Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Akman, O.E., Guerriero, M.L., Loewe, L., Troein, C.: Complementary approaches to understanding the plant circadian clock. In: FBTC. EPTCS, vol.Ā 19, pp. 1ā19 (2010)
Aziz, A., Sanwal, K., Singhal, V., Brayton, R.: Model-checking continuous-time Markov chains. ACM Transactions on Computational LogicĀ 1(1), 162ā170 (2000)
Barbuti, R., Cataudella, S., Maggiolo-Schettini, A., Milazzo, P., Troina, A.: A probabilistic model for molecular systems. Fundamenta InformaticaeĀ 67(1-3), 13ā27 (2005)
Bartocci, E., Grosu, R., Katsaros, P., Ramakrishnan, C.R., Smolka, S.A.: Model Repair for Probabilistic Systems. In: Abdulla, P.A., Leino, K.R.M. (eds.) TACAS 2011. LNCS, vol.Ā 6605, pp. 326ā340. Springer, Heidelberg (2011)
Batt, G., Belta, C., Weiss, R.: Temporal logic analysis of gene networks under parameter uncertainty. IEEE Transactions on Automatic ControlĀ 53, 215ā229 (2008)
Batt, G., Yordanov, B., Weiss, R., Belta, C.: Robustness analysis and tuning of synthetic gene networks. BioinformaticsĀ 23(18), 2415ā2422 (2007)
Belta, C., Habets, L., Kumar, V.: Control of multi-affine systems on rectangles with application to hybrid biomolecular networks. In: Proceedings of the 41st IEEE Conference on Decision and Control, pp. 534ā539. IEEE (2002)
Berman, S., HalĆ”sz, Ć.M., Kumar, V.: MARCO: A Reachability Algorithm for Multi-affine Systems with Applications to Biological Systems. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds.) HSCC 2007. LNCS, vol.Ā 4416, pp. 76ā89. Springer, Heidelberg (2007)
Bortolussi, L., Policriti, A.: (Hybrid) automata and (stochastic) programs The hybrid automata lattice of a stochastic program. J. Logic Computation, 2052 ā 2077 (2010)
Bortolussi, L., Policriti, A.: Hybrid dynamics of stochastic programs. Theoretical Computer ScienceĀ 411(20), 2052ā2077 (2010)
Cacciagrano, D.R., Corradini, F., Merelli, E., Tesei, L.: Multiscale Bone Remodelling with Spatial P Systems. In: Proceedings Compendium of the 4th Workshop on Membrane Computing and Biologically Inspired Process Calculi (MeCBIC 2010), pp. 69ā83 (2010)
Calder, M., Vyshemirsky, V., Gilbert, D., Orton, R.: Analysis of Signalling Pathways Using Continuous Time Markov Chains. In: Priami, C., Plotkin, G. (eds.) Transactions on Computational Systems Biology VI. LNCS (LNBI), vol.Ā 4220, pp. 44ā67. Springer, Heidelberg (2006)
Ciocchetta, F., Hillston, J.: Bio-pepa: A framework for the modelling and anal- ysis of biological systems. Theor. Comput. Sci.Ā 410(33-34), 3065ā3084 (2009)
Cook, B., Fisher, J., Krepska, E., Piterman, N.: Proving Stabilization of Biological Systems. In: Jhala, R., Schmidt, D. (eds.) VMCAI 2011. LNCS, vol.Ā 6538, pp. 134ā149. Springer, Heidelberg (2011)
Dayar, T., Mikeev, L., Wolf, V.: On the numerical analysis of stochastic Lotka-Volterra models. In: Proceedings of the 2010 International Multiconference on Computer Science and Information Technology (IMCSIT), pp. 289ā296. IEEE (2010)
DemattĆ©, L., Priami, C., Romanel, A.: Modelling and simulation of biological processes in BlenX. SIGMETRICS Perform. Eval. Rev.Ā 35(4), 32ā39 (2008)
Fages, F., Soliman, S., Chabrier-Rivier, N.: Modelling and querying interaction networks in the biochemical abstract machine biocham. Journal of Biological Physics and ChemistryĀ 4(2), 46ā73 (2004)
Gerhard, F., Webster, D., van Lenthe, G., MĆ¼ller, R.: In silico biology of bone modelling and remodelling: adaptation. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering SciencesĀ 367(1895), 2011 (2009)
Geris, L., Vander Sloten, J., Van Oosterwyck, H.: In silico biology of bone modelling and remodelling: regeneration. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering SciencesĀ 367(1895), 2031 (2009)
Gillespie, D.: Exact stochastic simulation of coupled chemical reactions. Journal of Physical ChemistryĀ 81(25), 2340ā2361 (1977)
Grosu, R., Batt, G., Fenton, F.H., Glimm, J., Le Guernic, C., Smolka, S.A., Bartocci, E.: From Cardiac Cells to Genetic Regulatory Networks. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol.Ā 6806, pp. 396ā411. Springer, Heidelberg (2011)
