Development of XCT & BLT

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2 Development of XCT & BLT Ge Wang, Wenxiang Cong, Hengyong Yu Biomedical Imaging Division VT-WFU School of Biomedical Engineering & Sciences Virginia Tech, Blacksburg, Virginia, USA October October 18, 2007 Pisa, Italy

3 Outline Introduction X-ray Computed Tomography (XCT) - Quasi-short Object Problem - Interior Problem Bioluminescence Tomography (BLT) - Phase-approximation approximation - Modulated Reconstruction Discussionsi

4 NIH Roadmap (10/03/03) New Pathways to Discovery Building Blocks, Pathways, and Networks Molecular Libraries and Imaging Structural Biology Bioinformatics and Computational Biology Nanomedicine Research Teams of the Future High-Risk Research Interdisciplinary Research Public Private Partnerships Re-engineering the Clinical Research Enterprise Clinical Research

5 Systems Biomedicine Gene s >35,000 Human Genome Project Protein Cell Tissue Organ Body Physiome Project

6 Biomedical Imaging Nuclear Imaging CT/X-Ray MRI Bioluminescence Imaging

7 Outline Introduction X-ray Computed Tomography (XCT) - Quasi-short Object Problem - Interior Problem Bioluminescence Tomography (BLT) - Phase-approximation approximation - Modulated Reconstruction Discussionsi

8 Long Object Problem Object Screen Filament E-beam Source Lens Computer Detector Stage Cone-Beam Data (AMIL, SUNY/Buffalo)

9 Implication for Medical CT Wang, G, Lin, TH, Cheng PC, Shinozaki DM, Kim, HG: Scanning cone-beam reconstruction algorithms for x-ray microtomography. Proc. SPIE Vol. 1556,,p p , July 1991 (Scanning Microscopy Instrumentation, Gordon S. Kino; Ed.)

10 Prototype of Spiral CBCT To solve the long-object object problem, a first level of improvement with respect to the 2D FBP algorithms was obtained by backprojecting the data in 3D, along the actual measurement rays. The prototype of this approach is the algorithm of Wang et al. Defrise, Noo, Kudo: A solution to the long-object problem in helical cone-beam tomography. Phys. Med. Biol. 45: , 2000 Many advances in CB reconstruction have been made recently thanks to the quest for an attractive reconstruction method in helical CB tomography. Pack, Noo, Clackdoyle: Cone-beam reconstruction using the backprojection of locally filtered projections. IEEE Trans. Medical Imaging g 24:1-16, 2005

11 Katsevich Theorem (2002) y( s 2 ) y( s 1 ) e u( s, x) γ Object f (x) β( s 0, x) y( s 0 ) Source Pi-Line Detector Plate f ( x ) 2π 1 1 = D 2π x y ( s ) q I PI ( x) 0 f ( y ( q ), Θ ( s, x, γ )) q = s 1 d γds sin γ e ( s, x) β ( s, x) u( s, x) Θ( s, x, γ ) cosγβ ( s, x) + sin γe( s, x) Katsevich A: A general scheme for constructing inversion algorithms for cone beam g g g CT. Int'l J. of Math. and Math. Sci. 21: , 2003

12 Bolus-chasing CT Angiography Control Predictive Filter Bolus Propagation Model Comparison Table On-Line CTF Image Reconstruction Image Analysis Off-Line CT Volume Reconstruction CT Angiography Wang G, Vannier MW, US Patent 6,535,821,2003 Bai EW, Wang G, Vannier MW, US patent application filed, 2005

13 Electron-Beam Micro-CT Generalized Tam window Electron gun Magnetic focus & deflection coils Cone-beam X-ray Animal chamber Vacuum chamber Taper Wang G et al., Journal of X-Ray Sci. and Tech. 12: , 2004 CCD camera

14 Nonstandard Spiral CBCT Wang G, Ye Y: Nonstandard spiral cone-beam scanning methods, apparatus, and applications (patent disclosure), 2003 Ye Y, Zhao S, Yu H, Wang G:. Exact image reconstruction for cone-beam CT along nonstandard spirals and other curves. SPIE Conf. on Development in X-ray Tomography IV, 2004 Zhao S, Yu H, Wang G: A family of analytic algorithms for cone-beam CT. SPIE Conf. on Development in X-ray Tomography IV, 2004

15 Generalized Katsevich Algorithm γ Object f (x) β( s 0, x) y( s 0 ) Source Chord Detector Plate f ( x) 2ππ 1 1 = D 2π x y( s) q I PI ( x) 0 f ( y( q), Θ( s, x, γ )) q= s 1 dγds sinγ Ye Y Wang G: A filtered backprojection formula for exact image reconstruction from Ye Y, Wang G: A filtered backprojection formula for exact image reconstruction from cone-beam data along a general scanning curve. Med. Phys. 32:42-48, 2005

16 Triple Sources Inter-PI Line Zhao, Jiang, Zhuang, Wang: Proc. of SPIE, Vol. 5535, pp , 2004 Zhao, Jiang, Zhuang, Wang: Journal of X-ray Science and Technology 14: ,

