Long-term monitoring of post-stroke plasticity after transient cerebral ischemia in mice using in vivo and ex vivo diffusion tensor MRI.

WE USED A MURINE MODEL OF TRANSIENT FOCAL CEREBRAL ISCHEMIA TO STUDY: 1) in vivo DTI long-term temporal evolution of the apparent diffusion coefficient (ADC) and diffusion fractional anisotropy (FA) at days 4, 10, 15 and 21 after stroke 2) ex vivo distribution of a plasticity-related protein (GAP-43) and its relationship with the ex vivo DTI characteristics of the striato-thalamic pathway (21 days). All animals recovered motor function. In vivo ADC within the infarct was significantly increased after stroke. In the stroke group, GAP-43 expression and FA values were significantly higher in the ipsilateral (IL) striatum and contralateral (CL) hippocampus compared to the shams. DTI tractography showed fiber trajectories connecting the CL striatum to the stroke region, where increased GAP43 and FA were observed and fiber tracts from the CL striatum terminating in the IL hippocampus.Our data demonstrate that DTI changes parallel histological remodeling and recovery of function.

Influence of the implanted pulse generator as reference electrode in finite element model of monopolar deep brain stimulation.

Electrical deep brain stimulation (DBS) is an efficient method to treat movement disorders. Many models of DBS, based mostly on finite elements, have recently been proposed to better understand the interaction between the electrical stimulation and the brain tissues. In monopolar DBS, clinically widely used, the implanted pulse generator (IPG) is used as reference electrode (RE). In this paper, the influence of the RE model of monopolar DBS is investigated. For that purpose, a finite element model of the full electric loop including the head, the neck and the superior chest is used. Head, neck and superior chest are made of simple structures such as parallelepipeds and cylinders. The tissues surrounding the electrode are accurately modelled from data provided by the diffusion tensor magnetic resonance imaging (DT-MRI). Three different configurations of RE are compared with a commonly used model of reduced size. The electrical impedance seen by the DBS system and the potential distribution are computed for each model. Moreover, axons are modelled to compute the area of tissue activated by stimulation. Results show that these indicators are influenced by the surface and position of the RE. The use of a RE model corresponding to the implanted device rather than the usually simplified model leads to an increase of the system impedance (+48%) and a reduction of the area of activated tissue (-15%).

An active strain electromechanical model for cardiac tissue

We propose a finite element approximation of a system of partial differential equations describing the coupling between the propagation of electrical potential and large deformations of the cardiac tissue. The underlying mathematical model is based on the active strain assumption, in which it is assumed that a multiplicative decomposition of the deformation tensor into a passive and active part holds, the latter carrying the information of the electrical potential propagation and anisotropy of the cardiac tissue into the equations of either incompressible or compressible nonlinear elasticity, governing the mechanical response of the biological material. In addition, by changing from an Eulerian to a Lagrangian configuration, the bidomain or monodomain equations modeling the evolution of the electrical propagation exhibit a nonlinear diffusion term. Piecewise quadratic finite elements are employed to approximate the displacements field, whereas for pressure, electrical potentials and ionic variables are approximated by piecewise linear elements. Various numerical tests performed with a parallel finite element code illustrate that the proposed model can capture some important features of the electromechanical coupling, and show that our numerical scheme is efficient and accurate.

A Thermodynamically Consistent Damage Model for Advanced Composites

A continuum damage model for the prediction of damage onset and structural collapse of structures manufactured in fiber-reinforced plastic laminates is proposed. The principal damage mechanisms occurring in the longitudinal and transverse directions of a ply are represented by a damage tensor that is fixed in space. Crack closure under load reversal effects are taken into account using damage variables established as a function of the sign of the components of the stress tensor. Damage activation functions based on the LaRC04 failure criteria are used to predict the different damage mechanisms occurring at the ply level. The constitutive damage model is implemented in a finite element code. The objectivity of the numerical model is assured by regularizing the dissipated energy at a material point using Bazant’s Crack Band Model. To verify the accuracy of the approach, analyses ofcoupon specimens were performed, and the numerical predictions were compared with experimental data

Analysis of diffusion tensor magnetic resonance imaging data using principal component analysis

