Nonlinear Dynamics in Physiology and Medicine

Je tiens impossible de connaître les parties sans connaître le tout, non plus que de connaître le tout sans connaître particulierement les parties -Pascal The eterna[ mystery of the world is its comprehensibility -Einstein This book deals with the application of mathematical tools to the study of physiological systems. It is directed toward an audience of physiologists, physicians, physicists, kinesiologists, psychologists, engineers, mathemati cians, and others interested in finding out more about the complexities and subtleties of rhythmic physiological processes from a theoretical per spective. We have attempted to give a broad view of the underlying notions behind the dynamics of physiological rhythms, sometimes from a theoretical perspective and sometimes from the perspective of the experimentalist. This book can be used in a variety of ways, ranging from a more tra ditional approach such as a textbook in a biomathematics course (at either the advanced undergraduate or graduatelevel) to a research re source in which someone interested in a particular problem might look at the corresponding discussion here to guide their own thinking. We hope that researchers at all levels will find inspiration from the way we have dealt with particular research problems to tackle completely new areas of investigation, or even approach these in totally new ways.

List of contents

1 Theoretical Approaches in Physiology.- 2 Introduction to Dynamics in Nonlinear Difference and Differential Equations.- 3 Bifurcations Involving Fixed Points and Limit Cycles in Biological Systems.- 4 Dynamics of Excitable Cells.- 5 Resetting and Entraining Biological Rhythms.- 6 Effects of Noise on Nonlinear Dynamics.- 7 Reentry in Excitable Media.- 8 Cell Replication and Control.- 9 Pupil Light Reflex: Delays and Oscillations.- 10 Data Analysis and Mathematical Modeling of Human Tremor.- A An Introduction to XPP.- Michael C. Mackey.- A.1 ODE Files.- A.2 Starting and Quitting XPP.- A.3 Time Series.- A.4 Numerics.- A.5 Graphic Tricks.- A.5.1 Axis.- A.5.2 Multiplotting.- A.5.3 Erasing.- A.5.4 Printing the Figures.- A.6 Examining the Numbers.- A.7 Changing the Initial Condition.- A.8 Finding the Fixed Points and Their Stability.- A.9 Drawing Nullclines and Direction Field.- A.10 Changing the Parameters.- A.11 Auto.- A.11.1 Bifurcation Diagram.- A.11.2 Scrolling Through the Points on theBifurcation Diagram.- A.12 Saving Auto Diagrams.- B An Introduction to Matlab.- Michèle S. Titcombe and Caroline Haurie.- R.1 Starting and Quitting Matlab.- B.2 Vectors and Matrices.- B 2 1 Creating Matrices and Vectors.- .B.3 Suppressing Output to the Screen (the Semicolon!).- B.4 Operations on Matrices.- B.5 Programs (M-Files).- B.5.1 Script Files.- B.5.2 Function Files.- B.6 The Help Command.- B.7 Loops.- B.8 Plotting.- B.8.1 Examples.- B.8.2 Clearing Figures and Opening New Figures.- B.8.3 Symbols and Colors for Lines and Points.- B.9 Loading Data.- B.9.1 Examples.- B.10 Saving Your Work.- C Time Series Analysis.- Roderick Edwards and Michèle S. Titcombe.- C.1 The Distribution of Data Points.- C.2 Linear Processes.- C.3 Fourier Analysis.

Summary

Je tiens impossible de connaître les parties sans connaître le tout, non plus que de connaître le tout sans connaître particulierement les parties -Pascal The eterna[ mystery of the world is its comprehensibility -Einstein This book deals with the application of mathematical tools to the study of physiological systems. It is directed toward an audience of physiologists, physicians, physicists, kinesiologists, psychologists, engineers, mathemati­ cians, and others interested in finding out more about the complexities and subtleties of rhythmic physiological processes from a theoretical per­ spective. We have attempted to give a broad view of the underlying notions behind the dynamics of physiological rhythms, sometimes from a theoretical perspective and sometimes from the perspective of the experimentalist. This book can be used in a variety of ways, ranging from a more tra­ ditional approach such as a textbook in a biomathematics course (at either the advanced undergraduate or graduatelevel) to a research re­ source in which someone interested in a particular problem might look at the corresponding discussion here to guide their own thinking. We hope that researchers at all levels will find inspiration from the way we have dealt with particular research problems to tackle completely new areas of investigation, or even approach these in totally new ways.

