M. Doblaré

Mechanical Stresses in Abdominal Aortic Aneurysms: Influence of Diameter, Asymmetry, and Material Anisotropy

Biomechanical studies suggest that one determinant of abdominal aortic aneurysm (AAA) rupture is related to the stress in the wall. In this regard, a reliable and accurate stress analysis of an in vivo AAA requires a suitable 3D constitutive model. To date, stress analysis conducted on AAA is mainly driven by isotropic tissue models. However, recent biaxial tensile tests performed on AAA tissue samples demonstrate the anisotropic nature of this tissue. The purpose of this work is to study the influence of geometry and material anisotropy on the magnitude and distribution of the peak wall stress in AAAs. Three-dimensional computer models of symmetric and asymmetric AAAs were generated in which the maximum diameter and length of the aneurysm were individually controlled. A five parameter exponential type structural strain-energy function was used to model the anisotropic behavior of the AAA tissue. The anisotropy is determined by the orientation of the collagen fibers (one parameter of the model). The results suggest that shorter aneurysms are more critical when asymmetries are present. They show a strong influence of the material anisotropy on the magnitude and distribution of the peak stress. Results confirm that the relative aneurysm length and the degree of aneurysmal asymmetry should be considered in a rupture risk decision criterion for AAAs.

On scaffold designing for bone regeneration: A computational multiscale approach

Scaffold design for bone tissue engineering applications involves many parameters that directly influence the rate of bone tissue regeneration onto its microstructural surface. To improve scaffold functionality, increasing interest is being focused on in vitro and in vivo research in order to obtain the optimal scaffold design for a specific application. However, the evaluation of the effect of each specific scaffold parameter on tissue regeneration using these techniques requires costly protocols and long-term experiments. In this paper, we elucidate the effect of some scaffold parameters on bone tissue regeneration by means of a mathematically based approach. By virtue of in silico experiments, factors such as scaffold stiffness, porosity, resorption kinetics, pore size and pre-seeding are analyzed in a specific bone tissue application found in the literature. The model predicts the in vivo rate of bone formation within the scaffold, the scaffold degradation and the interaction between the implanted scaffold and the surrounding bone. Results show an increasing rate of bone regeneration with increasing scaffold stiffness, scaffold mean pore size and pre-seeding, whereas the collapse of the scaffold occurs for a faster biomaterial resorption kinetics. Requiring further experimental validation, the model can be useful for the assessment of scaffold design and for the analysis of scaffold parameters in tissue regeneration.

Biomechanical modeling of refractive corneal surgery.

The aim of refractive corneal surgery is to modify the curvature of the cornea to improve its dioptric properties. With that goal, the surgeon has to define the appropriate values of the surgical parameters in order to get the best clinical results, i.e., laser and geometric parameters such as depth and location of the incision, for each specific patient. A biomechanical study before surgery is therefore very convenient to assess quantitatively the effect of each parameter on the optical outcome. A mechanical model of the human cornea is here proposed and implemented under a finite element context to simulate the effects of some usual surgical procedures, such as photorefractive keratectomy (PRK), and limbal relaxing incisions (LRI). This model considers a nonlinear anisotropic hyperelastic behavior of the cornea that strongly depends on the physiological collagen fibril distribution. We evaluate the effect of the incision variables on the change of curvature of the cornea to correct myopia and astigmatism. The obtained results provided reasonable and useful information in the procedures analyzed. We can conclude from those results that this model reasonably approximates the corneal response to increasing pressure. We also show that tonometry measures of the IOP underpredicts its actual value after PRK or LASIK surgery.

Overview and recent advances in natural neighbour galerkin methods

SummaryIn this paper, a survey of the most relevant advances in natural neighbour Galerkin methods is presented. In these methods (also known as natural element methods, NEM), the Sibson and the Laplace (non-Sibsonian) interpolation schemes are used as trial and test functions in a Galerkin procedure. Natural neighbour-based methods have certain unique features among the wide family of so-called meshless methods: a well-defined and robust approximation with no user-defined parameters on non-uniform grids, and the ability to exactly impose essential (Dirichlet) boundary conditions are particularly noteworthy.A comprehensive review of the method is conducted, including a description of the Sibson and the Laplace interpolants in two- and three-dimensions. Application of the NEM to linear and non-linear problems in solid as well as fluid mechanics is studied. Other issues that are pertinent to the vast majority of meshless methods, such as numerical quadrature, imposing essential boundary conditions, and the handling of secondary variables are also addressed. The paper is concluded with some benchmark computations that demonstrate the accuracy and the key advantages of this numerical method.

A finite element model to accurately predict real deformations of the breast

Most surgical procedures in breast plastic surgery are either reconstructive procedures following oncologic interventions (tumorectomy, quadrantectomy, mastectomy ...) or aesthetic ones, both augmentation and reduction. With current techniques, the results of such procedures cannot be fully guaranteed. Usually, surgical planning is based on a photographic and anthropometric study of the breast only. Among others, one of the difficulties that the plastic surgeons have is the noticeable change of the breast shape with the position of the patient. Thus, it is more and more necessary to plan a presurgical methodology to help the plastic surgeon and guarantee the patient a successful result of the intervention. In order to establish a reliable simulation method that could predict a patient-specific outcome after breast surgery, this study started trying to correlate spatial features of the breast between lying and standing up positions. A biomechanical model of breast was proposed and implemented into a finite element context to predict deformations, and from these the breast shape in different positions. The resulting shapes were compared with multimodal images, whereas the breast surface displacements were compared with manually identified landmarks and 3D scanner images. From the results, it can be concluded that the model hereby presented reasonably approximates breast response to gravity forces, therefore providing accurate and useful information to the surgeon planning such surgical procedures.

