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CLC number: TP391.41

On-line Access: 2012-01-19

Received: 2011-04-17

Revision Accepted: 2011-06-23

Crosschecked: 2011-12-29

Cited: 1

Clicked: 5126

Citations:  Bibtex RefMan EndNote GB/T7714

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Journal of Zhejiang University SCIENCE C 2012 Vol.13 No.2 P.90-98


Diffusion tensor interpolation profile control using non-uniform motion on a Riemannian geodesic

Author(s):  Chang-Il Son, Shun-ren Xia

Affiliation(s):  MOE Key Laboratory of Biomedical Engineering, Zhejiang University, Hangzhou 310027, China; more

Corresponding email(s):   srxia@zju.edu.cn

Key Words:  Diffusion tensor (DT), DT imaging (DTI), DT interpolation, Interpolation profile control, Riemannian geodesic

Chang-Il Son, Shun-ren Xia. Diffusion tensor interpolation profile control using non-uniform motion on a Riemannian geodesic[J]. Journal of Zhejiang University Science C, 2012, 13(2): 90-98.

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T1 - Diffusion tensor interpolation profile control using non-uniform motion on a Riemannian geodesic
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.C1100098

Tensor interpolation is a key step in the processing algorithms of diffusion tensor imaging (DTI), such as registration and tractography. The diffusion tensor (DT) in biological tissues is assumed to be positive definite. However, the tensor interpolations in most clinical applications have used a Euclidian scheme that does not take this assumption into account. Several Riemannian schemes were developed to overcome this limitation. Although each of the Riemannian schemes uses different metrics, they all result in a ‘fixed’ interpolation profile that cannot adapt to a variety of diffusion patterns in biological tissues. In this paper, we propose a DT interpolation scheme to control the interpolation profile, and explore its feasibility in clinical applications. The profile controllability comes from the non-uniform motion of interpolation on the riemannian geodesic. The interpolation experiment with medical DTI data shows that the profile control improves the interpolation quality by assessing the reconstruction errors with the determinant error, Euclidean norm, and Riemannian norm.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1]Alexander, D.C., Barker, G.J., 2005. Optimal imaging parameters for fiber-orientation estimation in diffusion MRI. NeuroImage, 27(2):357-367.

[2]Alexander, D.C., Pierpaoli, C., Basser, P.J., Gee, J.C., 2001. Spatial transformations of diffusion tensor MR images. IEEE Trans. Med. Imag., 20(11):1131-1139.

[3]Arsigny, V., Fillard, P., Pennec, X., Ayache, N., 2006. Log-Euclidean metrics for fast and simple calculus on diffusion tensors. Magn. Reson. Med., 56(2):411-421.

[4]Bansal, R., Staib, L.H., Xu, D.R., Laine, A.F., Royal, J., Peterson, B.S., 2008. Using perturbation theory to compute the morphological similarity of diffusion tensors. IEEE Trans. Med. Imag., 27(5):589-607.

[5]Basser, P.J., Mattiello, J., Bihan, D.L., 1994. MR diffusion tensor spectroscopy and imaging. Biophys. J., 66(1):259-267.

[6]Batchelor, P.G., Moakher, M., Atkinson, D., Calamante, F., Connelly, A., 2005. A rigorous framework for diffusion tensor calculus. Magn. Reson. Med., 53(1):221-225.

[7]Chefd’Hotel, C., Tschumperlé, D., Deriche, R., Faugeras, O., 2004. Regularizing flows for constrained matrix-valued images. J. Math. Imag. Vis., 20(1-2):147-162.

[8]Filley, C.M., 2001. The Behavioral Neurology of White Matter. Oxford University Press, New York, p.299.

[9]Fletcher, P.T., Sarang, J., 2007. Riemannian geometry for the statistical analysis of diffusion tensor data. Signal Process., 87(2):250-262.

[10]Hoptman, M.J., Nierenberg, J., Bertisch, H.C., Catalano, D., Ardekani, B.A., Branch, C.A., DeLisi, L.E., 2008. A DTI study of white matter microstructure in individuals at high genetic risk for schizophrenia. Schizophr. Res., 106(2-3): 115-124.

[11]Jones, D.K., Simmons, A., Williams, S.C.R., Horsfield, M.A., 1999. Non-invasive assessment of axonal fibre connectivity in the human brain via diffusion tensor MRI. Magn. Reson. Med., 42(1):37-41.

[12]Kindlmann, G., Estépar, R.S.J., Niethammer, M., Haker, S., Westin, C.F., 2007. Geodesic-loxodromes for diffusion tensor interpolation and difference measurement. LNCS, 4791:1-9.

[13]Pajevic, S., Basser, P.J., 2003. Parametric and non-parametric statistical analysis of DT-MRI. J. Magn. Reson., 161(1): 1-14.

[14]Peng, H., Orlichenkob, A., Dawe, R.J., Agam, G., Zhang, S., Arfanakis, K., 2009. Development of a human brain diffusion tensor template. NeuroImage, 46(4):967-980.

[15]Pennec, X., Fillard, P., Ayache, N., 2006. A Riemannian framework for tensor computing. Int. J. Comput. Vis., 66(1):41-66.

[16]Roosendaal, S.D., Geurts, J.J.G., Vrenken, H., Hulst, H.E., Cover, K.S., 2009. Regional DTI differences in multiple sclerosis patients. NeuroImage, 44(4):1397-1403.

[17]Schonberg, T., Pianka, P., Hendler, T., Pasternak, O., Assaf, Y., 2006. Characterization of displaced white matter by brain tumors using combined DTI and fMRI. NeuroImage, 30(4):1100-1111.

[18]Snook, L., Plewes, C., Beaulieu, C., 2007. Voxel based versus region of interest analysis in diffusion tensor imaging of neurodevelopment. NeuroImage, 34(1):243-252.

[19]Stejskal, E.O., Tanner, J.E., 1965. Spin diffusion measurements: spin echoes in the presence of a time-dependent field gradient. J. Chem. Phys., 42(1):288-292.

[20]Zhang, H., Yushkevich, P.A., Alexander, D.C., Gee, J.C., 2006. Deformable registration of diffusion tensor MR images with explicit orientation optimization. Med. Image Anal., 10(5):764-785.

[21]Zhou, Y.X., Dougherty, J.H., Hubner, K.F., Bai, B., Cannon, R.L., Hutson, R.K., 2008. Abnormal connectivity in the posterior cingulate and hippocampus in early Alzheimer’s disease and mild cognitive impairment. Alzheim. Dement., 4(4):265-270.

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