A Preliminary Numerical Study on the Interactions Between Nonlinear Ultrasonic Guided Waves and a Single Crack in Bone Materials With Motivation to the Evaluation of Micro Cracks in Long Bones

Abstract

Fatigue damage in a bone occurs in the form of micro-scale cracks with the lengths as small as to a few microns. The evaluation of cracks in bones has recently been a hot topic. However, the current most frequently used method is based on traditional linear ultrasound, which is just sensitive to gross damages rather than micro cracks. Nonlinear ultrasonic technique, which is capable of detecting microscale damages, has been widely used in metallic structures. However, few study has been directed to employing second harmonic generation of nonlinear ultrasound to evaluate fatigue damages in bones. In this study, a preliminary study is conducted on the interactions between nonlinear guided waves and a single crack in bone materials motivating to the evaluation of micro cracks in long bones. Considering the symmetry, asymmetry, location, orientation, length and width of the crack in bone materials, their influences on second harmonic responses are discussed in detail. Our results are presented as follows. Firstly, not only the primary S0 but also A0 mode Lamb wave generates the second harmonic component of S0 mode after interacting with a symmetric crack. Secondly, along the thickness direction, the primary S0 mode Lamb wave possesses almost the same detection sensitivity, no matter where the crack is located. Thirdly, the amplitudes of S0 mode second harmonic component are increased slightly when the oblique angle of the crack is set from 0º to 45º , while the amplitudes increase dramatically when the oblique angle changes to 67.5º and 90º .Lastly, the second harmonic amplitude and the relative acoustical nonlinear parameter are increased with the length of the crack, while they possess a monotonically decreasing relationship with the width of the crack. Our preliminary studies will provide priori knowledge when using nonlinear ultrasonic guided waves for detecting micro-scale cracks in long bones in future clinical inspections.INDEX TERMS Nonlinear ultrasonic Lamb waves, bone structures, the detection of cracks in bones, second harmonic component, the relative acoustical nonlinear parameter, ultrasonic signal processing

The Biomechanics of Musculoskeletal Tissues during Activities of Daily Living: Dynamic Assessment Using Quantitative Transmission-Mode Ultrasound Techniques

“…Animal, simulation, and clinical studies have demonstrated that axial-transmission parameters, such as the time of flight and propagation velocity of the first arriving ultrasound signal (i.e., fast wave), when measured across a fracture site, can be used as an indicator of bone fracture and healing [162,208,[255][256][257], with propagation velocity, rather than attenuation, being arguably more sensitive to changes in callus mineralization and porosity during the regeneration process [258,259]. Similarly, simulation and ex vivo studies have also suggested that guided waves, which are generally dispersive and influenced by both the periosteal and endosteal bone surfaces, may be even more useful for evaluating oblique and transverse fractures in cortical bone [241,[260][261][262][263] and may even have the potential to detect osseous micro-cracks [264]. The technique also allows waveguide characteristics of the bone, such as cortical thickness and/or porosity, to be estimated from dispersion curves by fitting a theoretical waveguide model [265][266][267][268].…”

Advances in nonlinear ultrasonic detection of microcracks

“…波混频的数值模拟均表明：非线性参量随微裂纹长度单调增加，随微裂纹宽度单调减小 [48,[57][58][59][60][61] ， 如图 4(a)和(b)。 Hirata 等人 [57] 和 Okada 等人 [58] 分别采用有限元模型和奇异单元模型模拟微裂纹与 体波的非线性相互作用，结果表明，裂纹越长、裂纹宽度越小，高次谐波幅值越大。Wan 等人 [59] 和 Xie 等人 [48] 针对金属材料和骨材料中的微裂纹开展了 Lamb 波二次谐波数值模拟研究。Jiao 等 人 [60] 和 Aslam 等人 [61] 分别采用 Lamb 波同向和对向混频信号表征了不同长度和宽度的微裂纹。 Lamb 波二次谐波和混频信号幅值随微裂纹长度和宽度的变化趋势与体波高次谐波一致。Wang 等人 [46] 进一步研究表明，Lamb 波传播方向与裂纹的夹角和激励信号周期数可以有效影响非线性 参量随裂纹长度的增加速率。 此外， 针对微裂纹引起的非线性信号弱、 易被背景噪声掩盖等问题，…”