A Fourth Order Tensor Statistical Model for Diffusion Weighted MRI - Application to Population Comparison

Theodosios Gkamas, Félix Renard, Christian Heinrich, Stéphane Kremer

Abstract

In this communication, we propose an original statistical model for diffusion-weighted magnetic resonance imaging, in order to determine new biomarkers. Second order tensor (T2) modeling of Orientation Distribution Functions (ODFs) is popular and has benefited of specific statistical models, incorporating appropriate metrics. Nevertheless, the shortcomings of T2s, for example for the modeling of crossing fibers, are well identified. We consider here fourth order tensor (T4) models for ODFs, thus alleviating the T2 shortcomings. We propose an original metric in the T4 parameter space. This metric is incorporated in a nonlinear dimension reduction procedure. In the resulting reduced space, we represent the probability density of the two populations, normal and abnormal, by kernel density estimation with a Gaussian kernel, and propose a permutation test for the comparison of the two populations. Application of the proposed model on synthetic and real data is achieved. The relevance of the approach is shown.

References

  1. Arsigny, V., Fillard, P., Pennec, X., and Ayache, N. (2006). Log-Euclidean metrics for fast and simple calculus on diffusion tensors. Magnetic Resonance in Medicine, 56(2):411-421.
  2. Barmpoutis, A., Bing, J., and Vemuri, B. (2009). Adaptive kernels for multi-fiber reconstruction. In Proceedings of the Information Processing in Medical Imaging conference (IPMI), volume 21, pages 338-349.
  3. Barmpoutis, A., Vemuri, B., and Forder, J. (2007). Registration of high angular resolution diffusion MRI images using 4th order tensors. In Int. Conf. on Medical Image Computing and Computer Assisted Intervention (MICCAI), volume 4791 of Lecture Notes in Computer Science, pages 908-915. Springer.
  4. Du, J., Goh, A., Kushnarev, S., and Qiu, A. (2014). Geodesic regression on orientation distribution functions with its application to an aging study. NeuroImage, 87:416-426.
  5. Duarte-Carvajalino, J., Sapiro, G., Harel, N., and Lenglet, C. (2013). A framework for linear and non-linear registration of diffusion-weighted MRIs using angular interpolation. Frontiers in Neuroscience, 7.
  6. Hastie, T., Tibshirani, R., and Friedman, J. (2011). The elements of statistical learning. Springer, second edition.
  7. He, X. and Niyogi, P. (2003). Locality preserving projections. In Advances in Neural Information Processing Systems 16 (NIPS), volume 16, pages 153-160.
  8. He, X., Yan, S., Hu, Y., Niyogi, P., and Zhang, H.-J. (2005). Face recognition using Laplacianfaces. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27(3):328-340.
  9. Horsfield, M. A. and Jones, D. K. (2002). Applications of diffusion-weighted and diffusion tensor MRI to white matter diseases - a review. NMR in Biomedicine, 15(7-8):570-577.
  10. Jenkinson, M., Beckmann, C., Behrens, T., Woolrich, M., and Smith, S. (2012). FSL. NeuroImage, 62(2):782- 790.
  11. Jones, D. K. (2011). Diffusion MRI: theory, methods, and applications. Oxford University Press.
  12. Ozarslan, E. and Mareci, T. H. (2003). Generalized diffusion tensor imaging and analytical relationships between diffusion tensor imaging and high angular resolution diffusion imaging. Magnetic Resonance in Medicine, 50(5):955-965.
  13. Scott, D. (1992). Multivariate Density Estimation: Theory, Practice, and Visualization. Wiley.
  14. Sfikas, G., Constantinopoulos, C., Likas, A., and Galatsanos, N. (2005). An analytic distance metric for Gaussian mixture models with application in image retrieval. In 15th International Conference on Artificial Neural Networks (IEEE ICANN 2005), volume 3697 of Lecture Notes in Computer Science, pages 835-840. Springer.
  15. Smith, S., Jenkinson, M., Johansen-Berg, H., Rueckert, D., Nichols, T., Mackay, C., Watkins, K., Ciccarelli, O., Cader, M. Z., Matthews, P., and Behrens, T. (2006). Tract-based spatial statistics: voxelwise analysis of multi-subject diffusion data. NeuroImage, 31(4):1487 - 1505.
  16. Tao, X. and Miller, J. (2006). A method for registering diffusion weighted magnetic resonance images. In Int. Conf. on Medical Image Computing and Computer Assisted Intervention (MICCAI), volume 4191 of Lecture Notes in Computer Science, pages 594- 602. Springer.
  17. Tarantola, A. (2005). Elements for physics: quantities, qualities, and intrinsic theories. Springer.
  18. Tenenbaum, J. B., Silva, V., and Langford, J. C. (2000). A Global Geometric Framework for Nonlinear Dimensionality Reduction. Science, 290(5500):2319-2323.
  19. Tuch, D. S. (2004). Q-ball imaging. Magnetic Resonance in Medicine, 52(6):1358-1372.
  20. Verma, R., Khurd, P., and Davatzikos, C. (2007). On analyzing diffusion tensor images by identifying manifold structure using isomaps. IEEE Transactions on Medical Imaging, 26(6):772-778.
  21. Weinberger, K. and Saul, L. (2006). Unsupervised learning of image manifolds by semidefinite programming. International Journal of Computer Vision, 70(1):77-90.
  22. Weldeselassie, Y., Barmpoutis, A., and Atkins, M. (2012). Symmetric positive-definite Cartesian tensor fiber orientation distribution (CT-FOD). Medical Image Analysis, 16(6):1121-1129.
Download


Paper Citation


in Harvard Style

Gkamas T., Renard F., Heinrich C. and Kremer S. (2015). A Fourth Order Tensor Statistical Model for Diffusion Weighted MRI - Application to Population Comparison . In Proceedings of the International Conference on Pattern Recognition Applications and Methods - Volume 2: ICPRAM, ISBN 978-989-758-077-2, pages 277-282. DOI: 10.5220/0005252602770282


in Bibtex Style

@conference{icpram15,
author={Theodosios Gkamas and Félix Renard and Christian Heinrich and Stéphane Kremer},
title={A Fourth Order Tensor Statistical Model for Diffusion Weighted MRI - Application to Population Comparison},
booktitle={Proceedings of the International Conference on Pattern Recognition Applications and Methods - Volume 2: ICPRAM,},
year={2015},
pages={277-282},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005252602770282},
isbn={978-989-758-077-2},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Pattern Recognition Applications and Methods - Volume 2: ICPRAM,
TI - A Fourth Order Tensor Statistical Model for Diffusion Weighted MRI - Application to Population Comparison
SN - 978-989-758-077-2
AU - Gkamas T.
AU - Renard F.
AU - Heinrich C.
AU - Kremer S.
PY - 2015
SP - 277
EP - 282
DO - 10.5220/0005252602770282