Bone ultrasound fractal dimension theory and experimental analysis with application to early osteoporosis prediction in cancellous bone

Fractal analysis and ultrasound techniques are pivotal in assessing osteoporosis by examining the complex structure of cancellous bone. Osteoporosis, marked by reduced bone mass and the degradation of bone microarchitecture, results in greater fragility and a higher risk of fractures. The poroelastodynamic model proposed in this study incorporates the Navier-Stokes equations of linear elasticity and Biot's theory of porous media, allowing the investigation of osteoporosis versus fractal dimension. Some mechanical properties of cancellous bone, such as porosity, density, elasticity, Poisson's ratio, and viscosity of bone marrow within the porous medium, are taken into account in this analysis. Our findings suggest that the fractal dimension of cancellous bone is a critical factor in predicting osteoporosis. Our study incorporates data from 84 women and 49 men to explore how fractal dimension can predict osteoporosis. We found that individuals with osteoporosis consistently exhibit lower fractal dimensions compared to those with normal bone, irrespective of gender or age. Analyzing rib data from three donors, we observed that an increase in fractal dimension correlates with a decrease in Young's modulus. Furthermore, examining lumbar spine data from 22 cadavers, we observed that increased bone mineral density is associated with higher fractal dimensions, while higher bone porosity correlates with reduced bone mineral density. Additionally, considering the attenuation of cancellous bone from 61 women, including 32 with osteoporotic bone and 29 with normal bone, shows that attenuation in normal bone is higher than in osteoporotic bone when accounting for porosity. Therefore, it can be concluded that increased porosity leads to a reduction in fractal dimension. From this study, the fractal dimension emerges as a critical metric in predicting osteoporosis, offering insights into the structural changes within cancellous bone that contribute to its fragility and susceptibility to fractures.