Adaptive bone remodeling using orthotropic Cosserat elasticity

The mechanical properties of bone are essential for supporting movement and protecting vital organs. Computational modeling is a key method for studying these properties. While some models address the anisotropic adaptive remodeling of bone, they often rely on classical elasticity theory, which inadequately describes materials with complex microstructures like bone. This study introduces a novel approach by incorporating the Cosserat elasticity theory into the adaptive remodeling framework, overcoming the limitations of classical elasticity. By modeling a proximal femur bone segment as an orthotropic material, we explore how Cosserat elasticity influences bone mechanics. The study also considers the adaptive behavior of the Cosserat parameters in relation to the stiffness modulus, Poisson's ratio, and the internal length scale. Our results indicate that Cosserat elasticity predicts bone behavior with a maximum displacement deviation of 36.33%, showing lower displacements compared to classical elasticity models, particularly at higher internal length scales. Furthermore, the Cosserat model shows a similar but lower average density distribution in the proximal femur, aligning well with existing literature, and more noticeable in localized stress areas. The study extends its analysis to a finite element model of a proximal femur specimen and concludes that the application of the Cosserat theory of elasticity in the context of adaptive bone remodeling yields more accurate results compared to classical elasticity. These findings suggest that the Cosserat theory offers a more realistic approach to bone modeling, particularly for materials where deformation is significantly influenced by microstructure. This advancement has important implications for biomechanics and materials science.