Mathematical Foundations and Biomechanics of the Digestive System

Name: Mathematical Foundations and Biomechanics of the Digestive System
Price: $100.90 USD
Availability: InStock
Author: Roustem N. Miftahof , Hong Gil Nam
ISBN: 9780521116626

by Roustem N. Miftahof , Hong Gil Nam

ISBN13:
9780521116626
ISBN10:
0521116627
Edition: 1st
Format: Hardcover
Copyright: 2010-06-07
Publisher: Cambridge University Press
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Summary

Mathematical modelling of physiological systems promises to advance our understanding of complex biological phenomena and pathophysiology of diseases. In this book, the authors adopt a mathematical approach to characterize and explain the functioning of the gastrointestinal system. Using the mathematical foundations of thin shell theory, the authors patiently and comprehensively guide the reader through the fundamental theoretical concepts, via step-by-step derivations and mathematical exercises, from basic theory to complex physiological models. Applications to nonlinear problems related to the biomechanics of abdominal viscera and the theoretical limitations are discussed. Special attention is given to questions of complex geometry of organs, effects of boundary conditions on pellet propulsion, as well as to clinical conditions, e.g. functional dyspepsia, intestinal dysrhythmias and the effect of drugs to treat motility disorders. With end of chapter problems, this book is ideal for bioengineers and applied mathematicians.

Author Biography

Roustem N. Miftahof is Professor and Head of the Department of Physiology at the Arabian Gulf University, Manama, Bahrain. He is a recognized leader in the areas of applied mathematics and gastrointestinal research, and has authored and co-authored two previous books in these fields. He has worked in both academia and industry across Europe, America and Asia.

Hong Gil Nam is Professor at Pohang University of science and Technology, Pohang, South Korea, Director of the National Core Research Centre for Systems Bio-Dynamics and President of the Association of Asian Societies for Bioinformatics. Professor Nam has received numerous awards for his research contributions and he has made several media appearances in South Korea.

Preface	p. xi
Notation	p. xv
Introduction	p. 1
Exercises	p. 4
The geometry of the surface	p. 6
Intrinsic geometry	p. 6
Extrinsic geometry	p. 8
The equations of Gauss and Codazzi	p. 13
General curvilinear coordinates	p. 15
Deformation of the surface	p. 18
Equations of compatibility	p. 22
Exercises	p. 26
Parameterization of shells of complex geometry	p. 28
Fictitious deformations	p. 28
Parameterization of the equidistant surface	p. 31
A single-function variant of the method of fictitious deformation	p. 33
Parameterization of a complex surface in preferred coordinates	p. 37
Parameterization of complex surfaces on a plane	p. 42
Exercises	p. 46
Nonlinear theory of thin shells	p. 47
Deformation of the shell	p. 47
Forces and moments	p. 50
Equations of equilibrium	p. 55
Exercises	p. 60
The continuum model of the biological tissue	p. 61
Structure of the tissue	p. 61
Biocomposite as a mechanochemical continuum	p. 62
The biological factor	p. 71
Exercises	p. 74
Boundary conditions	p. 76
The geometry of the boundary	p. 76
Stresses on the boundary	p. 78
Static boundary conditions	p. 81
Deformations of the edge	p. 84
Gauss-Codazzi equations for the boundary	p. 87
Exercises	p. 88
Soft shells	p. 89
Deformation of soft shell	p. 89
Principal deformations	p. 95
Membrane forces	p. 97
Principal membrane forces	p. 100
Corollaries of the fundamental assumptions	p. 101
Nets	p. 105
Equations of motion in general curvilinear coordinates	p. 106
Governing equations in orthogonal Cartesian coordinates	p. 109
Governing equations in cylindrical coordinates	p. 111
Exercises	p. 113
Biomechanics of the stomach	p. 115
Anatomical and physiological background	p. 115
Constitutive relations for the tissue	p. 119
A one-dimensional model of gastric muscle	p. 130
Myoelectrical activity	p. 132
Decrease in external Ca²⁺ concentration	p. 133
Effects of T- and L-type Ca²⁺-channel antagonists	p. 134
Acetylcholme-induced myoelectrical responses	p. 135
Effect of chloride-channel antagonist	p. 136
Effect of selective K⁺-channel antagonist	p. 136
The stomach as a soft biological shell	p. 137
Inflation of the stomach	p. 140
The electromechanical wave phenomenon	p. 142
The chronaxiae of pacemaker discharges	p. 145
Multiple pacemakers	p. 147
Pharmacology of myoelectrical activity	p. 155
Exercises	p. 155
Biomechanics of the small intestine	p. 157
Anatomical and physiological background	p. 157
A one-dimensional model of intestinal muscle	p. 158
Myoelectrical activity	p. 159
Effects of non-selective Ca²⁺-channel agonists	p. 160
Effects of Ca²⁺-activated K⁺-channel agonist	p. 160
Response to a selective K⁺-channel agonist	p. 161
Effect of selective K⁺-channel antagonist	p. 163
Conjoint effect of changes in Ca²⁺ dynamics and extracellular K⁺ concentrations	p. 164
The small intestine as a soft cylindrical shell	p. 165
Pendular movements	p. 166
Segmentation	p. 168
Peristaltic movements	p. 173
Self-sustained periodic activity	p. 173
Effect of lidocaine	p. 177
Exercises	p. 180
Biomechanics of the large intestine	p. 182
Anatomical and physiological background	p. 182
The colon as a soft shell	p. 184
Haustrai churning	p. 187
Contractions of the teniae coli	p. 187
Peristalsis and propulsive movements	p. 192
Pharmacology of colonic motility	p. 192
Effect of Lotronex	p. 192
Effect of Zelnorm	p. 194
Exercises	p. 194
Biological applications of mathematical modeling	p. 196
Biomechanics of hollow abdominal viscera	p. 196
Future developments and applications	p. 201
Exercises	p. 208
References	p. 210
Index	p. 217
Table of Contents provided by Ingram. All Rights Reserved.

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