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Title: Mathematical Modeling of Refractive Surgery of Eyes with Comprehensive Mathematical Description
Authors: Khan, Fareeha Sami
Keywords: Physical Sciences
Issue Date: 2021
Publisher: Federal Urdu University of Arts Sciences & Tech. Islamabad
Abstract: Vision plays a vital position in every aspect and phase of life in a modern com munity based upon the ability of seeing. Vision is the most powerful of the five senses and plays the significant part in many facets of our lives. Interpersonal and social experiences are central to face-to-face contact where information is communicated by non-verbal signs such as movements and facial expressions. Often few of us can’t clearly see distant or surrounding objects and have a vision disability. These vision disabilities require medical attention such as refractive surgery or Keratoplasty etc. Within this research, three mathematical models have been established. First model is a system of ordinary differential equation that predicts the effects of Descemet’s Stripping Endothelial Keratoplasty (DSEK) on eyes utilizing four ocular parameters interrelationship. The uniqueness and existence of its solutions were also confirmed and for this concept, steady states were addressed. This mathe matical model is validated and implemented on different ethnicities. Their findings are described graphically and in tabular representations. Questions answered about DSEK model are: ≫ To study the Keratoplasty of eyes by a system of ordinary differential equation by using the relationship among ocular parameters of anterior segment of eye instead of geometrical/statistical models. ≫ To construct and validate a mathematical model that can predict the changes in ocular parameters after Keratoplasty. ≫ Analyze the results of DSEK Mathematical model on data of different ethnic ities. Second mathematical model is a variation of the DSEK model that involves polyno mials of Zernike to analyze the ocular aberrations that occur during the refractive process. The uniqueness and existence of its solutions have also been confirmed, ix and for this concept, steady states have also been studied. This mathematical model is tested and extended to different ethnicities, too. Their results have been presented graphically and in table forms. Questions answered about DSEK model are: ≫ To modify the DSEK mathematical model for a medical condition called Aberration that occur as a side effect of refractive surgery. ≫ To check what type of aberration DSEK model can detect? ≫ Analyze the results of modified DSEK Mathematical model (EK model) on data of different ethnicities. ≫ To check which race is more likely to develop ocular aberration after En dothelial Keratoplasty. Third mathematical model is indeed a system of ordinary differential equation while it uses for computation the shape of the cornea. In this model a new equation of the cornea is created and used based on its shape. Its stability and steady states are discussed. Its findings have also been confirmed by the literature of previously published. Following are the questions to be answered in this work: ≫ To construct and validate another modified mathematical model that can predict the changes in ocular parameters after refractive surgery considering the shape of cornea that plays a major role in refractive surgery. ≫ Discuss the stability of modified DSEK mathematical model and obtain an equation for refractive power of eye. Above mentioned models have been constructed using the concepts of eye surgery and are dynamical non linear mathematical models. They are deterministic math ematical models and hence solved numerically using a mathematical software known as “Mathematica”.
Gov't Doc #: 23151
Appears in Collections:PhD Thesis of All Public / Private Sector Universities / DAIs.

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