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

Abstract

Computational studies on the evaluation of bone status in cases of pathologies have gained significant interest in recent years. This work presents a parametric and systematic numerical study on ultrasound propagation in cortical bone models to investigate the effect of changes in cortical porosity and the occurrence of large basic multicellular units, simply called non-refilled resorption lacunae (RL), on the velocity of the first arriving signal (FAS). Two-dimensional geometries of cortical bone are established for various microstructural models mimicking normal and pathological tissue states. Emphasis is given on the detection of RL formation which may provoke the thinning of the cortical cortex and the increase of porosity at a later stage of the disease. The central excitation frequencies 0.5 and 1 MHz are examined. The proposed configuration consists of one point source and multiple successive receivers in order to calculate the FAS velocity in small propagation paths (local velocity) and derive a variation profile along the cortical surface. It was shown that: (a) the local FAS velocity can capture porosity changes including the occurrence of RL with different number, size and depth of formation; and (b) the excitation frequency 0.5 MHz is more sensitive for the assessment of cortical microstructure.

Towards assessing cortical bone porosity using low-frequency quantitative acoustics: A phantom-based study

“…Unexpectedly, the relative changes in wave velocity due to porosity found in this study were comparable to results of experimental and computational studies measuring FAS at high frequencies between 500kHz and 2MHz: An experimental study on 10 human radii found FAS changes of -52 ± 12 m/(s %p), which corresponds to -1.5%v/%p [ 26 ], while two computational studies predicted changes between -0.6 and -1.0%v/%p [ 27 , 28 ]. Compared to these studies, limitations of the presented work (-0.5 to -1.5%v/%p) were the simple cylindrical shape, as well as the large size and the regular distribution of pores in the tested phantoms.…”

Estimation of Cortical Bone Microstructure From Ultrasound Backscatter

“…Not only the propagation medium, but also transmitter and receiver configurations and characteristics can be modeled close to real-life conditions. Previous studies have used Finite-Difference Time-Domain (FDTD) simulations based on two-dimensional maps derived from scanning acoustic microscopy images with a spatial resolution of approximately 20 µm to study i) ultrasound transmission in the femoral neck [32], ii) the effect of porosity on wave propagation in healthy and osteoporotic bones [33], iii) to estimate the effect of porosity and pore size on ultrasound multiple scattering and diffusion [30]. Most recently, three-dimensional FDTD models generated from second-generation HR-pQCT data have been proposed [34].…”

Computational modeling of long bones during the fracture healing process

“…In this section, the structural features of the computational models are described representing different cases of cortical porosity and pores' sizes as well as different number and distribution of RLs. The structural and material properties were derived from (Bourgnon et al, 2014;Potsika et al, 2016a), in which the Haversian canals of normal size were differentiated from the RLs to distinguish healthy bones (with no or few RL) from degenerated ones. As can be seen in Fig.…”

“…It was assumed that the soft tissues surrounding the cortical plate, as well as the circular pores are composed of water. Table 6.1 summarizes the material properties assigned to the cortical bone, scatterers and soft tissues which were derived from (Potsika et al, 2016a, Bourgnon et al, 2014.…”

“…Foiret et al, 2014;Talmant, 2009). The FAS velocity and attenuation have been used as the main quantitative parameters for bone characterization(Hata et al, 2016;Baron et al, 2007;Potsika et al, 2016a;Barbieri et al, 2011). However, when the wavelength is comparable to or smaller than the thickness of the cortex, the FAS propagates as a lateral wave reflecting only material and geometrical changes in the cortical surface.…”