Tensorlines: advection-diffusion based propagation through diffusion tensor fields

Abstract

Tracking linear features through tensor field datasets is an open research problem with widespread utility in medical and engineering disciplines. Existing tracking methods, which consider only the preferred local diffusion direction as they propagate, fail to accurately follow features as they enter regions of local complexity. This shortcoming is a result of partial voluming; that is, voxels in these regions often contain contributions from multiple features. These combined contributions result in ambiguities when deciding local primary feature orientation based solely on the preferred diffusion direction. In this paper, we introduce a novel feature extraction method, which we term tensorline propagation. Our method resolves the above ambiguity by incorporating information about the nearby orientation of the feature, as well as the anisotropic classification of the local tensor. The nearby orientation information is added in the spirit of an advection term in a standard diffusionbased propagation technique, and has the effect of stabilizing the tracking. To demonstrate the efficacy of tensorlines, we apply this method to the neuroscience problem of tracking white-matter bundles within the brain.

Fiber tracking: principles and strategies – a technical review

“…Deviation from cigar-shape anisotropy 58 The assumption that the direction of the largest principal axis aligns with a single local fiber orientation may not always be true. The most obvious case is when the data reveal two large eigenvalues and one small eigenvalue ( 1 = 2 > 3 ) or, in other words, when a diffusion ellipsoid has a pancake shape rather than a cigar shape.…”

“…38,58 In this approach, called 'tensorline', the incoming line orientation (v in ) is modulated according to the orientation of the diffusion ellipsoid, and the outgoing vector v out is calculated according to the equation, 38 The image in (B) shows examples of streamtube (red) and streamsurface (green) visualization of the tensor ®eld. 59 In (C), density of the streamtube was reduced to reveal internal structures.…”

A framework based on spin glass models for the inference of anatomical connectivity from diffusion‐weighted MR data – a technical review

“…In large crossing areas, the bundle inducing the highest diffusion direction is masking the crossing fascicles. Without highest angular resolution data, this con®guration seems very dif®cult to untangle line approach, namely the tensorlines 23,24 and the pathby-path approach proposed by Tuch et al,12 is the competition between neighboring trajectories. The global optimization gives the system a larger field of view when an ambiguous area has to be untangled.…”

“…The simplest one is the tensor-line method, which partly overcomes partial volume problems through an advection-diffusion based idea: isotropic or flat tensors do not modify the computed trajectory direction. 23,24 Other methods rely on simulations of a large scale diffusion process throughout white matter, either at the random walks level, 25 or at the macroscopic level using partial differential equation frameworks. [26][27][28] The methods mentioned above compute either one trajectory for each given input point (class T), [13][14][15]23 or a map of connectivity probability for each given input area related for instance to the time of arrival of a simulated large scale propagation process (class P).…”

“…23,24 Other methods rely on simulations of a large scale diffusion process throughout white matter, either at the random walks level, 25 or at the macroscopic level using partial differential equation frameworks. [26][27][28] The methods mentioned above compute either one trajectory for each given input point (class T), [13][14][15]23 or a map of connectivity probability for each given input area related for instance to the time of arrival of a simulated large scale propagation process (class P). [25][26][27] Hence, class P methods are able to detect several areas possibly connected to the input area, while branching is difficult to master with class T methods.…”