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E. Bartocci, P. Lio, E. Merelli, N. Paoletti:
"Multiple Verification in Complex Biological Systems: The Bone Remodelling Case Study";
Transactions on Computational Systems Biology, XIV (2012), S. 53 - 76.

We present a set of formal techniques and a methodology for a composite formal analysis at the tissue and organ level, focusing on the verification of quantitative properties in the process of bone remodelling. Starting from a differential equation model, we derive a stochastic model and a piecewise multi-affine approximation in order to perform model checking of stabilisation properties for the biological tissue, and to assess the differences between a regular remodelling activity and a defective activity typical of pathologies like osteoporosis. The complex nonlinear dynamics of bone remodelling is analysed with a variety of techniques: sensitivity analysis for the differential equation model; quantitative probabilistic model checking for the stochastic model; and classical model checking and parameter synthesis on the piecewise multi-affine model. Such analyses allow us to extract a wealth of information that is not only useful for a deeper understanding of the biological process but also towards medical diagnoses.

formal analysis,bone remodelling,model checking,sensitivity,piecewise multi-affine abstraction

http://dx.doi.org/10.1007/978-3-642-35524-0_3