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

The impact of signal-to-noise ratio, diffusion-weighted directions and image resolution in cardiac diffusion tensor imaging - insights from the ex-vivo rat heart

Background: Cardiac diffusion tensor imaging (DTI) is limited by scan time and signal-to-noise (SNR) restrictions. This invariably leads to a trade-off between the number of averages, diffusion-weighted directions (ND), and image resolution. Systematic evaluation of these parameters is therefore important for adoption of cardiac DTI in clinical routine where time is a key constraint. Methods: High quality reference DTI data were acquired in five ex-vivo rat hearts. We then retrospectively set 2 ≤ SNR ≤ 97, 7 ≤ ND ≤ 61, varied the voxel volume by up to 192-fold and investigated the impact on the accuracy and precision of commonly derived parameters. Results: For maximal scan efficiency, the accuracy and precision of the mean diffusivity is optimised when SNR is maximised at the expense of ND. With typical parameter settings used clinically, we estimate that fractional anisotropy may be overestimated by up to 13% with an uncertainty of ±30%, while the precision of the sheetlet angles may be as poor as ±31°. Although the helix angle has better precision of ±14°, the transmural range of helix angles may be under-estimated by up to 30° in apical and basal slices, due to partial volume and tapering myocardial geometry. Conclusions: These findings inform a baseline of understanding upon which further issues inherent to in-vivo cardiac DTI, such as motion, strain and perfusion, can be considered. Furthermore, the reported bias and reproducibility provides a context in which to assess cardiac DTI biomarkers

Advances in diffusion MRI acquisition and processing in the Human Connectome Project

The Human Connectome Project (HCP) is a collaborative 5-year effort to map human brain connections and their variability in healthy adults. A consortium of HCP investigators will study a population of 1200 healthy adults using multiple imaging modalities, along with extensive behavioral and genetic data. In this overview, we focus on diffusion MRI (dMRI) and the structural connectivity aspect of the project. We present recent advances in acquisition and processing that allow us to obtain very high-quality in-vivo MRI data, whilst enabling scanning of a very large number of subjects. These advances result from 2 years of intensive efforts in optimising many aspects of data acquisition and processing during the piloting phase of the project. The data quality and methods described here are representative of the datasets and processing pipelines that will be made freely available to the community at quarterly intervals, beginning in 2013

Tractography passes the test: Results from the diffusion-simulated connectivity (disco) challenge.

Estimating structural connectivity from diffusion-weighted magnetic resonance imaging is a challenging task, partly due to the presence of false-positive connections and the misestimation of connection weights. Building on previous efforts, the MICCAI-CDMRI Diffusion-Simulated Connectivity (DiSCo) challenge was carried out to evaluate state-of-the-art connectivity methods using novel large-scale numerical phantoms. The diffusion signal for the phantoms was obtained from Monte Carlo simulations. The results of the challenge suggest that methods selected by the 14 teams participating in the challenge can provide high correlations between estimated and ground-truth connectivity weights, in complex numerical environments. Additionally, the methods used by the participating teams were able to accurately identify the binary connectivity of the numerical dataset. However, specific false positive and false negative connections were consistently estimated across all methods. Although the challenge dataset doesn't capture the complexity of a real brain, it provided unique data with known macrostructure and microstructure ground-truth properties to facilitate the development of connectivity estimation methods

Manufacturing nanostructured YSZ coatings by suspension plasma spraying (SPS) : effect of injection parameters

International audienceThe suspension plasma spraying process is investigated using shadow imaging techniques to appreciate the different trajectories of the liquid jet interacting with a dc high-energy plasma flow. Then, the modelling of different liquid injections (isolated droplet, train of droplets and continuous jet) helps us to determine which injection type must be preferred. From that, coating depositions have been carried out with yttria zirconia suspension. Trajectory deviations at impact have been measured depending on the injection pressure and injection location. Coatings have been realized under the same operating investigations and their microstructures and mechanical properties have been characterize

Analysis by modeling of plasma flow interactions with liquid injection

International audienc

Modelling the interactions between a thermal plasma flow and a continuous liquid jet in a suspension spraying process

International audienc

Modeling liquid suspension injection in a thermal plasma flow for nanomaterial spraying: atomization, mechanical deformation and evaporation

International audienc

Modeling liquid suspension injection in a thermal plasma flow for nanomaterial spraying: atomization, mechanical deformation and evaporation

International audienc