17 Cone-Beam CT Roadmap

18 Outline Introduction X-ray Computed Tomography (XCT) - Quasi-short Object Problem - Interior Problem Bioluminescence Tomography (BLT) - Phase-approximation approximation - Modulated Reconstruction Discussionsi

19 Composite Circling Scan The helical scanning is the main mode to solve the long object problem What should be the main scanning mode to solve the quasi-short object problem? The composite circling trajectory/variants allow optimal balance of system compactness, mechanical stability, and imaging flexibility Wang, Yu: VT Patent Disclosure, US Provisional i Patent, t 2007

20 Outline Introduction X-ray Computed Tomography (XCT) - Quasi-short Object Problem - Interior Problem Bioluminescence Tomography (BLT) - Phase-approximation approximation - Modulated Reconstruction Discussionsi

21 Exact Reconstruction Condition Exact reconstruction conditions based on truncated Hilbert Transform: (a) the condition by Noo et al. (b) the condition by Defrise et al.; (c) the condition by our group. Wang, Yu, Ye: VT Patent Disclosure, US Provisional Patent, 2007 compact support of f ( x) reconstructible c3 c4 c 3 c1 2 gx ( ) is known compact support of reconstructible c 4 c 1 c 2 gx ( ) is known compact support of f ( x) c f ( x) x x (a) (b) Ye, Yu, Wei, Wang: International Journal of Biomedical Imaging; Article ID:63634, 2007 c 3 c 5 reconstructible c1 2 f( x) is known gx ( ) is known c 4 c x (c)

22 Exact Reconstruction Regions Exact interior reconstruction regions enabled by our latest finding for a given field of view. (a) by Noo et al.; (b) by Defrise et al.; (c) and (d) by ours.

23 Interior Reconstruction 1.4 Phantom Value Full Reconstruction Interior Reconstruction Known Known

24 Outline Introduction X-ray Computed Tomography (XCT) - Quasi-short Object Problem - Interior Problem Bioluminescence Tomography (BLT) - Phase-approximation approximation - Modulated Reconstruction Discussionsi

25 Ming s Work Uniqueness Results for Multi-spectral Bioluminescence Tomography Ming Jiang Peking University Ge Wang Virginia Tech CRM, Pisa, Italy 10/19/2007

26 Bioluminescence Tomography First initiative Pioneered by Wang et al. (2002) Funded by NIBIB (R21/R33)

27 Piwnica-Worms Statement "If you look at applications of molecular imaging strategies across the board, bioluminescence imaging has been galloping along at the fastest pace over the last 24 months for preclinical work. ""If you just look at the number of papers published and the way the techniques are being used-comparing MR, PET, SPECT, radiopharmaceutical, fluorescence, ultrasound, and bioluminescence-in preclinical studies and in basic science studies, bioluminescence imaging seems to be dominating the playing field." Molecular Imaging Outlook, March 2005

28 First BLT Prototype Bioluminescence Tomography prototype Designed by Wang, Hoffman, McLennan Built by us & UI Med. Inst. Facility in 2003 In Vivo Micro-CT scanner Designed by BIR, Hoffman, Wang Built by BIR in 2003 MicroCAT scanner under a pending agreement by Siemens & BLT Lab

29 Digital Spectral Separation t Red Spectrum Blue Spectrum Dichroic Coating Mirror bject Ob d Blue Virtual Image Red Virtual Image

30 Cone-mirror Design

31 Computed Tomography Individualized Volume Geometrical Model Optical Tomography Optical Model Bioluminescence Bioluminescent 3D Imaging Views Mapping Wang G, et al.: In vivo mouse studies with bioluminescence tomography. Optics Express 14: , 2006

32 Outline Introduction X-ray Computed Tomography (XCT) - Quasi-short Object Problem - Interior Problem Bioluminescence Tomography (BLT) - Phase-approximation approximation - Modulated Reconstruction Discussionsi

33 Multi-probe BLT Complicated biological network Multiple pathways and mechanisms Gene sequences and molecular library Multi-probes of different spectra Accurate and efficient transport models Innovative inversion strategies

34 Wavelength-Dependent Absorption Weissleder R, Ntziachristos V: Shedding light onto live molecular targets. Nat. Med. 9: , 2003

35 Radiative Transfer Equation 1 v L( rv, ) + ( μ ) (, ) (, ) (, ) a+ μs L rv = μ s L rv p v v dv + S( r), r Ω 2 4π L ( r, v) S ( r ) μ s ( r ) ( r ) Photon radiance Isotropic source Scattering coefficient μ r Absorption coefficient a p ( v,v ) Phase function Ishimaru: Wave Propagation and Scattering in Random Media. Academic Press, NY, 1978 S

36 Photon Fluence Rate Equation p 1 1 4π f 2π fδ ( v v ) = ( 1 ) + ( 1 v v ) r r 1 1 Φ ( r) = μs ( ) Φ ( ) + S( ) exp μ 2 t ( t ) dt d 4 r r r r β r π Ω r r 0 r r r d β n Φ( ) exp μ t ( t ) dt d 2 4π ( 1+ rd ) r r β r Ω 0 r r Cong W, Shen H, Cong A, Wang Y, Wang G: Modeling photon propagation in biological tissues using a generalized Delta-Eddington phase function. Physical Review E, 2007

