The measure of diffusion skewness and kurtosis in magnetic resonance imaging

Xinzhen Zhang, Chen Ling, Liqun Qi, Ed Xuekui Wu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

5 Citations (Scopus)


The diffusion tensor imaging (DTI) model is an important magnetic resonance imaging (MRI) model in biomedical engineering. It assumes that the water molecule displacement distribution is a Gaussian function. However, water movement in biological tissue is often non-Gaussian and this non-Gaussian behavior may contain useful biological and clinical information. In order to overcome this drawback, a new MRI model, the generalized diffusion tensor imaging (GDTI) model, was presented in [8]. In the GDTI model, even order tensors reflect the magnitude of the signal, while odd order tensors reflect the phase of the signal. In this paper, we propose to use the apparent skewness coefficient (ASC) value to measure the phase of non-Gaussian signals. We prove that the ASC values are invariant under rotations of co-ordinate systems. We discuss some further properties of the diffusion kurtosis tensor and present some preliminary numerical experiments for calculating the ASC values.
Original languageEnglish
Pages (from-to)391-404
Number of pages14
JournalPacific Journal of Optimization
Issue number2
Publication statusPublished - 1 May 2010


  • Eigenvalues
  • Generalized diffusion tensor imaging
  • Kurtosis
  • Signal processing
  • Skewness

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Control and Optimization


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