Book Review

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Book Information:

Editors: A. Beuter, L. Glass, M. C. Mackey and M. S. Titcombe

Title: Nonlinear dynamics in physiology and medicine

Additional book information: edited by A. Beuter, L. Glass, M. C. Mackey and M. S. Titcombe, Interdisciplinary Applied Mathematics, vol. 25, Springer-Verlag, New York, 2003, xxvi+434 pp., ISBN 0-387-00449-1, $69.95

**[1]**Francis Bacon (1620) Novum Organum, I, 95. Based on the standard translation of James Spedding, Robert Leslie Ellis, and Douglas Denon Heath in The Works (Vol. VIII), published in Boston by Taggard and Thompson in 1863. (Text given in http://www.constitution.org/bacon/nov_org.htm)**[2]**Daniel Bernoulli (1766) Essai d'une nouvelle analyse de la mortalité causée par la petite Vérole, & des avantages de l'Inoculation pour la prévenir. Mémoires de Mathématique et de Physique, Académie Royale des Sciences. English translation entitled ``An attempt at a new analysis of the mortality caused by smallpox and of the advantages of inoculation to prevent it" in: L. Bradley, Smallpox Inoculation: An Eighteenth Century Mathematical Controversy, Adult Education Department, Nottingham, 1971, p. 21. An excellent mathematical discussion of the controversy is given by K. Dietz and J.A.P. Heesterbeek, (2002) Daniel Bernoulli's epidemiological model revisited, Mathematical Biosciences, 180, 1-21.**[3]**Jean-le-Rond d'Alembert (1761) Sur l'application du calcul des probabilités à l'inoculation de la petite vérole; In Opuscules Mathématiques, vol. 2; p. 26 ff, David, Paris.**[4]**Otto Frank (1899) Die Grundform des Arteriellen Pulses, Zeitschrift für Biologie, 37: 483-526. A translation is given by K. Sagawa, R.K. Lie, and J. Schaefer (1990) J. Mol. Cell. Cardiol., 22, 253-277. Just as well, as I can't read German.**[5]**H. Helmholtz (1850) Note sur la vitesse de propagation de l'agent nerveux dans les nerfs rachidiens. C. R. Acad. Sci. (Paris), 30: 204-206. A fascinating discussion of the history of electrophysiology is given by M. Piccolino (1998) Animal electricity and the birth of electrophysiology: The legacy of Luigi Galvani, Brain Research Bulletin, 46: 381-407.**[6]**H. Helmholtz (1875) On the Sensations of Tone as a Physiological Basis for the Theory of Music, Longmans, Green and Co., London. I inherited a copy of this book from my grandfather, who was an accomplished violinist. I don't know how useful this book was for that, although I suspect not very.**[7]**Charles S. Peskin,*The immersed boundary method*, Acta Numer.**11**(2002), 479–517. MR**2009378**, https://doi.org/10.1017/S0962492902000077**[8]**Rall W., Rinzel J. (1973) Branch input resistance and steady attenuation for input to one branch of a dendritic neuron model, Biophysical Journal, 13: 648-87. J. Rinzel, J.B. Keller (1973) Traveling wave solutions of a nerve conduction equation. Biophysical Journal, 13: 1313-37. Not many physiological modellers have had papers with the most eminent people on both sides of the fence, and in the same journal volume, no less.**[9]**Christopher P. Fall, Eric S. Marland, John M. Wagner, and John J. Tyson (eds.),*Computational cell biology*, Interdisciplinary Applied Mathematics, vol. 20, Springer-Verlag, New York, 2002. MR**1911592****[10]**C.J. Meinrenken, J.G. Borst, B. Sakmann (2003) Local routes revisited: the space and time dependence of the Ca signal for phasic transmitter release at the rat calyx of Held. Journal of Physiology, 547: 665-89. E. Neher (1998) Vesicle pools and Camicrodomains: new tools for understanding their roles in neurotransmitter release. Neuron 20: 389-99. As it happens, a lot of the modeling of calcium in synapses has used some of Keizer's early work, particularly on the buffered diffusion equation.**[11]**Well, OK, I haven't got a proper reference for this quote (which Murray adapted from an Arab proverb), but he did say it. I promise. He even wrote it somewhere, as he will admit when pressed.**[12]**J.D. Murray (1977) Lectures on Nonlinear Differential Equation Models in Biology, Clarendon Press, Oxford. Mostly superseded by his more recent books and, sadly, out of print and difficult to find. A search on abebooks.com turns up only a single copy, for $136, with the lovely comment ``The text is printed in a font resembling Courier." Quite so. His later books used real fonts, I believe.**[13]**Anne Beuter, Leon Glass, Michael C. Mackey, and Michèle S. Titcombe (eds.),*Nonlinear dynamics in physiology and medicine*, Interdisciplinary Applied Mathematics, vol. 25, Springer-Verlag, New York, 2003. MR**2018243****[14]**The Springer Interdisciplinary Applied Mathematics Series has published (or republished) some of the most important and best-known books in mathematical biology, including Mathematical Biology (Murray), Mathematical Physiology (Keener and Sneyd), The Geometry of Biological Time (Winfree), Diffusion and Ecological Problems (Okubo and Levin), Branching Processes in Biology (Kimmel and Axelrod), Computational Cell Biology (edited by Fall et al.) and Molecular Modeling and Simulation; An Interdisciplinary Guide (Schlick). An impressive line-up by any standard, and Springer is to be commended. My bias is obvious, but my point valid nonetheless.

Review Information:

Reviewer: James Sneyd

Affiliation: University of Auckland

Email: sneyd@math.auckland.ac.nz

Journal: Bull. Amer. Math. Soc.

**41**(2004), 559-564

Published electronically: June 17, 2004

Review copyright: © Copyright 2004 American Mathematical Society