Accuracy barriers in mesh adaptation

The convergence rate of the approximation of a non-smooth, typically discontinuous function can be made higher than usual when an adaptative mesh refinement strategy is applied (in contrast to the uniform mesh refinemen- t). But, for isotropic mesh refinement, this order can be limited to d/p(d-1) for the L^p norm and a space dimension d

Global and directional activation maps for cardiac mapping in electrophysiology

Abstract Cardiac mapping is a necessary step for accurate diagnostics in cardiology. I

Finite volume scheme based on cell-vertex reconstructions for anisotropic diffusion problems with discontinuous coefficients

We propose a new second-order finite volume scheme for non-homogeneous and anisotropic diffusion problems based on cell to vertex reconstructions involving minimization of functionals to provide the coefficients of the cell to vertex mapping. The method handles complex situations such as large preconditioning number diffusion matrices and very distorted meshes. Numerical examples are provided to show the effectiveness of the method

Failure of human rhombic lip differentiation underlies medulloblastoma formation

Medulloblastoma (MB) comprises a group of heterogeneous paediatric embryonal neoplasms of the hindbrain with strong links to early development of the hindbrain 1–4. Mutations that activate Sonic hedgehog signalling lead to Sonic hedgehog MB in the upper rhombic lip (RL) granule cell lineage 5–8. By contrast, mutations that activate WNT signalling lead to WNT MB in the lower RL 9,10. However, little is known about the more commonly occurring group 4 (G4) MB, which is thought to arise in the unipolar brush cell lineage 3,4. Here we demonstrate that somatic mutations that cause G4 MB converge on the core binding factor alpha (CBFA) complex and mutually exclusive alterations that affect CBFA2T2, CBFA2T3, PRDM6, UTX and OTX2. CBFA2T2 is expressed early in the progenitor cells of the cerebellar RL subventricular zone in Homo sapiens, and G4 MB transcriptionally resembles these progenitors but are stalled in developmental time. Knockdown of OTX2 in model systems relieves this differentiation blockade, which allows MB cells to spontaneously proceed along normal developmental differentiation trajectories. The specific nature of the split human RL, which is destined to generate most of the neurons in the human brain, and its high level of susceptible EOMES +KI67 + unipolar brush cell progenitor cells probably predisposes our species to the development of G4 MB

Exponential multistep ODE solvers for stiff problems : convergence and stability analysis

Exponential multistep ODE solvers for stiff problems : convergence and stability analysi

Progress towards an electro-mechanical model of the heart for cardiac image analysis

We present a 3D numerical model of the heart ventricles which couples electrical and biomechanical activities. We have adopted a simpler formulation of previously published models to achieve a trade-off between biological accuracy and computational efficiency. To carry out computations, the FitzHugh-Nagumo equations are solved along with a constitutive law based on the Hill-Maxwell rheological law. Ultimately, the parameters of this generic model will be adjusted from the actual patient’s ECG and from the cardiac motion measured in 4D cardiac images. By including biological and physical a priori knowledge, we expect to extract quantitative ventricular function parameters from time sequences of cardiac images 1. 1

Optimized Schwarz algorithms in the framework of DDFV schemes

We are interested in this paper in anisotropic diffusion problems of the form −div(A∇u) = f on Ω; u=0 on ∂Ω. (1) A discretization of the Schwarz algorithm using Discrete Duality Finite Volume methods (DDFV for short) for such problems was developed in [3]. The DDF