Extreme diffusion values for non-Gaussian diffusions

Abstract

A new magnetic resonance imaging (MRI) model, called diffusion kurtosis imaging (DKI), was recently proposed, to characterize the non-Gaussian diffusion behaviour in tissues. DKI involves a fourth-order three-dimensional tensor and a second-order three-dimensional tensor. Similar to those in the diffusion tensor imaging (DTI) model, the extreme diffusion values and extreme directions associated to this tensor pair play important roles in DKI. In this paper, we study the properties of the extreme values and directions associated to such tensor pairs. We also present a numerical method and its preliminary computational results.

Keywords:

• diffusion kurtosis tensors
• extreme diffusion values
• extreme diffusion directions
• anisotropy

Acknowledgements

The authors wish to thank Professor Oleg Burdakov for his encouragement, Professor Regina Burachik and two referees for their comments and help. This work was supported by the Natural Science Foundation of China (Grant No. 10501024), the Natural Science Foundation of Jiangsu province (Grant No. BK2006214), the Hong Kong Research Grant Council, and a Chair Professor Fund of the Hong Kong Polytechnic University.