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

Diffusion Tensors Primary diffusion direction

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

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 0.5764 -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

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

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.

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

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.

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.

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

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

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.

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

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.

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 0.40. The region-ofinterest is the same as in Figure 6.

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

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.

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 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

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.