Additional text

From the reviews:

"As part of the Springer Interdisciplinary Applied Mathematics Series, this book joins a line of books that are leading the way in showing how mathematics can be usefully applied to biology and physiology." - Bulletin of the AMS, 2004

"This book is an excellent addition to the literature. Perhaps its greatest value is its appeal to a wide class of prospective readers who may range from the biologist (mathematician) who has a mild interest in mathematics (biology) to the researcher who works in one of the fields discussed. … There is a large bibliography, and there are analytical and computer exercises at the end of each chapter." (Jane Cronin, Zentralblatt MATH, Vol. 1050, 2005)

"The book «Nonlinear Dynamics in Physiology and Medicine» is a multi-author effort. … Each chapter is well grounded … . The book’s references list is thorough and valid … . This book is aimed at all scientists studying physiological systems in general … . It fits into curricula usually offered by bio-engineering departments and - happily more and more - also medical schools. … a book of high standards and is to be recommended. It is a title worth possessing as a collection of valuable reference material … ." (Prof. dr. sc. Vladimir Medved, IFMBE News, Vol. 69, November/December, 2004)

"Beuter, Glass, Mackey and Titcombe edit a book that provides an understanding of the theory and application of mathematical tools to the study of physiological systems. The book will be of interest to those involved in the modeling of such physiological systems. … The material is well written, clear and concise. … I liked the book. It makes an important contribution to the field … . I recommend this book. It makes a worthwhile addition to a biological/medical science library." (Paul Johnson, New Zealand Mathematical Society Newsletter, Issue 91, 2004)

 

Report

From the reviews:
"As part of the Springer Interdisciplinary Applied Mathematics Series, this book joins a line of books that are leading the way in showing how mathematics can be usefully applied to biology and physiology." - Bulletin of the AMS, 2004
"This book is an excellent addition to the literature. Perhaps its greatest value is its appeal to a wide class of prospective readers who may range from the biologist (mathematician) who has a mild interest in mathematics (biology) to the researcher who works in one of the fields discussed. ... There is a large bibliography, and there are analytical and computer exercises at the end of each chapter." (Jane Cronin, Zentralblatt MATH, Vol. 1050, 2005)
"The book «Nonlinear Dynamics in Physiology and Medicine» is a multi-author effort. ... Each chapter is well grounded ... . The book's references list is thorough and valid ... . This book is aimed at all scientists studying physiological systems in general ... . It fits into curricula usually offered by bio-engineering departments and - happily more and more - also medical schools. ... a book of high standards and is to be recommended. It is a title worth possessing as a collection of valuable reference material ... ." (Prof. dr. sc. Vladimir Medved, IFMBE News, Vol. 69, November/December, 2004)
"Beuter, Glass, Mackey and Titcombe edit a book that provides an understanding of the theory and application of mathematical tools to the study of physiological systems. The book will be of interest to those involved in the modeling of such physiological systems. ... The material is well written, clear and concise. ... I liked the book. It makes an important contribution to the field ... . I recommend this book. It makes a worthwhile addition to a biological/medical science library." (Paul Johnson, New Zealand Mathematical Society Newsletter, Issue 91, 2004)
 

Product details

• Assisted by: Anne Beuter (Editor), Michael C Mackey et al (Editor), Leo Glass (Editor), Leon Glass (Editor), Michael C. Mackey (Editor), Michele S. Titcombe (Editor)
• Publisher: Springer, Berlin
• Languages: English
• Product format: Hardback
• Released: 08.10.2003
• EAN: 9780387004495
• ISBN: 978-0-387-00449-5
• No. of pages: 436
• Weight: 786 g
• Illustrations: XXVI, 436 p.
• Series: Interdisciplinary Applied Mathematics; Mathematical Biology; Interdisciplinary Applied Mathematics; Mathematical Biology
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Analysis