Distance-driven binning for proton CT filtered backprojection along most likely paths

Transcription

1 Dstance-drven bnnng for proton CT fltered backprojecton along most lkely paths Smon Rt, Ncolas Freud, Davd Sarrut, Jean-Mchel Létang 12 1 CREATIS laboratory 2 Léon Bérard center May 25, 2012

2 Introducton Proton CT s not new [Cormack, 1963] Renewed nterest for proton therapy Reduce uncertanty on proton range ( 3% wth CT) Lower magng dose Improved dagnostc / delneaton Man drawbacks Cost but there are now proton accelerators for treatment Lack of spatal resoluton due to Multple Coulomb Scatterng whch nduces curved proton trajectores Man research effort of the past decade Dstance-drven bnnng for proton CT fltered backprojecton along most lkely paths May 25, 2012 Smon Rt 2

3 pct reconstructon problem - Physcs Energy loss va nelastc collsons [Schulte et al., 2005]: wth 1 S(I(x), E(x)) = K β 2 (E(x)) ( ) 2 E0 β(e) = 1 E + E 0 de (x) = η(x)s(i(x), E(x)) dx [ ( 2mec 2 ln I(x) β 2 ) ] (E(x)) 1 β 2 β 2 (E(x)) (E(x)) Approxmaton: I(x) I water = 69 ev, x R 3 Dstance-drven bnnng for proton CT fltered backprojecton along most lkely paths May 25, 2012 Smon Rt 3

4 pct reconstructon problem - Lne ntegral wth Γ η(x)dx = E n E out I Z the proton ndex, 1 S(I water, E) Γ R 3 ts curved path (measured), n de = G(E, E out ) η : R 3 R the relatve electron densty (sought), E out and E n the entrance and ext energes (measured). Dstance-drven bnnng for proton CT fltered backprojecton along most lkely paths May 25, 2012 Smon Rt 4

5 Most lkely path v Γ a(t) o Cone-beam scanner wth a crcular source trajectory a(t) R 3 around the axs defned by the socenter o R 3 and the unt axs v R 3. Dstance-drven bnnng for proton CT fltered backprojecton along most lkely paths May 25, 2012 Smon Rt 5

6 Most lkely path Ext detector v a(t) o x out Γ Spatal nformaton on the th proton: x out Dstance-drven bnnng for proton CT fltered backprojecton along most lkely paths May 25, 2012 Smon Rt 5

7 Most lkely path Entrance Ext v a(t) x n o x out Γ Spatal nformaton on the th proton: x out, ẋ n, x n, ẋ out Dstance-drven bnnng for proton CT fltered backprojecton along most lkely paths May 25, 2012 Smon Rt 5

8 Most lkely path Entrance Ext v Ω x out Γ a(t) o x n Spatal nformaton on the th proton: x out, ẋ n, x n, ẋ out, Ω Dstance-drven bnnng for proton CT fltered backprojecton along most lkely paths May 25, 2012 Smon Rt 5

9 Most lkely path Entrance Ext v Ω x out Γ a(t) o x n Spatal nformaton on the th proton: x out, ẋ n, x n, ẋ out, Ω Several solutons, [Schulte et al., 2008] used n ths work Dstance-drven bnnng for proton CT fltered backprojecton along most lkely paths May 25, 2012 Smon Rt 5

10 Most lkely path [Schulte et al., 2008] for 200 MeV protons Dstance-drven bnnng for proton CT fltered backprojecton along most lkely paths May 25, 2012 Smon Rt 6

11 State-of-the-art of pct reconstructon Fltered-backprojecton (FBP) along straght lnes Sometmes wth smart bnnng [Penfold, 2010] or cut to elmnate curved paths [Crrone et al., 2011] Iteratve reconstructon along most lkely paths Algebrac Reconstructon Technques [L and Lang, 2004] Statstcal, compressed sensng [Penfold, 2010], etc. Ether FBP along straght lnes or teratve reconstructon Dstance-drven bnnng for proton CT fltered backprojecton along most lkely paths May 25, 2012 Smon Rt 7

12 Not true n moton-compensated CT reconstructon Non-rgd moton durng acquston yelds a reconstructon problem along curved acquston lnes Both analytc (approxmate) and teratve technques [Rt et al., 2009] Dfference wth protons: lst-mode acquston Dstance-drven bnnng for proton CT fltered backprojecton along most lkely paths May 25, 2012 Smon Rt 8

13 Objectve Approxmate FBP algorthm for pct reconstructon along most lkely path Dstance-drven bnnng for proton CT fltered backprojecton along most lkely paths May 25, 2012 Smon Rt 9

14 Rotatng coordnate system Let I a I be the ndces of protons correspondng to the same source poston a(t) {u, v, w} s the rotatng coordnate system where u and w depend on the source poston. Entrance Ext u v w Ω x out a(t) o x n Dstance-drven bnnng for proton CT fltered backprojecton along most lkely paths May 25, 2012 Smon Rt 10

15 Grd of pxels for bnnng Let j J Z 2 be a set of spatal ndces correspondng to a grd of pxels of the ext detector. h : R 2 R the ndcator of pxel j,.e., { 1 f y R h j (y) = 2 s n the j th pxel, 0 else. Dstance-drven bnnng for proton CT fltered backprojecton along most lkely paths May 25, 2012 Smon Rt 11

16 Natural bnnng Entrance Ext u v a(t) w Ω o x out u out Γ x n w out g out j,a = I a h j (u out, v out h j(u out )G(E n, E out, v out ) ) Dstance-drven bnnng for proton CT fltered backprojecton along most lkely paths May 25, 2012 Smon Rt 12

