Acoustic diffusion constant of cortical bone: Numerical simulation study of the effect of pore size and pore density on multiple scattering

While osteoporosis assessment has long focused on the characterization of trabecular bone, the cortical bone micro-structure also provides relevant information on bone strength. This numerical study takes advantage of ultrasound multiple scattering in cortical bone to investigate the effect of pore size and pore density on the acoustic diffusion constant. Finite-difference time-domain simulations were conducted in cortical microstructures that were derived from acoustic microscopy images of human proximal femur cross sections and modified by controlling the density (Ct.Po.Dn) $∈[5−25] pore/mm2$ and size (Ct.Po.Dm) $∈[30−100] μm$ of the pores. Gaussian pulses were transmitted through the medium and the backscattered signals were recorded to obtain the backscattered intensity. The incoherent contribution of the backscattered intensity was extracted to give access to the diffusion constant D. At 8 MHz, significant differences in the diffusion constant were observed in media with different porous micro-architectures. The diffusion constant was monotonously influenced by either pore diameter or pore density. An increase in pore size and pore density resulted in a decrease in the diffusion constant (D $=285.9Ct.Po.Dm−1.49, R2=0.989 , p=4.96×10−5,RMSE=0.06; D=6.91Ct.Po.Dn−1.01, R2=0.94, p=2.8×10−3 , RMSE=0.09$⁠), suggesting the potential of the proposed technique for the characterization of the cortical microarchitecture.