This book introduces mathematicians to real applications from physiology. Using mathematics to analyze physiological systems, the authors focus on models reflecting current research in cardiovascular and pulmonary physiology. In particular, they present models describing blood flow in the heart and the cardiovascular system, as well as the transport of oxygen and carbon dioxide through the respiratory system and a model for baroreceptor regulation. Applied Mathematical Models in Human Physiology is the only book available that analyzes up-to-date models of the physiological system at several levels of detail. Some are simple "real-time" models that can be directly used in larger systems, while others are more detailed "reference" models that show the underlying physiological mechanisms and provide parameters for and validation of simpler models. The book also covers two-dimensional modeling of the fluid dynamics in the heart and its ability to pump, and includes a discussion of modeling wave-propagation throughout the systemic arteries.
The models presented can be used as case studies in courses on mathematical modeling or as an inspiration for the study and development of physiological models. The first two chapters of the book provide an excellent introduction to the physiologic concepts necessary for understanding the modeling assumptions and methodologies. The remaining chapters describe six different models of the cardiovascular and pulmonary system. Each model is introduced by a case study and can be studied individually.
Johnny T. Ottesen is a Professor of Mathematics and Physics at Roskilde University, Denmark. His main research interests include mathematical modeling of biological systems, biofluids, optimal control, scientific computing, and dynamical systems. He is a leading researcher in the area of modeling of physiological systems, especially in modeling the cardiovascular system and its control mechanisms. He has also contributed to research in the teaching of mathematical modeling at all university levels. He has been a Visiting Researcher at the University of California, Santa Barbara and at RIMS, Kyoto, Japan. Mette S. Olufsen is a Professor of Mathematics at North Carolina State University. Her research is in the fields of biofluid dynamics, computational neuroscience, scientific computation, and interdisciplinary research in mathematical biology. In particular she is interested in multiscale modeling including models from detailed fluid dynamics models to lumped compartmental models. Jesper K. Larsen is Director of Math-Tech and an applied mathematics educator at the department of Mathematics and Physics at Roskilde University, Denmark. His research areas include applied mathematical modeling, and he was one of the founders of the simulation project SIMA (SIMulation in Anesthesia), which was the project that brought together all the contributions documented in this book.