In the summer of 1997, the BioMath group at IMFUFA, Roskilde University, Denmark arranged the conference, “Mathematical Modelling in Medicine”. The goal of the conference was to present the state of the art on mathematical modelling in physiology and medicine. The speakers were all leading researchers educated in various traditional disciplines including mathematics, physics, engineering, physiology, medicine and cognitive engineering. The conference became a major success and the participants agreed to publish a proceeding of interests for graduate students as well as researchers in this interdisciplinary field.
The result is the current book. It 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. The articles can be read independently, but it may be an advantage to read some or all of the articles together, due to their close relationship.
In the last decade, we have observed a rapid increase in the popularity and success of mathematical models. This is not solely a consequence of the development and spread of fast computers, making easier access to simulations of complex systems. Another determining factor is the enormous increase in available clinical data. The precise continuous samplings of new data have generated experiments from which we can gain new insights into the dynamics of physiological systems and not only into their steady state behaviour patterns. Yet another important element is the attempts to focus on precise definitions of physiological concepts in order to avoid confusion, misunderstandings and waste of efforts. Most, if not all, concepts can only be clearly defined by use of mathematics. Otherwise obscurity and ambiguity will undoubtedly rise sooner or later. Mathematics may also provide a tool to structure thoughts, an area which have gained an increasing attention. Also, new important questions generated by the application of mathematical models, questions which could not be asked without such models, are believed to play a role in the interest of mathematical modelling. In addition to the importance of this interdisciplinary field in research, mathematical models have received an growing interest as an applied activity in industry, e.g. in the construction and use of simulators in training and education of medical doctors and nurses. Recently, the SIMA group in Denmark has developed a full scale anaesthesia simulator based on mathematical models. This simulator is currently in use at several hospitals in Denmark for the training of anaesthesiologists and anaesthetic nurses. Also, the simulator has become an obligatory part of their education.
Finally, we would like to thank the Moth-Lund foundation and the Danish Natural Science Research Council for supporting the conference, Mathematical Modelling in Medicine, as well as IMFUFA at Roskilde University for supporting this book. Also, we would like to thank the authors for their contributions and for being very co-operative, and our colleagues at IMFUFA, Roskilde University for many fruitful discussions.
JOHNNY T. OTTESEN