Volume-based non-continuum modeling of bone functional adaptation

Background: Bone adapts to mechanical strain by rearranging the trabecular geometry and bone density. The common finite element methods used to simulate this adaptation have inconsistencies regarding material properties at each node and are computationally demanding. Here, a volume-based, non-continuum formulation is proposed as an alternative. Adaptive processes corresponding to various external mechanical loading conditions are simulated for the femur. Results: Bone adaptations were modeled for one-legged stance, abduction and adduction. One-legged stance generally results in higher bone densities than the other two loading cases. The femoral head and neck are the regions where densities change most drastically under different loading conditions while the distal area always contains the lowest densities regardless of the loading conditions. In the proposed formulation, the inconsistency of material densities or strain energy densities, which is a common problem to finite element based approaches, is eliminated. The computational task is alleviated through introduction of the quasi-binary connectivity matrix and linearization operations in the Jacobian matrix and is therefore computationally less demanding. Conclusion: The results demonstrated the viability of the proposed formulation to study bone functional adaptation under mechanical loading.