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Uniformity in Multiscale Models: From Complex Automata to BioShape
Diletta Cacciagrano, Flavio Corradini, Emanuela Merelli and Luca Tesei

Many biological phenomena are inherently multiscale (MS) – i.e. they are characterised by interactions involving simultaneously different spatial and temporal scales. The needs of describing systems in a MS fashion and, more in general, MS problems across multiple scientific disciplines require a common modelling approach being able to (i) unify the common principles arising in general in MS scenarios (e.g. scale representation, scale separation and inter-scale interaction), (ii) support the effective combination of various single-scale models through well-defined scale coupling procedures, and consequently (iii) help to model and to simulate MS scenarios in a rigorous and systematic way.

Complex Automata (CxA) constitute a well-defined paradigm for multiscale modelling that goes towards the above mentioned characteristics. BIOSHAPE, a 3D spatial geometric-based simulator, has been also defined as an independent modelling and simulation environment naturally able to represent, in the same model, different levels of multiscale systems. In this work we show that BIOSHAPE can be used to perform multiscale modelling and simulation using the same core ideas of the CxA approach.

Bone remodelling (BR) is one of the most challenging (and intricate) multiscale phenomena to model and simulate. Both CxA and BIOSHAPE have been here exploited for modelling BR at cell and tissue scales. On the one hand, the two given MS models confirm an high expressiveness degree of both approaches to model MS scenarios in a uniform way. On the other hand, the possibility of expressing a quite complicated MS problem such as BR in both CxA and BIOSHAPE using the same underlying ideas highlights the existence of a mapping between them. This is enforced by the fact that both approaches are suitable for handling different scales in a uniform way, for including spatial information and for bypassing inter-scale homogenization problems.

Keywords: Multiscale modelling, multiscale simulation, uniform multiscale models, bone remodelling, complex automata, bioshape simulator, expressiveness of multiscale models.

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