This book presents models written as partial differential equations and originating from various questions in population biology, such as physiologically structured equations, adaptive dynamics, and bacterial movement. Its purpose is to derive appropriate mathematical tools and qualitative properties of the solutions. The book further contains many original PDE problems originating in biosciences.

This text is designed for a first course in biological mass transport, and the material in it is presented at a level that is appropriate to advanced undergraduates or early graduate level students. Its orientation is somewhat more physical and mathematical than a biology or standard physiology text, reflecting its origins in a transport course that I teach to undergraduate (and occasional graduate) biomedical engineering students in the Whiting School of Engineering at Johns Hopkins. The audience for my cours- and presumably for this text - also includes chemical engineering undergraduates concentrating in biotechnology, and graduate students in biophysics. The organization of this book differs from most texts that at tempt to present an engineering approach to biological transport. What distinguishes biological transport from other mass transfer processes is the fact that biological transport is biological. Thus, we do not start with the engineering principles of mass transport (which are well presented elsewhere) and then seek biological ap plications of these principles; rather, we begin with the biological processes themselves, and then develop the tools that are needed to describe them. As a result, more physiology is presented in this text than is often found in books dealing with engineering applica tions in the life sciences.

Transport in Biological Media is a solid resource of mathematical models for researchers across a broad range of scientific and engineering problems such as the effects of drug delivery, chemotherapy, or insulin intake to interpret transport experiments in areas of cutting edge biological research. A wide range of emerging theoretical and experimental mathematical methodologies are offered by biological topic to appeal to individual researchers to assist them in solving problems in their specific area of research. Researchers in biology, biophysics, biomathematics, chemistry, engineers and clinical fields specific to transport modeling will find this resource indispensible. - Provides detailed mathematical model development to interpret experiments and provides current modeling practices - Provides a wide range of biological and clinical applications - Includes physiological descriptions of models

Transport and Diffusion across Cell Membranes is a comprehensive treatment of the transport and diffusion of molecules and ions across cell membranes. This book shows that the same kinetic equations (with appropriate modification) can describe all the specialized membrane transport systems: the pores, the carriers, and the two classes of pumps. The kinetic formalism is developed step by step and the features that make a system effective in carrying out its biological role are highlighted. This book is organized into six chapters and begins with an introduction to the structure and dynamics of cell membranes, followed by a discussion on how the membrane acts as a barrier to the transmembrane diffusion of molecules and ions. The following chapters focus on the role of the membrane's protein components in facilitating transmembrane diffusion of specific molecules and ions, measurements of diffusion through pores and the kinetics of diffusion, and the structure of such pores and their biological regulation. This book methodically introduces the reader to the carriers of cell membranes, the kinetics of facilitated diffusion, and cotransport systems. The primary active transport systems are considered, emphasizing the pumping of an ion (sodium, potassium, calcium, or proton) against its electrochemical gradient during the coupled progress of a chemical reaction while a conformational change of the pump enzyme takes place. This book is of interest to advanced undergraduate students, as well as to graduate students and researchers in biochemistry, physiology, pharmacology, and biophysics.

Modeling of Microscale Transport in Biological Processes provides a compendium of recent advances in theoretical and computational modeling of biotransport phenomena at the microscale. The simulation strategies presented range from molecular to continuum models and consider both numerical and exact solution method approaches to coupled systems of equations. The biological processes covered in this book include digestion, molecular transport, microbial swimming, cilia mediated flow, microscale heat transfer, micro-vascular flow, vesicle dynamics, transport through bio-films and bio-membranes, and microscale growth dynamics. The book is written for an advanced academic research audience in the fields of engineering (encompassing biomedical, chemical, biological, mechanical, and electrical), biology and mathematics. Although written for, and by, expert researchers, each chapter provides a strong introductory section to ensure accessibility to readers at all levels.

These notes are based on a one-quarter course given at the Department of Biophysics and Theoretical Biology of the University of Chicago in 1916. The course was directed to graduate students in the Division of Biological Sciences with interests in population biology and neurobiology. Only a slight acquaintance with probability and differential equations is required of the reader. Exercises are interwoven with the text to encourage the reader to play a more active role and thus facilitate his digestion of the material. One aim of these notes is to provide a heuristic approach, using as little mathematics as possible, to certain aspects of the theory of stochastic processes that are being increasingly employed in some of the population biol ogy and neurobiology literature. While the subject may be classical, the nov elty here lies in the approach and point of view, particularly in the applica tions such as the approach to the neuronal firing problem and its related dif fusion approximations. It is a pleasure to thank Professors Richard C. Lewontin and Arnold J.F. Siegert for their interest and support, and Mrs. Angell Pasley for her excellent and careful typing. I . PRELIMINARIES 1. Terminology and Examples Consider an experiment specified by: a) the experiment's outcomes, ~, forming the space S; b) certain subsets of S (called events) and by the probabilities of these events.

This book presents several fundamental questions in mathematical biology such as Turing instability, pattern formation, reaction-diffusion systems, invasion waves and Fokker-Planck equations. These are classical modeling tools for mathematical biology with applications to ecology and population dynamics, the neurosciences, enzymatic reactions, chemotaxis, invasion waves etc. The book presents these aspects from a mathematical perspective, with the aim of identifying those qualitative properties of the models that are relevant for biological applications. To do so, it uncovers the mechanisms at work behind Turing instability, pattern formation and invasion waves. This involves several mathematical tools, such as stability and instability analysis, blow-up in finite time, asymptotic methods and relative entropy properties. Given the content presented, the book is well suited as a textbook for master-level coursework.

The idea for this book was conceived by the authors some time in 1988, and a first outline of the manuscript was drawn up during a summer school on mathematical physics held in Ravello in September 1988, where all three of us were present as lecturers or organizers. The project was in some sense inherited from our friend Marvin Shinbrot, who had planned a book about recent progress for the Boltzmann equation, but, due to his untimely death in 1987, never got to do it. When we drew up the first outline, we could not anticipate how long the actual writing would stretch out. Our ambitions were high: We wanted to cover the modern mathematical theory of the Boltzmann equation, with rigorous proofs, in a complete and readable volume. As the years progressed, we withdrew to some degree from this first ambition- there was just too much material, too scattered, sometimes incomplete, sometimes not rigor ous enough. However, in the writing process itself, the need for the book became ever more apparent. The last twenty years have seen an amazing number of significant results in the field, many of them published in incom plete form, sometimes in obscure places, and sometimes without technical details. We made it our objective to collect these results, classify them, and present them as best we could. The choice of topics remains, of course, subjective.

Introduction to Biotransport Principles is a concise text covering the fundamentals of biotransport, including biological applications of: fluid, heat, and mass transport.