# Shear-Actuation and Vibrometer Reception of Penetrating Ultrasonic Guided Wave Modes in Human Tibia
## 2 Methods
### Experimental Setup  
The experimental setup consists of a RAM 5000 pulser-receiver system from Ritec (Warwick, RI, USA), an omni-directional transducer from Guidedwave (Bellefonte, PA, USA), a synthetic composite tibia from Sawbones (Seattle, WA, USA), an OFV-5000 Modular Vibrometer from Polytec GmbH, and a digital oscilloscope (Tektronix MSO 2014). The shear transducer was originally designed to detect acoustic emissions [12] and has a central frequency close to 200 kHz, which, when coupled to a plate and used as an actuator in an active mode, excites shear-horizontal waves in all directions as a result of its piezoelectric shear ring element. The wave vector points outward in all directions from the center of the transducer, and the particle displacement is everywhere perpendicular to the wave vector. The result in an isotropic plate is circular-crested shear-horizontal waves that emanate from the transducer, as shown in Figure 1. Since the transducer sends waves in all directions, or receives waves coming from any direction, it is known as omni-directional. The fundamental shear-horizontal mode (SH0) is non-dispersive, i.e., SH0 propagates with a velocity independent of the thickness of the waveguide and the excitation frequency. This is a significant advantage in waveguides having a variable wall thickness in the wave propagation direction. For all these aforementioned reasons, omni-directional shear transducers [13; 14] are being investigated for many industrial applications. However, the geometry of long bones is very different from uniform plates or pipes commonly encountered in industry. The cross-section's lack of symmetry and the variation along the length results in propagating modes that are different from both SH0 waves in a plate, and the analogous torsional waves (i.e., T(0,1)) in a pipe. This is the first time this transducer has been used to generate guided waves in a long bone. The flat omni-directional shear transducer was coupled to the curved medial facet of the synthetic tibia using maple syrup as the couplant. Gaps exist between the transducer and the tibia due to the mismatching surfaces, but the setup works. We have found that maple syrup works very well as a couplant for shear transducers. Cortical bone is a lossy material; therefore, the relatively low frequency of 200 kHz was investigated in an attempt to minimize attenuation for propagation paths that cover a significant extent of the diaphysis [15; 16]. The test sample, a synthetic left tibia, was made from a composite material whose mechanical properties mimic those of a cortical bone in a healthy adult [17]. We did not have the full set of elastic properties for the synthetic bone material, but the supplier reports that the Young's moduli in the longitudinal and transverse directions are 16 GPa and 10 GPa [17], respectively. Some of the stiffness coefficients for the cortical bone-mimicking material, using the resonant ultrasound spectroscopy technique, are determined in [18]. The transversely isotropic material properties used in our finite element analysis are listed in Table 1[19; 20]. For detection, a 1D laser Doppler vibrometer (LDV) was used with the laser head oriented normal to the medial surface of the tibial diaphysis. Using the LDV, guided wave signals at multiple closely spaced locations were collected on the medial surface. Being a non-contact measurement, it was easy to scan along the long axis. The laser head was carefully oriented normal to the reflective tape, and maximum signal intensity was maintained. The experimental setup is shown in Figure 2. The LDV