Random noise in Diffusion Tensor Imaging, its Destructive Impact and Some Corrections

The empirical origin of random noise is described, its influence on DTI variables is illustrated by a review of numerical and in vivo studies supplemented by new simulations investigating high noise levels. A stochastic model of noise propagation is presented to structure noise impact in DTI. Finally, basics of voxelwise and spatial denoising procedures are presented. Recent denoising procedures are reviewed and consequences of the stochastic model for convenient denoising strategies are discussed

On Quantifying Local Geometric Structures of Fiber Tracts

International audienceIn diffusion MRI, fiber tracts, represented by densely distributed 3D curves, can be estimated from diffusion weighted images using tractography. The spatial geometric structure of white matter fiber tracts is known to be complex in human brain, but it carries intrinsic information of human brain. In this paper, inspired by studies of liquid crystals, we propose tract-based director field analysis (tDFA) with total six rotationally invariant scalar indices to quantify local geometric structures of fiber tracts. The contributions of tDFA include: 1) We propose orientational order (OO) and orientational dispersion (OD) indices to quantify the degree of alignment and dispersion of fiber tracts; 2) We define the local orthogonal frame for a set of unoriented curves, which is proved to be a generalization of the Frenet frame defined for a single oriented curve; 3) With the local orthogonal frame, we propose splay, bend, and twist indices to quantify three types of orientational distortion of local fiber tracts, and a total distortion index to describe distortions of all three types. The proposed tDFA for fiber tracts is a generalization of the voxel-based DFA (vDFA) which was recently proposed for a spherical function field (i.e., an ODF field). To our knowledge, this is the first work to quantify orientational distortion (splay, bend, twist, and total distortion) of fiber tracts. Experiments show that the proposed scalar indices are useful descriptors of local geometric structures to visualize and analyze fiber tracts

Generalized Wishart processes for interpolation over diffusion tensor fields

Diffusion Magnetic Resonance Imaging (dMRI) is a non-invasive tool for watching the microstructure of fibrous nerve and muscle tissue. From dMRI, it is possible to estimate 2-rank diffusion tensors imaging (DTI) fields, that are widely used in clinical applications: tissue segmentation, fiber tractography, brain atlas construction, brain conductivity models, among others. Due to hardware limitations of MRI scanners, DTI has the difficult compromise between spatial resolution and signal noise ratio (SNR) during acquisition. For this reason, the data are often acquired with very low resolution. To enhance DTI data resolution, interpolation provides an interesting software solution. The aim of this work is to develop a methodology for DTI interpolation that enhance the spatial resolution of DTI fields. We assume that a DTI field follows a recently introduced stochastic process known as a generalized Wishart process (GWP), which we use as a prior over the diffusion tensor field. For posterior inference, we use Markov Chain Monte Carlo methods. We perform experiments in toy and real data. Results of GWP outperform other methods in the literature, when compared in different validation protocols

Phase II trial of raltitrexed ('Tomudex') in advanced small-cell lung cancer.

Raltitrexed, a thymidylate synthase inhibitor, was given to 21 patients with advanced small-cell lung cancer, at a dose of 3 mg m(-2) as a 15-min intravenous infusion at 21-day intervals. All of the patients had extensive disease and 17 had received prior therapy. Patients with disease refractory to primary chemotherapy were excluded. Forty-one treatment cycles were given (median two, range one to four). The drug was well tolerated. No objective tumour response was documented. The patients had chemoresistant disease, as shown by a response in only one of ten patients who went on to receive alternative cytotoxic regimens. We conclude that raltitrexed given in this schedule is inactive as second line therapy for small-cell lung cancer

Measuring latency distribution of transcallosal fibers using transcranial magnetic stimulation

Background: Neuroimaging technology is being developed to enable non-invasive mapping of the latency distribution of cortical projection pathways in white matter, and correlative clinical neurophysiological techniques would be valuable for mutual verification. Interhemispheric interaction through the corpus callosum can be measured with interhemispheric facilitation and inhibition using transcranial magnetic stimulation. Objective: To develop a method for determining the latency distribution of the transcallosal fibers with transcranial magnetic stimulation. Methods: We measured the precise time courses of interhemispheric facilitation and inhibition with a conditioning-test paired-pulse magnetic stimulation paradigm. The conditioning stimulus was applied to the right primary motor cortex and the test stimulus was applied to the left primary motor cortex. The interstimulus interval was set at 0.1 ms resolution. The proportions of transcallosal fibers with different conduction velocities were calculated by measuring the changes in magnitudes of interhemispheric facilitation and inhibition with interstimulus interval. Results: Both interhemispheric facilitation and inhibition increased with increment in interstimulus interval. The magnitude of interhemispheric facilitation was correlated with that of interhemispheric inhibition. The latency distribution of transcallosal fibers measured with interhemispheric facilitation was also correlated with that measured with interhemispheric inhibition. Conclusions: The data can be interpreted as latency distribution of transcallosal fibers. Interhemispheric interaction measured with transcranial magnetic stimulation is a promising technique to determine the latency distribution of the transcallosal fibers. Similar techniques could be developed for other cortical pathways

