Osteoporosis is a skeletal disease characterized by reduced bone mass and microarchitectural deterioration, leading to increased fragility. This study presents a novel three-dimensional poroelastodynamic model for analyzing cancellous bone free vibration responses. The model incorporates the Navier-Stokes equations of linear elasticity and the Biot theory of porous media, allowing the investigation of osteoporosis-related changes. The analysis considers parameters like porosity, density, elasticity, Poisson ratio, and viscosity of bone marrow within the porous medium. Our findings indicate that natural frequencies of cancellous bone play a crucial role in osteoporosis prediction. By incorporating experimental data from 12 mouse femurs, we unveil insights into osteoporosis prediction. Increased porosity reduces bone stiffness, lowering natural frequencies. However, it also increases bone mass loss relative to stiffness, leading to higher frequencies. Therefore, the natural frequencies of osteoporotic bone are always higher than the natural frequencies of normal bone. Additionally, an increase in bone marrow within the pores, while increasing damping effects, also increases natural frequencies, which is another indication of osteoporosis growth in bone. The presence of bone marrow within the pores further influences natural frequencies, providing additional insights into osteoporosis growth. Thinner and smaller bones are found to be more susceptible to osteoporosis compared to larger and bigger bones due to their higher natural frequencies at equivalent porosity levels.
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