Mathematical Physiology (Interdisciplinary Applied Mathematics) 2 Vol Set [Hardcover]

James Keener (Author), James Sneyd (Author)

Book Description

ISBN-10: 0387094199 | ISBN-13: 978-0387094199 | Publication Date: December 31, 2008 | Edition: 2nd

There has been a long history of interaction between mathematics and physiology. This book looks in detail at a wide selection of mathematical models in physiology, showing how physiological problems can be formulated and studied mathematically, and how such models give rise to interesting and challenging mathematical questions. With its coverage of many recent models it gives an overview of the field, while many older models are also discussed, to put the modern work in context. In this second edition the coverage of basic principles has been expanded to include such topics as stochastic differential equations, Markov models and Gibbs free energy, and the selection of models has also been expanded to include some of the basic models of fluid transport, respiration/perfusion, blood diseases, molecular motors, smooth muscle, neuroendrocine cells, the baroreceptor loop, turboglomerular oscillations, blood clotting and the retina. Owing to this extensive coverage, the seond edition is published in two volumes. This first volume deals with the fundamental principles of cell physiology and the second with the physiology of systems. The book includes detailed illustrations and numerous excercises with selected solutions. The emphasis throughout is on the applications; because of this interdisciplinary approach, this book will be of interest to students and researchers, not only in mathematics, but also in bioengineering, physics, chemistry, biology, statistics and medicine. Reviews of the first edition: “...probably the best book ever written on the interdisciplinary field of mathematical physiology.” Mathematical Reviews, 2000 “In addition to being good reading, excellent pedagogy, and appealing science, the exposition is lucid and clear, and there are many good problem sets to choose from... Highly recommended.” Mathematical Biosciences, 1999 “Both authors are seasoned experts in the field of mathematical physiology and particularly in the field of excitability, calcium dynamics and spiral waves. It directs students to become not merely skilled technicians in biological research but masters of the science.” SIAM, 2004 The first edition was the winner of the prize for The Best Mathematics book of 1998 from the American Association of Publishers.

Editorial Reviews

Review

From the reviews: “Probably the best book ever written on the subject of mathematical physiology … It contains numerous exercises, enough to keep even the most diligent student busy, and a comprehensive list of approximately 600 references … highly recommended to anybody interested in mathematical or theoretical physiology.” Mathematical Reviews “In addition to being good reading, excellent pedagogy, and appealing science, the exposition is lucid and clear, and there are many good problem sets to choose from … Highly recommended.” Journal of the Society of Mathematical Biology “Most of the chapters, especially those outined in the second part of the book, can constitute whole monographs by themselves, and Keener and Sneyd have attempted to cover some of the fundamental modeling concepts within the respective areas.” Bulletin of Mathematical Biology, 2000 “Both authors are seasoned experts in the field of mathematical physiology and particularly in the field of excitability, calcium dynamics and spiral waves. It directs students to become not merely skilled technicians in biological research but masters of the science.” SIAM, 2004 From the reviews of the second edition: "This massive new edition … offers an introduction to mathematical physiology that emphasizes work conducted by Keener (Univ. of Utah), Sneyd (Univ. of Auckland, New Zealand), and others over the past 20 years. It is designed as a course resource for beginning graduate students who have … some mathematical background. … Keener and Sneyd have made very reasonable choices in their subject selections. This work is an admirable resource for students with the appropriate prerequisites. Chapters include exercises … . Summing Up: Recommended. Graduate students." (P. Cull, Choice, Vol. 46 (10), June, 2009) "The texts provide a comprehensive summary of the important concepts in mathematical physiology. … For those actively working in the field of mathematical physiology … is a must have. The new edition includes updated descriptions, new models, and new figures adding to the breadth of the first edition. One of the most beneficial aspects … is the addition of about a decade’s worth of work and references (over 350!). … more advanced questions were added giving more flexibility when used as a course textbook." (Joe Latulippe, The Mathematical Association of America, July, 2009) “This second edition of Mathematical physiology, ten years after the first one … provides information on recent works in mathematical physiology. … It is a very interesting book dealing with the interdisciplinary field of mathematical physiology. … Mathematical physiology, with the consequent number of exercises given at the end of each chapter, could be used in particular for a full-year course in mathematical physiology. It is also suitable for researchers and graduate students in applied mathematics, bioengineering and physiology.” (Fabien Crauste, Mathematical Reviews, Issue 2010 b) --This text refers to an alternate Hardcover edition.

