A biphasic hyperelastic model for the analysis of fluid and mass transport in brain tissue.

A biphasic hyperelastic finite element model is proposed for the description of the mechanical behavior of brain tissue. The model takes into account finite deformations through an Ogden-type hyperelastic compressible function and a hydraulic conductivity dependent on deformation. The biphasic equations, implemented here for spherical symmetry using an updated Lagrangian algorithm, yielded radial coordinates and fluid velocities that were used with the convective-diffusive equation in order to predict mass transport in the brain. Results of the model were equal to those of a closed-form solution under infinitesimal deformations, however, for a wide range of material parameters, the model predicted important increments in the infusion sphere, reductions of the fluid velocities, and changes in the species content distribution. In addition, high localized deformation and stresses were obtained at the infusion sphere. Differences with the infinitesimal solution may be mainly attributed to geometrical nonlinearities related to the increment of the infusion sphere and not to material nonlinearities.

Simulation of high tensile Poisson's ratios of articular cartilage with a finite element fibril-reinforced hyperelastic model.

Analyses with a finite element fibril-reinforced hyperelastic model were undertaken in this study to simulate high tensile Poisson's ratios that have been consistently documented in experimental studies of articular cartilage. The solid phase was represented by an isotropic matrix reinforced with four sets of fibrils, two of them aligned in orthogonal directions and two oblique fibrils in a symmetric configuration respect to the orthogonal axes. Two distinct hyperelastic functions were used to represent the matrix and the fibrils. Results of the analyses showed that only by considering non-orthogonal fibrils was it possible to represent Poisson's ratios higher than one. Constrains in the grips and finite deformations played a minor role in the calculated Poisson's ratio. This study also showed that the model with oblique fibrils at 45 degrees was able to represent significant differences in Poisson's ratios near 1 documented in experimental studies. However, even considering constrains in the grips, this model was not capable to simulate Poisson's ratios near 2 that have been reported in other studies. The study also confirmed that only with a high relation between the stiffness of the fibers and that of the matrix was it possible to obtain high Poisson's ratios for the tissue. Results suggest that analytical models with a finite number of fibrils are appropriate to represent main mechanical effects of articular cartilage.

A biphasic viscohyperelastic fibril-reinforced model for articular cartilage: formulation and comparison with experimental data.

Experiments in articular cartilage have shown highly nonlinear stress-strain curves under finite deformations, nonlinear tension-compression response as well as intrinsic viscous effects of the proteoglycan matrix and the collagen fibers. A biphasic viscohyperelastic fibril-reinforced model is proposed here, which is able to describe the intrinsic viscoelasticity of the fibrillar and nonfibrillar components of the solid phase, the nonlinear tension-compression response and the nonlinear stress-strain curves under tension and compression. A viscohyperelastic constitutive equation was used for the matrix and the fibers encompassing, respectively, a hyperelastic function used previously for the matrix and a hyperelastic law used before to represent biological connective tissues. This model, implemented in an updated Lagrangian finite element code, displayed good ability to follow experimental stress-strain equilibrium curves under tension and compression for human humeral cartilage. In addition, curve fitting of experimental reaction force and lateral displacement unconfined compression curves showed that the inclusion of viscous effects in the matrix allows the description of experimental data with material properties for the fibers consistent with experimental tensile tests, suggesting that intrinsic viscous effects in the matrix of articular cartilage plays an important role in the mechanical response of the tissue.

A nonlinear biphasic viscohyperelastic model for articular cartilage.

Experiments on articular cartilage have shown nonlinear stress-strain curves under finite deformations as well as intrinsic viscous effects of the solid phase. The aim of this study was to propose a nonlinear biphasic viscohyperelastic model that combines the intrinsic viscous effects of the proteoglycan matrix with a nonlinear hyperelastic constitutive equation. The proposed equation satisfies objectivity and reduces for uniaxial loading to a solid type viscous model in which the actions of the springs are represented by the hyperelastic function proposed by Holmes and Mow [1990. J. Biomechanics 23, 1145-1156.]. Results of the model, that were efficiently implemented in an updated Lagrangian algorithm, were compared with experimental infinitesimal data reported by DiSilverstro and Suh [2001. J. Biomechanics 34, 519-525.] and showed acceptable fitting for the axial force (R(2)=0.991) and lateral displacement (R(2)=0.914) curves in unconfined compression as well as a good fitting of the axial indentation force curve (R(2)=0.982). In addition, the model showed an excellent fitting of finite-deformation confined compression stress relaxation data reported by Ateshian et al. [1997. J. Biomechanics 30, 1157-1164.] and Huang et al. [2005. J. Biomechanics 38, 799-809.] (R(2)=0.993 and R(2)=0.995, respectively). The constitutive equation may be used to represent the mechanical behavior of the proteoglycan matrix in a fiber reinforced model of articular cartilage.

Sistema de fijación externa atlas para tratamiento de fracturas óseas. Características mecánicas de un fijador con seis grados de libertad / External fixation system atlas for bone fracture treatment. Mechanical characterization of a fixation with six degrees of freedom

Se describe un sistema de fijación externa desarrollado en la Universidad del Valle que ofrece una gran versatilidad para diferentes tipos de fracturas, es de costo muy competitivo y cumple los requisitos de estabilidad y rigidez. La base del sistema consiste en una prensa de seis grados de libertad que permite construir configuraciones de doble barra, que brindan buena estabilidad. El sistema está complementado por anillos de aluminio y otros accesorios que permiten configurar desde fijadores monoplanares para fracturas diafisarias hasta fijadores híbridos para tratar fracturas complejas como las del pilón tibial. Se presentan los componentes del sistema, algunas configuraciones típicas, sus caractericas mecánicas realizadas mediante procedimientos computacionales validados experimentalmente en el laboratorio, buscando la matriz de flexibilidad ínterfragmentaria. Los resultados indicaron una rigidez y una estabilidad comparables con las de otros fijadores internacionalmente probados y aceptados, en nuestro medio. Desde el punto de vista biomecánico el sistema está listo para ser probado clínicamente.