Visualizing Diffusion Tensor Imaging Data with Merging Ellipsoids
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Visualizing Diffusion Tensor Imaging Data with Merging Ellipsoids
Wei Chen, Zhejiang UniversitySong Zhang, Mississippi State University
Stephen Correia, Brown UniversityDavid 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
1321
3
2
1
3211 )()(
eeeeeeEE
DDD
DDD
DDD
D
zzzyzx
yzyyyx
xzxyxx
)(max)(3
1k
kiii reigenvectoe
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Fractional anisotropy
• Degree of anisotropy
-represents the deviation from
isotropic diffusion
10)()()(
2
3
3:
23
22
21
23
22
21
321
FA
let
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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 0.0012Eigenvector: 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
λ1 = λ2 = λ3 λ1 > λ2 > λ3 λ1 > λ2 = λ3
isotropic anisotropic
Eigenvectors define alignment of axes
Courtesy: G. Kindlmann
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• Integral Curves– Show topography– Lost information because
a tensor is reduced to a vector
– Error accumulates over curves
• Glyphs– Shows entire diffusion tensor
information– Topography information may
be lost or difficult to interpret– Too many glyphs visual
clutter; too few poor representation
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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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Methods1) 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
4) Construct a metaball function:
R = truncation radius, si is the center of the ith ellipitical function. a = −4:0/9:0; b = 17:0/9:0; c = −22:0/9:0.
3) Sampling an integral curve, and place an elliptical function at each si :
Streamball method [Hagen1995] employs spherical functions
λ1 = λ2 = λ3, e1 = e2 = e3
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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 > 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
sagittal coronal
coronalcoronal
sagittalsagittal
axialaxial
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• Box = 17mm3
• Min path distance = 3.4mm
• b = streamtubes
• c = ellipsoids
• d = merging ellipsoids
• Note greater detail in d
coronalcoronal
sagittalsagittal
axialaxial
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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
axialaxial
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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 curves0, s1 = starting & end points of sdist(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.