1 PET reconstruction software testGiovanni Pirrone INSIDE meeting, 14/06/2016, Roma

2 MLEM algorithm: iterative method for Tomographic Image ReconstructionWhy iterative? Can handle complex acquisition geometries Do not need complete projection data Can account for the type of measurement statistics Can model both the geometry and the physics of the acquisition system From continuous to discrete The image is discretised: fj=1,…,N with N as the number of voxels/pixels The data is discretised: pi=1,…,M with M as the number of measured projection The imaging system is modeled vie the system matrix A Є RM X N . System matrix entry expresses the contribution of image pixel j to detector bin i.

3 Basic concepts: how to recover the imageImaging process is expressed as linear system of equations 𝐴𝑓=𝑝 𝑓= 𝐴 −1 𝑝 but A might not be invertible! i.e. not square or bad conditioned More practical approach: search for the solution f iteratively by guessing f and improving it iteratively using only A and AT: 𝑓 𝑘+1 = 𝑓 𝑘 ∙ 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑡𝑒𝑟𝑚 Where k is the iteration number, and the system matrix A is used in the «correction term»

4 Basic concepts: how to recover the imageFor k=1 start with a guess Image (fk) Project A ‘artificial’ projection data Measurement data (p) Compute next image (k=k+1) compare Correction data Backproject AT Correction data Divide by the sensitivity Loop notation Operator notation 𝑓 𝑗 𝑘∗1 = 𝑓 𝑗 𝑘 𝑖=1 𝑀 𝑎 𝑖𝑗 𝑖=1 𝑀 𝑎 𝑖𝑗 𝑝 𝑖 𝑙=1 𝑁 𝑎 𝑖𝑙 𝑓 𝑙 𝑘 𝑓 𝑘+1 = 1 𝐴 𝑓 𝑘 ∙ 𝐴 𝑇 𝑝 𝐴 𝑓 𝑘

5 INSIDE 5x2 System matrix System matrix informations Reference systemHead-to-Head distance (mm): 500 FOV dimension (in voxels): 140,70,165 FOV spacing (mm): 1.6 Crystals size (mm2): 3 x 3 Crystals pitch (mm): 3.2 Detector size (mm): 51.2 Detector pitch (mm): 54.5 Model size (Mb): 458 PET 1 Y Reference system Z X PET 2

6 Sensitivity image 𝑊 2 > 𝑊 1 Sensitivity evaluation LOR2 LOR1Lines Of Response (LORs) backprojection into the Field Of View (FOV) For each image voxel a value is assigned. This value is given by LORs that are crossing the voxel If the voxel is crossed by j LORs, the value for that voxel is computed by a weighted sum of j terms The weights Wj are given by the lines length within the voxel LOR2 𝑊 2 > 𝑊 1 LOR1

7 Sensitivity image Sensitivity image orthogonal views (central slices)Z X X Sensitivity image orthogonal views (central slices) Z

8 Sensitivity image: symmetryZ Horizontal flip No visible pattern. Image values ~ 10-9 ÷ Y Z Vertical flip No visible pattern. Image values ~ 10-9 ÷ Y

9 Sensitivity profiles Y Z

10 Sensitivity: computed VS simulatedGate simulations F-18 point source (cube of 500 μm) within a PMMA phantom (cube of 10 mm side) Activity: 100 μCi ( Bq) Simulation time: 120 s The source was positioned in different points of the FOV along the x, y and z directions

11 Point source reconstructionGate simulations A ROI was selected for each slice along all the orthogonal planes and the arrays of the average counts values were calculated Profile plot and gaussian fit were performed to determine the reconstructed position as a function of the nominal position Z Z X Y X Y

12 Point source reconstruction Profiles along Y (plane YZ)Gate simulations F-18 point source (cube of 500 μm) within a PMMA phantom (cube of 10 mm side) Activity: 100 μCi ( Bq) Simulation time: 120 s Source positions: 0, 10, 20, 30, 40 mm along the Y direction (with the coordinates X and Z equal to 0) The std of the profiles gaussian fit goes from 0.9 mm to 1.3 mm for the positions y=0 mm and y=40 mm respectively Same behaviour along the Z direction

13 Point source reconstruction Profiles along X (plane XY)Gate simulations F-18 point source (cube of 500 μm) within a PMMA phantom (cube of 10 mm side) Activity: 100 μCi ( Bq) Simulation time: 120 s Source positions: 0, 25, 50, 75, 100 mm along the Y direction (with the coordinates X and Z equal to 0) The std of the profiles gaussian fit goes from 4.3 mm to 6.2 mm for the positions x=0 mm and x=100 mm respectively. Worst results (but satisfying) on the position reconstruction

14 Limits of our system…

15 CNAO data reconstruction Single spot, 124 MeV (111 mm in H2O), high statisticX Y Z Y

16 PET-CT image fusion fusion Treatment plan information Radiation typeProton Target prescription dose 55.8 Gy Number of fraction planned 31 Fraction dose 1.8 Gy Number of beam 2 (B1, B2) Measurements information Beam B1 Dose delivered 0.9 Gy Nominal beam energy range 73.93 ÷ MeV Rando CT PET image fusion