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Visualizing Diffusion Tensor Imaging Data with Merging Ellipsoids

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Title: Visualizing Diffusion Tensor Imaging Data with Merging Ellipsoids


1
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

2
Background
  • Diffusion Tensor Imaging (DTI)
  • Water diffusion in biological tissues.
  • Indirect information about the integrity of the
    underlying white matter.

3
Diffusion Tensors
  • Primary diffusion direction

4
Fractional anisotropy
  • Degree of anisotropy
  • -represents the deviation from
  • isotropic diffusion

5
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)
6
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
7
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
8
  • 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

9
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.

10
Methods
1) Compute diffusion tensors
2) Compute integral curves
p(0) the initial point e1 major vector
field p(t) generated curve
11
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.
12
Methods
5) Define a scalar influence field
6) The merging ellipsoids representation denotes
an isosurface extracted from a scalar influence
field F(S x)
13
Methods
Visualizing eight diffusion tensors along an
integral curve with (a) glyphs, (b) standard
spherical streamballs Hagen1995, and (c)
merging ellipsoids
14
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

15
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.
16
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.
17
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

18
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.

19
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.

20
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.

21
  • Box 34mm3
  • Minimum path distance 1.7mm
  • Anatomic structures and relationships between
    tensors

axial
coronal
sagittal
22
  • Box 17mm3
  • Min path distance 3.4mm
  • b streamtubes
  • c ellipsoids
  • d merging ellipsoids
  • Note greater detail in d

23
  • 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

24
  • 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

25
  • 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

26
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

27
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

28
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

29
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

30
Acknowledgements
  • This work is partially supported by NSF of China
    (No.60873123), the Research Initiation Program at
    Mississippi State University.

31
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.
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