Mathematical Modelling in Medicine is divided into four distinct parts which cover mathematical models of heart, arterial tree, baroreceptor control and applications for simulators. The mathematical models covering these four topics are contained in a number of articles in each part. In addition, historical reviews on the heart, arterial tree and baroreceptors are also included in the articles offering a broader view and understanding of the current physiological models. The models presented are all based on fundamental physiological principles. This common guideline may result in more solid models from which we can obtain new physiological insights. Mathematical Modelling in Medicine demonstrates that the increase in popularity and success of mathematical models, is not solely a consequence of the development and spread of fast computers, making easier access to simulations of complex systems. An important element for this success is the precise continuous samplings of new clinical data have generated experiments, from which one can gain new insights into the dynamics of physiological systems and not only into their steady state behaviour patterns. Another important element is the attempts to focus on precise definitions of physiological concepts in order to avoid confusion, misunderstandings and waste of efforts. Furthermore, it is shown, that mathematics may also provide a tool to structure thoughts, an area which have gained an increasing attention lately. This book will be of interest to graduate students as well as researchers in the interdisciplinary fields of bioengeneering, biophysics and mathematical physiology.

The idea of writing this book appeared when I was working on some problems related to representations of physically relevant infinite - mensional groups of operators on physically relevant Hilbert spaces. The considerations were local, reducing the subject to dealing with representations of infinite-dimensional Lie algebras associated with the associated groups. There is a large number of specialized articles and books on parts of this subject, but to our suprise only a few represent the point of view given in this book. Moreover, none of the written material was self-contained. At present, the subject has not reached its final form and active research is still being undertaken. I present this subject of growing importance in a unified manner and by a fairly simple approach. I present a route by which students can absorb and understand the subject, only assuming that the reader is familliar with functional analysis, especially bounded and unbounded operators on Hilbert spaces. Moreover, I assume a little basic knowledge of algebras , Lie algebras, Lie groups, and manifolds- at least the definitions. The contents are presented in detail in the introduction in Chap. The manuscript of this book has been succesfully used by some advanced graduate students at Aarhus University, Denmark, in their "A-exame'. I thank them for comments.