StatisticallyBased Reorientation of Diffusion Tensor Field

1
Statistically-Based Reorientation of Diffusion
Tensor Field
July 10, 2002

• XU, DONGRONG
• SUSUMU MORI
• DINGGANG SHEN
• CHRISTOS DAVATZIKOS

JOHNS HOPKINS UNIVERSITY SCHOOL OF MEDICINE
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Outline

• Introduction
• Motivation
• Preliminaries
• Our Method
• Experiment Results
• Conclusion
• Acknowledgement

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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

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Introduction (cont.)
Example 1 3D ellipsoid view
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Introduction (cont.)
Example 2 Primary direction view
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Introduction (cont.)

• Existing DTI warping methods
• - Small Strain Method
• - Finite Strain Method
• Preservation of Principal Direction (PPD)
• Our Method
• Reorientation based on Procrustean Estimation

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Motivation

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

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Motivation (cont.)

• To process DTI in a different space, e.g. track
  neural fibers

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Preliminaries
Tensor reorientation is a must
Wrong
Correct
Deformed fiber
Deformed Fiber
Original Fiber
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Preliminaries (cont.)
Scaling component needs to be removed
Wrong
Correct
Deformed fiber
Deformed Fiber
Original Fiber
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Preliminaries (cont.)
Tensors original orientation is important
Shear Force
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Preliminaries (cont.)

• Difficulties
• Tensor reorientation
• De-noise estimate the true orientation
• DTI warping
• Relocation Reorientation

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Our Method

• Reorientation by Procrustean Estimation in an
  optimized neighborhood, based on estimated PDF()

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Our Method (cont.)

• Procrustean Estimation
• Let A,B ?Mmxn ,We need to find a unitary
  matrix U, so that
• A U . B or minimize (A-U.B)
• where
• U V . WT
• by singular value decomposition (SVD)
• A . BT V . S . WT

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Our Method (cont.)
Neighborhood

• Estimate an optimized neighborhood for
• True PD
• PDF resample
• Keep neighborhood volume a constant

Underlying Fiber
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Our Method (cont.)
Resample

• Directly take samples from neighborhood
• They implicitly follow the local PDF()

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Our Method (cont.)
Weight Procrustean Estimation

• Reasons
• Sample importance varies with distance
• Tensors fractional anisotropy (FA) factor

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Experiment 1
Simulated data to demonstrate the
effectiveness of our algorithm
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Experiment 2
With Real Case Before After Warping
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Experiment 3
With Simulation Data on 5 Individual Subjects
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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

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Acknowledgement

• Thanks to Mr. Meiyappan Solaiyappan

Thank you ! - END -
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)
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Experiment 4
Preserve 1st 2nd PD
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Experiment 5
1. Improve SNR with 9 real cases



The nine normal subjects
2. Target abnormal areas by FA-map
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Our Method (cont.)