From the Back Cover

There has been a long history of interaction  between mathematics and physiology. This book looks in detail at a wide selection of mathematical models in physiology, showing how physiological problems can be formulated and studied mathematically, and how such models give rise to interesting and challenging mathematical questions. With its coverage of many recent models it gives an overview of the field, while many older models are also discussed, to put the modern work in context.  In this second edition the coverage of basic principles has been expanded to include such topics as stochastic differential equations, Markov models and Gibbs free energy, and the selection of models has also been expanded to include some of the basic models of fluid transport, respiration/perfusion, blood diseases, molecular motors, smooth muscle, neuroendrocine cells, the baroreceptor loop, turboglomerular oscillations, blood clotting and the retina.   Owing to this extensive coverage, the second edition is published in two volumes. This first volume deals with the fundamental principles of cell physiology and the second with the physiology of systems.   The book includes detailed illustrations and  numerous excercises with selected solutions. The emphasis throughout is on the applications; because of this interdisciplinary  approach, this book  will be of  interest to students and researchers, not only in mathematics, but also in bioengineering, physics, chemistry, biology, statistics and medicine. James Keener is a Distinguished Professor of Mathematics at the University of Utah. He and his wife live in Salt Lake City, but don't be surprised if he moves to the mountains. James Sneyd is the Professor of Applied Mathematics at the University of Auckland in New Zealand, where he has worked for the past six years. He lives with his wife and three children beside a beach, and would rather be swimming. Reviews of the first edition: ...probably the best book ever written on the interdisciplinary field of mathematical physiology. Mathematical Reviews, 2000 In addition to being good reading, excellent pedagogy, and appealing science, the exposition is lucid and clear, and there are many good problem sets to choose from... Highly recommended. Mathematical Biosciences, 1999 Both authors are seasoned experts in the field of mathematical physiology and particularly in the field of excitability, calcium dynamics and spiral waves. It directs students to become not merely skilled technicians in biological research but masters of the science. SIAM, 2004 The first edition was the winner of the 1998 Association of American Publishers "Best New Title in Mathematics." --This text refers to an alternate Hardcover edition.

Product Details

• Hardcover: 1160 pages
• Publisher: Springer; 2nd edition (December 31, 2008)
• Language: English
• ISBN-10: 0387094199
• ISBN-13: 978-0387094199
• Product Dimensions: 9.6 x 7.1 x 2.4 inches
• Shipping Weight: 4.8 pounds
• Average Customer Review: 4.0 out of 5 stars  See all reviews (5 customer reviews)
• Amazon Best Sellers Rank: #1,116,295 in Books (See Top 100 in Books)

More About the Author

Discover books, learn about writers, read author blogs, and more.

Customer Reviews

Most Helpful Customer Reviews

23 of 25 people found the following review helpful:

4.0 out of 5 stars Graduate level Mathematical Physiology text, April 11, 2000

By A Customer

This review is from: Mathematical Physiology (Hardcover)

This is a very good graduate level text on mathematical physiology. It covers a broad range of topics from cardiac electrophysiology to the cell cycle. The authors have written the closest thing to a mathematical version of Guyton's Human Physiology text that I have seen. The prospective reader of this text should be aware that it assumes a background in PDE ,ODE, and asymptotics, as well as introductory molecular Biology. The structure of DNA, RNA, and the central dogma DNA to RNA to Protein are described in less than 3 pages without diagrams. Terms from Biochemistry are used at times without definition or explanation. Each Chapter concludes with a very nice collection of interesting problems. Supplement the text with the outstanding elementary text by Leah - Edelstein - Keshet , lecture notes by C. Peskin ,the applied math texts by Keener and Cole, Molecular biology texts by Lodish et al or Baltimore et al ,and of course Guyton's Human Physiology for a fascinating introduction to mathematical biology with an emphasis on differential equation models in physiology.

17 of 18 people found the following review helpful:

5.0 out of 5 stars All of it fascinating...., May 22, 2001

By 

Dr. Lee D. Carlson (Baltimore, Maryland USA) - See all my reviews
(VINE VOICE)    (HALL OF FAME REVIEWER)    (REAL NAME)   

This review is from: Mathematical Physiology (Hardcover)

This book is an excellent overview of the major research into the mathematics of physiological processes. The first part of the book covers cellular physiology beginning with a discussion of biochemical reactions in the first chapter. Some of the applications of dynamical systems are nicely illustrated here, especially bifurcation theory.

