In this study, we investigated the impact of various simulated skull bone geometries on the determination of skull speed of sound and acoustic attenuation values via optimization using transmitted pressure amplitudes beyond the bone. Using the hybrid angular spectrum method (HAS), we simulated ultrasound transmission through four model sets of different geometries involving sandwiched layers of diploë and cortical bone in addition to three models generated from CT images of ex-vivo human skull-bones. We characterized cost-function solution spaces for each model and, using optimization, found that when a model possessed appreciable variations in resolvable layer thickness, the predefined attenuation coefficients could be found with low error (RMSE < 0.01 Np/cm). However, we identified a spatial frequency cutoff in the models' geometry beyond which the accuracy of the property determination begins to fail, depending on the frequency of the ultrasound source. There was a large increase in error of the attenuation coefficients determined by the optimization when the variations in layer thickness were above the identified spatial frequency cutoffs, or when the lateral variations across the model were relatively low in amplitude. For our limited sample of three CT-image derived bone models, the attenuation coefficients were determined successfully. The speed of sound values were determined with low error for all models (including the CT-image derived models) that were tested (RMSE < 0.4 m/s). These results illustrate that it is possible to determine the acoustic properties of two-component models when the internal bone structure is taken into account and the structure satisfies the spatial frequency constraints discussed.

中文翻译：

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骨模型几何形状对颅骨声学特性测定的影响


在这项研究中，我们通过使用骨外传输的压力幅度进行优化，研究了各种模拟颅骨几何形状对确定颅骨声速和声衰减值的影响。使用混合角谱方法 (HAS)，除了根据离体人类颅骨 CT 图像生成的三个模型之外，我们还通过四个不同几何形状的模型集（涉及夹层板和皮质骨）模拟超声传输。我们对每个模型的成本函数解空间进行了表征，并通过优化发现，当模型的可解析层厚度具有明显变化时，可以以较低的误差找到预定义的衰减系数（RMSE < 0.01 Np/cm）。然而，我们在模型的几何形状中发现了一个空间频率截止点，超过该截止频率，属性确定的准确性开始下降，具体取决于超声源的频率。当层厚度的变化高于确定的空间频率截止值时，或者当模型的横向变化幅度相对较低时，优化确定的衰减系数的误差会大幅增加。对于我们有限的三个 CT 图像衍生骨模型样本，成功确定了衰减系数。所有测试模型（包括 CT 图像衍生模型）的声速值均以低误差确定（RMSE<<0.4m/s）。这些结果表明，当考虑内部骨骼结构并且该结构满足所讨论的空间频率约束时，可以确定二元模型的声学特性。