Visualization of HARDI data

Transcription

1 Visualization of HARDI data bmia.bmt.tue.nl/research/mviav Anna Vilanova

2 Introduction PAGE 1

3 What HARDI data? Diffusion Propagator P ( x ) Probability that a particle arrive to x given a fixed time. For each voxel we have a full probability density function. Diffusion Spectrum Imaging (a volume per voxel) PAGE 2

4 What HARDI data? Orientation Distribution Function O D F ( g) P ( rg) r d r 2 rg g rg g 0 Probability that a molecule is found in a given direction. is a unit vector. g g Fiber Orientation Distribution fo D F ( g ) Fraction of fiber portions in a given orientation within a voxel //Biomedical Engineering PAGE 3

5 Functions on the sphere Most of the HARDI models can be represented by functions on the sphere. (, ) ( g) w here g 1 Spherical Harmonics (SH) or Higher-Order Tensors (HOT) are used as representations. During this tutorial we will talk about one or the other, but remember that they represent the same and are interchangeable / Bimedical Engineering PAGE 4

6 Multi-Tensor Model Multi-Tensor Model does not use SH or HOT (Bergman et al. 2006) The weighted sum of k second-order tensors represent the signal /Biomedical Engineering PAGE 5

7 Visualizations Anisotropy Indices Glyphs Tractography PAGE 6

8 Anisotropy Indices (DTI) Based on eigenvalues of the tensor Most used quantities in clinic It is assumed that these indices give information about the quality of the underlying fibrous structure. FA /Biomedical Engineering PAGE 7

9 Anisotropy indices for HARDI Extended Anisotropy measures: Generalized Anisotropy (Ozarslan et al 2005 ), Generalized Fractional Anisotropy (Tuch 2004, Leow et al ), Cumulative Residual Entropy (Rao et al. 2004, Chen et al ), Fractional Multifiber Index (Frank 2002 ),R0,R2,Ri (Descoteaux 2006) M n ( g) ( g) n n d g d g 1 n Moments are used as anisotropy indices. M 2 is GFA Higher-order moments can also be used (Seunarine et al. 2009) Apply to different spherical diffusion functions ADC (Signal) Q-Ball, DOT, etc. /Biomedical Engineering PAGE 8

10 Anisotropy Indices for HARDI Reduce information to one scalar, easy to visualize Give an easy quantitative way to evaluate data They are not as widely used as DTI measures (FA) What extra information are they giving? (Prckovska et al 2008) This line of research is underdeveloped in HARDI literature. /Biomedical Engineering PAGE 9

11 Glyph Representation DTI Shows local information In 3D, clutter is a problem 1 e 1 (Kindlmann 2004) Ellipsoids Superquadrics e e Cuboids /Biomedical Engineering PAGE 10

12 Glyph Representation HARDI HARDI information is more complex. What the Glyph represents depends on the model. DTI Ellipsoid Algebraic surfaces { x xd x ct} 2 /Biomedical Engineering PAGE 11

13 Glyph Representation HARDI Easy to build with DTI using eigenanalysis Not easy to generalize to HARDI due to the inverse General algebraic surfaces for second-order tensors (Strang 1998) DTI Ellipsoid General algebraic surfaces { x x D x ct} Generalisation (Qi 2006), maxima are minima. Contraintuitive T /Biomedical Engineering PAGE 12

14 Glyph Representation HARDI Spherical Polar Plots S ( g ) ( g ) g g 1 T S ( g ) ( g D g ) g S ( g ) ( g ) g /Biomedical Engineering PAGE 13

15 Maxima enhancement The maxima in (, ) are of interest Normalization is needed in most of the models QBall Normalized Showing arrows at maxima (Hlawitschka et al. 2005) Maxima enhancement by color coding XYZ - RGB color coding Distance to center based color coding (Hlawitschka et al. 2005) (Prckovska et al. 2010) /Biomedical Engineering PAGE 14

16 Maximum Enhancing Glyphs (Schultz et al 2009,Schultz et al 2010) Use the linear mapping defined by tensors DTI - It defines an Ellipsoid D S ( g ) D g D HARDI maxima enhancement glyphs (HOME) g 1 T tensor of order l S ( g ) T g T l 1 g 1 /Biomedical Engineering PAGE 15

