Inferring Porosity from Frequency Dependent Attenuation in Cortical Bone Mimicking Porous Media

Osteoporosis affects porosity in cortical bone. Quantifying levels of osteoporosis by inferring the micro-architectural properties from ultrasonic wave attenuation in cortical bone has yet to be done. In this work we use a phenomenological, power law model to describe the frequency dependent attenuation in non-absorbing porous media mimicking a simplified cortical bone structure. We optimize this model to fit data generated using a finite-difference, time domain (FDTD) numerical simulation. Model parameters are estimated using an ordinary least squares (OLS) formulation of the inverse problem. With these we determine linear, functional relationships between the model parameter estimates and the micro-architectural parameters, pore density and pore diameter. These relationships allow us to infer ranges of porosity from simulated attenuation data. Repeating this process for attenuation data collected from cortical bone samples could allow one to characterize the micro-architectural properties of bone.