Mathematical challenges in integrative physiology

Traditional approaches to biomedical research are based on the subdivision of biological systems—by length (or time) scales (body, organ, tissue, cell, and molecule), discipline (biology, physiology, bioengineering, etc.), or sub-systems (cardiovascular, musculoskeletal, gastrointestinal, etc.). These subdivisions, however, make it difficult to unravel the systemic nature of the mechanisms that govern many of the (patho-) physiological processes in the human body. The challenge now is to complement this traditional approach with an integrative approach that makes it possible to combine observations, theories and predictions across dimensional scales, scientific disciplines, and anatomical sub-systems. This realisation has led to initiatives such as integrative biology [1], systems biology [2,3], the Physiome [4–6] and the Virtual Physiological Human [7]. These have highlighted the need to create a virtual infrastructure which should make it possible to interconnect predictive models defined at different scales, with different methods and with different levels of detail to enable investigation of systemic hypotheses. Such a framework should also facilitate validation of theoretical or computational models by comparison with clinical or laboratory observations, by making the observation data easily accessible to the modelling community. Model validation is regularly overlooked and cannot be integrated fully into multi-scale models unless there is sufficient communication and exchange of data between the mathematical and life scientists