PhysiologyChap - Applied Mathematical Models in Human...

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Unformatted text preview: Applied Mathematical Models in Human Physiology October 3, 2006 J.T. Ottesen, M.S. Olufsen, and J.K. Larsen • U N I V E R S IT A S RO S K I L D E N S I S • I N T R A N Q U I L L O M OR S • IN F L U C T U V I T A BioMath-Group Department of Mathematics and Physics Roskilde University Denmark Preface The purpose of this book is to study mathematical models of human physiology. The book is a result of work by Math- Tech (in Copenhagen, Denmark) and the BioMath group at the Department of Mathematics and Physics at Roskilde University (in Roskilde, Denmark) on mathematical models related to anesthesia simulation. The work presented in this book has been carried out as part of a larger project SIMA (SIMulation in Anesthesia) 1 , which has resulted in the production of a commer- cially available anesthesia simulator and several scientific research publications contributing to the understanding of human physiology. This book contains the scientific contributions and does not discuss the details of the models implemented in the SIMA project. In order to develop an anesthesia simulator it is necessary to model many aspects of the physiology in the human body. This book is devoted to presenting models reflecting current research relevant to cardiovascular and pulmonary physiology. In particular this book presents models describing blood flow in the heart and the cardiovascular system, as well as transport of oxygen and carbon dioxide through the respiratory system. The models presented describes several aspects of the physiology and it is our hope that this book may provide inspiration for researchers entering this area of study, and for advanced undergrad- uate and graduate students in applied mathematics, biophysics, physiology and bio-engineering. Each of the chapters present a unique model that can be read independently of the other chapters. Chapters 5 and 6 have been used in graduate level courses in applied mathematics at Roskilde University, at Boston University, and at North Carolina State University. Moreover, most of Chapters 2-8 have been used in project organized and problem based student activities at graduate and advanced undergraduate levels at Roskilde University. When using the book in a traditional organized course, we suggest that the students use the models as a collection of examples that can serve as inspiration in their own modeling. Since we find it important that, in a modeling situation, students are involved in both formulating and solving problems we have not included traditional exercises at the end of each chapter. The mathematical background used to derive our models is not presented in detail in this book, however, each chapter includes references to pertinent background material. It is expected that the reader has some knowledge of ordinary and partial differential equations, which are used in the models and are solved using numerical methods. The equations are not subject to analytical mathematical scrutiny, therefore a limited understanding of the methods underlying the use of these equations is...
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PhysiologyChap - Applied Mathematical Models in Human...

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