Genetic algorithms-based inversion of multimode guided waves for cortical bone characterization

Recent progress in quantitative ultrasound has exploited the multimode waveguide response of long bones. Measurements of the guided modes, along with suitable waveguide modeling, have the potential to infer strength-related factors such as stiffness (mainly determined by cortical porosity) and cortical thickness. However, the development of such model-based approaches is challenging, in particular because of the multiparametric nature of the inverse problem. Current estimation methods in the bone field rely on a number of assumptions for pairing the incomplete experimental data with the theoretical guided modes (e.g. semi-automatic selection and classification of the data). The availability of an alternative inversion scheme that is user-independent is highly desirable. Thus, this paper introduces an efficient inversion method based on genetic algorithms using multimode guided waves, in which the mode-order is kept blind. Prior to its evaluation on bone, our proposal is validated using laboratory-controlled measurements on isotropic plates and bone-mimicking phantoms. The results show that the model parameters (i.e. cortical thickness and porosity) estimated from measurements on a few ex vivo human radii are in good agreement with the reference values derived from x-ray micro-computed tomography. Further, the cortical thickness estimated from in vivo measurements at the third from the distal end of the radius is in good agreement with the values delivered by site-matched high-resolution x-ray peripheral computed tomography.