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Mathematical models of bone externally excited remodelling

Periodic Reporting for period 1 - MMoBEER (Mathematical models of bone externally excited remodelling)

Reporting period: 2017-11-02 to 2019-11-01

The interesting phenomena of bone adaptation to external loading are being addressed by mathematical modelling of externally excited bone cell communication processes. In an adult organism, the adaptation process predominantly depends on bone cellular organization and communication processes that are highly driven by external mechanical loading. How physical forces and changes in the mechanical properties of cells and tissues contribute to development, cell differentiation, physiology, and disease, in general, is a major interest of mechanobiology. Mathematical modelling and in-silico experiments underpinned with mechanobiology discoveries of mechanosensing, recognition, transduction and down streaming of external signals on the level of bone bаsic multi-cellular unit (BMU) were the main objectives of the project. The project develops computational analytical models in order to address and better understand mechanotransduction - the molecular mechanisms by which bone cells sense and respond to mechanical signals.
At least three different bone cell lineages loaded by the external signal together with the numerous parameters of their biochemical secretory activities are involved in this complex process of mutual interactions. This complexity can be better understood and predicted by the employment of the developed mathematical model which is capable to cover a number of the necessary parameters and aspects of the process and give the results that can predict which kind of the external signal is the most desirable for healthy bone cell activities when the bone resorption and formation contents are in balance. Once verified a mathematical model is also a good tool in personalized medicine since the calculation is easy for an entirely different set of input parameters belongs to the specific conditions of patients.
The collaboration between in-silico and in-vitro experiments is inevitable for further success of the field. With this research, we wish to emphasize the importance, reliability and credibility of mathematical models which are a great way of cementing biological intuition. Specifically, they provide causative mechanisms linking inputs and outputs and illuminating underlying assumptions that determine a biological system’s dynamics. Finally, they offer a means of predicting new outcomes, as well as highlighting the most sensitive modelled components, resulting in the construction of new experimental hypotheses and experimentations that are more efficient.
The research started with the investigation of contemporary theories of bone tissue processes by attendance to the Course at Bone cellular biology (Basic Course in Bone and Cartilage Biology and Disease, 23rd – 24th November 2017, Sheffield University.) and extensive study of the bone biology literature and the numerous published scientific articles on the theme of mathematical models of bone remodelling. On the base of a large number of these readings, the few knowledge gaps and challenges of the adequate number of parameters have been identified and considered in the discussion with collaborators from School of Biosciences at Cardiff Univesity during the Lab meeting. We agreed that the simpler mathematical model with osteocyte number time changes needs to be tested with data from in vitro cell-collagen gel culture experiment with Human Mesenchymal stem cell (MSC) derived line Y201. Such an experiment has been planned, and several stages of the experiment have been successful growing, feeding, counting and identifying osteocyte cells population, followed with collagen gel embedding and distribution in the plastic plate wells, preparation of measurements 1-hour pre and after loading of 1 Hz, the results of the experiment are still being processed. We finalized the following tasks:
Sublimation of contemporary theories and methods of bone cellular modelling to their essences with all their advantages and consequences; Identifying knowledge gaps and challenges
Coordination with mathematical and mechanical possibilities and biological needs relevant for a model, the definition of different language interpretation of terms- nomenclature of all relevant parameters.
Developing a mathematical model of bone turnover concerning osteocyte role and respond to mechanical loading;
The five conference papers were prepared, submitted and presented (by the poster presentation and conference talks) for this first-year period of research.
The next stage, over the second year of project development, was parametrisation and characterisation of the developed mathematical model of bone turnover concerning osteocyte role and respond to mechanical loading. During this period there has been established intensive collaboration with the colleagues from the School of Mathematics at Cardiff University and from the University of Oxford's Institute of Musculoskeletal Sciences. By presenting an experimentally evidenced mathematical model of bone, which includes externally forced turnover, we contribute to the realism of modelling. Critically, we approach the modelling through both deterministic and stochastic methods, which allow us to consider the intrinsic noisiness of the discrete process. We also agreed that it will be necessary for validation of the model to compare the results with results of a 3D physicochemical map of key osteocyte markers to locate the osteocytic response in time and space from the ongoing experiments. Although the results wait for validation with biological organ-on-chip human osteocyte experiment, the in-silico experiments have already given explanations and predictions that fit nicely with already discovered and published findings of total bone content increase under the influence of mechanical strains and loading.
The five conference papers were prepared, submitted and presented (by a poster presentation and conference talks) for the second-year period of research.
Part of the research plans was also to continue research in the field of nonlinear dynamical systems modelling. This part of the research was realized by two conferences attendance and talks.
The special concern was dedicated to the public engagement and dissemination of the obtained results, thus JS has been trained for public speaking and engagement at Coaching session “Communication and Public Speaking” organized by the European Commission within the event “MSCA Satellite event ESOF 2018” Toulouse, 7-8th July 2018. This session improved her skills and presenting techniques for TED talk presentation and public engagement. This experience she applied during her participation in the photography Chinese Whisper project and Tea with a Researcher session for European Researcher`s Night in Bristol, on the 28th Sept. 2018.
We introduce an adapted mathematical model for bone remodelling that maintains those fundamental mechanisms captured in existing models while incorporating biological aspects of bone mechanosensitivity that have not previously been considered deterministically and stochastically. In particular, this model includes bone cells mechanobiology, which, apart from their biochemical processes and their interactions with other bone remodelling cells, includes external periodic signal transduction and influence that represents a significant advance to the field.