Rational invariants of even ternary forms under the orthogonal group

In this article we determine a generating set of rational invariants of minimal cardinality for the action of the orthogonal group $\mathrm{O}_3$ on the space $\mathbb{R}[x,y,z]_{2d}$ of ternary forms of even degree $2d$. The construction relies on two key ingredients: On one hand, the Slice Lemma allows us to reduce the problem to dermining the invariants for the action on a subspace of the finite subgroup $\mathrm{B}_3$ of signed permutations. On the other hand, our construction relies in a fundamental way on specific bases of harmonic polynomials. These bases provide maps with prescribed $\mathrm{B}_3$-equivariance properties. Our explicit construction of these bases should be relevant well beyond the scope of this paper. The expression of the $\mathrm{B}_3$-invariants can then be given in a compact form as the composition of two equivariant maps. Instead of providing (cumbersome) explicit expressions for the $\mathrm{O}_3$-invariants, we provide efficient algorithms for their evaluation and rewriting. We also use the constructed $\mathrm{B}_3$-invariants to determine the $\mathrm{O}_3$-orbit locus and provide an algorithm for the inverse problem of finding an element in $\mathbb{R}[x,y,z]_{2d}$ with prescribed values for its invariants. These are the computational issues relevant in brain imaging.Comment: v3 Changes: Reworked presentation of Neuroimaging application, refinement of Definition 3.1. To appear in "Foundations of Computational Mathematics

Fiber-Flux Diffusion Density for White Matter Tracts Analysis: Application to Mild Anomalies Localization in Contact Sports Players

We present the concept of fiber-flux density for locally quantifying white matter (WM) fiber bundles. By combining scalar diffusivity measures (e.g., fractional anisotropy) with fiber-flux measurements, we define new local descriptors called Fiber-Flux Diffusion Density (FFDD) vectors. Applying each descriptor throughout fiber bundles allows along-tract coupling of a specific diffusion measure with geometrical properties, such as fiber orientation and coherence. A key step in the proposed framework is the construction of an FFDD dissimilarity measure for sub-voxel alignment of fiber bundles, based on the fast marching method (FMM). The obtained aligned WM tract-profiles enable meaningful inter-subject comparisons and group-wise statistical analysis. We demonstrate our method using two different datasets of contact sports players. Along-tract pairwise comparison as well as group-wise analysis, with respect to non-player healthy controls, reveal significant and spatially-consistent FFDD anomalies. Comparing our method with along-tract FA analysis shows improved sensitivity to subtle structural anomalies in football players over standard FA measurements

DeepTract: A Probabilistic Deep Learning Framework for White Matter Fiber Tractography

We present DeepTract, a deep-learning framework for estimating white matter fibers orientation and streamline tractography. We adopt a data-driven approach for fiber reconstruction from diffusion weighted images (DWI), which does not assume a specific diffusion model. We use a recurrent neural network for mapping sequences of DWI values into probabilistic fiber orientation distributions. Based on these estimations, our model facilitates both deterministic and probabilistic streamline tractography. We quantitatively evaluate our method using the Tractometer tool, demonstrating competitive performance with state-of-the art classical and machine learning based tractography algorithms. We further present qualitative results of bundle-specific probabilistic tractography obtained using our method. The code is publicly available at: https://github.com/itaybenou/DeepTract.git

Topography of the Chimpanzee Corpus Callosum

The corpus callosum (CC) is the largest commissural white matter tract in mammalian brains, connecting homotopic and heterotopic regions of the cerebral cortex. Knowledge of the distribution of callosal fibers projecting into specific cortical regions has important implications for understanding the evolution of lateralized structures and functions of the cerebral cortex. No comparisons of CC topography in humans and great apes have yet been conducted. We investigated the topography of the CC in 21 chimpanzees using high-resolution magnetic resonance imaging (MRI) and diffusion tensor imaging (DTI). Tractography was conducted based on fiber assignment by continuous tracking (FACT) algorithm. We expected chimpanzees to display topographical organization similar to humans, especially concerning projections into the frontal cortical regions. Similar to recent studies in humans, tractography identified five clusters of CC fibers projecting into defined cortical regions: prefrontal; premotor and supplementary motor; motor; sensory; parietal, temporal and occipital. Significant differences in fractional anisotropy (FA) were found in callosal regions, with highest FA values in regions projecting to higher-association areas of posterior cortical (including parietal, temporal and occipital cortices) and prefrontal cortical regions (p<0.001). The lowest FA values were seen in regions projecting into motor and sensory cortical areas. Our results indicate chimpanzees display similar topography of the CC as humans, in terms of distribution of callosal projections and microstructure of fibers as determined by anisotropy measures