# Shear-Actuation and Vibrometer Reception of Penetrating Ultrasonic Guided Wave Modes in Human Tibia
## 4 Discussion  
The results presented in the previous section illustrate that the 200 kHz shear transducer actuated ultrasonic guided waves in a synthetic tibia that were received due to particle displacement normal to the medial surface at distances of 45-85 mm. While the transducer will generate omni-directional SH waves in a plate, the waves generated in the synthetic tibia bear no resemblance to torsional waves in a pipe. Even though the signal is attenuated over the propagation distance, it is measurable. The phase velocity spectrum computed from the received signals reveals that the propagating modes have phase velocities of \(\sim\)1500-2000 m/s. The dispersion curves obtained for the tibial cross-section at the mid-diaphysis reveal that these modes are in the low phase velocity region and nearly non-dispersive. Thus, they can be expected to penetrate the lossy material relatively well. These wave modes, which are actuated by a shear transducer, are received by particle motion normal to the surface because the wave structures for the propagating modes consist partially of this displacement. The wave propagation simulation in the time domain confirms that the wave packet, which consists of multiple modes, has particle motion normal to the surface.  
In the Results section, the wave structures for just five modes in the cluster were investigated. The displacement field for a mode is distributed over the entire cross-section, but not in a uniform way. Relatively large displacement values are localized. These fields suggest that if all the propagating modes were superposed together, the resulting displacement field might be more uniform. If this is the case, then the reception position would be more arbitrary, and the wave energy would interact with cracks located anywhere in the cross-section.  
Deep-penetrating guided wave modes could be important for monitoring the fracture-healing process in long bones. Fractures can occur at many different locations, but non-invasive access points for transducers are somewhat limited. Therefore, the guided waves could be used to transport ultrasonic energy reasonably long distances in order for it to interact with the healing fracture. The wave-discontinuity interaction would be indicative of the state of the healing process.  
Based on these findings, it is clear that penetrating guided wave propagation in long bones is complicated by the material properties and the geometry of the long bone waveguide. However, the fact that simulations conducted on the geometry of a human tibia and the properties of a human tibia showed good agreement with the results of an experiment conducted on a synthetic tibia suggests that at least some of the wave propagation characteristics for a population of human tibial bones are common. Future research is needed to quantify the guided wave characteristics in a diverse population of long bones.  
The experiments presented herein used a laser Doppler vibrometer to conveniently scan along the synthetic bone. This would not be practical for a human subject, but a simple linear array of piezoelectric receivers should function in the same way, permitting percutaneous measurements at the medial facet. Finally, neither experiments nor simulations had soft tissue adjacent to the bone surfaces, as would be the case for in vivo measurements. Future research is needed to address whether wave energy leaks into the soft tissue. Preliminary experiments with this shear transducer give cause for optimism.