Computational Chemotaxis Models For Neurodegenerative Disease

The mathematical model presented in this book, based on partial differential equations (PDEs) describing attractant-repellent chemotaxis, is offered for a quantitative analysis of neurodegenerative disease (ND), e.g., Alzheimer's disease (AD). The model is a representation of basic phenomena (mechanisms) for diffusive transport and biochemical kinetics that provides the spatiotemporal distribution of components which could explain the evolution of ND, and is offered with the intended purpose of providing a small step toward the understanding, and possible treatment of ND. The format and emphasis of the presentation is based on the following elements: A statement of the PDE system, including initial conditions (ICs), boundary conditions (BCs) and the model parameters.Algorithms for the calculation of numerical solutions of the PDE system with a minimum of mathematical formality.A set of R routines for the calculation of numerical solutions, including a detailed explanation of all of the sections of the code. The R routines can be executed after a straightforward download of R, an open-source scientific computing system available from the Internet.Presentation of the numerical solutions, particularly in graphical (plotted) format to enhance the visualization of the solution.Summary and conclusions concerning the principal results from the model that might serve as the basis for a next step in the modeling of ND. In other words, a methodology for numerical PDE modeling is presented that is flexible, open ended and readily implemented on modest computers. If the reader is interested in an alternate model, it might possibly be implemented by: (1) modifying and/or extending the current model (for example, by adding terms to the PDEs or adding additional PDEs), or (2) using the reported routines as a prototype for the model of interest. These suggestions illustrate an important feature of computer-based modeling, that is, the readily available procedure of numerically experimenting with a model. The current model is offered as only a first step toward the resolution of this urgent medical problem. Request Inspection Copy

Invertebrates have proven to be extremely useful model systems for gaining insights into the neural and molecular mechanisms of sensory processing, motor control and higher functions such as feeding behavior, learning and memory, navigation, and social behavior. A major factor in their enormous contributions to neuroscience is the relative simplicity of invertebrate nervous systems. In addition, some invertebrates, primarily the molluscs, have large cells, which allow analyses to take place at the level of individually identified neurons. Individual neurons can be surgically removed and assayed for expression of membrane channels, levels of second messengers, protein phosphorylation, and RNA and protein synthesis. Moreover, peptides and nucleotides can be injected into individual neurons. Other invertebrate model systems such as Drosophila and Caenorhabditis elegans offer tremendous advantages for obtaining insights into the neuronal bases of behavior through the application of genetic approaches. The Oxford Handbook of Invertebrate Neurobiology reviews the many neurobiological principles that have emerged from invertebrate analyses, such as motor pattern generation, mechanisms of synaptic transmission, and learning and memory. It also covers general features of the neurobiology of invertebrate circadian rhythms, development, and regeneration and reproduction. Some neurobiological phenomena are species-specific and diverse, especially in the domain of the neuronal control of locomotion and camouflage. Thus, separate chapters are provided on the control of swimming in annelids, crustaea and molluscs, locomotion in hexapods, and camouflage in cephalopods. Unique features of the handbook include chapters that review social behavior and intentionality in invertebrates. A chapter is devoted to summarizing past contributions of invertebrates to the understanding of nervous systems and identifying areas for future studies that will continue to advance that understanding.

Advances in semi-automated high-throughput image data collection routines, coupled with a decline in storage costs and an increase in high-performance computing solutions have led to an exponential surge in data collected by biomedical scientists and medical practitioners. Interpreting this raw data is a challenging task, and nowhere is this more evident than in the field of opthalmology. The sheer speed at which data on cataracts, diabetic retinopathy, glaucoma and other eye disorders are collected, makes it impossible for the human observer to directly monitor subtle, yet critical details. This book is a novel and well-timed endeavor to present, in an amalgamated format, computational image modeling methods as applied to various extrinsic scientific problems in ophthalmology. It is self-contained and presents a highly comprehensive array of image modeling algorithms and methodologies relevant to ophthalmologic problems. The book is the first of its kind, bringing eye imaging and multi-dimensional hyperspectral imaging and data fusion of the human eye, into focus. The editors are at the top of their fields and bring a strong multidisciplinary synergy to this visionary volume. Their "inverted-pyramid" approach in presenting the content, and focus on core applications, will appeal to students and practitioners in the field.

In this book, the clinical chapters are organized into sections by defined developmental pathways or gene families, and each section is preceded by a general overview. For each disorder the authors cover the disease-causing genes, the role of these genes in development as elucidated in model organisms, the human mutations that have been identified, and the developmental pathogenesis of the condition. Clinical descriptions, along with discussions of therapy and counseling, are provided. This book will be an invaluable resource for physicians, dentists, and other health professionals and for basic scientists interested in developmental processes and genetic perturbations that affect them.

Presents numerical methods and computer code in Matlab for the solution of ODEs and PDEs with detailed line-by-line discussion.

This book is directed toward the numerical integration (solution) of a system of partial differential equations (PDEs) that describes a combination of chemical reaction and diffusion, that is, reaction-diffusion PDEs. The particular form of the PDEs corresponds to a system discussed by Alan Turing and is therefore termed a Turing model. Specifically, Turing considered how a reaction-diffusion system can be formulated that does not have the usual smoothing properties of a diffusion (dispersion) system, and can, in fact, develop a spatial variation that might be interpreted as a form of morphogenesis, so he termed the chemicals as morphogens. Turing alluded to the important impact computers would have in the study of a morphogenic PDE system, but at the time (1952), computers were still not readily available. Therefore, his paper is based on analytical methods. Although computers have since been applied to Turing models, computer-based analysis is still not facilitated by a discussion of numerical algorithms and a readily available system of computer routines. The intent of this book is to provide a basic discussion of numerical methods and associated computer routines for reaction-diffusion systems of varying form. The presentation has a minimum of formal mathematics. Rather, the presentation is in terms of detailed examples, presented at an introductory level. This format should assist readers who are interested in developing computer-based analysis for reaction-diffusion PDE systems without having to first study numerical methods and computer programming (coding). The numerical examples are discussed in terms of: (1) numerical integration of the PDEs to demonstrate the spatiotemporal features of the solutions and (2) a numerical eigenvalue analysis that corroborates the observed temporal variation of the solutions. The resulting temporal variation of the 2D and 3D plots demonstrates how the solutions evolve dynamically, including oscillatory long-term behavior. In all of the examples, routines in R are presented and discussed in detail. The routines are available through a download link so that the reader can execute the PDE models to reproduce the reported solutions, then experiment with the models, including extensions and application to alternative models.