1. proton Computed Tomography images with algebraic reconstruction M. Bruzzi 1,2, D. Bonanno 3, M. Brianzi 2, M. Carpinelli 4,9, G.A.P. Cirrone 5, C. Civinini 2, G. Cuttone 5, D. Lo Presti 3,8,G. Maccioni 4, S. Pallotta 2,7,8, N. Randazzo 3, M. Scaringella 2, F. Romano 5, V. Sipala 4,9, C. Talamonti 2,7,8, E. Vanzi 10 Prima – RDH – IRPT Collaboration 1 Physics and Astronomy Department, University of Florence, Florence, Italy 2 INFN - Florence Division, Florence, Italy 3 INFN - Catania Division, Catania, Italy 4 INFN Cagliari Division, Cagliari, Italy 5 INFN - Laboratori Nazionali del Sud, Catania, Italy 6 Physics and Astronomy Department, University of Catania, Catania, Italy 7 Department of Biomedical, Experimental and Clinical Sciences, University of Florence, Florence, Italy 8 SOD Fisica Medica, Azienda Ospedaliero-Universitaria Careggi, Firenze, Italy 9 Chemistry and Pharmacy Department, University of Sassari, Sassari, Italy 10 Fisica Sanitaria, Azienda Ospedaliero-Universitaria Senese, Siena, Italy

2. Introduction The proton Computed Tomography principle The PRIMA/RDH INFN proton Computed Tomography device Algebraic Reconstruction Techniques Test beam and phantom configuration Data analysis: – BI-SART reconstructed tomographies – Spatial and density resolutions starting from {0} using FBP as seed Conclusions Mara Bruzzi Univ. Firenze - VCI Conference, Wien, 15-19 February 2

3. Proton Radiotherapy → f irst proposed by R.R. Wilson in 1946 "Radiological Use of Fast Protons", Radiology, 47:487-491 (1946) 3 Advantage : Highly conformational dose distribution i) lower dose to healthy tissues in front of it; ii) healthy tissues beyond tumor not damaged; Inaccuracies: Treatment planning presently performed by X-CT → expected errors typically of a few millimeters B. Schaffner and E. Pedroni Phys. Med. Biol. 43 (1998) 1579–1592 Direct measure of the stopping power maps Precision improvement when positioning and treatment are made in one go The proton Computed Tomography - principle pCT Mara Bruzzi Univ. Firenze - VCI Conference, Wien, 15-19 February

4. Tracks with multiple scattering L Measurements: entry position and angle Proton true trajectory L  straight line with confidence limits Measurements: entry and exit positions and angles L’ L’  straight line with confidence limits Measurements: entry and Exit position and angle + Most Likely Path (MLP) calculation L’’ L’’ curved trajectory with Norrower confidence limits 4 Mara Bruzzi Univ. Firenze - VCI Conference, Wien, 15-19 February

5. PARAMETERVALUE Proton beam kinetic energy 200 -270 MeV Proton beam rate 1 MHz Spatial resolution < 1 mm Electronic density resolution <1% Detector radiation hardness >1000 Gy Dose per scan < 5 cGy P1P1 P2P2 P3P3 P4P4 z x y Single particle proton tracking: silicon strip detectors → MLP Residual energy measurement: crystal calorimeter → energy loss A set of single event information can be processed by appropriate reconstruction algorithms to produce tomographic images. 5 pCT system design Mara Bruzzi Univ. Firenze - VCI Conference, Wien, 15-19 February

6. Most Likely Path in a pCT geometry Mara Bruzzi Univ. Firenze - VCI Conference, Wien, 15-19 February 6 MLP example with 200MeV kinetic energy protons in 20cm of water: Entry: Y(0) = 0.2cm Y’(0) = -10mrad Exit: Y(20) = -0.1cm Y’(20) = +10mrad Silicon microstrip detectors: 320  m thick 200  m strip pitch MLP error envelope plus contributions from detector position measurement error (~ pitch/√12) and MCS inside the silicon sensors  The sensor thickness contribution affects only the MLP error at the edge of the phantom  ~ 150-250  m 200MeV in 90MeV out Starting from D.C. Williams Phys. Med. Biol. 49 (2004) and R.W. Shulte at al. Med. Phys. 35 (11) (2008) 5 cm of air have been inserted in front and behind the 20cm H 2 O phantom

