Mathematical models of bone externally excited remodelling

2026-07-22

For describing complex systems as bone tissue, with their inner interactions and their interactions with environment the mathematical models become even more complex, that puts demands on theories, methods and assumptions used and the efficiency of numerical methods employed for solving as well as the management of data. The complexity of bone models depends not only on the number of parameters describing different biochemistry and Multi-physics influences but also on different time scales and rate of periodicity of processes involved. In structural analysis non-linearity plays important role for realistic description of real world phenomena. Incorporated the parametric nonlinear analysis of periodically excited hybrid systems into a structural models of bone would be a great advantages for prediction of a more realistic situation for description of the bone mass distribution, delay in the osteoblasts and osteoclasts coupling, osteocytes transferring of signals and more other issues related to the bone adaptively and strength. The aim of the project would be that on the base of existing level of known parameters in bone turnover guided by external loading provide an analytical approach to be solve and interpreted for real description and prediction of bone adaptive behavior. Hybrid systems treat cellular level as discrete system of particles described with system of coupled ordinary differential equations and environmental conditions as a continuous system described with a system of coupled partial differential equations affected with different external signals. The established, measured and explored model will also give an approach closer to the realistic situation and real needs and suggestions for patients with bone problems but also for those who want to have healthy and strong skeleton.

United Kingdom (UK)

2026-01-15