Functional adaptation of bone mechanical properties using a diffusive stimulus originated by dynamic loads in bone remodelling

The present study proposes a mathematical model elucidating some aspects of the bio-mechanical stimulus involved in bone remodelling, which, in our assumptions, acts as a diffusive signalling agent for bones. The proposed mathematical model aims to scrutinize the behaviour of bone tissues and their evolution over time by better understanding the mechanisms of bone remodelling and offering new theoretical tools for developing more effective and efficient treatment strategies for bone defects, trauma, or diseases. The bone remodelling process involves adapting bone mechanical properties in response to dynamic loads. This adaptation is achieved through the diffusive stimulus created by these loads. The result is a functional adaptation of the bone, wherein it acquires the mechanical properties required to withstand the loads to which it is subjected. This phenomenon has significant implications for the study of bone physiology and biomechanics. As such, it is a topic of great interest to researchers and practitioners in the fields of orthopaedics, sports medicine, and related disciplines. In this contribution, the mechanical behaviour is modelled through a generalized three-dimensional deformable continuum that also takes into account the porous nature of the bone tissue with a nonlinear constitutive law. Since we have focused the study on the model of the stimulus and its interplay with the evolution of the tissue, an isotropic material symmetry is adopted to simplify the problem. This formulation is promising because it permits the bone tissue to evolve depending on the time variability of the external mechanical loads, even if the source of the stimulus is assumed to be the strain energy density. The proposed model exhibits great potential, and its scope extends to several other applications, including the integration of anisotropic material symmetry and damage. Further research in this area can unlock new possibilities and enable the development of more advanced models with these new features. We plan future investigations to focus on these areas to exploit the full potential of this model entirely.