Three-Dimensional Finite Element Analysis of Several Internal and External Pelvis Fixations

The Finite Element Method (FEM) can be used to analyze very complex geometries, such as the pelvis, and complicated constitutive behaviors, such as the heterogeneous, nonlinear, and anisotropic behavior of bone tissue or the noncompression, nonbending character of ligaments. Here, FEM was used to simulate the mechanical ability of several external and internal fixations that stabilize pelvic ring disruptions. A customized pelvic fracture analysis was performed by computer simulation to determine the best fixation method for each individual treatment. The stability of open-book fractures with external fixations at either the iliac crests or the pelvic equator was similar, and increased greatly when they were used in combination. However, external fixations did not effectively stabilize rotationally and vertically unstable fractures. Adequate stabilization was only achieved using an internal pubis fixation with two sacroiliac screws.

Permeability evaluation of 45S5 Bioglass®-based scaffolds for bone tissue engineering

Permeability is a key parameter for microstructural design of scaffolds, since it is related to their capability for waste removal and nutrients/oxygen supply. In this framework, Darcys experiments were carried out in order to determine the relationship between the pressure drop gradient and the fluid flow velocity in Bioglass-based scaffolds to obtain the scaffolds permeability. Using deionised water as working fluid, the measured average permeability value on scaffolds of 90-95% porosity was 1.96 x 10(-9) m(2). This value lies in the published range of permeability values for trabecular bone.

Mechanical behaviour of synthetic surgical meshes: Finite element simulation of the herniated abdominal wall

The material properties of meshes used in hernia surgery contribute to the overall mechanical behaviour of the repaired abdominal wall. The mechanical response of a surgical mesh has to be defined since the haphazard orientation of an anisotropic mesh can lead to inconsistent surgical outcomes. This study was designed to characterize the mechanical behaviour of three surgical meshes (Surgipro®, Optilene® and Infinit®) and to describe a mechanical constitutive law that accurately reproduces the experimental results. Finally, through finite element simulation, the behaviour of the abdominal wall was modelled before and after surgical mesh implant. Uniaxial loading of mesh samples in two perpendicular directions revealed the isotropic response of Surgipro® and the anisotropic behaviour of Optilene® and Infinit®. A phenomenological constitutive law was used to reproduce the measured experimental curves. To analyze the mechanical effect of the meshes once implanted in the abdomen, finite element simulation of the healthy and partially herniated repaired rabbit abdominal wall served to reproduce wall behaviour before and after mesh implant. In all cases, maximal displacements were lower and maximal principal stresses higher in the implanted abdomen than the intact wall model. Despite the fact that no mesh showed a behaviour that perfectly matched that of abdominal muscle, the Infinit® mesh was able to best comply with the biomechanics of the abdominal wall.

Modeling mechanosensing and its effect on the migration and proliferation of adherent cells.

The behavior of normal adherent cells is influenced by the stiffness of the substrate they are anchored to. Cells are able to detect substrate mechanical properties by actively generating contractile forces and use this information to migrate and proliferate. In particular, the speed and direction of cell crawling, as well as the rate of cell proliferation, vary with the substrate compliance and prestrain. In this work, we present an active mechanosensing model based on an extension of the classical Hills model for skeletal muscle behavior. We also propose a thermodynamical approach to model cell migration regulated by mechanical stimuli and a proliferation theory also depending on the mechanical environment. These contributions give rise to a conceptually simple mathematical formulation with a straightforward and inexpensive computational implementation, yielding results consistent with numerous experiments. The model can be a useful tool for practical applications in biology and medicine in situations where cell-substrate interaction as well as substrate mechanical behavior play an important role, such as the design of tissue engineering applications.

Finite element simulation of arcuates for astigmatism correction

In order to simulate the corneal incisions used to correct astigmatism, a three-dimensional finite element model was generated from a simplified geometry of the anterior half of the ocular globe. A hyperelastic constitutive behavior was assumed for cornea, limbus and sclera, which are collagenous materials with a fiber structure. Due to the preferred orientations of the collagen fibrils, corneal and limbal tissues were considered anisotropic, whereas the sclera was simplified to an isotropic one assuming that fibrils are randomly disposed. The reference configuration, which includes the initial strain distribution that balances the intraocular pressure, is obtained by an iterative process. Then the incisions are simulated. The final positions of the nodes belonging to the incised meridian and to the perpendicular one are fitted by both radii of curvature, which are used to calculate the optical power. The simulated incisions were those specified by Lindstroms nomogram [Chu, Y., Hardten, D., Lindquist, T., Lindstrom, R., 2005. Astigmatic keratotomy. Duanes Ophthalmology. Lippincott Williams and Wilkins, Philadelphia] to achieve 1.5, 2.25, 3.0, 4.5 and 6.0D of astigmatic change, using the next values for the parameters: length of 45 degrees , 60 degrees and 90 degrees , an optical zone of 6mm, single or paired incisions. The model gives results similar to those in Lindstroms nomogram [Chu et al., 2005] and can be considered a useful tool to plan and simulate refractive surgery by predicting the outcomes of different sorts of incisions and to optimize the values for the parameters involved: depth, length, position.