# Shear-Actuation and Vibrometer Reception of Penetrating Ultrasonic Guided Wave Modes in Human Tibia
## 1 Introduction  
Ultrasonic guided waves have played a major role in recent advances in non-destructive evaluation and structural health monitoring. The technology for long-range pipeline inspection using guided waves has already been commercialized [1; 2; 3; 4; 5]. The industrial success of ultrasonic guided waves for non-destructive evaluation has prompted its adaptation to health monitoring of human long bones. The hollow pipe-like geometry of the appendicular bones in the human skeleton causes them to act like ultrasonic waveguides [6; 7; 8]. The inherent sensitivity of ultrasonic guided waves to changes in the material and geometric properties of a waveguide suggest their strong potential to characterize bone fracture healing as well as cortical wall thinning due to developing osteoporosis [9]. Ultrasonic guided waves can potentially supplement state-of-the-art radiological imaging techniques such as dual-energy X-ray absorptiometry (DEXA) and computed tomography (CT) scans, or possibly provide a portable, low-cost alternative.  
Exploiting this potential necessitates a careful characterization of guided wave propagation in long bones. The hollow long bones are unlike regular uniform geometries such as plates and hollow cylinders [10]. Long bones exhibit complexities in both material behavior (anisotropy and internal damping) and geometric features (lack of axisymmetry and variation along the length). For instance, the cross-section of a long bone is irregular in shape and changes along the long axis [11]. This makes it difficult to identify the nature of the propagating modes in a cortical bone; hence, plate and shell approximations are often adopted.  
We investigated the use of a shear transducer to generate guided waves in a long bone that may be less prone to leak into the soft tissue surrounding the bone. This idea was inspired by the practice of using torsional waves for long-distance pipe inspection because, unlike longitudinal wave modes, the shear-based torsional waves do not leak into the enclosed fluid. The objective was to assess whether a single omni-directional shear transducer can generate guided waves in a long bone that propagate long distances axially. As will be seen, the guided waves generated in a synthetic tibia are detected by a laser Doppler vibrometer, which only senses the displacement component normal to the surface at a point. It is curious that a shear transducer generates guided waves that have a significant displacement component normal to the surface. Thus, finite element simulations were conducted to understand these experimental results. The novelties of the research described herein are (i) the use of a unique shear transducer to actuate guided waves in a tibia, and (ii) analysis of wave propagation in a geometrically realistic model rather than a surrogate plate or pipe. In the remainder of this article, Section 2 describes the experimental setup and numerical modeling, while Section 3 presents the experimental and numerical results. Then, Section 4 discusses the findings, and finally Section 5 gives a brief summary and states the conclusions.