17 Bnnng drven by entrance poston u v a(t) w Entrance Ω x out x n un w n w out o Ext Γ g n j,a = I h j (un a, v n h j(u n, v n ) )G(E n, E out ) Dstance-drven bnnng for proton CT fltered backprojecton along most lkely paths May 25, 2012 Smon Rt 13

18 Dstance-drven bnnng Entrance Ext u v a(t) w x n Ω o x out u out Γ u (w) w w out g j,a (w) = I a h j (u (w), v (w))g(e n h j(u (w), v (w)), E out ) Dstance-drven bnnng for proton CT fltered backprojecton along most lkely paths May 25, 2012 Smon Rt 14

19 Dstance-drven bnnng Named from dstance-drven (back)projecton [De Man and Basu, 2004]. In practce, bnnng s computed for several dstances w between w n and w out. 4D snogram g : R 3 Z R nstead of a standard 3D snogram, e.g., g out : R 2 Z R. The 3D slce for w = w out s equal to the natural bnnng g out. Dstance-drven bnnng for proton CT fltered backprojecton along most lkely paths May 25, 2012 Smon Rt 15

20 Experments Monte-Carlo smulatons wth GATE. Ideal pct scanner 200 MeV mono-energetc pont source placed at w s = 1 m Proton characterstcs at w n = 60 cm and w out = 60 cm (E n, E out, x n, ẋ n, x out and ẋ out ) MLP: straght path outsde Ω, [Schulte et al., 2008] n Ω Assumes homogeneous object of water Dstance-drven bnnng for proton CT fltered backprojecton along most lkely paths May 25, 2012 Smon Rt 16

21 Experment #1: one projecton only a(t) v u w Entrance Bone Water o Ext Sphercal object and nserts centered on source Projecton s a rectangular functon f partcles follow straght lnes (e.g. prmary photons) Dstance-drven bnnng for proton CT fltered backprojecton along most lkely paths May 25, 2012 Smon Rt 17

22 Experment #1: one projecton only u (mm) G (mm 1 ) w (mm) u (mm) Dstance-drven bnnng for proton CT fltered backprojecton along most lkely paths May 25, 2012 Smon Rt 18

23 Reconstructon usng dstance-drven backprojecton If FDK formula s wrtten [Feldkamp et al., 1984] η(x) = 2π 0 ( ) 2 a 2 g a out (u(x), v(x)) dθ a, w(x) t becomes, η(x) = 2π 0 ( ) 2 a 2 g a (u(x), v(x), w(x)) dθ a. w(x) Local compensaton as n moton-compensated CT Dstance-drven bnnng for proton CT fltered backprojecton along most lkely paths May 25, 2012 Smon Rt 19

24 Experment #2: Catphan CTP528 Dstance-drven bnnng for proton CT fltered backprojecton along most lkely paths May 25, 2012 Smon Rt 20

25 Relatve electron densty (no unt) g(110cm) g(90cm) g Poston (mm)

26 Relatve electron densty (no unt) g(110cm) g(90cm) g Poston (mm)

27 Conclusons Improved spatal resoluton n FBP algorthm usng most lkely paths by means of dstance-drven bnnng No effect on densty resoluton of homogeneous areas s expected snce only hgh frequences of projectons are modfed Beng evaluated... Use of most-lkely paths seems essental for short scans Dstance-drven bnnng for proton CT fltered backprojecton along most lkely paths May 25, 2012 Smon Rt 23

28 Bblography G.A.P. Crrone, M. Buccoln, M. Bruzz, G. Candano, C. Cvnn, G. Cuttone, P. Guarno, D. Lo Prest, S.E. Mazzagla, S. Pallotta, N. Randazzo, V. Spala, C. Stancampano, and C. Talamont. Monte carlo evaluaton of the fltered back projecton method for mage reconstructon n proton computed tomography. Nuclear Instruments and Methods n Physcs Research Secton A: Accelerators, Spectrometers, Detectors and Assocated Equpment, 658(1):78 83, ISSN do: /j.nma URL A.M. Cormack. Representaton of a functon by ts lne ntegrals, wth some radologcal applcatons. Journal of Appled Physcs, 34(9): , do: / B. De Man and S. Basu. Dstance-drven projecton and backprojecton n three dmensons. Phys Med Bol, 49(11): , Jun L.A. Feldkamp, L.C. Davs, and J.W. Kress. Practcal cone-beam algorthm. J Opt Soc Am A, 1(6): , T. L and J.Z. Lang. Reconstructon wth most lkely trajectory for proton computed tomography. volume 5370, pages SPIE, do: / URL S. Penfold. Image reconstructon and Monte Carlo smulatons n the development of proton computed tomography for applcatons n proton radaton therapy. PhD thess, Centre for Medcal Radaton Physcs, Unversty of Wollongong, URL S. Rt, D. Sarrut, and L. Desbat. Comparson of analytc and algebrac methods for moton-compensated cone-beam CT reconstructon of the thorax. IEEE Trans Med Imag, 28(10): , R. W. Schulte, S. N. Penfold, J. T. Tafas, and K. E. Schubert. A maxmum lkelhood proton path formalsm for applcaton n proton computed tomography. Med Phys, 35(11): , Nov R.W. Schulte, V. Bashkrov, M.C. Loss Klock, T. L, A.J. Wroe, I. Evseev, D.C. Wllams, and T. Satogata. Densty resoluton of proton computed tomography. Med Phys, 32(4): , Apr Dstance-drven bnnng for proton CT fltered backprojecton along most lkely paths May 25, 2012 Smon Rt 24