**Edited by Riccardo Sacco, Giovanna Guidoboni, and Aurelio Giancarlo Mauri, Academic Press, 2019, ISBN: 978-0-128-12518-2 (Paperback), xxiii + 830 pages, $200**

**When this reviewer** opted to receive and review this text, it was hoped that it would present as a complementary text to those of Drs. Carson and Cobelli [Modelling Methodology for Physiology and Medicine (2013) and Introduction to Modeling in Physiology and Medicine, 2nd ed. (2019)]. This was not to be the case.

This text was written by three authors, two of whom have Ph.D. degrees and specialize in applied mathematics. The authors collectively have experience in computational biology, semiconductor device modeling, ophthalmology modeling, and several related fields, these experiences are reflected in the several examples in the text. The text itself consists of some 30 chapters, which are reported in eight sections.

Part 1 of the text [Mathematical, Computational, and Physical Foundations (four chapters)] gives a quick overview of mathematical modeling, mathematical and computational modeling methods, and physics. One is immediately presented with such terms as vector calculus, tensors, manifolds, etc., in a form not normally seen by most undergraduate students, while the two introductory chapters on modeling are more typical of many sophomore-level presentations. Part 2 of the text [Balance Laws (four chapters)] covers laws of mass and energy balances with (again) a nonundergraduate use of strain and deformation tensors.

Part 3 of the text [Constitutive Relations (five chapters)] covers modeling of fluids, solids, and mixtures, as well as electromagnetism and ion electrodynamics. Some of the mathematical concepts are at a typical undergraduate level, though not all. One does finally see Nernst potentials, but next to a discussion on semiconductors. With half the text done, Part 4 of the text [Model Reduction of System Complexity (two chapters)] finally gives the reader Kirchhoff current laws and fluid flow modeling, including compliant and collapsible tubing discussions.

Part 5 of the text [Mathematical Models of Basic Biological Units and Complex Systems (four chapters)] gives a useful overview of neuron functions, action potentials, the Hodgkin–Huxley equations, cable models, and astrocyte mechanics. Part 6 of the text [Advanced Mathematical and Computational Methods (six chapters)] gives an overview of function spaces, partial differential equations, and approximations of functions. Much of this material is very high-level, in terms of the math involved.

Part 7 of the text [Simulation Examples and Clinical Applications (two chapters)] covers ion pumps (with an example of aqueous humor production) and ocular perfusion. Part 8 of the text [Examples, Exercises, and Projects (three chapters)] gives 49 MATLAB scripts used in the text (chapter 28), 51 MATLAB functions (chapter 29), and a series of exercises and projects for parts 1–7 above.

The text then includes an appendix on curvilinear coordinate laws and a bibliography for the text (244 references, with no mention of the above Carson and Cobelli texts!).

**While this text** is touted as being for “Biomedical engineers, life sciences researchers, as well as undergraduate and graduate students in Biomedical Engineering, Electrical Engineering, Mathematics, Biology, and Medicine” (Academic Press website), this reviewer suggests that the text be mainly considered as a reference text, to be used primarily by those with an adequate mathematical and MATLAB background.

*—Review by Paul H. King, Vanderbilt University*