1. Iterative reconstruction for metal artifact reduction in CT 1 the problem projection completion polychromatic ML model for CT local models, bowtie,… examples the problem projection completion polychromatic ML model for CT local models, bowtie,… examples Katrien Van Slambrouck, Johan Nuyts Nuclear Medicine, KU Leuven

2. the problem 2 y y CT ln(b/y) iron

3. the problem Double hip prosthesis Double knee prosthesisDental fillings Cause of metal artifacts: Beam hardening Nonlinear partial volume effects Noise Scatter resolution (crosstalk, afterglow) (Motion) Mouse bone and titanium screw (microCT) 3

4. I.Beam hardening Polychromatic spectrum, beam hardens when going through the object Low energy photons are more likely absorbed Artifacts in CT Energy (keV) 10 cm water Energy (keV) Normalized intensity (%) Typical artifact appearance: dark streaks in between metals, dark shades around metals (and cupping) Iron in waterAmalgam in PMMA

5. II.(Non)-linear partial volume effects Linear: voxels only partly filled with particular substance Non-linear: averaging over beam width, focal spot, … I0I0 I µ1µ1 µ2µ2 Artifacts in CT Typical artifact appearance: dark and white streaks connecting edges Iron in waterAmalgam in PMMA

6. III. Scatter Compton scatter: deviation form original trajectory Scatter grids? Artifacts in CT I0I0 Iron in waterAmalgam in PMMA Typical artifact appearance: dark streaks in between metals, dark shades around metals (and cupping)

7. IV. Noise Quantum nature: ± Poisson distribution Artifacts in CT Iron in waterAmalgam in PMMA Typical artifact appearance: streaks around and in between metals

8. projection completion  Initial FBP reconstruction  Segment the metals and project  Remove metal projections for sinogram  Interpolate (e.g. linear, polynomial, …)  Reconstruct (FBP) and paste metal parts 8 Kalender W. et aI. "Reduction of CT artifacts caused by metallic impants." Radiology, 1987 Glover G. and Pelc N. "An algorithm for the reduction of metal clip artifacts in CT reconstructions." Med. Phys., 1981 Mahnken A. et al, "A new algoritbm for metal artifact reduction in computed tomogrpaby, In vitro and in vivo evaluation after total hip replacement." Investigative Radiology, 2003

9. projection completion 9 window 600 HU Fe PMMA H2OH2O

10. projection completion 10 true object FBP projection completion window 600 HU

11. 1 projection completion 11 2 Muller I., Buzug T.M., "Spurious structures created by interpolation-based Ct metal artifact reduction." Proc. of SPIE, 2009 Meyer E. et al, "Normalized metal artifact reduction (NMAR) in computed tomography." Med. Phys., 2010 zeroed metal trace linear interpolation

12. NMAR 12 Muller I., Buzug T.M., "Spurious structures created by interpolation-based Ct metal artifact reduction." Proc. of SPIE, 2009 Meyer E. et al, "Normalized metal artifact reduction (NMAR) in computed tomography." Med. Phys., 2010 sinograminterpolatedsinogram of segmentation normalized sinogram window 600 HU

13. NMAR 13 1 2 sinogram, metals erased sinogram, metals erased sinogram of the segmented reconstruction sinogram of the segmented reconstruction

14. NMAR 14 1 2 normalized sinogram, metals erased normalized sinogram, metals erased interpolated sinogram interpolated sinogram

15. NMAR 15 unnormalized interpolated sinogram unnormalized interpolated sinogram

16. proj.completion and NMAR 16 true object FBP projection completion projection completion window 300 HU NMAR

17. 17 CT Maximum Likelihood for CT

18. 18 CT datarecon

19. computing p(recon | data)difficult inverse problem computing p(data | recon)“easy” forward problem one wishes to find recon that maximizes p(recon | data) Bayes: p(recon | data) = p(data | recon) p(recon) p(data) datarecon ~ Maximum Likelihood for CT 19 MAP ML

20. Maximum Likelihood for CT p(recon | data) ~ p(data | recon) projectionPoisson jj j = 1..J i = 1..I ln ( p(data | recon) ) = L(data | recon) = ~ p(data | recon) recon data 20

21. Maximum Likelihood for CT L(data | recon) 21 iterative maximisation of L:

22. 22 MLTR convex algorithm [1] [1] Lange, Fessler, “Globally convergent algorithms for maximum a posteriori transmission tomography”, IEEE Trans Image Proc, 1995 [2] JA Fessler et al, "Grouped-coordinate ascent algorithm for penalized likelihood transmission image reconstruction." IEEE Trans Med Imaging 1997. [3] Fessler, Donghwan, "Axial block coordinate descent (ABCD) algorithm for X-ray CT image reconstruction.“ Fully 3D 2011 patchwork: local update [2,3]

