A computational two-scale approach to cancellous bone remodelling - Steinmann, Paul; Schmidt, Ina; Pivonka, Peter; Papastavrou, Areti (Advanced Modeling and Simulation in Engineering Sciences, 2024)
We propose a novel two-scale (meso-macro-scale) approach to computationally capture cancellous bone remodelling allowing for efficient and effective numerical implementation. Therein, the macro-scale is governed by the well-established kinematics and kinetics of one-scale continuum bone remodelling. However, the constitutive behaviour is not postulated phenomenologically at the macro-scale, but rather follows from the meso-scale. There, for the sake of computational efficiency, the trabecular architecture is idealised as a truss network with the cross-sectional area of the trabeculae adapting to mechanical loading. Then, the meso- and the macro-scale are coupled through up- and down-scaling. Computational results on benchmark problems from bio-mechanics demonstrate that the proposed two-scale approach is effective from a modelling perspective and efficient from a computational perspective. In particular, it automatically captures anisotropy resulting from the irregular trabecular architecture at the meso-scale, and, most importantly, enables the direct investigation of different trabecular structures at the meso-scale, thereby serving as a virtual “magnifiying glass”. As an outlook, the proposed two-scale approach to cancellous bone remodelling provides an excellent launch pad for further extension, e.g., by considering more complex trabecular architectures and/or through inclusion of micro-scale bone cellular activities.
CRIS-Team Scopus Importer:2025-02-04
Keywords: Anisotropy; Cancellous bone; Computational bone remodelling; Trabecular architecture; Two-scale approach

On biological availability dependent bone remodeling - Papastavrou, Areti; Schmidt, Ina; Steinmann, Paul (Computer Methods in Biomechanics and Biomedical Engineering, 2020)
Modeling the evolution of bone density is relevant for understanding, simulation and possible prediction of bone response to external and internal influences. In this work we present a formulation for the bone density evolution process that takes into account not only the commonly considered mechanical stimulus, but, as novelty, also the influence of the availability of nutrients and hormones, with its implementation pursued within the finite element method. A simple uni-axial extension test is used to illustrate and compare our novel model against the classical approach. The results of the proposed modified model are promising for application to real-life problems.
CRIS-Team Scopus Importer:2020-03-17
Keywords: biological availability; Bone remodeling; density change; finite element method; growth