A Uniform Multiscale Meta-model of BIOSHAPE

Existing approaches in multiscale (MS) science and engineering have evolved from a range of ideas and solutions that are reflective of their original problem domains. As a result, research in MS science has followed widely diverse and disjoint paths, which present a barrier to cross pollination of ideas and application of methods outside their application domains. The status of the research environment calls for a methodological framework able to (i) provide a common language to modelling and simulating MS problems across a range of scientific and engineering disciplines and, consequently, (ii) characterize critical common issues arising in MS problems in an uniform setting. In this paper, we contribute in this sense. Taking inspiration from the Complex Automata (CxA) MS approach, we formally define and enrich the meta-model of BioShape-put forward as a scale-independent MS simulation environment-and we exploit it to give a uniform treatment of generally defined coupling schemes, in particular the micro-macro one applied to the bone remodelling process. Similarly to CxA, also the BioShape meta-model enjoys two important features: namely, (i) a MS system can be decomposed in uniform single-scale models, each one described by a generic sequence of calls to well-defined operators, and (ii) the link between any two single-scale models can be expressed as a flow of data between a pair of these operators by well-defined coupling schemes. As a consequence, such features not only enforce and formally prove the scale-independence property of the BioShape simulator, but also makes the BioShape meta-model a common and uniform MS modelling paradigm across a range of heterogeneous application domains.