| Popis: |
The Theory of Porous Media is applied in this thesis to two different biomechanical problems. First, a computational model of the diabetic foot is developed by taking advantage of patient specific geometries and time-dependent loads experimentally measured. Differently from the state-of-the-art hyperelastic behavior, the plantar tissue is modelled as a fully saturated porohyperelastic porous medium. In this way, time becomes a variable with a real physical meaning, allowing to consider the peculiarities of the subject specific gait cycles. In addition, thanks to the two different phases constituting the medium (i.e. solid and fluid phases), total stress can be split into interstitial fluid pressure and effective stress contributions. Thus, the position and the value of peaks is different, whether total or effective stress are considered, and the peaks in effective counterparts are increasing with the number of gait cycles, as a result of the fluid-structure interaction. By taking advantage of these results we hypothesized that the development of the ulceration phenomenon in the diabetic foot is guided by the excess of an average effective pressure limit. Due to the lack in literature of specific ulceration triggering stress value, maximum average pressure values found for a healthy subject are used as triggering values for the diabetic foot model. As a result, the development of the ulcers within the plantar tissue is mimicked, showing ulcer positions that are in good agreement with the one observed by clinicians. The second application is the scaffold for the spinal fusion: starting from experimental results, a computational model of tissue differentiation is developed, guided by mechanical stimuli applied. The model obtained is capable to predict the tissue formation in post-surgery period, reducing the velocity of tissue transformation depending on stress values found in literature. It can be used by clinicians as a tool for defining subject specific scaffold dimensions and after surgery loading guidelines. The last biomechanical application is the three layer composite scaffold for the articular defect repair. Due to the complexity of the problem, a scaffold with final tissue developed is taken into account and its behavior as a function of loads applied is studied. By taking advantage of the experimental loads from the diabetic foot, we hypothesized to place the scaffold in a knee joint. Thus, it is loaded with vertical and shear loads, studying the development of effective stresses and interstitial fluid pressure within the domain. The numerical results allowed us to suggest an enhancement of the composite scaffold configuration, to avoid stress peaks patterns in the bone layer of the scaffold. The Theory of Porous Media allowed us to make a step forward with respect to the state of the art modelling in different biomechanical fields, by developing computational models that can be used by physicians as effective tools in conjunction with experimental results. |
