Diffusion tensor magnetic resonance imaging (DT-MRI) is a technique used to quantify the microstructural organization of biological tissues. Multiple images are necessary to reconstruct the tensor data and each acquisition is subject to complex thermal noise. As such, measures of tensor invariants, which characterize components of tensor shape, derived from the tensor data will be biased from their true values. Previous work has examined this bias, but over a narrow range of tensor shape. Herein, we define the mathematics for constructing a tensor from tensor invariants, which permits an intuitive and principled means for building tensors with a complete range of tensor shape and salient microstructural properties. Thereafter, we use this development to evaluate by simulation the effects of noise on characterizing tensor shape over the complete space of tensor shape for three encoding schemes with different SNR and gradient directions. We also define a new framework for determining the distribution of the true values of tensor invariants given their measures, which provides guidance about the confidence the observer should have in the measures. Finally, we present the statistics of tensor invariant estimates over the complete space of tensor shape to demonstrate how the noise sensitivity of tensor invariants varies across the space of tensor shape as well as how the imaging protocol impacts measures of tensor invariants.

The structure of fiber tracts in DT-MRI data presents a challenging problem for visualization and analysis. We derive visualization of such traces from a local coherence measure and achieve much improved visual segmentation. We introduce a coherence measure defined for fiber tracts. This quantitative assessment is based on infinitesimal deviations of neighboring tracts and allows identification and segmentation of coherent fiber regions. We use a hardware-accelerated implementation to achieve interactive visualization on slices and provide several approaches to visualize coherence information. Furthermore, we enhance existing techniques by combining them with coherence. We demonstrate our method on both a canine heart, where the myocardial structure is visualized, and a human brain, where we achieve detailed visualization of major and minor fiber bundles in a quality similar to and exceeding fiber clustering approaches. Our approach allows detailed and fast visualization of important anatomical structures in DT-MRI data sets.