Ultrasonic guided wave propagation in long bones with varying cortical thickness

The propagation of ultrasonic guided wave (GW) in the long bone is very sensitive to the bones´ shapes, properties and cortical thicknesses (CTh). Most of the previous studies on the GW propagation in long bones mainly focused on the bones with uniform CTh. However, it is necessary to understand the impacts of CTh variation, such as mode conversion. Therefore, an adequate analysis on GW propagating in long bones with varying CTh is essential for the precise calibration of the quantitative measurement of it. The aim of this study is to use a modified boundary element method (BEM) to analyze the GW propagation characteristics in long bones with varying CTh. Numerical analysis implemented by the BEM and cylindrical mode expansion method was employed to calculate the transmission coefficient (TC) for various incident GW modes, frequencies, and CTh. In the cases of incident longitudinal tube modes L(0,1) and L(0,2) at frequencies 0.05 - 1.2 MHz, gradual CTh variations from 4 mm to 8 mm were considered. Mode conversion phenomena due to varying CTh were investigated. The direction of the GW propagation is very important due to significant differences in resulting mode conversion phenomena, when using the GW to assess the actual long bones. The modified BEM method used enabled the optimization of GWs for the long bone assessment. Results of this work can potentially be used to improve inspection sensitivity for the assessment of long bones with varying CTh.