An analysis method for diffusion tensor (DT) magnetic resonance imaging data is described, which, contrary to the standard method (multivariate fitting), does not require a specific functional model for diffusion-weighted (DW) signals. The method uses principal component analysis (PCA) under the assumption of a single fibre per pixel. PCA and the standard method were compared using simulations and human brain data. The two methods were equivalent in determining fibre orientation. PCA-derived fractional anisotropy and DT relative anisotropy had similar signal-to-noise ratio (SNR) and dependence on fibre shape. PCA-derived mean diffusivity had similar SNR to the respective DT scalar, and it depended on fibre anisotropy. Appropriate scaling of the PCA measures resulted in very good agreement between PCA and DT maps. In conclusion, the assumption of a specific functional model for DW signals is not necessary for characterization of anisotropic diffusion in a single fibre.

A continuum anisotropic model of sea-ice dynamics

We develop the essential ingredients of a new, continuum and anisotropic model of sea-ice dynamics designed for eventual use in climate simulation. These ingredients are a constitutive law for sea-ice stress, relating stress to the material properties of sea ice and to internal variables describing the sea-ice state, and equations describing the evolution of these variables. The sea-ice cover is treated as a densely flawed two-dimensional continuum consisting of a uniform field of thick ice that is uniformly permeated with narrow linear regions of thinner ice called leads. Lead orientation, thickness and width distributions are described by second-rank tensor internal variables: the structure, thickness and width tensors, whose dynamics are governed by corresponding evolution equations accounting for processes such as new lead generation and rotation as the ice cover deforms. These evolution equations contain contractions of higher-order tensor expressions that require closures. We develop a sea-ice stress constitutive law that relates sea-ice stress to the structure tensor, thickness tensor and strain rate. For the special case of empty leads (containing no ice), linear closures are adopted and we present calculations for simple shear, convergence and divergence.

Dimensionality reduction assisted tensor clustering

This paper is concerned with tensor clustering with the assistance of dimensionality reduction approaches. A class of formulation for tensor clustering is introduced based on tensor Tucker decomposition models. In this formulation, an extra tensor mode is formed by a collection of tensors of the same dimensions and then used to assist a Tucker decomposition in order to achieve data dimensionality reduction. We design two types of clustering models for the tensors: PCA Tensor Clustering model and Non-negative Tensor Clustering model, by utilizing different regularizations. The tensor clustering can thus be solved by the optimization method based on the alternative coordinate scheme. Interestingly, our experiments show that the proposed models yield comparable or even better performance compared to most recent clustering algorithms based on matrix factorization.

Joint multiple dictionary learning for tensor sparse coding

Traditional dictionary learning algorithms are used for finding a sparse representation on high dimensional data by transforming samples into a one-dimensional (1D) vector. This 1D model loses the inherent spatial structure property of data. An alternative solution is to employ Tensor Decomposition for dictionary learning on their original structural form —a tensor— by learning multiple dictionaries along each mode and the corresponding sparse representation in respect to the Kronecker product of these dictionaries. To learn tensor dictionaries along each mode, all the existing methods update each dictionary iteratively in an alternating manner. Because atoms from each mode dictionary jointly make contributions to the sparsity of tensor, existing works ignore atoms correlations between different mode dictionaries by treating each mode dictionary independently. In this paper, we propose a joint multiple dictionary learning method for tensor sparse coding, which explores atom correlations for sparse representation and updates multiple atoms from each mode dictionary simultaneously. In this algorithm, the Frequent-Pattern Tree (FP-tree) mining algorithm is employed to exploit frequent atom patterns in the sparse representation. Inspired by the idea of K-SVD, we develop a new dictionary update method that jointly updates elements in each pattern. Experimental results demonstrate our method outperforms other tensor based dictionary learning algorithms.