23. MLTR MEASUREMENT REPROJECTION COMPARE UPDATE RECON 23

24. MLTR 24 validation Siemens Sensation 16 SiemensMLTR

25. models for iterative reconstruction 25 Poisson Likelihood: measured data data computed from current reconstruction image Projection model: monochromatic: bibi

26. models for iterative reconstruction Poisson Likelihood: Projection model: monochromatic: 1 material polychromatic: 26 energy k intensity b ik measured data data computed from current reconstruction image energy “water correction” MLTR_C

27. models for iterative reconstruction 27 Full Polychromatic Model – IMPACT Poisson Likelihood: energy k intensity b ik Projection model:

28.  jk =  j ∙ photo k +  j ∙ Compton k models for iterative reconstruction 28 Full Polychromatic Model – IMPACT water Compton photo-electric attenuation al  jk = photo-electric + Compton at energy k Compton k = Klein-Nishina (energy) Photo k ≈ 1 / energy 3

29. models for iterative reconstruction 29 Full Polychromatic Model – IMPACT  and  (1/cm)  mono (1/cm)    jk =  j ∙ photo k +  j ∙ Compton k  jk =  j  ∙ photo k +  j  ∙ Compton k

30.    and  (1/cm)  mono (1/cm) models for iterative reconstruction 30  

31. patches, local models 31 MLTR convex algorithm [1] [1] Lange, Fessler, “Globally convergent algorithms for maximum a posteriori transmission tomography”, IEEE Trans Image Proc, 1995 [2] JA Fessler et al, "Grouped-coordinate ascent algorithm for penalized likelihood transmission image reconstruction." IEEE Trans Med Imaging 1997. [3] Fessler, Donghwan, "Axial block coordinate descent (ABCD) algorithm for X-ray CT image reconstruction.“ Fully 3D 2011 patchwork: local update [2,3]

32. bowtie, BHC 32 e-e- energy k intensity b ik raw CT data not corrected for beam hardening send spectrum through filter and bowtie b ik = spectrum(k) x bowtie(i)

33. patches, local models IMPACT is complex and slow, MLTR and MLTR_C are simpler and faster Find the metals PATCH 3 PATCH 2 PATCH 1 Define patches IMPACT in metals MLTR_C elsewhere IMPACT in metals MLTR_C elsewhere 33 PATCH 4

34. clinical CT (Siemens Sensation 16) Body shaped phantom 34

35. sequential CT (Siemens Sensation 16) Body shaped phantom 35 FBP Regular PCPC NMAR IMPACT PATCHMLTR_C + IMPACTIMPACT 20 iter x 116 subsets

36. sequential CT (Siemens Sensation 16) Body shaped phantom 36 Black = FBP Blue = PC-NMAR Red = IMPACT PATCH wateraluminumCoCr..Ti Al VPMMAwater

37. helical CT 37 sequential 2 x 1mmhelical 16 x 0.75mm

38. helical CT 38 MIP IMPACT FBP NMAR metal patches, uniform init. metal patches, uniform init. no patches, NMAR init. no patches, NMAR init. metal patches, NMAR init. metal patches, NMAR init. 5 iter x 116 subsets

39. helical CT 39 IMPACT FBP NMAR metal patches, uniform init. metal patches, uniform init. no patches, NMAR init. no patches, NMAR init. metal patches, NMAR init. metal patches, NMAR init. MIP

40. helical CT 40 FBP NMAR 5 it 10 it IMPACT

41. helical CT 41 We give patches same x-y sampling but increased z-sampling: z-sampling x 3 impact, regular z

42. to do 42 after 5..10 x 100 iterations with patches still incomplete convergence persistent artifacts near flat edges of metal implants we currently think it is not o scatter o non-linear partial volume effect o crosstalk, afterglow o detector dead space

43. 43 thanks better physical model better reconstruction Katrien Van Slambrouck Bruno De Man Karl Stierstorfer, David Faul, Siemens

44. sequential CT (Siemens Sensation 16) 44 no energy corr. IMPACT no energy corr. IMPACT no energy, no bowtie corr. IMPACT + blank adjusted for bowtie no energy, no bowtie corr. IMPACT + blank adjusted for bowtie clinical scan IMPACT clinical scan IMPACT clinical scan, uncorrected IMPACT + bowtie clinical scan, uncorrected IMPACT + bowtie

45. microCT: soft tissue, cartilage, Ti FDKIMPACT SKYSCAN SPECTRUM Black = without filter Blue = 0.5 mm Al and 0.038 mm Cu Ti-cage, culture of soft tissue and cartilage 45