Modeling and biomechanical characterization of femur and tibia bones using the Extended Mooney-Rivlin approach with mathematical validation.

BACKGROUND

Understanding the non-linear mechanical behavior of human bone is critical for improving orthopedic modeling and developing personalized treatment strategies. The Mooney-Rivlin model, traditionally used in soft matters, has been extended to capture the complex stress-strain relationships of hard biological materials like bone.

OBJECTIVE

To apply the Extended Mooney-Rivlin model to human bone specimens and quantify regional variations in mechanical parameters, with the goal of improving finite element simulations and biomechanical interpretations.

PARTICIPANTS AND

SETTING

The study analyzed bone specimens from the proximal femur as well as the midshaft, distal, and proximal sections of long bones in the lower limb, based on data obtained from the literature.

METHODS

Experimental stress-strain data were collected from bone samples subjected to uniaxial loading. The Extended Mooney-Rivlin model was fitted to the data to extract four key parameters: B (overall stiffness), C 1 (shear resistance), C 2 (damping/energy dissipation), and H (non-linearity).

RESULTS

The model demonstrated strong goodness-of-fit across all specimens (R 2  > 0.95). Stiffness (B) was significantly higher in midshaft regions compared to distal regions. Damping capacity (C 2 ) and linearity (H) were elevated in distal regions C 2 , indicating enhanced shock-absorbing properties. Surprisingly, shear resistance (C 1 ) was also greater in trabecular-rich regions, reflecting greater adaptability to complex loading environments.

CONCLUSIONS

The Extended Mooney-Rivlin model effectively captures regional variations in bone mechanics, with clear distinctions between cortical and trabecular bone behavior. These findings support its application in advanced biomechanical modeling and suggest new directions for personalized orthopedic treatment. Future work should explore the influence of age, bone mineral density, and pathological changes on these mechanical parameters.