Background: Pathophysiological mechanisms that contribute to neurodegeneration in Amyotrophic Lateral Sclerosis (ALS) include oxidative stress and inflammation. We conducted a preliminary study to explore these mechanisms, to discuss their link in ALS, and to determine the feasibility of incorporating this combined analysis into current biomarkers research. Methods: We enrolled 10 ALS patients and 10 controls. We measured the activities of glutathione peroxidase, glutathione reductase, superoxyde dismutase (SOD), and the levels of serum total antioxidant status (TAS), malondialdehyde (MDA), 8-hydroxy-2’-deoxyguanosine (8-OHdG), and glutathione status (e.g. glutathione disulfide, GSSG/reduced glutathione, GSH). We analysed the concentrations of homocysteine, several cytokines, vitamins and metals by standard methods used in routine practice. Results: There was a significant decrease in TAS levels (p=0.027) and increase in 8-OHdG (p=0.014) and MDA (p=0.011) levels in ALS patients. We also observed a significantly higher GSSG/GSH ratio (p=0.022), and IL-6 (p=0.0079) and IL-8 (p=0.009) concentrations in ALS patients. Correlations were found between biological and clinical markers (homosysteine vs. clinical status at diagnosis, p=0.02) and between some biological markers such as IL-6 vs. GSSG/GSH (p=0.045) or SOD activity (p=0.017). Conclusion: We confirmed the systemic alteration of both the redox and the inflammation status in ALS patients, and we observed a link with some clinical parameters. These promising results encourage us to pursue this study with collection of combined oxidative stress and inflammatory markers.

In this article, we investigate numerical schemes for solving a three component Cahn-Hilliard model. The space discretization is performed by using a Galerkin formulation and the finite element method. Concerning the time discretization, the main difficulty is to write a scheme ensuring, at the discrete level, the decrease of the free energy and thus the stability of the method. We study three different schemes and prove existence and convergence theorems. Theoretical results are illustrated by various numerical examples showing that the new semi-implicit discretization that we propose seems to be a good compromise between robustness and accuracy.

This study concerns some asymptotic models used to compute the flow outside and inside fractures in a bidimensional porous medium. The flow is governed by the Darcy law both in the fractures and in the porous matrix with large discontinuities in the permeability tensor. These fractures are supposed to have a small thickness with respect to the macroscopic length scale, so that we can asymptotically reduce them to immersed polygonal fault interfaces and the model finally consists in a coupling between a 2D elliptic problem and a 1D equation on the sharp interfaces modelling the fractures. A cell-centered finite volume scheme on general polygonal meshes fitting the interfaces is derived to solve the set of equations with the additional differential transmission conditions linking both pressure and normal velocity jumps through the interfaces. We prove the convergence of the FV scheme for any set of data and parameters of the models and derive existence and uniqueness of the solution to the asymptotic models proposed. The models are then numerically experimented for highly or partially immersed fractures. Some numerical results are reported showing different kinds of flows in the case of impermeable or partially/highly permeable fractures. The influence of the variation of the aperture of the fractures is also investigated. The numerical solutions of the asymptotic models are validated by comparing them to the solutions of the global Darcy model or to some analytic solutions.

In this paper, we propose a new diffuse interface model for the study of three immiscible component incompressible viscous flows. The model is based on the Cahn-Hilliard free energy approach. The originality of our study lies in particular in the choice of the bulk free energy. We show that one must take care of this choice in order for the model to give physically relevant results. More precisely, we give conditions for the model to be well-posed and to satisfy algebraically and dynamically consistency properties with the two-component models. Notice that our model is also able to cope with some total spreading situations. We propose to take into account the hydrodynamics of the mixture by coupling our ternary Cahn-Hilliard system and the Navier-Stokes equation supplemented by capillary force terms accounting for surface tension effects between the components. Finally, we present some numerical results which illustrate our analysis and which confirm that our model has a better behavior than other possible similar models.

This paper is concerned with the finite volume approximation of the p-Laplacian equation with homogeneous Dirichlet boundary conditions on rectangular meshes. A reconstruction of the norm of the gradient on the mesh's interfaces is needed in order to discretize the p-Laplacian operator. We give a detailed description of the possible nine points schemes ensuring that the solution of the resulting finite dimensional nonlinear system exists and is unique. These schemes, called admissible, are locally conservative and in addition derive from the minimization of a strictly convexe and coercive discrete functional. The convergence rate is analyzed when the solution lies in W2,p. Numerical results are given in order to compare different admissible and non-admissible schemes.