Renaud G, Calle S, Remenieras J P, Defontaine M
Lab. Ultrasons Signaux et Instrum., Univ. Francois Rabelais, Tours, France. renau
IEEE Trans Ultrason Ferroelectr Freq Control. 2008 Jul;55(7):1497-507. doi: 10.1109/TUFFC.2008.825.
Bone tissue contains microcracks that may affect its mechanical properties as well as the whole trabecular structure. The relationship between crack density and bone strength is nevertheless poorly understood. Linear ultrasound techniques being almost insensitive to the level of damage, we propose a method to measure acoustic non- linearity in trabecular bone using time-of-flight modulation (TOFM) measurements. Ultrasonic short bursts times-of- flight (TOF) are modulated as a result of nonlinear interaction with a low-frequency (LF) wave in the medium. TOF variations are directly related to elastic modulus variations. Classical and nonclassical nonlinear parameters beta, delta, and alpha can be derived from these measurements. The method was validated in materials with classical, quadratic, nonlinear elasticity. In dense trabecular bone region, TOFM related to classical, quadratic, nonlinear elasticity as a function of the LF pressure exhibits tension-compression asymmetry. The TOFM amplitude measured in dense areas of trabecular bone is almost one order of magnitude higher than in a low-density area, but the linear parameters show much smaller variations: 5% for ultrasound propagation velocity and 100% for broadband ultrasonic attenuation (BUA). In high-density trabecular bone regions, beta depends on the LF pressure amplitude and can reach 400 at 50 kPa.
骨组织中含有微裂纹，这些微裂纹可能会影响其力学性能以及整个小梁结构。然而，裂纹密度与骨强度之间的关系却鲜为人知。由于线性超声技术对损伤程度几乎不敏感，我们提出了一种利用飞行时间调制（TOFM）测量来检测小梁骨声学非线性的方法。超声短脉冲的飞行时间（TOF）会因与介质中的低频（LF）波发生非线性相互作用而受到调制。TOF变化与弹性模量变化直接相关。经典和非经典非线性参数β、δ和α可从这些测量中得出。该方法在具有经典二次非线性弹性的材料中得到了验证。在致密小梁骨区域，与经典二次非线性弹性相关的TOFM作为低频压力的函数呈现出拉压不对称性。在小梁骨致密区域测量的TOFM幅度比低密度区域高出近一个数量级，但线性参数的变化要小得多：超声传播速度变化5%，宽带超声衰减（BUA）变化100%。在高密度小梁骨区域，β取决于低频压力幅度，在50 kPa时可达到400。
