J OHNS H OPKINS U NIVERSITY S CHOOL O F M EDICINE Statistically-Based Reorientation of Diffusion Tensor Field XU, D ONGRONG S USUMU M ORI D INGGANG S HEN C HRISTOS D AVATZIKOS July 10, 2002

Outline Introduction Motivation Preliminaries Our Method Experiment Results Conclusion Acknowledgement

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

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

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

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

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

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

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

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

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

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

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

Our Method (cont.) Procrustean Estimation: Let A,B  M mxn,We need to find a unitary matrix U, so that: A = U. B or minimize (A-U. B) where: U = V. W T by singular value decomposition (SVD): A. B T = V. Σ. W T

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

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

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

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

Experiment 2 With Real Case Before & After Warping before after

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

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

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

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

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

Our Method (cont.)