Mathematical Models of Retinal Development PDF Download

Author: Erika Tatiana Camacho
Publisher:
ISBN:
Category :
Languages : en
Pages : 280

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Author: William E. Schiesser
Publisher: Academic Press
ISBN: 0128184531
Category : Science
Languages : en
Pages : 144

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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: Christopher Andrew Graesser
Publisher:
ISBN:
Category :
Languages : en
Pages : 120

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Author: Paul Allen Roberts
Publisher:
ISBN:
Category : Retina
Languages : en
Pages : 0

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Author: Giovanna Guidoboni
Publisher: Springer Nature
ISBN: 3030258866
Category : Mathematics
Languages : en
Pages : 606

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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: Xuemin Shen
Publisher: Springer
ISBN: 9780387097510
Category : Technology & Engineering
Languages : en
Pages : 0

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Peer-to-peer networking is a disruptive technology for large scale distributed app- cations that has recently gained wide interest due to the successes of peer-to-peer (P2P) content sharing, media streaming, and telephony applications. There are a large range of other applications under development or being proposed. The - derlying architectures share features such as decentralizaton, sharing of end system resources, autonomy, virtualization, and self-organization. These features constitute the P2P paradigm. This handbook broadly addresses a large cross-section of c- rent research and state-of-the-art reports on the nature of this paradigm from a large number of experts in the ?eld. Several trends in information and network technology such as increased perf- mance and deployment of broadband networking, wireless networking, and mobile devices are synergistic with and reinforcing the capabilities of the P2P paradigm. There is general expectation in the technical community that P2P networking will continue to be an important tool for networked applications and impact the evo- tion of the Internet. A large amount of research activity has resulted in a relatively short time, and a growing community of researchers has developed. The Handbook of Peer-to-Peer Networking is dedicated to discussions on P2P networks and their applications. This is a comprehensive book on P2P computing.

Author: Sarah P. Otto
Publisher: Princeton University Press
ISBN: 1400840910
Category : Science
Languages : en
Pages : 745

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Thirty years ago, biologists could get by with a rudimentary grasp of mathematics and modeling. Not so today. In seeking to answer fundamental questions about how biological systems function and change over time, the modern biologist is as likely to rely on sophisticated mathematical and computer-based models as traditional fieldwork. In this book, Sarah Otto and Troy Day provide biology students with the tools necessary to both interpret models and to build their own. The book starts at an elementary level of mathematical modeling, assuming that the reader has had high school mathematics and first-year calculus. Otto and Day then gradually build in depth and complexity, from classic models in ecology and evolution to more intricate class-structured and probabilistic models. The authors provide primers with instructive exercises to introduce readers to the more advanced subjects of linear algebra and probability theory. Through examples, they describe how models have been used to understand such topics as the spread of HIV, chaos, the age structure of a country, speciation, and extinction. Ecologists and evolutionary biologists today need enough mathematical training to be able to assess the power and limits of biological models and to develop theories and models themselves. This innovative book will be an indispensable guide to the world of mathematical models for the next generation of biologists. A how-to guide for developing new mathematical models in biology Provides step-by-step recipes for constructing and analyzing models Interesting biological applications Explores classical models in ecology and evolution Questions at the end of every chapter Primers cover important mathematical topics Exercises with answers Appendixes summarize useful rules Labs and advanced material available

Author: Evelyne Sernagor
Publisher: Cambridge University Press
ISBN: 1139459732
Category : Medical
Languages : en
Pages : 369

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This advanced text, first published in 2006, takes a developmental approach to the presentation of our understanding of how vertebrates construct a retina. Written by experts in the field, each of the seventeen chapters covers a specific step in the process, focusing on the underlying molecular, cellular, and physiological mechanisms. There is also a special section on emerging technologies, including genomics, zebrafish genetics, and stem cell biology that are starting to yield important insights into retinal development. Primarily aimed at professionals, both biologists and clinicians working with the retina, this book provides a concise view of vertebrate retinal development. Since the retina is 'an approachable part of the brain', this book will also be attractive to all neuroscientists interested in development, as processes required to build this exquisitely organized system are ultimately relevant to all other parts of the central nervous system.

Author: Erika Tatiana Camacho
Publisher:
ISBN: 9780496292202
Category :
Languages : en
Pages : 134

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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: Lindsey C. Macdougall
Publisher:
ISBN:
Category :
Languages : en
Pages :

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