A study of the mechanical behaviour of the human aortic artery by means of non-linear finite element models

En la presente tesis desarrollamos una estrategia para la simulación numérica del comportamiento mecánico de la aorta humana usando modelos de elementos finitos no lineales. Prestamos especial atención a tres aspectos claves relacionados con la biomecánica de los tejidos blandos. Primero, el análisis del comportamiento anisótropo característico de los tejidos blandos debido a las familias de fibras de colágeno. Segundo, el análisis del ablandamiento presentado por los vasos sanguíneos cuando estos soportan cargas fuera del rango de funcionamiento fisiológico. Y finalmente, la inclusión de las tensiones residuales en las simulaciones en concordancia con el experimento de apertura de ángulo. El análisis del daño se aborda mediante dos aproximaciones diferentes. En la primera aproximación se presenta una formulación de daño local con regularización. Esta formulación tiene dos ingredientes principales. Por una parte, usa los principios de la teoría de la fisura difusa para garantizar la objetividad de los resultados con diferentes mallas. Por otra parte, usa el modelo bidimensional de Hodge-Petruska para describir el comportamiento mesoscópico de los fibriles. Partiendo de este modelo mesoscópico, las propiedades macroscópicas de las fibras de colágeno son obtenidas a través de un proceso de homogenización. En la segunda aproximación se presenta un modelo de daño no-local enriquecido con el gradiente de la variable de daño. El modelo se construye a partir del enriquecimiento de la función de energía con un término que contiene el gradiente material de la variable de daño no-local. La inclusión de este término asegura una regularización implícita de la implementación por elementos finitos, dando lugar a resultados de las simulaciones que no dependen de la malla. La aplicabilidad de este último modelo a problemas de biomecánica se estudia por medio de una simulación de un procedimiento quirúrgico típico conocido como angioplastia de balón. In the present thesis we develop a framework for the numerical simulation of the mechanical behaviour of the human aorta using non-linear finite element models. Special attention is paid to three key aspects related to the biomechanics of soft tissues. First, the modelling of the characteristic anisotropic behaviour of the softue due to the collagen fibre families. Secondly, the modelling of damage-related softening that blood vessels exhibit when subjected to loads beyond their physiological range. And finally, the inclusion of the residual stresses in the simulations in accordance with the opening-angle experiment The modelling of damage is addressed with two major and different approaches. In the first approach a continuum local damage formulation with regularisation is presented. This formulation has two principal ingredients. On the one hand, it makes use of the principles of the smeared crack theory to avoid the mesh size dependence of the structural response in softening. On the other hand, it uses a Hodge-Petruska bidimensional model to describe the fibrils as staggered arrays of tropocollagen molecules, and from this mesoscopic model the macroscopic material properties of the collagen fibres are obtained using an homogenisation process. In the second approach a non-local gradient-enhanced damage formulation is introduced. The model is built around the enhancement of the free energy function by means of a term that contains the referential gradient of the non-local damage variable. The inclusion of this term ensures an implicit regularisation of the finite element implementation, yielding mesh-objective results of the simulations. The applicability of the later model to biomechanically-related problems is studied by means of the simulation of a typical surgical procedure, namely, the balloon angioplasty.

A study of the non-uniform convergence of the inverse of a doubly-infinite matrix associated with a boundary value problem in a waveguide /

"Contract AF33(616)-6079 Project No. 9-(13-6278), Task No. 40572. Sponsored by: Aeronautical Systems Division"

Wave velocity method of depth determination for non-uniform short crested wave systems by aerial photography /

Mode of access: Internet.

Correlation of non-uniform protein expression with variation in transmitter release probability

The strength of synaptic transmission is highly variable between different synapses. The present study examined some factors that may contribute to this variation in the strength of neurotransmission in sympathetic varicosities of the mouse vas deferens. Transmitter release was measured using a focal macropatch electrode placed over pairs of visualised varicosities. By regulating the calcium concentration of the solutions inside the recording electrode and in the bath independently of each other, transmitter release was restricted to one or two surface varicosities at each recording site. Using this technique, transmitter release probability was shown to be highly variable, even between adjacent varicosities on single axon branches. Very little variation was observed in the calcium influx following single impulse nerve stimulation between adjacent Oregon Green BAPTA-1 loaded varicosities. However, the staining intensities of three vesicular proteins, SV2, synaptophysin, and synaptotagmin 1, showed considerable variation between adjacent varicosities on single axon branches. This variation in staining intensity may be partly explained by variation in the density of synaptic vesicles. However, double staining experiments using two vesicular antigens showed some varicosities staining for one vesicular antigen, but not for the second, suggesting that the expression of these release machinery proteins is regulated locally within the varicosities. The results of the present study strengthen suggestions that synaptic strength is at least in part, regulated by variation in the expression of vesicular proteins. (C) 2004 Wiley-Liss, Inc.

Sparse signal representation by adaptive non-uniform B-spline dictionaries on a compact interval

Non-uniform B-spline dictionaries on a compact interval are discussed in the context of sparse signal representation. For each given partition, dictionaries of B-spline functions for the corresponding spline space are built up by dividing the partition into subpartitions and joining together the bases for the concomitant subspaces. The resulting slightly redundant dictionaries are composed of B-spline functions of broader support than those corresponding to the B-spline basis for the identical space. Such dictionaries are meant to assist in the construction of adaptive sparse signal representation through a combination of stepwise optimal greedy techniques.

Impact of design of sharp non-uniform fibre Bragg gratings on system performance

The impact of design of sharp non-uniform fiber Bragg gratings on system performance was presented. The evolution of the Q-value of the worst channel against the propagation distance was shown. The results suggested that to apply approximated flat-dispersion gratings as inline filters in a periodic system, some post-compensation was included to account for the extra dispersion introduced by the gratings.

Caputo Derivatives in Viscoelasticity: A Non-Linear Finite-Deformation Theory for Tissue

Mathematics Subject Classification: 26A33, 74B20, 74D10, 74L15