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)*
Eigenvalue=
0.0003
0.0008
0.0012
Eigenvector:
Primary diffusion direction:
( )

6. FA at (155,155,30) Diffusion tensor: 10^(-3)* 0.5764 -0.3668 0.1105
Eigenvalue=
0.0003
0.0008
0.0012
FA =

7. Tensor Displayed as Ellipsoid
isotropic
anisotropic
Courtesy: G. Kindlmann
λ1 = λ2 = λ3
λ1 > λ2 > λ3
λ1 > λ2 = λ3
Eigenvectors define alignment of axes

8. Glyphs Integral Curves 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. 1) Compute diffusion tensors:
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
λ1 = λ2 = λ3, e1 = e2 = e3
4) Construct a metaball function:
An ellipsoid fx is constructed for each tensor on each curve.
Define a blobby object with respect to the ellipsoid;
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.

12. 5) Define a scalar influence field:
Methods
5) Define a scalar influence field:
6) The merging ellipsoids representation denotes an isosurface extracted from a scalar influence field F(S; x)
Define a scalar influence field which is given as the sum at a give point x of weighted influence functions Ii(x) generated by a set of blobby objects: where ωi denotes the strength of the ith influence function.
4) Compute a global surface representation of the entire diffusion field by extracting the isosurfaces interactively.
Depicts shape and orientation of individual diffusion tensors locally but illustrates connectivity in a smooth, visually plausible fashion.

13. Methods
Merge together in anisotropic regions; separate in isotropic regions.
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
Optimal truncation radius: Dt = distance threshold between curves; Dl is the maximal distance between two consecutive tensors for all curves

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 > 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. Minimum path distance = 1.7mm
Box = 34mm3
Minimum path distance = 1.7mm
Anatomic structures and relationships between tensors
coronal
sagittal
axial
axial
Figure 5: The merging ellipsoids method was applied to the DTI data
of a normal subject. (a) The red box indicates the horizontal view of
the region-of-interest on the fractional anisotropy map of the brain.
(b) The merging ellipsoids capture the connectivity information as
well as the tensor details. (c) Sagittal view of the merging ellipsoids.
(d) Coronal view of the merging ellipsoids.
sagittal
coronal

22. Note greater detail in d
Box = 17mm3
Min path distance = 3.4mm
b = streamtubes
c = ellipsoids
d = merging ellipsoids
Note greater detail in d
coronal
sagittal
axial
Figure 6: Comparison of the integral curves method, the simple ellipsoids
glyph method, and the merging ellipsoids method in a corpus
callosum region of the brain. (a) The red box indicates the horizontal
view of the region-of-interest in the brain. The dimension of the region
is 17mm17mm17mm. (b) The integral curves show the connectivity
information but lack the tensor details. These curves also
accumulate integration error. (c) Ellipsoid glyphs placed on the integral
curves reveal more details in the individual tensors but reduce
the connectivity information. (d) The merging ellipsoids capture the
connectivity information as well as the tensor details.

23. Same ROI Different iso-values
b = 0.80
c = 0.60
d = 0.40
Different emphases on local diffusion tensor info vs. connectivity info
Figure 7: The iso-value parameter was adjusted interactively by the
user to produce a continuous set of merging ellipsoids models that
provide information with different emphases on the connectivity information
and the tensor details. (a), (b), (c), and (d) were produced
by the iso-values set to 0.90, 0.80, 0.60, and The region-ofinterest
is the same as in Figure 6.

24. More isotropic tensors vs. corpus callosum
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
Figure 8: The comparison of the three visualization methods in another
region-of-interest close to the forceps major. (a) The regionof-
interest. (b) The integral curves method. (c) The simple ellipsoid
glyph method. (d) The merging ellipsoids method.
axial

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
Figure 9: This picture shows the difference in tensors along an integral
curve. The blue arrow points to the region where the tensors are
more anisotropic and well aligned while the red arrow points to the
region with more isotropy and uncertainty.

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 Intra-individual variability
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 ), 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.