Numerical evaluation of the backward propagating acoustic field in healing long bones.

The propagation of ultrasound in healing long bones induces complex scattering phenomena due to the interaction of an ultrasonic wave with the composite nature of callus and osseous tissues. This work presents numerical simulations of ultrasonic propagation in healing long bones using the boundary element method aiming to provide insight into the complex scattering mechanisms and better comprehend the state of bone regeneration. Numerical models of healing long bones are established based on scanning acoustic microscopy images from successive postoperative weeks considering the effect of the nonhomogeneous callus structure. More specifically, the scattering amplitude and the acoustic pressure variation are calculated in the backward direction to investigate their potential to serve as quantitative and qualitative indicators for the monitoring of the bone healing process. The role of the excitation frequency is also examined considering frequencies in the range 0.2-1 MHz. The results indicate that the scattering amplitude decreases at later stages of healing compared to earlier stages of healing. Also, the acoustic pressure could provide supplementary qualitative information on the interaction of the scattered energy with bone and callus.

Evaluation of ultrasonic scattering for different cortical bone porosities and excitation frequencies: A numerical study.

Quantitative ultrasound is a promising and relative recent method for the assessment of bone. In this work, the interaction of ultrasound with the porosity of cortical bone is investigated for different frequencies. Emphasis is given on the study of complex scattering effects induced by the propagation of an ultrasonic wave in osseous tissues. Numerical models of cortical bone are established with a porosity of 0, 5 and 10% corresponding to healthy homogeneous bone, healthy inhomogeneous bone and normal ageing, respectively. Different excitation frequencies are applied in the range 0.2-1 MHz. The scattering amplitude and the acoustic pressure are calculated for multiple angles and receiving positions focusing on the backward direction. The results indicate that the application of higher frequencies can better distinguish changes in the energy distribution in the backward direction due to alterations of the cortical porosity.