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Statistically-Based Reorientation of Diffusion Tensor Field

July 10, 2002. Statistically-Based Reorientation of Diffusion Tensor Field. XU, D ONGRONG S USUMU M ORI D INGGANG S HEN C HRISTOS D AVATZIKOS. J OHNS H OPKINS U NIVERSITY S CHOOL O F M EDICINE. Outline. Introduction Motivation Preliminaries Our Method Experiment Results

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Statistically-Based Reorientation of Diffusion Tensor Field

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  1. July 10, 2002 Statistically-Based Reorientation of Diffusion Tensor Field XU, DONGRONG SUSUMU MORI DINGGANG SHEN CHRISTOS DAVATZIKOS JOHNS HOPKINS UNIVERSITY SCHOOL OF MEDICINE

  2. Outline • Introduction • Motivation • Preliminaries • Our Method • Experiment Results • Conclusion • Acknowledgement

  3. Introduction • DTI : second order tensor at each voxel • A 3 x 3 symmetric matrix • The tensor describes local water diffusion • DT provides insight into white matter region structure

  4. Introduction (cont.) Example –1: 3D ellipsoid view

  5. Introduction (cont.) Example –2: Primary direction view

  6. Introduction (cont.) • Existing DTI warping methods: - Small Strain Method - Finite Strain Method • Preservation of Principal Direction (PPD) • ……… • Our Method • Reorientation based on Procrustean Estimation

  7. Atlas Atlas Motivation • Spatial registration of diffusion tensor images (DTI) for statistical analysis, based on noisy observations

  8. Motivation (cont.) • To process DTI in a different space, e.g. track neural fibers

  9. Preliminaries Tensor reorientation is a must Wrong Correct Deformed fiber Deformed Fiber Original Fiber

  10. Preliminaries (cont.) Scaling component needs to be removed Wrong Correct Deformed fiber Deformed Fiber Original Fiber

  11. Preliminaries (cont.) Tensor’s original orientation is important Shear Force

  12. Preliminaries (cont.) • Difficulties: • Tensor reorientation • De-noise: estimate the true orientation • DTI warping: Relocation + Reorientation

  13. Estimate Optimized Neighborhood Estimate True Orientation PDF Vector Resample Procrustean Estimation Tensor Reorientation Our Method • Reorientation by Procrustean Estimation in an optimized neighborhood, based on estimated PDF(•)

  14. Our Method (cont.) Procrustean Estimation: LetA,B Mmxn,We need to find a unitary matrix U, so that: A = U . Bor minimize(A-U.B) where: U = V . WT by singular value decomposition (SVD): A . BT = V . Σ . WT

  15. Underlying Fiber Our Method (cont.) Neighborhood • Estimate an optimized neighborhood for: • True PD • PDF resample • Keep neighborhood volume a constant Underlying Fiber

  16. displacement field A = U .B ( ) = U . ( ) U: Pure rotation normalized PD displaced PD (normalized) Our Method (cont.) Resample • Directly take samples from neighborhood • They implicitly follow the local PDF(•)

  17. A = U .B ( ) = U . ( ) U: Pure rotation N(x): Neighborhood at location x V : original vec.;v’: displace vec. w : weight Our Method (cont.) Weight Procrustean Estimation • Reasons: • Sample importance varies with distance • Tensor’s fractional anisotropy (FA) factor

  18. Displacement Field1 (DF-1) Displacement Field2 (DF-2) Original Zoomed in of Warped by DF-2 Warped by DF-2 Warped by DF-1 Experiment 1 Simulated data to demonstrate the effectiveness of our algorithm

  19. before after Experiment 2 With Real Case Before & After Warping

  20. Lots thin small branches Thick branches Fibers defined in template Colormap 1 2 3 5 individual configurations One DTI with noise 5 Accuracy Demonstration Average after normalization Colormap of the Average DTI of the 5 normalized ones Ground truth 4 Normalization Experiment 3 With Simulation Data on 5 Individual Subjects

  21. Conclusion • Procrustean estimation for tensor reorientation • Relatively robust in noisy environment • Fiber pathway preserved after warping • Preservation of tensor shape (both 1st and 2nd PD) • No “small displacement” requirement

  22. Acknowledgement • Thanks to Mr. Meiyappan Solaiyappan Thank you ! - END -

  23. : )

  24. Warped PD1 Original PD1 & PD2 PD2 preserved during warping PD2 NOT considered Displacement field Warped PD2 Experiment 4 Preserve 1st & 2nd PD

  25. template Colormap of one individual DTI Colormap of the Average of the 9 after normalization Simulated abnormalities by decreasing FA 10% ~ 40% 10% 20% FA map of the average tensor field of the 9 warped individuals Detected abnormalities 30% 40% Experiment 5 1. Improve SNR with 9 real cases The nine normal subjects 2. Target abnormal areas by FA-map

  26. Our Method (cont.)

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