Computational Models for the Human Body Special Volume

This series of volumes covers all the major aspects of numerical analysis, serving as the basic reference work on the subject. Each volume concentrates on one to three, particular topics. Each article, written by an expert, is an in-depth survey, reflecting the most recent trends in the field, and is essentially self-contained. The handbook will cover the basic methods of numerical analysis, under the following general headings: Solution of Equations in Rn Finite Difference Methods Finite Element Methods Techniques of Scientific Computing Optimization Theory and Systems Science. It will also cover the numerical solution of actual problems of contemporary interest in Applied Mathematics, under the following headings: Numerical Methods for Fluids Numerical Methods for Solids Specific Applications - including meteorology, seismology, petroleum mechanics and celestial mechanics. Computational Models for the Human Body is a recent and rapidly progressing area of research whose primary objective is to provide a better understanding of the physiological and mechanical behavior of the human body and to design tools for their realistic numerical simulations. This book describes concrete examples of such computational models. Although far from being exhaustive, the book covers a large range of methods and an illustrative set of applications, and proposes a number of well defined mathematical and numerical modeling of physical problems, (including formal analysis of existence and unicity of solutions for instance), followed by various numerical simulations. Medical applications are addressed first, because physiological and biomechanical models of the human body already play a prominent role in the prevention, diagnosis and therapy of many diseases. The generalized introduction of such models in medicine will in fact strongly contribute to the development of a more individualized and preventive medicine. In effect, through the continuous progress of medical imaging during the past decades, it is currently possible to extract an increasing flow of anatomical or functional information on any individual, with an increasing resolution in space and time. The overwhelming quantity of available signals and images makes a direct analysis of the data more and more difficult, when not impossible. New computational models are necessary to capture those parameters pertinent to analyze the human system under study or to stimulate it. There is also a number of important non medical applications of these in silico human models, covering numerous human activities, like driving (safer design of vehicles), working (better ergonomy of workplaces), exercising (more efficient training of athletes), entertaining (simulation for movies), etc. There are basically three levels of design for human models. The first level is mainly geometrical, and addresses the construction of a digital description of the anatomy, often acquired from medical imagery. The second level is physical, involving mainly the biomechanical modeling of various tissues, organs, vessels, muscles or bone structures. The third level is physiological, involving a modeling of the functions of the major biological systems (e.g. cardiovascular, respiratory, digestive, hormonal, muscular, central or peripheral nervous system, etc.) or some pathological metabolism (e.g. evolution of cancerous or inflammatory lesions, formation of vessel stenoses, etc.). A fourth level (not described in this book) would be cognitive, modeling the higher functions of the human brain. These different levels of modeling are closely related to each other, and several physiological systems may interact together (e.g. the cardiopulmonary interaction). The choice of the resolution at which each level is described is important, and may vary from microscopic to macroscopic, ideally through multiscale descriptions. The first three chapters of the book study three important physiological models (vascular, cardiac, and tumoral).Ciarlet, P. G. is the author of 'Computational Models for the Human Body Special Volume', published 2004 under ISBN 9780444515667 and ISBN 0444515666.