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

Background• Diffusion Tensor Imaging (DTI)

– Water diffusion in biological tissues.

– Indirect information about the integrity of the underlying white matter.

Diffusion Tensors

Primary diffusion direction

1321

3

2

1

3211 )()(

eeeeeeEE

DDD

DDD

DDD

D

zzzyzx

yzyyyx

xzxyxx

)(max)(3

1k

kiii reigenvectoe

Fractional anisotropy

• Degree of anisotropy

-represents the deviation from

isotropic diffusion

10)()()(

2

3

3:

23

22

21

23

22

21

321

FA

let

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)

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

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

isotropic anisotropic

Eigenvectors define alignment of axes

Courtesy: G. Kindlmann

• 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

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.

Methods1) Compute diffusion tensors:

2) Compute integral curves:

p(0) = the initial point

e1 = major vector field

p(t) = generated curve

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

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

axial

sagittal coronal

coronalcoronal

sagittalsagittal

axialaxial

• Box = 17mm3

• Min path distance = 3.4mm

• b = streamtubes

• c = ellipsoids

• d = merging ellipsoids

• Note greater detail in d

coronalcoronal

sagittalsagittal

axialaxial

• 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

axialaxial

• 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• 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

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

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 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.