7. Proton Computed Tomography devices Four x-y silicon microstrip based tracking planes Proton entry and exit positions and directions Proton residual energy Mara Bruzzi Univ. Firenze - VCI Conference, Wien, 15-19 February 7 Yag:Ce calorimeter p on n single sided Fz 200  m thick / 200  m pitch Phase 1 ~ 5x5cm 2 active area Phase 2 : 5x20cm 2 Results in the following refers to the small area device

8. Algebraic Reconstruction Techniques Iterative algorithm to reconstruct tomographic images (proton stopping power maps) from ‘projections’ (for pCT set of single proton events) Starting point (S(x,y,E) stopping power): Introducing the mass stopping power S/  : E 0 fixed energy Mara Bruzzi Univ. Firenze - VCI Conference, Wien, 15-19 February 8

9. Algebraic Reconstruction Techniques Dividing by S/  at energy E: The left hand side doesn’t depend too much on the material composition (~2-4*10 -3 ) and could be replaced by the one measured for liquid water (NIST pstar tables - http://physics.nist.gov/PhysRefData/Star/Text/PSTAR.html ) : Mara Bruzzi Univ. Firenze - VCI Conference, Wien, 15-19 February 9

10. Algebraic Reconstruction Techniques Integrating along the proton path: E in is given by the accelerator, E out by the calorimeter and the ‘path’ by the tracker (Most Likely Path) Subdividing the object into a set of pixels, for the i th proton: Where w ij is the path length of proton i inside the pixel j Mara Bruzzi Univ. Firenze - VCI Conference, Wien, 15-19 February 10 Wang, Med.Phys. 37(8), 2010: 4138

11. Mara Bruzzi Univ. Firenze - VCI Conference, Wien, 15-19 February 11 Pixel 1 w ij Pixel j Pixel N Computational challenge: find the simplest (fastest) way to build the w ij matrix (could have billions of elements, most of them equal to zero) p in 200 MeV p out 90 MeV Phantom: 20 cm of water

12. Algebraic Reconstruction Techniques The problem is then to solve, for S j, the following set of equations: N = number of pixels; M number of protons In our case: – N = (128x128)=16384 pixels – M ~ 40(angles)*1.5x10 6 events Mara Bruzzi Univ. Firenze - VCI Conference, Wien, 15-19 February 12

13. Algebraic Reconstruction Techniques The system could be solved using an iterative formula: Mara Bruzzi Univ. Firenze - VCI Conference, Wien, 15-19 February 13 S k image vector at iteration k (stopping power) w i i th track length in each pixel (vector)  Tracker p i stopping power integral (number)  Calorimeter k relaxing factor (constant value or  0 as ~k -1 ) S 0 initial image: {0} or approx (i.e., from FBP reconstruction). ART implementations: A k = {1-event}: ART  too much ‘salt-pepper’ noise A k = {full data set}: SART (simultaneous ART)  better noise A k = {1/n of the full data set}: BI-SART (n-Block iterative SART)  good noise performance with faster convergence Gordon, R; Bender, R; Herman, GT J. Theor. Biol. (1970) 29 (3): 471–81.

14. Test beam @ The Svedberg Laboratory (Uppsala) Beam energy at pCT detector ~ 175 MeV Instantaneous beam intensity 10kHz protons – 40 angles (0 o -351°): 1.5*10 6 events per angle Mara Bruzzi Univ. Firenze - VCI Conference, Wien, 15-19 February14

15. Phantom Dimensions limited by the system field of view To have a reasonable energy measurement error the phantom material should not be tissue eqivalent:  E PMMA (5cm)~22MeV (to be compared with the calorimeter resolution at 200MeV  E calo ~4-5MeV) → Aluminium for the phantom body with Iron and Copper insert to simulate high constrast material (e.g., muscle-bone structure). Mara Bruzzi Univ. Firenze - VCI Conference, Wien, 15-19 February 15 An empty hole and a uniform section added to evaluate space resolution for different constrasts and to get density r.m.s. measurements.

