José Manuel García Aznar

External bone remodeling through boundary elements and damage mechanics

The most recent advances in external bone remodeling are shown using strain energy density (SED) and damage mechanics variables as stimulus functions. The Boundary Element Method (BEM) is used to obtain the tractions and displacements in each iteration.In this paper it is assumed that the level of damage and the strain energy near the periosteum and endosteum control the external bone remodeling response in the cortical of long bones. The boundary is modified as a function of time and the numerical analysis is solved through the method before mentioned for each variation of the boundary coordinates, then the geometry is evaluated and adapted. Smoothing techniques are used ([β-spline surfaces) to prevent sudden variations in the boundary that may hinder a solution convergence. To validate this model a numerical example is shown with previously validated experimental data from other authors.

Numerical simulation of solid deformation driven by creeping flow using an immersed finite element method

An immersed finite element method for solid–fluid interaction is presented with application focus on highly deformable elastic bodies in a Stokes flow environment. The method is based on a global balance equation which combines the solid and fluid momentum balances, the fluid mass balance and, in weak form, the interface conditions. By means of an Updated Lagrangian description for finite elasticity, only one analysis mesh is used, where the solid particles are backtracked in order to preserve the deformation history. The method results in a full coupling of the solid-fluid system which is solved by an exact Newton method. The location of the material interface is captured by a signed distance function and updated according to the computed displacement increments and the help of an explicit surface parameterisation; no body-fitted volume meshes are needed. Special emphasis is placed on the accurate integration of finite elements traversed by the interface and the related numerical stability of the shape function basis. A number of applications for compressible Neo-Hookean solids subject to creeping flow are presented, motivated by microfluidic experimentation in mechanobiology.

Involvement of Cellular Prion Protein in α-Synuclein Transport in Neurons

The cellular prion protein, encoded by the gene Prnp, has been reported to be a receptor of β-amyloid. Their interaction is mandatory for neurotoxic effects of β-amyloid oligomers. In this study, we aimed to explore whether the cellular prion protein participates in the spreading of α-synuclein. Results demonstrate that Prnp expression is not mandatory for α-synuclein spreading. However, although the pathological spreading of α-synuclein can take place in the absence of Prnp, α-synuclein expanded faster in PrPC-overexpressing mice. In addition, α-synuclein binds strongly on PrPC-expressing cells, suggesting a role in modulating the effect of α-synuclein fibrils.

An unstructured immersed finite element method for nonlinear solid mechanics

We present an immersed finite element technique for boundary-value and interface problems from nonlinear solid mechanics. Its key features are the implicit representation of domain boundaries and interfaces, the use of Nitsche’s method for the incorporation of boundary conditions, accurate numerical integration based on marching tetrahedrons and cut-element stabilisation by means of extrapolation. For discretisation structured and unstructured background meshes with Lagrange basis functions are considered. We show numerically and analytically that the introduced cut-element stabilisation technique provides an effective bound on the size of the Nitsche parameters and, in turn, leads to well-conditioned system matrices. In addition, we introduce a novel approach for representing and analysing geometries with sharp features (edges and corners) using an implicit geometry representation. This allows the computation of typical engineering parts composed of solid primitives without the need of boundary-fitted meshes.

An affine micro-sphere based constitutive model, accounting for junctional sliding, can capture F-actin network mechanics

Actin filaments are a major component of the cytoskeleton and play a crucial role in cell mechanotransduction. F-actin networks can be reconstituted in vitro and their mechanical behaviour has been studied experimentally. Constitutive models that assume an idealised network structure, in combination with a non-affine network deformation, have been successful in capturing the elastic response of the network. In this study, an affine network deformation is assumed, in which we propose an alternative 3D finite strain constitutive model. The model makes use of a micro-sphere to calculate the strain energy density of the network, which is represented as a continuous distribution of filament orientations in space. By incorporating a simplified sliding mechanism at the filament-to-filament junctions, premature filament locking, inherent to affine network deformation, could be avoided. The model could successfully fit experimental shear data for a specific cross-linked F-actin network, demonstrating the potential of the novel model.

Localized tissue mineralization regulated by bone remodelling: A computational approach

Bone is a living tissue whose main mechanical function is to provide stiffness, strength and protection to the body. Both stiffness and strength depend on the mineralization of the organic matrix, which is constantly being remodelled by the coordinated action of the bone multicellular units (BMUs). Due to the dynamics of both remodelling and mineralization, each sample of bone is composed of structural units (osteons in cortical and packets in cancellous bone) created at different times, therefore presenting different levels of mineral content. In this work, a computational model is used to understand the feedback between the remodelling and the mineralization processes under different load conditions and bone porosities. This model considers that osteoclasts primarily resorb those parts of bone closer to the surface, which are younger and less mineralized than older inner ones. Under equilibrium loads, results show that bone volumes with both the highest and the lowest levels of porosity (cancellous and cortical respectively) tend to develop higher levels of mineral content compared to volumes with intermediate porosity, thus presenting higher material densities. In good agreement with recent experimental measurements, a boomerang-like pattern emerges when plotting apparent density at the tissue level versus material density at the bone material level. Overload and disuse states are studied too, resulting in a translation of the apparent–material density curve. Numerical results are discussed pointing to potential clinical applications.