Principal invariants and inherent parameters of diffusion kurtosis tensors

Liqun Qi, Deren Han, Ed X. Wu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

28 Citations (Scopus)


A diffusion kurtosis (DK) tensor is a fourth order three-dimensional fully symmetric tensor, which is used in diffusion kurtosis imaging (DKI), a new model in medical engineering. To understand the biological and clinical meaning of the DK tensor, we have to measure and calculate some quantities and parameters which are independent from coordinate system choices. In this paper we study such quantities and parameters. They include the largest, the smallest and the average apparent kurtosis coefficients (AKC) values, which are invariant from the coordinate system choices, and some parameters measured in the inherent coordinate system, which is formed by the eigenvector system of the second order diffusion tensor. We study their computational formulas and relationships.
Original languageEnglish
Pages (from-to)165-180
Number of pages16
JournalJournal of Mathematical Analysis and Applications
Issue number1
Publication statusPublished - 1 Jan 2009


  • Average apparent kurtosis coefficient values
  • Diffusion kurtosis tensors
  • Eigenvalues
  • Inherent parameters
  • Invariants

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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