[PDF] Mathematical Models Of Retinal Dynamics eBook

Author : R. Collins
Publisher : Springer Science & Business Media
Page : 111 pages
File Size : 14,53 MB
Release : 2013-03-08
Category : Mathematics
ISBN : 3642501532

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A rich and abundant literature has developed during the last half century dealing with mechanical aspects of the eye, mainly from clinical and, experimental points of view. For the most part, workers have attempted to shed light on the complex set of conditions known by the general term glaucoma. These conditions are characterised by an increase in intraocular pressure sufficient to cause de generation of the optic disc and concomitant defects in the visual field, which, if not controlled, lead to inevitable permanent blindness. In the United States alone, an estimated 50,000 persons are blind as a result of glaucoma, which strikes about 2% of the population over 40 years of age (Vaughan and Asbury, 1974). An understanding of the underlying mechanisms of glaucoma is hindered by the fact that elevated intraocular pressure, like a runny nose, is but a symptom which may have a variety of causes. Only by turning to the initial pathology can one hope to understand this important class of medical problems.

Author : Erika Tatiana Camacho
Publisher :
Page : 134 pages
File Size : 39,3 MB
Release : 2003
Category :
ISBN : 9780496292202

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In this work, we investigate the circadian rhythms of the avian chick eye. Diurnal rhythms in melatonin and dopamine in the retina have been shown to be affected both by a circadian oscillator as well as by changes in local light levels. The Preliminary Models we first consider ignore the influence of the circadian rhythm and do not yield results which agree with the experimental data. The Retinal Oscillator Model is a mathematical formulation of a descriptive model of the nature of the biochemistry of retinal dynamics and is given by: m & d2;= -c1Rt 1-ft m-m0-c2 md, g & d2;= -c3ft g-g0-c6 gd, d & d2;= -c4gd-d0 -c5md. Here m(t) = melatonin concentration, g(t) = glutamate concentration at the amacrine cells, d(t) = dopamine concentration, f(t) is the light load with ft=1 forlightON, ft=0fo rlightOFF, and R(t) is the effect of the circadian rhythm on the melatonin synthesis. The circadian oscillator may be reset by light loadings. We numerically integrate the equations for various light loading and obtain qualitative agreement with the experiments performed with White Leghorn Chicks, thus showing the need of including the circadian oscillator.

Author : Giovanna Guidoboni
Publisher : Springer Nature
Page : 606 pages
File Size : 23,25 MB
Release : 2019-11-25
Category : Mathematics
ISBN : 3030258866

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The chapters in this contributed volume showcase current theoretical approaches in the modeling of ocular fluid dynamics in health and disease. By including chapters written by experts from a variety of fields, this volume will help foster a genuinely collaborative spirit between clinical and research scientists. It vividly illustrates the advantages of clinical and experimental methods, data-driven modeling, and physically-based modeling, while also detailing the limitations of each approach. Blood, aqueous humor, vitreous humor, tear film, and cerebrospinal fluid each have a section dedicated to their anatomy and physiology, pathological conditions, imaging techniques, and mathematical modeling. Because each fluid receives a thorough analysis from experts in their respective fields, this volume stands out among the existing ophthalmology literature. Ocular Fluid Dynamics is ideal for current and future graduate students in applied mathematics and ophthalmology who wish to explore the field by investigating open questions, experimental technologies, and mathematical models. It will also be a valuable resource for researchers in mathematics, engineering, physics, computer science, chemistry, ophthalmology, and more.

