3R41. Physics of Pulsatile Flow. Biological Physics Series. - M Zamir (Dept of Appl Math, Univ of W Toronto, London ON, N6A 5B7, Canada). Springer-Verlag, Wien, Austria. 2000. 220 pp. ISBN 0-387-98925-0. $69.95.

Reviewed by RS Budwig (Mech Eng Dept, Univ of Idaho, Moscow ID 83844-0902).

This is the first book, to my knowledge, to give a detailed description of the basic physics and mathematics of pulsatile flow in a tube. While the focus of the monograph is the physics and mathematics of pulsatile flow, the author does refer often to the application of this knowledge to the subject of blood flow in the conduits of the mammalian circulatory system. There are two monographs that write on this subject from a medical perspective (Hemodynamics, by WR Milnor, and Blood Flow in Arteries, by DA McDonald) and two monographs that give a broader view of the physics of circulation (The Fluid Mechanics of the Large Blood Vessels, by TJ Pedley, and Biodynamics–Circulation, by YC Fung). Finally, there is a non-mathematical, but highly descriptive monograph on this subject (Vital Circuits, by S Vogel).

The six chapters of the present book may be divided into two categories: Chapters 1 and 2 focus on fundamental concepts and Chapters 3 through 6 describe four cases of tube flows. The first chapter of the book provides a presentation of the background concepts that are required to study tube flows. This reviewer was pleased to find that, in addition to the required basic concepts, the author has included a section on whether or not blood may be treated as a Newtonian fluid. He also provides a brief discussion on when blood flow might be turbulent. The second chapter is a standard development of the equations of motion for fluid flow—the author derives the equations in polar cylindrical coordinates so they may be readily applied to tube flow.

Chapter 3 focuses on the subject of steady tube flow. The Hagen-Poiseuille solution is developed and discussed. The author goes on to discuss entry length of a tube flow and then devotes the remainder of the chapter to the application of modeling flow in the arterial tree. The chapter has an insightful discussion of the concept of the energy expenditure that is required to move a fluid through a tube and the implications of this on the diameter of blood vessels in the arterial tree. One area for improvement in this chapter and throughout the book would be the addition of a few examples with realistic numerical values for viscosity, diameter, etc. The reader would then get an idea of the order of magnitude of quantities that are being discussed (for example, does it require 1 watt or 100 watts to pump blood through the human aorta at typical conditions?).

Chapter 4 goes on to consider the case of pulsatile flow in a rigid tube. The author presents a detailed development of the solution for the case of a flow driven by a purely sinusoidal pressure waveform. He includes a section on how Fourier analysis can be used to represent waveforms that are more complicated than a simple sine wave (such as the waveforms that occur in the flow of blood in the arteries). The author presents graphical results of the velocity profiles. This reviewer was surprised that the author did not present and discuss the near-wall velocity overshoot (Richardson’s annular effect) that is a hallmark of oscillatory tube flow. On the other hand, this reviewer compliments the author for his unique contribution in writing an entire section on the power required to drive a pulsatile flow. Chapter 5 gives a clear and unique presentation of the analysis and results for pulsatile flow in an elastic tube. Chapter 6 presents the theory of wave reflection for pulsatile flow in a system of elastic tubes. Both Chapters 5 and 6 include a level of detail that is not found in other books.

On the whole, this reviewer found the topics in this book to be presented with clarity. The unique features of the monograph include the presentations on pumping power and the level of detail in the presentations on flow in an elastic tube and on the theory of wave reflections. The author has chosen to limit the book’s scope—he does not address the secondary flow patterns that develop at bends, bifurcations, constrictions, or other morphologies that exist in the cardiovascular system. The author has included excellent problems at the end of each chapter, solution summaries at the end of the book, and a valuable list of references with each chapter. This reviewer is pleased to recommend Physics of Pulsatile Flow for the library of anyone involved in the study or teaching of internal pulsatile flows.