Tensor regression based on linked multiway parameter analysis

Classical regression methods take vectors as covariates and estimate the corresponding vectors of regression parameters. When addressing regression problems on covariates of more complex form such as multi-dimensional arrays (i.e. tensors), traditional computational models can be severely compromised by ultrahigh dimensionality as well as complex structure. By exploiting the special structure of tensor covariates, the tensor regression model provides a promising solution to reduce the model’s dimensionality to a manageable level, thus leading to efficient estimation. Most of the existing tensor-based methods independently estimate each individual regression problem based on tensor decomposition which allows the simultaneous projections of an input tensor to more than one direction along each mode. As a matter of fact, multi-dimensional data are collected under the same or very similar conditions, so that data share some common latent components but can also have their own independent parameters for each regression task. Therefore, it is beneficial to analyse regression parameters among all the regressions in a linked way. In this paper, we propose a tensor regression model based on Tucker Decomposition, which identifies not only the common components of parameters across all the regression tasks, but also independent factors contributing to each particular regression task simultaneously. Under this paradigm, the number of independent parameters along each mode is constrained by a sparsity-preserving regulariser. Linked multiway parameter analysis and sparsity modeling further reduce the total number of parameters, with lower memory cost than their tensor-based counterparts. The effectiveness of the new method is demonstrated on real data sets.

CMB and LSS constraints on a single-field model of inflation

A new inflationary scenario whose exponential potential V (Phi) has a quadratic dependence on the field Phi in addition to the standard linear term is confronted with the five-year observations of the Wilkinson-Microwave Anisotropy Probe and the Sloan Digital Sky Survey data. The number of e-folds (N), the ratio of tensor-to-scalar perturbations (r), the spectral scalar index of the primordial power spectrum (n(s)) and its running (dn(s)/d ln k) depend on the dimensionless parameter a multiplying the quadratic term in the potential. In the limit a. 0 all the results of the exponential potential are fully recovered. For values of alpha not equal 0, we find that the model predictions are in good agreement with the current observations of the Cosmic Microwave Background (CMB) anisotropies and Large-Scale Structure (LSS) in the Universe. Copyright (C) EPLA, 2008.

Numerical solution of the eXtended Pom-Pom model for viscoelastic free surface flows

In this paper we present a finite difference method for solving two-dimensional viscoelastic unsteady free surface flows governed by the single equation version of the eXtended Pom-Pom (XPP) model. The momentum equations are solved by a projection method which uncouples the velocity and pressure fields. We are interested in low Reynolds number flows and, to enhance the stability of the numerical method, an implicit technique for computing the pressure condition on the free surface is employed. This strategy is invoked to solve the governing equations within a Marker-and-Cell type approach while simultaneously calculating the correct normal stress condition on the free surface. The numerical code is validated by performing mesh refinement on a two-dimensional channel flow. Numerical results include an investigation of the influence of the parameters of the XPP equation on the extrudate swelling ratio and the simulation of the Barus effect for XPP fluids. (C) 2010 Elsevier B.V. All rights reserved.

Numerical Solution of the Upper-Convected Maxwell Model for Three-Dimensional Free Surface Flows

This work presents a finite difference technique for simulating three-dimensional free surface flows governed by the Upper-Convected Maxwell (UCM) constitutive equation. A Marker-and-Cell approach is employed to represent the fluid free surface and formulations for calculating the non-Newtonian stress tensor on solid boundaries are developed. The complete free surface stress conditions are employed. The momentum equation is solved by an implicit technique while the UCM constitutive equation is integrated by the explicit Euler method. The resulting equations are solved by the finite difference method on a 3D-staggered grid. By using an exact solution for fully developed flow inside a pipe, validation and convergence results are provided. Numerical results include the simulation of the transient extrudate swell and the comparison between jet buckling of UCM and Newtonian fluids.

Absence of gluonic components in axial and tensor mesons

A quarkonium-gluonium mixing scheme previously developed to describe the characteristic of the pseudoscalar mesons is applied to axial and tensor mesons. The parameters of the model are determined by fitting the eigenvalues of a mass matrix. The corresponding eigenvectors give the proportion of light quarks, strange quarks and glueball in each meson. However, the predictions of the model for the branching ratios and electromagnetic decays are incompatible with the experimental results. These results suggest the absence of gluonic components in the states of axial and tensor isosinglet mesons analyzed here.

Mass generation for Abelian spin-1 particles via a symmetric tensor

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A new spin-2 self-dual model in D=2+1

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)