This work proposes the use of two physics-based models for wave attenuation to infer the microstructure of cortical bone-like structures. One model for ultrasound attenuation in porous media is based on the independent scattering approximation (ISA) and the other model is based on the Waterman Truell (WT) approximation. The microstructural parameters of interest are pore radius and pore density. Attenuation data are simulated for three-dimensional structures mimicking cortical bone using the finite-difference time domain package SimSonic. These simulated structures have fixed sized pores (monodisperse), allowing fine-tuned control of the microstructural parameters. Structures with pore radii ranging from 50 to $100\hspace{0.17em}\hspace{0.17em}\mu \mathrm{m}$ and densities ranging from 20 to 50 pores/mm³ are generated in which only the attenuation due to scattering is considered. From here, an inverse problem is formulated and solved, calibrating the models to the simulated data and producing estimates of pore radius and density. The estimated microstructural parameters closely match the values used to simulate the data, validating the use of both the ISA and WT approximations to model ultrasonic wave attenuation in heterogeneous structures mimicking cortical bone. Furthermore, this illustrates the effectiveness of both models in inferring pore radius and density solely from ultrasonic attenuation data.

中文翻译：

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使用基于物理的建模从超声波衰减推断孔隙半径和密度

这项工作建议使用两种基于物理学的波衰减模型来推断皮质骨样结构的微观结构。多孔介质中超声衰减的一种模型基于独立散射近似 (ISA)，另一种模型基于 Waterman Truell (WT) 近似。感兴趣的微观结构参数是孔半径和孔密度。使用有限差分时域包SimSonic模拟模拟皮质骨的三维结构的衰减数据。这些模拟结构具有固定大小的孔（单分散），允许微调控制微观结构参数。孔径范围为 50 到$100\hspace{0.17em}\hspace{0.17em}\mu \mathrm{米}$生成的密度范围为 20 至 50 个孔/mm ³，其中仅考虑散射引起的衰减。从这里开始，一个逆问题被制定和解决，将模型校准到模拟数据并产生孔隙半径和密度的估计值。估计的微结构参数与用于模拟数据的值非常匹配，验证了使用 ISA 和 WT 近似来模拟模拟皮质骨的异质结构中的超声波衰减。此外，这说明了两种模型仅从超声衰减数据推断孔隙半径和密度的有效性。