Computational study of the influence of callus porosity on ultrasound propagation in healing bones

Abstract

In the process of fracture healing, several phases of recovery are observed as the mechanical stability, continuity and normal load carrying capacity are gradually restored. The ultrasonic monitoring and discrimination of different healing stages is a complex process due to the significant microstructure and porous nature of osseous and callus tissues. In this study, we investigate the influence of the callus pores' size and concentration on ultrasound propagation in a long bone at a late healing stage. Different excitation frequencies are applied in the range of 300 kHz-1 MHz. A 2D geometry is developed and axial transmission calculations are performed based on a Finite Element Method. The velocity of the first arriving signal (FAS) and the propagation of guided waves are used as the estimated parameters. It was shown that the FAS velocity can reflect callus porosity changes, while the propagation of guided waves is sensitive to pores' distribution for higher frequencies.

Computational Study of the Effect of Cortical Porosity on Ultrasound Wave Propagation in Healthy and Osteoporotic Long Bones

“…This work presents a 2D parametric and systematic computational study aiming to investigate the effect of cortical porosity on ultrasound wave propagation in healthy and osteoporotic long bones. In comparison to previous studies [ 2 , 14 , 26 ], we established more realistic scenarios, as this is the first time that the distribution of the pores was randomized including normal pores, as well as pores with diameters larger than the Haversian canal size. Moreover, the analysis was not limited to a small segment of cortical bone with the presence of only one large basic multicellular unit as in [ 14 ].…”

“…When multiple receivers are considered, the change in the FAS arrival time Δt (μs) can be calculated using Δt(x) = t(x i ) − t(x i-1 ) , where i is the number of the receiving position, t(x i ) is the arrival time of the signal at receiver i and t(x i-1 ) is the arrival time at the previous receiver [ 25 ]. For the detection of the FAS a threshold was applied to the receiving waveforms corresponding to the identification of the first signal extremum ( Figure 2 ) [ 26 ].…”

Ultrasound Radiation Force for the Assessment of Bone Fracture Healing in Children: An In Vivo Pilot Study

“…The decomposed modes, though, could have been different from the waves propagating in the bone tissue material. The results of simulation and experimental ex vivo studies on cortical bone for analyzing the lamb modes using guided waves have also been reported [ 41 , 42 , 43 , 44 ].…”

The Biomechanics of Musculoskeletal Tissues during Activities of Daily Living: Dynamic Assessment Using Quantitative Transmission-Mode Ultrasound Techniques

“…The latter waves arise from the reflection, mode conversion, and interference of longitudinal and shear waves within the cortical structure [241]. Animal, simulation, and clinical studies have demonstrated that axial-transmission parameters, such as the time of flight and propagation velocity of the first arriving ultrasound signal (i.e., fast wave), when measured across a fracture site, can be used as an indicator of bone fracture and healing [162,208,[255][256][257], with propagation velocity, rather than attenuation, being arguably more sensitive to changes in callus mineralization and porosity during the regeneration process [258,259]. Similarly, simulation and ex vivo studies have also suggested that guided waves, which are generally dispersive and influenced by both the periosteal and endosteal bone surfaces, may be even more useful for evaluating oblique and transverse fractures in cortical bone [241,[260][261][262][263] and may even have the potential to detect osseous micro-cracks [264].…”