MODELING OF BIOLOGICAL MATERIALS

One of the greatest challenges of science is to assist in enhancing the quality and longevity of life. To be able to meaningfully meet such an expectation it is necessary to meld the preventive and curative aspects of medicine and to provide the practitioner of medicine with predictive capabilities that can be brought by the development of interdisciplinary activities involving various basic sciences: biology, physics, chemistry and mathematics. Significant strides have been taken during the past decade to the developments above and some important steps forward have been possible primarily due to an understanding of the interplay between mechanics and the other basic sciences. This collection of survey articles addresses this aspect to the advance in the medical sciences. In particular, these survey articles bring to the forefront the central role played by modelling in general and the modeling of mechanical considerations that have a bearing in the biology, chemistry and physics of living matter, in particular. This book develops with the idea that it is necessary to potentiate a research field which represents a keystone between engineering and medical sciences and to prepare a professional figure able to understand the medical needs and to handle numerical simulations and technological innovations in order to complete the modelling process which goes from phenomenological observation to computer simulation, through the development of mechanical and mathematical models and the related investigative methods. One of the aims of this book is the development of the just mentioned modelling cycle for several biomedical applications. In this respect the models are tested on realistic and typical examples and situations, explicit theoretical results are extracted either in analytical or in numerical form, and a comparison with the experimental findings is performed. The degree of the observed coincidence between theory and experiments serves as an obvious test on the adequacy of the modeling. From a different perspective, it can be remarked that in modeling and subsequent mathematical treatment many biomechanical problems related to different parts of the human body are either very close or share very similar basic ideas. However, as the final applications are very different, many different backgrounds, ways of thinking and ``languages'' are used, and as a result the pertinent literature is widely spread over journals possessing different styles and often mutually nonintersecting communities of readers, e.g. engineers, biologists, medical doctors. Another ambitious aim of this book is to alleviate this situation to a certain degree, through collecting several survey papers of actively working specialists, dealing with some of the most important, both theoretically and practically, problems in biomechanics: tumor growth, blood flow, mechanics of circulatory system, cell rheology, mechanical properties of hard tissues, membranes modelling and modelling of natural tissues substitute, i.e. biomaterials. Each chapter will focus on a specific biomedical application and will explain as simply as possible both the biological and mechanical background, together with the basic ideas of the appropriate models, the peculiarities of their implementation, the basic features of the discussed phenomena and their explanation by the models, as well as certain basic theoretical results and simulations, compared with experimental data. The authors tried to avoid more cumbersome mathematical techniques, giving at the same time a glimpse for them with the needed and most important references for the interested reader. The book is addressed to graduate and PhD students in applied mathematics, engineering and bio-medicine and to young researcher with a multidisciplinary attitude or eager to apply mathematical and numerical methods to understand and describe the mechanics of living tissues.