Geometric Assessment of Structural Coherence in DTI

Geometric Assessment of Structural Coherence in DTI • Xavier Tricoche1, Gordon Kindlmann2, Christoph Garth3 (1) SCI Institute, University of Utah (2) LMI, Harvard Medical School (3) University of Kaiserslautern

Motivation • Extract and characterize structural contents of DT images • “salient”, “coherent” structures in fibrous tissue • simplified representations for visual inspection • cardiac tissue  brain white matter • derive quantitative information for statistical analysis • “comparative study in health and disease” (cf. Jim’s talk)

DTI Post-processing • Tractography: from tensors to fibers • Weinstein and Kindlmann, IEEE Visualization ’99 • Zhukov and Barr, IEEE Visualization ’02, ’03 • Hlawitschka and Scheuermann, IEEE Visualization ‘05 • Application to clustering and segmentation • Brun et al., MICCAI ‘04

DTI Post-processing • Mostly applied to the brain white matter • Growing interest in DTI to study cardiac tissue architecture • Zhukov and Barr, IEEE Visualization ’03 • Hsu et al., Magn. Reson. Med. ’04 • Helms et al., Magn. Reson. Med. ’05, Circ. Res. ’06

Tensor Structure Definitions • Topology • Delmarcelle, IEEE Visualization ’94 • Tricoche, Zheng, Pang, Tensor Dagstuhl ‘04

Tensor Structure Definitions • Creases of anisotropy, Kindlmann et al., MICCAI ‘06

Alternative Approach • Combine tractography and crease-based method • Value at each point defined w.r.t. properties of fibers • Global behavior attached to local attribute • Define local coherence in terms of geometric similarity of neighboring fiber pathways • Boundaries = locations where neighboring fibers exhibit incoherent behaviors • Quantitative assessment: crease extraction

Quantifying Coherence • Bidirectional flow map: • Jacobian computation at each point • Requires consistent orientation of neighboring fibers • Impossible to do globally (in general) • Done locally on-the-fly along with numerical derivative computation Integration length seed 2 end points

Quantifying Coherence • Dispersion measured in each direction as spectral norm of corresponding Jacobian • Need symmetric measure in the (arbitrary) local choice of orientation: • Integration length is used to control the scale of the extracted structures

Implementation • Dense set of fibers integrated from vertices of regular grid • Upsampling with respect to resolution of DTI scan • Numerical integration using RK4 and GK’s Teem (tensorlines) • Jacobian of flow map computed at each point • Comparison of initial eigenvector direction to assign consistent orientation • Least Squares fit over 26 direct neighbors

Results

Future Work • Study second eigenvector • Identify coherent laminar structure in cardiac tissue • Investigate impact of fiber length on structures • Properly incorporate information about inhomogeneous fiber lengths in quantification of dispersion • Crease extraction • Computational speed

Acknowledgments • Teem library: http://teem.sourceforge.net • Ed Hsu, University of Utah • Center for Integrative Biomedical Computing, NIH NCRR Project 2-P41-RR12553-07

Geometric Assessment of Structural Coherence in DTI