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 Dxx Dxy Dxz 1 D D yx D yy D yz EE 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: 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. 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 • 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 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.