The measure of diffusion skewness and kurtosis in magnetic resonance imaging

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.