Author : William E. Schiesser
Publisher : Academic Press
Page : 144 pages
File Size : 37,93 MB
Release : 2019-06-14
Category : Science
ISBN : 0128184531

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Numerical PDE Analysis of Retinal Neovascularization Mathematical Model Computer Implementation in R provides a methodology for the analysis of neovascularization (formation of blood capillaries) in the retina. It describes the starting point—a system of three partial differential equations (PDEs)—that define the evolution of (1) capillary tip density, (2) blood capillary density and (3) concentration of vascular endothelial growth factor (VEGF) in the retina as a function of space (distance along the retina), x, and time, t, the three PDE dependent variables for (1), (2) and (3), and designated as u1(x, t), u2(x, t), u3(x, t), amongst other topics. Includes PDE routines based on the method of lines (MOL) for computer-based implementation of PDE models Offers transportable computer source codes for readers in R, with line-by-line code descriptions as it relates to the mathematical model and algorithms Authored by a leading researcher and educator in PDE models

Author : Rebecca Segal
Publisher : Springer Nature
Page : 221 pages
File Size : 32,8 MB
Release : 2020-12-29
Category : Mathematics
ISBN : 3030571297

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This volume tackles a variety of biological and medical questions using mathematical models to understand complex system dynamics. Working in collaborative teams of six, each with a senior research mentor, researchers developed new mathematical models to address questions in a range of application areas. Topics include retinal degeneration, biopolymer dynamics, the topological structure of DNA, ensemble analysis, multidrug-resistant organisms, tumor growth modeling, and geospatial modeling of malaria. The work is the result of newly formed collaborative groups begun during the Collaborative Workshop for Women in Mathematical Biology hosted by the Institute of Pure and Applied Mathematics at UCLA in June 2019. Previous workshops in this series have occurred at IMA, NIMBioS, and MBI.

Author : Nikos Paragios
Publisher : Springer Science & Business Media
Page : 648 pages
File Size : 31,72 MB
Release : 2005-10-31
Category : Computers
ISBN : 9780387263717

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Abstract Biological vision is a rather fascinating domain of research. Scientists of various origins like biology, medicine, neurophysiology, engineering, math ematics, etc. aim to understand the processes leading to visual perception process and at reproducing such systems. Understanding the environment is most of the time done through visual perception which appears to be one of the most fundamental sensory abilities in humans and therefore a significant amount of research effort has been dedicated towards modelling and repro ducing human visual abilities. Mathematical methods play a central role in this endeavour. Introduction David Marr's theory v^as a pioneering step tov^ards understanding visual percep tion. In his view human vision was based on a complete surface reconstruction of the environment that was then used to address visual subtasks. This approach was proven to be insufficient by neuro-biologists and complementary ideas from statistical pattern recognition and artificial intelligence were introduced to bet ter address the visual perception problem. In this framework visual perception is represented by a set of actions and rules connecting these actions. The emerg ing concept of active vision consists of a selective visual perception paradigm that is basically equivalent to recovering from the environment the minimal piece information required to address a particular task of interest.

Author : E. Y. K. Ng
Publisher : CRC Press
Page : 432 pages
File Size : 28,47 MB
Release : 2012-06-05
Category : Technology & Engineering
ISBN : 1439869936

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Advanced image processing and mathematical modeling techniques are increasingly being used for the early diagnosis of eye diseases. A comprehensive review of the field, Human Eye Imaging and Modeling details the latest advances and analytical techniques in ocular imaging and modeling. The first part of the book looks at imaging of the fundus as well as infrared imaging. It begins by exploring developments in the analysis of fundus images, particularly for the diagnosis of diabetic retinopathy and glaucoma. It also reviews anterior segment imaging and reports on developments in ocular thermography, especially the use of thermal imaging as the basis of tear evaporimetry and dry eye diagnosis. The second part of the book delves into mathematical modeling of the human eye. Coverage includes modeling of the eye during retinal laser surgery, a framework for optical simulation, heat distribution using a 3D web-splines solution, and exposure to laser radiation. The text also examines computer simulation of the human eye based on principles of heat transfer, as well as various bioheat equations to predict interior temperatures based on the surface temperature. Featuring contributions by established experts in eye imaging, this is a valuable reference for medical personnel and researchers who want to know more about state-of-the-art computer-based imaging and detection methods. It presents novel imaging and modeling algorithms that can aid in early diagnosis, with the aim of enriching the lives of people suffering from eye abnormalities.