Visualizing Diffusion Tensor Imaging Data with Merging Ellipsoids

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Visualizing Diffusion Tensor Imaging Data with
Merging Ellipsoids

• Wei Chen, Zhejiang University
• Song Zhang, Mississippi State University
• Stephen Correia, Brown University
• David Tate, Harvard University
• 22 April 2009, Beijing

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Background

• Diffusion Tensor Imaging (DTI)
• Water diffusion in biological tissues.
• Indirect information about the integrity of the
  underlying white matter.

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Diffusion Tensors

• Primary diffusion direction

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Fractional anisotropy

• Degree of anisotropy
• -represents the deviation from
• isotropic diffusion

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Tensor at (155,155,30)
Diffusion tensor 10(-3) 0.5764 -0.3668
0.1105 -0.3668 0.8836 -0.1152
0.1105 -0.1152 0.8373 Eigenvalue
0.0003 0.0008
0.0012 Eigenvector
0.8375 -0.1734 0.5182 0.5432 0.3669
-0.7552 -0.0592 0.9140 0.4015 Primary
diffusion direction (0.5182 -0.7552
0.4015)
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FA at (155,155,30)
Diffusion tensor 10(-3) 0.5764 -0.3668
0.1105 -0.3668 0.8836 -0.1152
0.1105 -0.1152 0.8373 Eigenvalue
0.0003 0.0008
0.0012 FA 0.5133
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Tensor Displayed as Ellipsoid
anisotropic
isotropic
Courtesy G. Kindlmann
?1 ?2 ?3
?1 gt ?2 gt ?3
?1 gt ?2 ?3
Eigenvectors define alignment of axes
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• Glyphs
• Shows entire diffusion tensor information
• Topography information may be lost or difficult
  to interpret
• Too many glyphs ? visual clutter too few ? poor
  representation

• Integral Curves
• Show topography
• Lost information because a tensor is reduced to a
  vector
• Error accumulates over curves

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Our contributions

• A merging ellipsoid method for DTI visualization.
• Place ellipsoids on the paths of DTI integral
  curves.
• Merge them to get a smooth representation
• Allows users to grasp both white matter
  topography/connectivity AND local tensor
  information.
• Also allows the removal of ellipsoids by using
  the same method used to cull redundant fibers.

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Methods
1) Compute diffusion tensors
2) Compute integral curves
p(0) the initial point e1 major vector
field p(t) generated curve
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Methods
3) Sampling an integral curve, and place an
elliptical function at each si
Streamball method Hagen1995 employs spherical
functions
?1 ?2 ?3, e1 e2 e3
4) Construct a metaball function
R truncation radius, si is the center of the
ith ellipitical function. a -40/90 b
170/90 c -220/90.
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Methods
5) Define a scalar influence field
6) The merging ellipsoids representation denotes
an isosurface extracted from a scalar influence
field F(S x)
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Methods
Visualizing eight diffusion tensors along an
integral curve with (a) glyphs, (b) standard
spherical streamballs Hagen1995, and (c)
merging ellipsoids
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Parameters

• The degree of merging or separation depends on
  three factors.
• 1st the iso-value C adjusted interactively
• Shows merging or un-merging
• 2nd the truncation radius R
• 3rd the placement of the ellipsoids.
• Currently, uniform sampling

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Parameters
Visualizing eight diffusion tensors with
different iso-values (a) 0.01, (b) 0.25, (c)
0.51, (d) 0.75, (e) 0.85, (f) 0.95. The
truncation radius R is 1.0.
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Parameters
The results with different truncation radii (a)
0.3, (b) 0.5, (c) 1.0. In all cases, the
iso-value is 0.5.
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Properties

• The entire merging ellipsoid representation is
  smooth.
• A diffusion tensor produces one elliptical
  surface.
• When two diffusion tensors are close, their
  ellipsoids tend to merge smoothly. If they
  coincide, a larger ellipsoid is generated.
• Provide iso-value parameters for users to
  interactively change sizes of ellipsoids.
• Larger ellipsoids merge with neighbors and
  provide a sense of connectivity
• Smaller provide better sense of individual
  tensors but has limited connectivity information

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Comparison

• If the three eigenvectors are set as identical,
  our method becomes the standard streamball
  approach.
• If a sequence of ellipsoids are continuously
  distributed along an integral curve, the
  hyperstreamline representation is yielded.
• An individual elliptical function can be extended
  into other superquadratic functions, yielding the
  glyph based DTI visualization representation.

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Experiments

• Scalar field pre-computed
• Running time dependent on the grid resolution and
  number of tensors
• Construction costs 15 minutes to 150 minutes with
  the volume dimension of 2563.
• Visualization of ellipsoids done interactively
• Reconstruction of isosurface takes 0.5 seconds
  using un-optimized software implementation.

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Experiments

• DTI data from adult healthy control participant
  (age gt 55).
• DTI protocol
• b 0, 1000 mm/s2
• 12 directions
• 1.5 Tesla Siemens
• Experimental results performed on laptop P4 2.2
  GHz CPU 2G host memory.

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• Box 34mm3
• Minimum path distance 1.7mm
• Anatomic structures and relationships between
  tensors

axial
coronal
sagittal
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• Box 17mm3
• Min path distance 3.4mm
• b streamtubes
• c ellipsoids
• d merging ellipsoids
• Note greater detail in d

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• Same ROI
• Different iso-values
• a 0.90
• b 0.80
• c 0.60
• d 0.40
• Different emphases on local diffusion tensor info
  vs. connectivity info

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• Forceps major
• Box 17mm3
• Min path distance 3.4mm
• Renderings
• b streamtubes
• c ellipsoids
• d merging ellipsoids
• More isotropic tensors vs. corpus callosum
• Change from high to low anisotropy on same fiber
  seen with merging ellipsoid method

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• Differences between tensors on a single curve.
• Blue more anisotropic
• Red more isotropic
• Improves ability to identify problematic fibers
  or problematic sections on a curve

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Evaluation

• Identify regions within a fiber that has low
  anisotropy and thus might be problematic.
• Normal anatomy (e.g., crossing fibers)?
• Injured?
• At risk?
• Adjunct to conventional quantitative tractography
  methods

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Evaluation

• Adjunct to conventional quantitative tractography
  methods
• Activate merging ellipsoids after tract selection
  to visually evaluate and select fibers with low
  or high anisotropy, even if length is same

• Group comparison and statistical correlation with
  cognitive and/or behavioral measures
• May reveal effects otherwise masked by larger
  number of normal fibers in the tract-of-interest

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Conclusions

• A simple method for simultaneous visualization of
  connectivity and local tensor information in DTI
  data.
• Interactive adjustment to enhance information
  about local anisotropy.
• Full spectrum from individual glyphs to
  continuous curves

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Future Directions

• Statistical tests
• Cingulum bundle in vascular cognitive impairment
• Association with apathy?
• Circularity?
• Select fibers at risk based on visual inspection
  and then enter into statistical models?
• Intra-individual variability
• Inter-individual variability
• Interhemispheric differences

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Acknowledgements

• This work is partially supported by NSF of China
  (No.60873123), the Research Initiation Program at
  Mississippi State University.

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Distance between integral curves
s The arc length of shorter curve s0, s1
starting end points of s dist(s) shortest
distance from location s on the shorter curve to
the longer curve. Tt ensures two trajectories
labeled different if they differ significantly
over any portion of the arc length.