16. Mara Bruzzi Univ. Firenze - VCI Conference, Wien, 15-19 February 16 Top Fe Cu Air Back Phantom design - Aluminum + Cu / Air / Fe inserts - one empty hole and a few uniform sections to evaluate space resolution for different constrast and density r.m.s. Expected Stopping Power values: Aluminium: 10.38 MeV/cm (we used Anticorodal  5% discrepancy) Iron: 27.03 MeV/cm Copper: 29.53 MeV/cm φ=4mm φ=6mm φ=3mm φ=2mm 45mm

17. pCT dose evaluation 1234512345 CategoryRelative abundance to Cat. 3DE PhantomEvent type 10.088200 MeVNucl. Int. Phantom 20.21350 MeVNucl Int. Calorimeter 3150 MeVUseful event 40.06950 MeVToo much scattering 50.04150 MeVGeometry leakage Dose required for total tomography ( 10 6 p/cm 2 ) : ~ 2mGy

18. BI-SART reconstructed tomographies BI-SART algorithm - data divided into 4 blocks; No a-priori knowledge of the phantom boundary required (only an external, larger, container); proton tracks calculated using MLP formulas; GPU parallelism implemented to reduce computing time: iteration ~1’ for a 512x512 pixels image with 2x10 6 events; Relaxation parameters chosen to get best density r.m.s. resolution in approx 10 iterations. Mara Bruzzi Univ. Firenze - VCI Conference, Wien, 15-19 February 18

19. BI-SART starting for empty picture Mara Bruzzi Univ. Firenze - VCI Conference, Wien, 15-19 February 19 Iteration 11 color palette : Stopping Power (at 175 MeV) as calculated by the algorithm

20. Resolutions Mara Bruzzi Univ. Firenze - VCI Conference, Wien, 15-19 February 20 0.96% @ iter. #11 650  m @ iter. # 11 The edge resolution has been obtained fitting the edge of the tomography with an error function and quoting the sigma The density resolution is the r.m.s. of the pixel stopping power distribution in a uniform region of the phantom BI-SART (from {0}

21. Mara Bruzzi Univ. Firenze - VCI Conference, Wien, 15-19 February21 960  m at iter. # 11 The internal insert resolution has been obtained fitting the edge of the inserts with an error function and quoting sigma BI-SART (from {0} Internal Hole Resolution 45mm φ=4mm φ=2mm φ=6mm φ=3mm

22. FBP reconstructed tomographies The Filter Back Projection algorithm use only straigth tracks This is not true for protons because of multiple scattering Nonetheless we apply the FBP algorithm* to reconstruct a pCT image This image can be compared with BI-SART images and/or used as a starting point for the iterative algorithm Mara Bruzzi Univ. Firenze - VCI Conference, Wien, 15-19 February 22 400  m pixel size, RSP normalize to SART image FBP – hard filter *E. Vanzi et al. NIM A 730 (2013) 184–190

23. BI-SART starting from {0} or FBP Mara Bruzzi Univ. Firenze - VCI Conference, Wien, 15-19 February 23 Starting from {0} Starting from FBP-Hard filter Much more uniform Better spatial resolution

24. Mara Bruzzi Univ. Firenze - VCI Conference, Wien, 15-19 February 24 Starting from FBP Better spatial resolution starting from FBP- hard filter 650  m at 11 400  m at 50 400  m at 11 340  m at 50 Edge resolution BI-SART starting from {0} / FBP Starting from {0}

25. Mara Bruzzi Univ. Firenze - VCI Conference, Wien, 15-19 February 25 More uniform when starting from {0} Density resolution BI-SART starting from {0} or FBP Starting from FBP-hard filter Starting from {0}

26. Conclusions A small-area proton Computed Tomography device has been tested in 175 MeV proton beam; BI-SART reconstruction algorithms implemented with GPU; Reconstructed tomographies with density and spatial resolutions fitting medical requirements (~1% ; < 1mm) ; Total time processing ~ 15’ for a 512x512 pixels image with 2x10 6 events; FBP-hard filter used as a seed improve image spatial resolution but worsen density resolution. In near future filter will be used to control the trade-off between resolution and noise. Forthcoming : Large-area pCT test beams with tissue equivalent non-homogeeneous phantoms. Mara Bruzzi Univ. Firenze - VCI Conference, Wien, 15-19 February 26

27. FBP -filtering Mara Bruzzi Univ. Firenze - VCI Conference, Wien, 15-19 February 27 n = order c = cut off frequency of the filter Decreasing order filter becomes harder. Spatial resolution improve but noise becomes more relevant. E. Vanzi et al. NIM A 730 (2013) 184–190