Ultrasonic transmission through small tubes such as rat tibias for axial Young’s modulus estimation: Discussion and recommendations

In the framework of in vitro osteoporosis investigation with ultrasound on rat model, we propose a study of axisymmetric modes guided in small cylindrical structures such as rat tibias. The main objective is to analyze how an ultrasonic pulse (with a frequency close to the MHz) transmitted through the cortical bone diaphysis can be used to obtain a rapid estimation of the axial Young's modulus. Thanks to a numerical approach and experimentations on bone phantoms we show that the velocity of the first arrival signal (VFAS) measured with a simple time of flight method corresponds to the maximum of the group velocity of the axisymmetric L0,2 mode. Considering the geometry of the cylinders analyzed, we show that it is possible to use this velocity to estimate the axial Young's modulus. The ratio (internal radius / thickness) is an important parameter for small tubes such as rat tibias and has to be considered for results analysis. In this framework, µCT measurements are of first interest. At the end of this communication, preliminary experiments on rat tibias are presented and discussed.