Applications of the diffusion equation follow in the next chapter on cellular homeostasis. The Nernst-Planck electrodiffusion equation is discussed but not derived, and is solved in the constant field approximation.

This is complicated somewthat in the next chapter on membrane ion channels, where the potential across the membrane is not assumed to have a constant gradient. There is a discussion of channel blocking drugs in the last section, but unfortunately it is too short. This is an important area of application, with the experimental validation of the mathematical results of upmost importance.

The Hodgkin-Huxley and the FitzHugh-Nagumo equations dominate the next chapter on electrical signaling in cells. The phase space analysis of these models is discussed, along with an interesting treatment of the excitability of cardiac cells in the Appendix of the chapter.

A very well-written treatment, along with helpful diagrams, of calcium dynamics is given in Chapter 5. The authors show how ignoring the fast variables and transients lead one to a solution of they dynamical problem of the receptor model.

Phase space analysis is used extensively in the next chapter on electrical bursting, with emphasis on bursting in pancreatic beta-cells. An interesting discussion on the classification of bursting oscillations is given purely in terms of bifurcation theory.

That synaptic transimission is quantal in nature is one of the topics of the next chapter on intercellular communication. This is the first time in the book that probabilistic methods are introduced into the modeling. The authors quote some very old references on the experimental verification of the quantal model, leaving the reader wondering if more modern experiments have been done. In calculating the effective diffusion coefficients, the authors introduce the technique of homogenization, and give a explanation of the rationale behind the technique. The strategy of determining the behavior at a particular scale without solving completely the details at a finer scale is one that has proven to be quite productive, especially in physics.

The use of partial differential equations is increased in the next chapter on electrical flow in neurons, with the linear cable equation playing the dominant role. The authors use transform methods to obtain the solutions in the main text and exercises, giving references for the reader not familiar with these techniques.

The nonlinear cable equation is the subject of the next chapter, with traveling waves solutions of the bistable equation given the main emphasis. Shooting methods are employed in the solution of this equation, and the authors also treat the more difficult case of the discrete bistable equation.

Wave propagation in higher dimensions is the subject of the next chapter, with spiral waves discussed along with a brief discussion of scroll waves.

The fascinating subject of cardiac propagation is the subject of Chapter 11. The mathematical techniques are not much more complicated, but mathematicians coming to cardiac biology for the first time will need to pay attention to the details. One of the most interesting subjects of the book is treated in Chapter 13 on cell function regulation. Mathematical models of the G1 and G2 checkpoint processes are given.

Part two of the book emphasizes the mathematical modeling of the biological systems, rather than at the cellular level. This part begins with a consideration of how cellular activity can be coordinated to produce a regular heartbeat and how failure can occur. Interestingly, a Schrodinger-like equation appears when linearizing the FitzHugh-Nagumo equations for oscillating cells. And, interestingly, dynamical systems via circle maps appear in the model of the AV modal signal. This is followed by a lengthy and fascinating discussion of the mathematics of the circulatory system. Unfortunately, the discussion on the dangers of high blood pressure is not justified by any mathematical models in the book. It would have been very interesting to see a model developed that would predict the effects of hypertension on the heart, kidneys, etc and one that would be compared with historical and clinical data.

The next chapters discuss physiology of the blood, respiration, and muscles. A very interesting discussion of hormone physiology and mammal ovulation is given. The mathematical models of the kidneys and gastrointestinal systems are very detailed and very enlightening for individuals not in these fields.

The book ends with chapters on the physiology of sight and hearing. The discussion of the light reflex mechanism is very interesting as the authors use linear stability analysis. The oscillations of the basilar membrane in the inner ear are good reading for the physicist.

This book would be of great interest to mathematicians who are entering the field of computational physiology or computational biologists who need an understanding of the modeling required. Very captivating reading........

1 of 1 people found the following review helpful:

4.0 out of 5 stars Good book, recommended for everyone with a science background entering physiology/biology, February 23, 2010

By 

Jordi (Netherlands) - See all my reviews

This review is from: Mathematical Physiology (Interdisciplinary Applied Mathematics) 2 Vol Set (Hardcover)

I wish I had this book when I started in this field. It is so much nicer to learn from such a well written and comprehensive textbook than to try to extract all the information from journal articles. Some background in physiology and, particularly, mathematics (ODE's, algebra, etc.) is required though to make the most out of this book. (Parts of) the book are/is well suited for an advanced course in computational biology.