In vivo Imaging of Kurtosis Tensor Eigenvalues in the Brain at 3 T

Background Diffusion tensor imaging (DTI), a gaussian anisotropic diffusion model, provides mean diffusivity (MD) and fractional anisotropy (FA) metrics that describe diffusion in brain tissue (white and gray matter). However, the widely recognized non-gaussian diffusion behavior in tissue has motivated higher order schemes (q-ball, HARDI, DSI) to accurately describe the tissue structure. In generalized DTI, higher order tensors are invoked to represent the orientational diffusion profile [1-3]. Diffusional kurtosis imaging (DKI) measures the displacement non-gaussianity or “kurtosis” [4,5]. The directionally averaged mean kurtosis (MK) has been shown to be a potentially valuable disease marker in such illnesses as Alzheimer’s and ADHD [6,7]. Recent work has also used kurtosis projections along the diffusion tensor [8], and the kurtosis tensor has been used to estimate the full orientation distribution function (ODF) [9]. Another strategy, analogous to the principal diffusivities of the diffusion tensor, is to seek eigenvalues/tensors/vectors of the kurtosis tensor as its characteristic features. Though this is challenging for a rank-4 object, there are mathematical prescriptions for deriving such parameters [10,11]. The present study employed spectral decomposition [10] of the diffusion kurtosis tensor, in order to understand the kurtosis variation in the brain and supplement tractography techniques. Methods Scans were performed on a healthy volunteer in a full body Siemens Tim Trio 3 T scanner with a 12-channel head coil. DKI data used a twice-refocused bipolar diffusion gradient EPI sequence (2 x 2 x 2.5 mm resolution, 100 x 100 matrix, 50 slices, iPat = 2, 64 directions, b = 0 (11 avgs.) ,1000, 2000 s/mm (2 avgs ea.)) Analysis was performed using code written in Igor Pro. For each direction n̂ , apparent diffusion (D ( n̂ )) and apparent kurtosis (K( n̂ )) were extracted: