Application of simplified ray method for the determination of the cortical bone elastic coefficients by the ultrasonic wave inversion

Abstract

This work contributes to the methodology of an evaluation of elastic properties of cortical bones by ultrasonic wave inversion, whilst the bone is considered to be a linear elastic anisotropic continuum. Velocities of acoustic waves are used as an input data into inverse problem and they are experimentally detected by means of the ultrasonic based pulseecho immersion technique. The geometry of bone specimens is also implicated into algorithm by the model of wave propagation through curvilinear anisotropic sample based on the simplified ray method. The stability of resulting data is evaluated by the statistical method based on the Monte-Carlo simulation. The immersion method based on the wave inversion has shown to be a reliable tool for determination of some elastic constants only, the remaining coefficients need to be measured or improved by another experimental method. The ultrasonic contact pulse through transmission technique was rated as an acceptable experimental approach for this purposes. The RUS was found to be an unsuitable method for the measurement of the elastic coefficients of the cortical bone tissue.