Numerical study of the fluid motion and mixing processes in the vitreous cavity

The vitreous cavity, the largest chamber of the eye, is delimited anteriorly by the lens and posteriorly by the retina and is filled by the vitreous humour. Under normal conditions the vitreous humour has the consistency of a gel, however, typically, with advancing age a disintegration of the gel structure occurs, leading to a vitreous liquefaction. Moreover, after a surgical procedure called vitrectomy the vitreous body may be completely removed and replaced by tamponade fluids. Besides allowing the establishment of an unhindered path of light from the lens to the retina, the vitreous also has important mechanical functions. In particular, it has the role of supporting the retina in contact to the outer layers of the eye, and of acting as a diffusion barrier for molecule transport between the anterior and the posterior segments of the eye. Studying the dynamics of the vitreous induced by eye rotations (saccadic movements) is important in connection of both the above aspects. On the one hand indications exist that the shear stress exerted by the vitreous on the retina may be connected with the occurrence of retinal detachment. On the other hand, if the vitreous motion is intense enough (a situation occurring either when the vitreous is liqueed or when it has been replaced with a uid after vitrectomy), advective transport may be by far more important than diffusion and may have complex characteristics. Advection has indeed been shown to play an important role in the transport phenomena within the vitreous cavity, but, so far, only advection due to the slow overall fluid ux from the anterior to the posterior segments of the eye has been accounted for, while fluid motion due to eye rotations, even if it is generally believed to play an important role, has been invariably disregarded. Some recent contributions have pointed out the importance of accounting for the real vitreous cavity shape in studying uid motion induced by eye rotations. Modelling the vitreous cavity as a deformed sphere, showed that the flow field displays very complex three- dimensional characteristics to which effective fluid mixing is likely to be associated. The purpose of the thesis is to model numerically the motion of the liqueed vitreous within the vitreous cavity induced by different eye movements. Create the model in the Comsol interface, compare the results with theoretical, experimental measurements and do some ow visualizations. Finally show the dependence of the streaming intensity from the amplitude of rotations and the Womersley number .The vitreous cavity, the largest chamber of the eye, is delimited anteriorly by the lens and posteriorly by the retina and is filled by the vitreous humour. Under normal conditions the vitreous humour has the consistency of a gel, however, typically, with advancing age a disintegration of the gel structure occurs, leading to a vitreous liquefaction. Moreover, after a surgical procedure called vitrectomy the vitreous body may be completely removed and replaced by tamponade fluids. Besides allowing the establishment of an unhindered path of light from the lens to the retina, the vitreous also has important mechanical functions. In particular, it has the role of supporting the retina in contact to the outer layers of the eye, and of acting as a diffusion barrier for molecule transport between the anterior and the posterior segments of the eye. Studying the dynamics of the vitreous induced by eye rotations (saccadic movements) is important in connection of both the above aspects. On the one hand indications exist that the shear stress exerted by the vitreous on the retina may be connected with the occurrence of retinal detachment. On the other hand, if the vitreous motion is intense enough (a situation occurring either when the vitreous is liqueed or when it has been replaced with a uid after vitrectomy), advective transport may be by far more important than diffusion and may have complex characteristics. Advection has indeed been shown to play an important role in the transport phenomena within the vitreous cavity, but, so far, only advection due to the slow overall fluid ux from the anterior to the posterior segments of the eye has been accounted for, while fluid motion due to eye rotations, even if it is generally believed to play an important role, has been invariably disregarded. Some recent contributions have pointed out the importance of accounting for the real vitreous cavity shape in studying uid motion induced by eye rotations. Modelling the vitreous cavity as a deformed sphere, showed that the flow field displays very complex three- dimensional characteristics to which effective fluid mixing is likely to be associated. The purpose of the thesis is to model numerically the motion of the liqueed vitreous within the vitreous cavity induced by different eye movements. Create the model in the Comsol interface, compare the results with theoretical, experimental measurements and do some ow visualizations. Finally show the dependence of the streaming intensity from the amplitude of rotations and the Womersley number .

Classification of probability density functions in the framework of Bayes spaces : methods and applications

The process of supervised classification when the data set consists of probability density functions is studied. Due to the relative information contained in densities, it is necessary to convert the functional data analysis methods into an appropriate framework, here represented by the Bayes spaces. This work develops Bayes space counterparts to a set of commonly used functional methods with a focus on classification. Hereby, a clear guideline is provided on how some classification approaches can be adapted for the case of densities. Comparison of the methods is based on simulation studies and real-world applications, reflecting their respective strengths and weaknesses

Simple enough, but not simpler : reconsidering additive logratio coordinates in compositional analysis

Compositional data, multivariate observations carrying relative information, are popularly expressed in additive logratio coordinates which are easily interpretable as they use one of the components as ratioing part to produce pairwise logratios. These coordinates are however oblique and they lead to issues when applying multivariate methods on them, including widely-used techniques such as principal component analysis and linear regression. In this paper we propose a way to redefine alr coordinates with respect to an orthonormal system and we also extend the idea to the case of compositional tables. The new approach is demonstrated in an application to movement behavior data