17 Maximum Enhancing Glyphs HOME Glyphs Surface partition Color saturation modulation /Biomedical Engineering PAGE 16

18 Glyph s Rendering Polygonal meshes (Schultz et al. 2010): Simple Calculate geometry when changing seed points Accuracy depends on tessellation order Speed depends on tessellation order and amount of glyphs Ray-Casting for Spherical Harmonics: (Peeters et al. 2009, Almsick et al. 2010) Complex (GPU implementation) Quality depends on ray sampling steps Speed depends mainly on screen resolution, and number of glyphs. /Biomedical Engineering PAGE 17

19 Fiber population and multi-tensor glyphs Fiber population Spherical Deconvolution Maxima detection Multi-tensor model (Bergman et al 2006) (Schultz et al. 2008) /Biomedical Engineering PAGE 18

20 HARDI Tractography Deterministic HARDI Streamline Riemannian Framework Probabilistic Bayesian Bootstraping /Biomedical Engineering PAGE 19

21 HARDI Deterministic Tractography Extension of DTI streamlines Detection of Maxima Spherical Deconvolution ODF Multi-tensor model Interpolation Decide what fiber to follow PAGE 20 /Biomedical Engineering

22 HARDI Deterministic Tractography (Blyth et al Hagmann et al 2007 Perrin et al Jeurissen et al ) /Biomedical Engineering PAGE 21

23 HARDI Riemannian Framework DTI metric HARDI metric (Finsler) 1 G ( x ) D ( x ) G ( x, g ) f ( ( x, g )) [L. O Donnell et al. 02] [N.Wotawa et al. 05] (Melanakos et al. 2007) (Pichon et al 2005) /Biomedical Engineering PAGE 22

24 Probabilistic tractography :Bayesian p ( v D W d a ta, v ) p ( D W d a ta v ) p ( v v ) k k 1 k k k 1 Posterior Next step direction Given noise and previous direction Likelihood Models noise given a fiber orientaiton Prior Next direction given previous direction v k 1 (Friman et al ) Cortesy of (CF Westin 2008) /Biomedical Engineering PAGE 23

25 Probabilistic tractography :Bayesian p ( v D W d a ta, v ) p ( D W d a ta v ) p ( v v ) k k 1 k k k 1 are used to randomly define the next step v k 1 Randomly trace thousand paths v k Challenge good estimation of the likelihood and prior (Parker et al 2003)(Cook et al ) (Seunarine et al. 2007) Courtesy of (CF Westin 2008) Log(probability of connection) /Biomedical Engineering PAGE 24

26 Probabilistic tractography :Bootstraping Resampling method : random sampling with replacement Measure in several directions and several times Random selection of perturbations of the directions and generate large number of datasets Calculate the variance of derived measures like Anisotropy indices, Eigenvalues, Eigenvectors, etc. Calculate the fibers generated from one seed point. (Haroon et al. 2007) (Berman et al. 2008) (Hosey et al. 2005) (Behrens et al 2007) (Jeurissen et al. 2010) /Biomedical Engineering PAGE 25

27 Hybrid Visualization Scheme (Prckovska et al. 2010) /Biomedical Engineering PAGE 26

28 Visualizations Scalar Indices Glyphs Tractography PAGE 27

29 Challenges Modeling (Signal Diffusion Fiber characteristics) Spliting, kissing fibers, diameter of fibers,... Identifying relevant quantitative measures (DTI FA) the visualization should consider this goal Information overload Interactive tools for visual data analysis (DSI, ODF, etc) Reduce memory and computational costs /Biomedical Engineering PAGE 28

30 Challenges Visual comparison between subjects Uncertainty estimation and visualization Mainly used in research environments What is the real value of HARDI? Validation /Biomedical Engineering PAGE 29

31 Acknowledgements Vesna Prckovska Paulo Rodrigues Neda Sepasian, Tim Peeters Ralph Brecheisen. Alard Roebroeck from Maastricht Brain Imaging Center Pim Pullens from Brain Innovation B.V., Maastricht Maxime Descoteaux from MOIVRE Centre for their valuable input and collaboration More information: bmia.bmt.tue.nl DTI Visualization Techniques and Applications