Hahn, E.M., Hermanns, H., Wachter, B., Zhang, L.: PARAM: A Model Checker for Parametric Markov Models. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol.Ā 6174, pp. 660ā664. Springer, Heidelberg (2010)
Komarova, S., Smith, R., Dixon, S., Sims, S., Wahl, L.: Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling. BoneĀ 33(2), 206ā215 (2003)
Krivine, J., Danos, V., Benecke, A.: Modelling Epigenetic Information Maintenance: A Kappa Tutorial. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol.Ā 5643, pp. 17ā32. Springer, Heidelberg (2009)
Kwiatkowska, M., Norman, G., Parker, D.: Using probabilistic model checking in systems biology. ACM SIGMETRICS Performance Evaluation ReviewĀ 35(4), 14ā21 (2008)
Kwiatkowska, M., Norman, G., Parker, D.: PRISM 4.0: Verification of Probabilistic Real-Time Systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol.Ā 6806, pp. 585ā591. Springer, Heidelberg (2011)
Li, L., Yokota, H.: Application of Petri Nets in Bone Remodeling. Gene Regulation and Systems BiologyĀ 3, 105 (2009)
Lin, J., Unbehauen, R.: Canonical piecewise-linear approximations. IEEE Transactions on Circuits and Systems I: Fundamental Theory and ApplicationsĀ 39, 697ā699 (1992)
LiĆ², P., Merelli, E., Paoletti, N.: Multiple verification in computational modeling of bone pathologies. In: Proceedings of the 3rd International Workshop on Computational Models for Cell Processes (CompMod 2011), pp. 82ā96 (2011)
Voit, E.O., Ferreira, A.E.: Computational Analysis of Biochemical Systems. Cambridge University Press (2000)
Paoletti, N., LiĆ², P., Merelli, E., Viceconti, M.: Osteoporosis: a multiscale mod- eling viewpoint. In: Proceedings of the 9th International Conference on Computational Methods in Systems Biology (CMSB 2011), pp. 183ā193. ACM (2011)
Paoletti, N., LiĆ², P., Merelli, E., Viceconti, M.: Multi-level computational modeling and quantitative analysis of bone remodeling. IEEE/ACM Transactions on Computational Biology and BioinformaticsĀ 9(5), 1366ā1378 (2012)
Parfitt, A.: Osteonal and hemi-osteonal remodeling: The spatial and temporal framework for signal traffic in adult human bone. Journal of Cellular BiochemistryĀ 55(3), 273ā286 (1994)
Parfitt, M., Qiu, S., Palnitkar, S., Rao, D.: Abnormal bone remodeling in patients with spontaneous painful vertebral fracture. Journal of Bone and Mineral ResearchĀ 26(3), 475ā485 (2011)
Pivonka, P., Komarova, S.: Mathematical modeling in bone biology: From intracellular signaling to tissue mechanics. BoneĀ 47(2), 181ā189 (2010)
Pnueli, A.: The temporal logic of programs. In: 18th IEEE Annual Symposium on Foundations of Computer Science, pp. 46ā57. IEEE (1977)
Pronk, T., de Vink, E., BoÅ”naÄki, D., Breit, T.: Stochastic modeling of codon bias with PRISM. In: Proceedings of the 3rd International Workshop Methods and Tools for Coordinating Concurrent, Distributed and Mobile Systems, MTCoord 2007 (2007)
Soetaert, K., Petzoldt, T., et al.: Inverse modelling, sensitivity and monte carlo analysis in R using package FME. Journal of Statistical SoftwareĀ 33(3), 1ā28 (2010)
Stewart, W.: Introduction to the numerical solution of Markov chains. Princeton University Press, NJ (1994)
Tovar, A.: Bone remodeling as a hybrid cellular automaton optimization process. PhD thesis, University of Notre Dame (2004)
Viceconti, M., Bellingeri, L., Cristofolini, L., Toni, A.: A comparative study on different methods of automatic mesh generation of human femurs. Medical Engineering & PhysicsĀ 20(1), 1ā10 (1998)
Whitfield, J.: Growing bone. Landes Bioscience (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
Ā© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bartocci, E., LiĆ², P., Merelli, E., Paoletti, N. (2012). Multiple Verification in Complex Biological Systems: The Bone Remodelling Case Study. In: Priami, C., Petre, I., de Vink, E. (eds) Transactions on Computational Systems Biology XIV. Lecture Notes in Computer Science(), vol 7625. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35524-0_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-35524-0_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35523-3
Online ISBN: 978-3-642-35524-0
eBook Packages: Computer ScienceComputer Science (R0)