Multiple Verification in Complex Biological Systems: The Bone Remodelling Case Study

  • Ezio Bartocci
  • Pietro Liò
  • Emanuela Merelli
  • Nicola Paoletti
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7625)


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 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Ezio Bartocci
    • 1
  • Pietro Liò
    • 2
  • Emanuela Merelli
    • 3
  • Nicola Paoletti
    • 3
  1. 1.Department of Computer EngineeringVienna University of TechnologyAustria
  2. 2.Computer LaboratoryUniversity of CambridgeUK
  3. 3.School of Science and Technology, Computer Science DivisionUniversity of CamerinoItaly

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