The interplay between BMU activity linked to mechanical stress, specific surface and inhibitory theory dictate bone mass distribution: Predictions from a 3D computational model

Bone mechanical and biological properties are closely linked to its internal tissue composition and mass distribution, which are in turn governed by the purposeful action of the basic multicellular units (BMUs). The orchestrated action of osteoclasts and osteoblasts, the resorbing and forming tissue cells respectively, in BMUs is responsible for tissue maintenance, repair and adaptation to changing load demands through the phenomenon known as remodelling. In this work, a computational mechano-biological model of bone remodelling based on the inhibitory theory and a new scheme of bone resorption introduced previously in a 2D model, is extended to a 3D model of the real external geometry of a femur under normal walking loads. Starting from a uniform apparent density (ratio of tissue local mass to total local volume) distribution, the BMU action can be shown to lead naturally to an internal density distribution similar to that of a real bone, provided that the initial density value is high enough to avoid unrealistic final mass deposition in zones of high energy density and excessive damage. Physiological internal density values are reached throughout the whole 3D geometry, and at the same time a ‘boomerang’-like relationship between apparent and material density (ratio of tissue mass to tissue volume) emerges naturally under the proposed remodelling scheme. It is also shown here that bone-specific surface is a key parameter that determines the intensity of BMU action linked to the mechanical and biological requirements. Finally, by engaging in simulations of bone in disuse, we were able to confirm the appropriate selection of the model parameters. As an example, our results show good agreement with experimental measurements of bone mass on astronauts a fact that strengthens our belief in the insightful nature of our novel 3D computational model.