Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지
DOI QR코드

DOI QR Code

MEDICAL IMAGE ANALYSIS USING HIGH ANGULAR RESOLUTION DIFFUSION IMAGING OF SIXTH ORDER TENSOR

  • K.S. DEEPAK (Department of Mathematics, Alva's College) ;
  • S.T. AVEESH (Department of Mathematics, PES Institute of Technology and Management)
  • Received : 2022.08.23
  • Accepted : 2022.12.17
  • Published : 2023.05.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, the concept of geodesic centered tractography is explored for diffusion tensor imaging (DTI). In DTI, where geodesics has been tracked and the inverse of the fourth-order diffusion tensor is inured to determine the diversity. Specifically, we investigated geodesic tractography technique for High Angular Resolution Diffusion Imaging (HARDI). Riemannian geometry can be extended to a direction-dependent metric using Finsler geometry. Euler Lagrange geodesic calculations have been derived by Finsler geometry, which is expressed as HARDI in sixth order tensor.

Keywords

Acknowledgement

The authors wish to express their sincere thanks to the reviewer for the valuable suggestions.

References

  1. N. Sepasian, H.M. Jan, T. Boonkkamp, Luc M.J. Florack, Bart M. Ter Haar Romeny and Anna Vilanova, Riemann-FinslerMulti-valued Geodesic Tractography for HARDI. Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data, Springer, Berlin, Heidelberg, 2014, 209-225.
  2. L. Astola, Multi-Scale Riemann-Finsler Geometry Applications to Diffusion Tensor Imaging and High Angular Resolution Diffusion Imaging, Ph.D. Thesis , Eindhoven University of Technology, the Netherlands, 2010.
  3. I. Aganj, C. Lenglet, and G. Sapiro, ODF reconstruction in q-ball imaging with solid angle consideration, Proceedings of the Sixth IEEE International Symposium on Biomedical Imaging 47 (2009), 392-397.
  4. L. Astola and L. Florack, Finsler geometry on higher order tensor fields and applications to high angular resolution diffusion imaging, International Journal of Computer Vision 42 (2011), 325-336. https://doi.org/10.1007/s11263-010-0377-z
  5. D.E. Blarr, Inversion Theory and Conformal Mapping, American Mathematical Society, Proceedings, 2000.
  6. S. Chern, Z. Shen, Lectures on Finsler geometry, Nankai Tracts Math. 25 (2003), 63-76,139-147,203-215.
  7. M. Descoteaux, High angular resolution diffusion MRI: from local estimation to segmentation and tractography, Ph.D. Thesis, Universite de Nice, Sophia Antipolis, 2005.
  8. M. Descoteaux, E. Angelino, S. Fitzgibbons, R. DericheR, Regularized, fast and robust analytical q-ballimaging, Magn. Reson. Med. 58 (2007), 498-508. https://doi.org/10.1002/mrm.21277
  9. A. Tristan Vega, C.F. Westin, S. Aja-Farnandez, Estimation of fiber orientation probability density functions in high angular resolution diffusion imaging, Neuro Image 47 (2009), 638-650. https://doi.org/10.1016/j.neuroimage.2009.04.049
  10. P.J. Basser, J. Mattiello, R. Turner, D. LeBihan, Diffusion tensor echo-planar imaging of human brain, Proceedings of the SMRM 56 (1993), 584-592.
  11. P.J. Basser, J. Mattiello, D. Lebihan, Estimation of the effective self-diffusion tensor from the NMR spin echo, Journal of Magnetic Resonance Series B 103 (1994), 247-254. https://doi.org/10.1006/jmrb.1994.1037
  12. P.J. Basser, J. Mattiello, D. Lebihan, MR diffusion tensor spectroscopy and imaging, Biophysical Journal 66 (1994), 259-267. https://doi.org/10.1016/S0006-3495(94)80775-1