Mathematical Sciences Department Theses and Dissertations

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Browsing Mathematical Sciences Department Theses and Dissertations by Author "Arciero, Julia Concetta"

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    Blood circulation and aqueous humor flow in the eye : multi-scale modeling and clinical applications
    (2016-06-14) Cassani, Simone; Guidoboni, Giovanna; Arciero, Julia Concetta; Harris, Alon
    Glaucoma is a multi-factorial ocular disease associated with death of retinal ganglion cells and irreversible vision loss. Many risk factors contribute to glaucomatous damage, including elevated intraocular pressure (IOP), age, genetics, and other diseases such as diabetes and systemic hypertension. Interestingly, alterations in retinal hemodynamics have also been associated with glaucoma. A better understanding of the factors that contribute to these hemodynamic alterations could lead to improved and more appropriate clinical approaches to manage and hopefully treat glaucoma patients. In this thesis, we develop several mathematical models aimed at describing ocular hemodynamics and oxygenation in health and disease. Precisely we describe: (i) a time-dependent mathematical model for the retinal circulation that includes macrocirculation, microcirculation, phenomenological vascular regulation, and the mechanical effect of IOP on the retinal vasculature; (ii) a steady-state mathematical model for the retinal circulation that includes macrocirculation, microcirculation, mechanistic vascular regulation, the effect of IOP on the central retinal artery and central retinal vein, and the transport of oxygen in the retinal tissue using a Krogh cylinder type model; (iii) a steady-state mathematical model for the transport of oxygen in the retinal microcirculation and tissue based on a realistic retinal anatomy; and (iv) a steady-state mathematical model for the production and drainage of aqueous humor (AH). The main objective of this work is to study the relationship between IOP, systemic blood pressure, and the functionality of vascular autoregulation; the transport and exchange of oxygen in the retinal vasculature and tissue; and the production and drainage of AH, that contributes to the level of IOP. The models developed in this thesis predict that (i) the autoregulation plateau occurs for different values of IOP in hypertensive and normotensive patients. Thus, the level of blood pressure and functionality of autoregulation affect the changes in retinal hemodynamics caused by IOP and might explain the inconsistent outcomes of clinical studies; (ii) the metabolic and carbon dioxide mechanisms play a major role in the vascular regulation of the retina. Thus, the impairment of either of these mechanisms could cause ischemic damage to the retinal tissue; (iii) the multi-layer description of transport of oxygen in the retinal tissue accounts for the effect of the inner and outer retina, thereby improving the predictive ability of the model; (iv) a greater reduction in IOP is obtained if topical medications target AH production rather that AH drainage and if IOP-lowering medications are administrated to patients that exhibit a high initial level of IOP. Thus, the effectiveness of IOP-lowering medications depend on a patient’s value of IOP. In conclusion, the results of this thesis demonstrate that the insight provided by mathematical modeling alongside clinical studies can improve the understanding of diseases and potentially contribute to the clinical development of new treatments.
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    Multiscale mathematical modeling of ocular blood flow and oxygenation and their relevance to glaucoma
    (2016-06-14) Carichino, Lucia; Guidoboni, Giovanna; Harris, Alon; Arciero, Julia Concetta
    Glaucoma is a multifactorial ocular disease progressively leading to irreversible blindness. There is clear evidence of correlations between alterations in ocular hemodynamics and glaucoma; however, the mechanisms giving rise to these correlations are still elusive. The objective of this thesis is to develop mathematical models and methods to help elucidate these mechanisms. First, we develop a mathematical model that describes the deformation of ocular structures and ocular blood flow using a reduced-order fluid-structure interaction model. This model is used to investigate the relevance of mechanical and vascular factors in glaucoma. As a first step in expanding this model to higher dimensions, we propose a novel energy-based technique for coupling partial and ordinary differential equations in blood flow, using operator splitting. Next, we combine clinical data and model predictions to propose possible explanations for the increase in venous oxygen saturation in advanced glaucoma patients. We develop a computer-aided manipulation process of color Doppler images to extract novel waveform parameters to distinguish between healthy and glaucomatous individuals. The results obtained in this work suggest that: 1) the increase in resistance of the retinal microcirculation contributes to the influence of intraocular pressure on retinal hemodynamics; 2) the influence of cerebrospinal fluid pressure on retinal hemodynamics is mediated by associated changes in blood pressure; 3) the increase in venous oxygen saturation levels observed among advanced glaucoma patients depends on the value of the patients’ intraocular pressure; 4) the normalized distance between the ascending and descending limb of the ophthalmic artery velocity profile is significantly higher in glaucoma patients than in healthy individuals.