j pixel i distance sinogram angle

 System matrix: with attenuation

ML-EM 4 iterations OS-EM 1 iteration Update 1Update 2Update 3Update 4 ML-EM: each update involves BP and FP for all projection angles OSEM: each update only uses a subset of projection angles EM iterations = OS-EM iterations x no of subsets OS-EM

Image courtesy of Bettinardi et al, Milan

FBPFBPML-EMML-EM Poisson Uniform FBPFBPML-EMML-EM a) ML-EM: noise is proportional to activity b) ML-EM: noise assumes a Poisson model

Problems with pre-correction acquired data assumed to be Poisson processing of projections likely to destroy assumption e.g. scatter correction, randoms correction in PET instead incorporate all corrections inside model Historical Subtract measured randoms and scatter; increases noise Instead Add measured randoms and scatter in forward model

True image 20 iterations100 iterations Courtesy Johan Nuyts, KU Leuven, Belgium iteration Non-uniform convergence J Nucl Med, 2005; 46:469P (abs) Convergence rate for 20 lesions (UCL)

8 iter 100 iter FBP true image sinogram with noise with noise smoothed Image courtesy of J Nuyts, Leuven

detector (projection) object  Courtesy: Panin et al IEEE Trans Med Imaging 2006; 25: potentially improves resolution requires many iterations slow to compute Modelling resolution w/o resn model with resn model stabilises solution better noise properties

 System matrix: including resolution model

Modelling system resolution (UltraSPECT, Astonish, Flash, Evolution) FBP WBR FBP 10 min scan WBR 5 min scan D-SPECT: reconstruction includes resolution model

FWHM total 2 = FWHM det 2 + FWHM range 2 + FWHM  positron range colinearity detector PET resolution depth of interaction results in asymmetric point spread function fan depth of interaction

 Modelling resolution noise contrast/recovery Simple model: assumes no loss of resolution Account for resolution: exactly accounts for resolution involves higher uncertainty Contrast v noise: noise increases with iteration no contrast reaches max value With resolution model: need more iterations to reach max noise less for same contrast better model; better quality

Reconstruction on 256 pixels x 256 pixels, 28 subsets, 5 iterations PSF-OSEM Clinical studies Courtesy Rapisardi, Bettinardi, Milan FWHM=5 mm FWHM=4 mm OSEM OSEM + smooth

Townsend, Phys Med Biol 2008; 53: R1-R39 Clinical studies: 14subsets 2 iterations 3D-OP-OSEM 3D-OSEM with PSF

 detector 1 detector 2 coincidence window time (ns) Time-of-flight d t1t1 t2t2 t1t1 t2t2 both gammas travel with speed of light (c) difference in time of detection is (t 2 -t 1 ) emission origin is at distance d from centre where d = (t 2 -t 1 ).c/2 (t 2 -t 1 ) but uncertainty in determining time (  t) therefore also uncertainty in determining d (  d)  t 600ps 8ns  d9cm dd Time-of-flight

Adapted from Mike Casey, Siemens white paper Time-of-flight  Normal back projection: no knowledge of position blurred result Using TOF: some knowledge of position much less blurring

Improving signal-to-noise: time-of-flight PET  t (ps)  d (cm) SNR * * SNR gain for 40 cm phantom = SNR TOF / SNR non-TOF Detector B Detector A e-e- e+e+ Patient outline (diameter D) t1t1 t2t2 SNR TOF  √(D/  d) · SNR non-TOF d1d1 d  d is uncertainty in position due to limited timing resolution  t ; D is diameter of object (patient) dd

35-cm diameter phantom; 5 minute scan time 10, 13, 17, 22-mm hot spheres (6:1 contrast); 28, 37-mm cold spheres noTOF TOF #iter = TOF converges faster and achieves better contrast for given noise Philips Gemini TF

TOF benefit is more significant as timing resolution improves TOF: 400ps TOF: 650ps Non- TOF 1.4M2.8M5.6M8.5M12.7M16.9M 35-cm diameter phantom La-PET proto-type: LaBr

HD·PETultraHD·PET BMI: D: FORE+OSEM3D: HD3D: ultraHD HD·PET images show improved spatial resolution when compared with 2D reconstruction. The ultraHD·PET images show incremental improvement in signal-to-noise such as better liver uniformity and lower background in cold areas.

1990 BMI 30 15%–19% 20%–24% 25%–29% ≥30% <10% 10%–14% 2006 Body Mass Index (BMI) SNR Gain HD·PETultraHD·PET Time-of-flight gain

Summary Iterative reconstruction is increasingly used in clinical practice ML-EM iteration = OS-EM iterations x no of subsets Need to be aware of limitations - bias with low counts - convergence varies across object - need to preserve Poisson statistics Resolution models potentially improve contrast AND noise - needs extra iterations Time-of-flight information further improves signal to noise - needs less iterations! - gain dependent on patient size, application

Acknowledgements Thanks to Joel Karp, Dave Townsend, Johan Nuyts for use of material for slides.

OS-EM bias: non-negativity constraint 10:15:1 Striatal Phantom with 10:1 and 5:1 striatal-to-background uptake ratio Background count concentration in 10:1 study half that of 5:1 study Convergent striatal count concentration Non-convergent background count concentration at low count level in 10:1 study Apparent peaking of measured uptake ratio in 10:1 study Data courtesy of J Dickson, UCL

Meaningful evaluation evaluation is difficult! wide range of algorithms and parameters comparing only two sets of images meaningless! conventional performance measures inappropriate (e.g. resolution, sensitivity) measurement is object dependent performance is task dependent: ROC analysis! FBP OS-EM

Comparing performance: noise contrast/recovery

Contrast versus noise myocardium to ventricle contrast recovery COV from 10 independent noise realisations values vary with iteration number / filter parameters Data courtesy K Kacperski, UCL no rr rr+filter