Although the three examples have identical average diffusion tensors they have different covariance tensors ℂ. In these graphical representations, green is positive, black is zero, and red is negative. The DTD model includes average diffusion tensors, shown by 3×3 matrices, and covariance tensors, shown as 6×6 matrices, along with the scalar invariants from Eqs. The second row shows the DTD model corresponding to each synthetic example. As a consequence, these different structures are indistinguishable with conventional DTI. The first row shows synthetic examples of diffusion tensor distributions within a voxel that yield an isotropic average diffusion tensor 〈 D〉. Synthetic examples of diffusion tensor distributions that cannot be differentiated using conventional SDE-based dMRI sequences such as DTI, HARDI, DSI, and DKI, but can be distinguished using the proposed QTI framework. The ability to measure and model the distribution of diffusion tensors, rather than a quantity that has already been averaged within a voxel, has the potential to provide a powerful paradigm for the study of complex tissue architecture.ĭDE DTI Diffusion MRI Diffusion tensor distribution Microscopic anisotropy Microscopic fractional anisotropy μFA QTI SDE TDE q-space q-space trajectory.Ĭopyright © 2016 Elsevier Inc. The parameter maps derived from QTI were compared between the groups, and 9 out of the 14 parameters investigated showed differences between groups. To demonstrate the feasibility of QTI on a clinical scanner, we performed a small pilot study comparing a group of five healthy controls with five patients with schizophrenia. We derive rotationally invariant scalar quantities describing intuitive microstructural features including size, shape, and orientation coherence measures. The QTI framework has been designed to improve discrimination of the sizes, shapes, and orientations of diffusion microenvironments within tissue. We show that b-tensors of rank 2 or 3 enable estimation of the mean and covariance of the DTD model in terms of a second order tensor (the diffusion tensor) and a fourth order tensor. In our analysis of QTI, we find that the well-known scalar b-value naturally extends to a tensor-valued entity, i.e., a diffusion measurement tensor, which we call the b-tensor. We show that the QTI framework enables microstructure modeling that is not possible with the traditional pulsed gradient encoding as introduced by Stejskal and Tanner. Then we propose a microstructure model, the diffusion tensor distribution (DTD) model, which takes advantage of additional information provided by QTI to estimate a distributional model over diffusion tensors. First we propose q-space trajectory encoding, which uses time-varying gradients to probe a trajectory in q-space, in contrast to traditional pulsed field gradient sequences that attempt to probe a point in q-space. The QTI framework consists of two parts: encoding and modeling. This work describes a new diffusion MR framework for imaging and modeling of microstructure that we call q-space trajectory imaging (QTI).
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