Abstract
One of the important steps of analysis of any mathematical model is the sensitivity analysis. The most frequently used type of sensitivity analysis is the local parametric sensitivity analysis that answers the question how changes of model’s parameters influence the solution of the model. It is routinely used but it can be applied only for constant parameters. It cannot be applied for non-stationary parameters nor for varying in time external input signals. The full information about the sensitivity in such a case can be given by the sensitivity analysis using Green’s function. This work describes a toolbox written in MATLAB environment, which can be useful in sensitivity analysis of biomedical models described by system of ordinary differential equations. To illustrate this type of sensitivity analysis, we use the created tool to analyze a model of cell signaling pathway of p53 protein, which plays crucial role in the response of tumor and healthy cells to radiotherapy.
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References
Fujarewicz, K.: Estimation of initial functions for systems with delays from discrete measurements. Math. Biosci. Eng. 14(1), 165–178 (2017). https://doi.org/10.3934/mbe.2017011
Fujarewicz, K., Galuszka, A.: Generalized backpropagation through time for continuous time neural networks and discrete time measurements. In: Rutkowski, L., Siekmann, J., Tadeusiewicz, R., Zadeh, L.A. (eds.) Artificial Intelligence and Soft Computing - ICAISC 2004. Lecture Notes in Computer Science, vol. 3070, pp. 190–196 (2004). https://doi.org/10.1007/978-3-540-24844-6_24
Fujarewicz, K., Kimmel, M., Lipniacki, T., Swierniak, A.: Adjoint systems for models of cell signaling pathways and their application to parameter fitting. IEEE ACM Trans. Comput. Biol. Bioinform. 4(3), 322–335 (2007). https://doi.org/10.1109/tcbb.2007.1016
Fujarewicz, K., Kimmel, M., Swierniak, A.: On fitting of mathematical models of cell signaling pathways using adjoint systems. Math. Biosci. Eng. 2(3), 527–534 (2005). https://doi.org/10.3934/mbe.2005.2.527
Fujarewicz, K., Łakomiec, K.: Parameter estimation of systems with delays via structural sensitivity analysis. Discr. Continuous Dyn. Syst. Ser. B 19(8), 2521–2533 (2014). https://doi.org/10.3934/dcdsb.2014.19.2521
Fujarewicz, K., Łakomiec, K.: Adjoint sensitivity analysis of a tumor growth model and its application to spatiotemporal radiotherapy optimization. Math. Biosci. Eng. 13(6), 1131–1142 (2016). https://doi.org/10.3934/mbe.2016034
Garcia, V.: Sensitivity analysis for ODEs and DAEs, MATLAB central file exchange. https://www.mathworks.com/matlabcentral/fileexchange/1480-sensitivity-analysis-for-odes-and-daes. Accessed 25 Mar 2016
Hendrickson, R.: A Survey of Sensitivity Analysis Methodology. National Bureau of Standards, NBSIR 84-28114, Washington DC (1984)
Jakubczak, M., Fujarewicz, K.: Application of adjoint sensitivity analysis to parameter estimation of age-structured model of cell cycle. In: Pietka, E., Badura, P., Kawa, J., Wieclawek, W. (eds.) Advances in Intelligent Systems and Computing, vol. 472, pp. 123–131. Springer (2016). https://doi.org/10.1007/978-3-319-39904-1_11
Jonak, K., Kurpas, M., Szoltysek, K., Janus, P., Abramowicz, A., Puszynski, K.: A novel mathematical model of ATM/p53/NF-\(\kappa \)b pathways points to the importance of the DDR switch-off mechanisms. BMC Syst. Biol. 10(1), 75 (2016). https://doi.org/10.1186/s12918-016-0293-0
Kumala, S., Fujarewicz, K., Jayaraju, D., Rzeszowska-Wolny, J., Hancock, R.: Repair of DNA strand breaks in a minichromosome in vivo: kinetics, modeling, and effects of inhibitors. Plos One 8(1), 1–12 (2013). https://doi.org/10.1371/journal.pone.0052966
Łakomiec, K., Fujarewicz, K.: Parameter estimation of non-linear models using adjoint sensitivity analysis. In: Advanced Approaches to Intelligent Information and Database Systems, Studies in Computational Intelligence, vol. 551, pp. 59–68. Springer (2014). https://doi.org/10.1007/978-3-319-05503-9_6
Łakomiec, K., Kumala, S., Hancock, R., Rzeszowska-Wolny, J., Fujarewicz, K.: Modeling the repair of DNA strand breaks caused by \(\gamma \)-radiation in a minichromosome. Phys. Biol. 11(4), 045003 (2014). https://doi.org/10.1088/1478-3975/11/4/045003
MathWorks MATLAB SimBiology release 2015b, Natick, Massachusetts, United States (2015)
Perumal, T.M., Wu, Y., Gunawan, R.: Dynamical analysis of cellular networks based on the green’s function matrix. J. Theor. Biol. 261(2), 248–259 (2009). https://doi.org/10.1016/j.jtbi.2009.07.037
Puszynski, K., Hat, B., Lipniacki, T.: Oscillations and bistability in the stochastic model of p53 regulation. J. Theor. Biol. 254(2), 452–465 (2008). https://doi.org/10.1016/j.jtbi.2008.05.039
Puszynski, K., Lachor, P., Kardynska, M., Smieja, J.: Sensitivity analysis of deterministic signaling pathways models. Bull. Pol. Acad. Sci. Tech. Sci. 60(3), 471–479 (2012)
Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Saisana, M., Tarantola, S.: Global Sensitivity Analysis: The Primer. Wiley, New York (2008)
Acknowledgement
This work was supported by the Polish National Science Centre under grant DEC-2016/21/B/ST7/02241 (K.F.) and by the Silesian University of Technology under grants BKM-508/RAU1/2017/12 (K.K.), BK-204/RAU1/2017/3 (K.Ł.). Calculations were performed using the infrastructure supported by the computer cluster Ziemowit (www.ziemowit.hpc.polsl.pl) funded by the Silesian BIO-FARMA project No. POIG.02.01.00-00-166/08 and expanded in the POIG.02.03.01-00-040/13 in the Computational Biology and Bioinformatics Laboratory of the Biotechnology Centre at the Silesian University of Technology.
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Łakomiec, K., Kurasz, K., Fujarewicz, K. (2019). Sensitivity Analysis of Biomedical Models Using Green’s Function. In: Pietka, E., Badura, P., Kawa, J., Wieclawek, W. (eds) Information Technology in Biomedicine. ITIB 2018. Advances in Intelligent Systems and Computing, vol 762. Springer, Cham. https://doi.org/10.1007/978-3-319-91211-0_42
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