37 Photon Flux Vector Equation p 1 ( s s ) = ( 1 )( 1 3 ) 2 ( 1 ) 4 f + h + f δ π s s s s 1 J( r) = β( )( ( ) 3 hμ ( a )) G(, ) d 4π Ω r J r + v J r rr v r 1 + ( 1+ β ( )) Q( ) G(, ) d 4π Ω r r rr v r r ( ) 3 v + ( 2A 6 n v ) n G ( rr, )( ) d J r n v v r d J r 4π Ω Cong WX, Cong A, Shen H, Liu Y, Wang G: Flux vector formulation for photon propagation in the biological tissue. Optics Letters 32, , 2007

38 Fluence & Flux Equations p 1 ( s s ) = ( 1 )( 1 3 ) 2 ( 1 ) 4 f + h + f δ π s s s s 1 Φ ( r) = { μ s ( ) 3h ( ) Q( )} G(, ) d 4π Φ r v J r + r r r r Ω rd + Φ ( ) + 3 ( ) G (, )( ) d r v J r rr v n r 4π Ω 1 J( r) = { μ s Φ ( ) 3h ( ) + Q( )} G(, ) d 4π r v J r r r r v r Ω r + d Φ ( ) + 3 ( ) G (, ) ( ) d 4π Ω r v J r rr v v n r Cong WX, Shen H, Cong A, Wang G: Integral equations of the photon fluence rate and flux based on a generalized ed Delta-Eddington phase function. J of Biomedical Optics, 2007

39 Problems with DA Diffusion approximation dominates in biophotonics Diffusion equation is inaccurate in important cases 1 (b) 1 (b) 0.8 DA MC 0.8 DA MC Rate Normaliz zed Fluence µ = 0.2 mm 1 µ a = 0.35 mm 1 a µ s = 14.5 mm 1 µ s = 12.5 mm 1 Error 14.6% Error 31.2% Detector Position Rate Normaliz zed Fluence Detector Position

40 Merits with PA Novel phase function to simplify the radiative transfer equation Outperform DA over a broad range of biological optical properties 1 1 (a) (a) 0.8 PA MC 0.8 PA MC Rate ized Fluence µ = 1 = 1 a 0.2 mm µ 0.6 a 0.35 mm µ s = 14.5 mm 1 µ s = 12.5 mm 1 Error < 4% Error < 4% Rate ized Fluence 0.4 Normali 0.2 Normali Detector Position i Detector Position i Patent disclosure filed in May 2007

41 Comparative Study DA based Reconstruction Localization Error 2.3 mm Energy Error 25% Optical Properties: µ a = 0.2 mm 1, µ s = 14.5 mm 1, g = 0.9 PA based Reconstruction Localization Error 0.2 mm Energy Error 5%

42 Outline Introduction X-ray Computed Tomography (XCT) - Quasi-short Object Problem - Interior Problem Bioluminescence Tomography (BLT) - Phase-approximation approximation - Modulated Reconstruction Discussionsi

43 Spectral Data of Fluc Zhao H, Doyle T, Coquoz O, Kalish F, Rice B, Contag C: Emission spectra of bioluminescent reporters and interaction with mammalian tissue determine the sensitivity of detection in vivo. J. Biomed. Opt. 10: , 2005

44 Focused US Heating The ultrasound pressure field at position X can be expressed as: p ( X ) iρc = λ S ( α e u ' X X ' + ik ) X X ' ds The induced d temperature t distribution ib ti T is governed by the steady state bioheat transport equation: κ 2 T cbω( T T a ) + Q = 0 W G Sh HO C WX Zh S W i GW T t d l t d bi l i Wang G, Shen HO, Cong WX, Zhao S, Wei GW: Temperature-modulated bioluminescence tomography. Optics Express 14: , 2006

45 Temperature-modulated BLT (TBT) TBT Reconstruction Spatial Error < 0.2 mm, Power Error < 22%

46 Outline Introduction X-ray Computed Tomography (XCT) - Quasi-short Object Problem - Interior Problem Bioluminescence Tomography (BLT) - Phase-approximation approximation - Modulated Reconstruction Discussionsi

47 Number Games 0 = Circular scanning g( (Feldkamp) 0+1 = Helical scanning (Long object) 0+00 = Composite circling (Short object) 0 = Diffusion approximation 0+1 = Phase approximation

48 Fundamental Questions Demand Sophisticated Tools Not Cheap

49 Local Heating In Vitro 1 cm o C

50 Acknowledgment The results in this presentation are of collaborative nature. Important collaborators include Drs. M Jiang, EW Bai, YB Ye, YLi Li, WHan, EAHoffman, G McLennan, M Henry, GW Wei, J Zhao, SY Zhao, P Dubey and many others.

51 Thank You for Invitation!