Mathematical Biosciences 257 (2014) 1

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Mathematical methods and models in system biomedicine Medical and biological technology has advanced rapidly in recent years and its impact is expected to rise further in the future. These technological innovations have led to a significant progress in health care along with improvement of life quality. Mathematical modeling plays an important role in modern biomedical research and is predicted to become even more crucial in the coming years. Models, analysis techniques and numerical simulation, combined with experimental validation, facilitate advances in medical knowledge by providing additional tools that can be used to improve the understanding of living systems including prediction of basic physiological and pathological processes. Models have also started to play a role in diagnosis and treatment planning, in strategies for choosing personalized and optimized therapeutic options, and for analysis of medical/biological data. The latter require adaptation of models to individual patients, as well as methods for prediction of both model and parameter uncertainty. Development of models that can help in the above tasks is difficult since biological functions result from complex interaction across multiple scales, from the molecular to the organelle and cellular levels, extended to tissues, organs and whole organisms. Theoretical concepts, along with modeling and computational efforts are invaluable for examining underlying biological mechanisms allowing us to track interdependencies across multiple scales in a quantitative, integrative and computationally efficient way. They include, but are not limited to, techniques for theoretical analysis of system dynamics, algorithms designed for mapping diagnostic and therapeutic procedures, scale models developed for instrumentation design, as well as decision algorithms for interpretation of imaging results. In addition to insights gained directly from modeling, it should be emphasized that knowledge extracted from measurements is usually interpreted using mathematical and statistical models. Frequently these are hidden in the equipment, implicating that what is collected experimentally are not the raw data, but model based analysis of some derived quantity. Moreover only selected variables at given times are measurable during experiments, and modeling can disclose aspects of the system not directly available: shortly, modelling makes somewhat accessible an otherwise inaccessible world. Furthermore, it is important to remember that modeling, especially in biomedical research, has to be carried out in an iterative manner, and that tomorrow’s models will build on today’s progress. 0025-5564/Ó 2014 Published by Elsevier Inc.

This special issue offers a selection of articles discussing models and computational methodologies for analyzing biomedical systems. These studies have been chosen over a variety of applications on different space and time-scales: from intracellular phenomena, cell structures and signals to system level models describing hemodynamics, organ function, drug delivery. These specific studies provide a broad platform for researchers to communicate their mathematical models and computational tools predicting various aspects of the complex biological system. Finally, these models also identify potential clinical questions that can be addressed in future investigations. This special issue includes a total of 12 manuscripts by leading researchers in mathematical biology discussing both modeling methodologies and applications. These studies tackle several aspects of multiscale problems with an exchange of information between theoretical and applied fields in an interdisciplinary perspective, bridging simulation capabilities and biotechnological demands. This multidisciplinary effort, including expertise from different areas such as engineering, mathematics, biophysics, medicine, and computer science is a real challenge of today’s science. The collected papers cover a wide spectrum of topics and represent a good, although not exhaustive, example of the possibilities offered in the field of mathematical modeling in biomedicine. The editors are grateful to all the authors for their excellent contributions. We truly hope the issue will increase the awareness of the potential of the computing amongst medical doctors, engineers and scientists working in the field. The Editors Giuseppe Pontrelli Istituto per le Applicazioni del Calcolo, CNR via dei Taurini, 19 – 00185 Roma, Italy E-mail address: [email protected] Mette S. Olufsen Department of Mathematics, NC State University, Campus Box 8205, Raleigh, NC 27502, USA Johnny T. Ottesen Department of Science, Systems and Models, Roskilde University, Building 27.1, 4000 Roskilde, Denmark

Mathematical methods and models in system biomedicine.

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