PVis2009_Talk_merged

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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
Background
• Diffusion Tensor Imaging (DTI)
– Water diffusion in biological
tissues.
integrity of the underlying white
matter.
Diffusion Tensors
 Dxx    Dxy    Dxz                            1         
                    
D   D yx   D yy   D yz   EE 1  (e1 e2   e3 ) 
   2       (e e
 1 2    e3 ) 1
 Dzx    Dzy    Dzz                            
        3 

                    

Primary diffusion direction
3
ei  eigenvector (i )  i  max(k )
k 1
Fractional anisotropy
• Degree of anisotropy
-represents the deviation from
isotropic diffusion

1  2  3
let :  
3
(1   ) 2  (2   ) 2  (3   ) 2
 0 1
3
FA 
2               
2     2
1   2
2
3
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)
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
Tensor Displayed as Ellipsoid
isotropic                               anisotropic

Courtesy: G. Kindlmann

λ1 = λ2 = λ3                λ1 > λ2 > λ3                 λ1 > λ2 = λ3

Eigenvectors define alignment of axes
• Integral Curves               • Glyphs
– Show topography              – Shows entire diffusion tensor
information
– Lost information because
a tensor is reduced to a     – Topography information may
vector                         be lost or difficult to interpret
– Error accumulates over       – Too many glyphs  visual
curves                         clutter; too few  poor
representation
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.
Methods
1) Compute diffusion tensors:

2) Compute integral curves:

p(0) = the initial point

e1 = major vector field

p(t) = generated curve
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:

si is the center of the ith ellipitical function.
a = −4:0/9:0; b = 17:0/9:0; c = −22:0/9:0.
Methods
5) Define a scalar influence field:

6) The merging ellipsoids representation denotes an isosurface
extracted from a scalar influence field F(S; x)
Methods

Visualizing eight diffusion tensors along an integral curve with (a) glyphs, (b)
standard spherical streamballs [Hagen1995], and (c) merging ellipsoids
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
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.
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.
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
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.
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.
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.
• Box = 34mm3
• Minimum path
distance = 1.7mm
• Anatomic
structures and
relationships
between tensors

sagittal                             axial

coronal

axial

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

sagittal

coronal

axial
•   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
•   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
axial
•   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
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
Evaluation
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
Conclusions
• A simple method for simultaneous
visualization of connectivity and local
tensor information in DTI data.
– Full spectrum from individual glyphs to
continuous curves
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
Acknowledgements
• This work is partially supported by NSF of
China (No.60873123), the Research
Initiation Program at Mississippi State
University.
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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