Wear Keith, Nagatani Yoshiki, Mizuno Katsunori, Matsukawa Mami
U.S. Food and Drug Administration, Silver Spring, Maryland 20993.
Department of Electronics, Kobe City College of Technology 8-3, Gakuen Higashi-cho, Nishiku, Kobe, 651-2194 Japan.
J Acoust Soc Am. 2014 Oct;136(4):2015-24. doi: 10.1121/1.4895668.
Fast and slow waves were detected in a bovine cancellous bone sample for thicknesses ranging from 7 to 12 mm using bandlimited deconvolution and the modified least-squares Prony's method with curve fitting (MLSP + CF). Bandlimited deconvolution consistently isolated two waves with linear-with-frequency attenuation coefficients as evidenced by high correlation coefficients between attenuation coefficient and frequency: 0.997 ± 0.002 (fast wave) and 0.986 ± 0.013 (slow wave) (mean ± standard deviation). Average root-mean-squared (RMS) differences between the two algorithms for phase velocities were 5 m/s (fast wave, 350 kHz) and 13 m/s (slow wave, 750 kHz). Average RMS differences for signal loss were 1.6 dB (fast wave, 350 kHz) and 0.4 dB (slow wave, 750 kHz). Phase velocities for thickness = 10 mm were 1726 m/s (fast wave, 350 kHz) and 1455 m/s (slow wave, 750 kHz). Results show support for the model of two waves with linear-with frequency attenuation, successful isolation of fast and slow waves, good agreement between bandlimited deconvolution and MLSP + CF as well as with a Bayesian algorithm, and potential variations of fast and/or slow wave properties with bone sample thickness.
使用带限反卷积和带曲线拟合的改进最小二乘 Prony 方法（MLSP + CF），在厚度范围为 7 至 12 毫米的牛松质骨样本中检测到了快波和慢波。带限反卷积始终分离出两个具有随频率线性衰减系数的波，衰减系数与频率之间的高相关系数证明了这一点：快波为 0.997 ± 0.002，慢波为 0.986 ± 0.013（平均值 ± 标准差）。两种算法的相速度平均均方根（RMS）差异为：快波（350 kHz）为 5 m/s，慢波（750 kHz）为 13 m/s。信号损失的平均 RMS 差异为：快波（350 kHz）为 1.6 dB，慢波（750 kHz）为 0.4 dB。厚度 = 10 毫米时的相速度为：快波（350 kHz）为 1726 m/s，慢波（750 kHz）为 1455 m/s。结果表明支持具有随频率线性衰减的两个波的模型，成功分离出快波和慢波，带限反卷积与 MLSP + CF 以及贝叶斯算法之间具有良好的一致性，并且快波和/或慢波特性可能随骨样本厚度而变化。
