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Multi-parametric analysis of bone turnover

Simonovic, Julijana 2019. Multi-parametric analysis of bone turnover. Presented at: The International Workshop on Recent Trends in Applied Mathematics (RTM’19), jointly with the International Conference on Digital Image and Signal Processing, St Hugh's College, University of Oxford, Oxford, UK, 19-20 April 2019. -.

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This paper describes bone cell signalling processes at the level of basic multicellular unit (BMU). Using the bone cell population mathematical model of the system of coupled ordinary differential equations (ODEs) with power-law nonlinearities it is possible to properly interpret and analyse bone cell communication dynamics. The system of bone cellular communication is complex and not yet properly described and revealed. Mathematical interpretation and models of this system become even more important as the higher resolution screening discovers the new players involved in the process, what puts demands on theories, methods and assumptions used and the efficiency of numerical methods employed for solving as well as managing of parameters and data. The structural analysis has been used here for stability analyses of the problem, as like as for analyses of system sensibility to small parameters changes. The usage of the multi-parametric synchronous analysis presented in this paper is the advantage of Mathematica ODE solver that provides the functional interpretation of important parameters of dynamics. Such a representation with easily changeable values of parameters and visible system dynamic responses is useful for fast and reliable choice of significant and relevant parameters for every particular set of variable initial conditions and parameters values. The models explored in numerous numerical (in-silico) experiments also provide more realistic approaches to interpreting either the physiological and pathological pathways but also the development of various possible interventions for patients with bone trauma and diseases. This research is a very practical and clear example of nonlinear theory application for bone cell signalling processes modelling and interpretation. Especially, because every system of ODE is accompanied with a particular functional model of described processes, what clearly bridges the gap between the biological and mathematical way of interpretations of the same phenomena of bone cellular signalling. The functional models are important as necessary explanations of the significant and important terms and parameters that have to be adjusted and fitted to the model according to the new knowledge of the involved aspects. Moreover, obtained conclusions and discussions for parameter values and ranges are very applicable for the justification of effectiveness of mathematical models and their compliance with in-vivo experiments of bone cells. Keywords Bone cell population model, regular bone turnover, simultaneous parameter changes, parameters sensitivity, nonlinear system of ordinary differential equations. Acknowledgements These results are part of research on project MMoBEER (nov.2017-nov.2019) that has received funding from the European Union's H2020 MGA MSCA-IF-2016 under grant agreement No. 752793.

Item Type: Conference or Workshop Item (Speech)
Date Type: Completion
Status: Unpublished
Schools: Engineering
Subjects: Q Science > QA Mathematics
Date of Acceptance: 11 January 2019
Last Modified: 05 Feb 2020 03:15

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