32 Bibliography (Bergman et al. 2006) Ø. Bergmann, G. Kindlmann, A. Lundervold, and C.- F.Westin. Diffusion k-tensor estimation from Q-Ball imaging using discretized principal axes. In Proc. Medical Image Computing and Computer-Assisted Intervention (MICCAI 06), volume 4191 of LNCS, pages , (Ozarslan et al. 2005) Ozarslan, E., Shepherd, T.M., Vemuri, B.C., Blackband, S.J., Mareci, T.H.: Resolution of complex tissue microarchitecture using the diffusion orientation transform (DOT). NeuroImage 36(3) (July 2006) (Tuch 2004) Tuch, D.: Q-ball imaging. Magn Reson Med 52 (2004) (Leow et al. 2008) Leow, A., Zhu, S., Zhan, L., McMahon, K., de Zubicaray, G., Meredith, M.,Wright, M., Thompson, P.: A study of information gain in high angular resolution diffusion imaging (HARDI). In: Computational Diffusion MRI Workshop,MICCAI. (2008) (Rao et al. 2004) Rao, M., Chen, Y., Vemuri, B.C., Wang, F.: Cumulative residual entropy: A new measure of information. IEEE Transactions on Information Theory 50(6) (June 2004) (Chen et al. 2005) Chen, Y., Guo, W., Zeng, Q., Yan, X., Rao, M., Liu, Y.: Apparent diffusion coefficient approximation and diffusion anisotropy characterization in DWI. In: Information Processing in Medical Imaging. (2005) /Biomedical Engineering PAGE 31

33 Bibliography (Seunarine et al 2009) Seunarine, K. K., Alexander, D. C. (2009). Multiple fibers: beyond the diffusion tensor. In Diffusion MRI: from quantitative measurement to in vivo neuroanatomy Oxford,U.K.: Elsevier,2009; (Frank 2002 ) Frank, L.R.: Anisotropy in high angular resolution diffusionweighted MRI. Magn Reson Med 45(6) (2002) o (Descoteaux et al 2006) Descoteaux, M., Angelino, E., Fitzgibbons, S., Deriche, R.: Apparent diffusion coefficients from high angular resolution diffusion imaging: Estimation and applications. Magn. Reson. Med. 56(2) (2006) (Prckovska et al 2008) Prckovska, V., Roebroeck, A.F., Pullens,W., Vilanova, A., ter Haar Romeny, B.M.:Optimal acquisition schemes in high angular resolution diffusion weighted imaging. In: MICCAI. Vol of LNCS.Springer (2008) (Kindlmann 2004) Kindelmann G.: Superquadric tensor glyphs. In EG/IEEE Symposium on Visualization (SymVis) (2004), pp (Strang 1998) Strang G.: Linear algebra and its applications, 3rd ed. Harcourt Brace Jovanovich, (Qi 2006) Qi L.: Rank and eigenvalues of a supersymmetric tensor, the multivariate homogeneous polynomial and the algebraic hypersurface it defines. Journal of Symbolic Computation 41 (2006), /Biomedical Engineering PAGE 32

34 Bibliography (Prckovska et al. 2010) V. Prckovska, T.H.J.M. Peeters, M.A. van Almsick, B.M. ter Haar Romeny, A. Vilanova: Fused DTI/HARDI visualization, IEEE Transactions in Visualization and Computer Graphics (to appear) (2010) (Hlawitschka et al. 2005) M. Hlatwitschka, g. Scheuermann: HOT-lines tracking lines in higher order tensor fields. In Proceedings IEEE Visualization (2005), (Schultz et al 2009) ) T. Schultz Feature Extraction for DW-MRI Visualization: The State of the Art and Beyond Accepted for publication in Proc. Schloss Dagstuhl Scientific Visualization Workshop (Schultz et al 2010) T. Schultz and G. Kindlmann: A Maximum Enhancing Higher-Order Tensor Glyph. Computer Graphics Forum (Proc. EuroVis) 29(3): , (Peeters et al. 2009) T.H.J.M. Peeters, V. Prckovska, M.A. van Almsick, A. Vilanova, B.M. ter Haar Romeny, Fast and Sleek Glyph Rendering for Interactive HARDI Data Exploration, in IEEE Pacific Visualization Symposium; Beijing, China, , (2009) /Biomedical Engineering PAGE 33

