Frequency-dependent analysis of ultrasound apparent absorption coefficient in multiple scattering porous media: application to cortical bone

Abstract

The effect of matrix viscoelastic absorption on frequency-dependent attenuation in porous structures mimicking simplified cortical bone is addressed in this numerical study. An apparent absorption is defined to quantify the difference between total attenuation (resulting from both absorption and scattering) and attenuation exclusively due to scattering. A power-law model is then used to describe the frequency-dependent apparent absorption as a function of pore diameter and density. The frequency response of the porous structures to a Gaussian pulse is studied to determine the frequency range over which the system can be considered linear. The results show that for low scattering regimes (normalized frequency < 0.80), the system and its apparent absorption can be considered linear. Hence, the total attenuation coefficient results from the summation of scattering and absorption coefficients. However, for highly scattering regimes, the system can no longer be considered linear, as the apparent absorption vs. frequency deviates from a linear trend. As the pore density increases, the apparent absorption coefficient increases as well.

In vivo pulse-echo measurement of apparent broadband attenuation and Q factor in cortical bone: a preliminary study

“…This frequency may need to be adapted for smaller or larger thicknesses in order to remain with an endosteal echo clearly separated and not too much attenuated. As attenuation in cortical bone may have a nonlinear dependence on frequency (Yousefian et al, 2021), attenuation values obtained at different frequencies may not be directly compared with the values obtained in the present study.…”

“…The complex wavenumber is denoted (k + iα), where α is the imaginary part and is assumed to present a linear attenuation with frequency in cortical bone, i.e., α = β f (Minonzio et al, 2011). This linear approximation, or first order Taylor expansion, is valid around a central frequency f 0 as long as the frequency deviation ∆f is narrow, i.e., ∆f /f 0 << 1, even if the attenuation variation for larger frequency is not linear (Szabo, 1995;Yousefian et al, 2021). Note that the real part k of the wavenumber is assumed to be frequency independent within the considered bandwidth.…”

“…Ex vivo studies on cuboid specimens have established that ultrasonic attenuation of bulk waves in cortical bone is related to mass density (Bernard et al, 2015) and to Ct.vBMD (Sasso et al, 2008). Also, simulations have suggested that the scattering of ultrasound by the cavities of the pore network is one important mechanism of attenuation (Yousefian et al, 2018(Yousefian et al, , 2021Iori et al, 2020). It follows that, in addition to ultrasonic velocities measured with QUS approaches (Grimal and Laugier, 2019), attenuation could be indicative of the mechanical quality of cortical bone as it is related to Ct.Po and Ct.vBMD.…”

The influence of intra-cortical microstructure on the contrast in ultrasound images of the cortex of long bones: A 2D simulation study

“…Ultrasound attenuation in cortical bone is due to a combination of absorption by dissipative mechanisms in particular in the mineralized matrix and scattering by the pores [24]. Following the models of Yousefian et al [18,25], a frequency-independent absorption within the bone matrix with an absorption coefficient of 19.0 dB/cm at 2.5 MHz was modeled.…”

Pore‐Size Distribution and Frequency‐Dependent Attenuation in Human Cortical Tibia Bone Discriminate Fragility Fractures in Postmenopausal Women With Low Bone Mineral Density

“…In that study, monodisperse pore radii ranging from 50 to 100 µm and densities ranging from 20 to 50 pores per mm³ were investigated. The same group also proposed a model that aims at decoupling the effects of viscoelastic absorption and scattering (44) . Although forward and backscatter characteristics are not identical, the same concept could be integrated into the cortical backscatter model in the future to assess the relative contributions of structural and viscoelastic tissue alterations to the fragility fracture discrimination independently.…”