35 (Almsick et al. 2010) M.A. van Almsick, T.H.J.M. Peeters, V. Prckovska, A. Vilanova Bartroli, B.M. ter Haar Romeny, GPU-Based Ray-Casting of Spherical Functions Applied to High Angular Resolution Diffusion Imaging, IEEE Transactions on Visualization and Computer Graphics, (to appear) (2010) (Schultz et al. 2008) T.Schultz, H.-P. Seidel: Estimating Crossing Fibers: A Tensor Decomposition Approach IEEE Transactions on Visualization and Computer Graphics (Proc. IEEE Visualization) 14(6): , 2008 (Blyth et al. 2003) R. Blyth, P. Cook, and D. Alexander, Tractography with multiple fibre directions, in Proc. ISMRM, (Hagmann et al 2007) P. Hagmann, L. Jonasson, T. Deffieux, R. Meuli, J-P. Thiran, and V.J. Wedeen, Fibertract segmentation in position orientation space from high angular resolution diffusion MRI, Neuroimage, no. 32, pp , (Perrin et al. 2005) Perrin M, Poupon C, Cointepas Y, Rieul B, Golestani N, Pallier C, Rivie`re D, Constantinesco A, LeBihan D, Mangin JF: Fiber tracking in q-ball fields using regularized particle trajectories. Inf Process Med Imaging (2005),19: /Biomedical Engineering PAGE 34

36 Bibliography (Jeurissen et al. 2010) Ben Jeurissen, Alexander Leemans,, Derek K. Jones, Jacques-Donald Tournier, and Jan Sijbers: Probabilistic Fiber Tracking Using the Residual Bootstrap with Constrained Spherical Deconvolution, Human Brain Mapping (2010) DOI: /hbm (Melanakos et al. 2007) J. Melonakos, V. Mohan, M. Niethammer, K. Smith, M. Kubicki and A. Tannenbaum, Finsler tractography for white matter connectivity of the cingulum bundle, Medical Image Computing and Computer Assisted Intervention (MICCAI) Vol of LNCS, Springer-Verlag (2007), (Pichon et al 2005) Pichon, E., Westin, C., Tannenbaum, A.: A Hamilton-Jacobi- Bellman approach to high angular resolution diffusion tractography. In: Duncan, J.S., Gerig, G. (eds.) MICCAI LNCS, vol. 3749, pp Springer, Heidelberg (2005) (Friman et al. 2006) Friman, O., Farneback, G., Westin, C.-F.; A Bayesian approach for stochastic white matter tractography, IEEE Transactions on Medical Imaging, (2006) 25: /Biomedical Engineering PAGE 35

37 Bibliography (Parker et al 2003) Parker GJ, Haroon HA, Wheeler-Kingshott CA: A framework for a streamline-based probabilistic index of connectivity (PICo) using a structural interpretation of MRI diffusion measurements. J Magn Reson Imaging (2003)18: (Cook et al. 2005) P. A. Cook et al. An automated approach to connectivitybased partitioning of brain structures. In Proc MICCAI, pages , Palm Springs, (Cook et al. 2006) P. A. Cook and D. C. Alexander. Modelling uncertainty in two fibre-orientation estimates within a voxel. In Proc ISMRM, page 1629, Seattle, (Seunarine et al. 2007) Seunarine KK, Cook PA, Hall MG, Embleton KV, Parker GJM, Alexander DC: Exploiting peak anisotropy for tracking through complex structures. In: IEEE 11th International Conference on Computer Vision, Rio de Janeiro. (2007) pp 1 8. (Haroon et al. 2007) H. A. Haroon and G. J. Parker. Using the wild bootstrap to quantify uncertainty in fibre orientations from q-ball analysis. In Proc ISMRM, Berlin, /Biomedical Engineering PAGE 36

38 Bibliography (Berman et al. 2008) Berman JI, Chung S, Mukherjee P, Hess CP, Han ET, Henry RG (2008): Probabilistic streamline q-ball tractography using the residual bootstrap. NeuroImage 39: (Hosey et al. 2005) T. Hosey, G.Williams, and R. Ansorge, Inference of multiple fiber orientations in high angular resolution diffusion imaging, Magn. Reson. Med., (2005) vol. 54, pp (Behrens et al 2007) Behrens T, Johansen-Berg H, Jbabdi S, Rushworth M, Woolrich M. Probabilistic diffusion tractography with multiple fibre orientations: What can we gain? NeuroImage 2007;34: /Biomedical Engineering PAGE 37