A unified model for the speed of sound in cranial bone based on genetic algorithm optimization

The density and structure of bone is highly heterogeneous, causing wide variations in the reported speed of sound for ultrasound propagation. Current research on the propagation of high intensity focused ultrasound through an intact human skull for non-invasive therapeutic action on brain tissue requires a detailed model for the acoustic velocity in cranial bone. Such models have been difficult to derive empirically due to the aforementioned heterogeneity of bone itself. We propose a single unified model for the speed of sound in cranial bone based upon the apparent density of bone by CT scan. This model is based upon the coupling of empirical measurement, theoretical acoustic simulation and genetic algorithm optimization. The phase distortion caused by the presence of skull in an acoustic path is empirically measured. The ability of a theoretical acoustic simulation coupled with a particular speed-of-sound model to predict this phase distortion is compared against the empirical data, thus providing the fitness function needed to perform genetic algorithm optimization. By performing genetic algorithm optimization over an initial population of candidate speed-of-sound models, an ultimate single unified model for the speed of sound in both the cortical and trabecular regions of cranial bone is produced. The final model produced by genetic algorithm optimization has a nonlinear dependency of speed of sound upon local bone density. This model is shown by statistical significance to be a suitable model of the speed of sound in bone. Furthermore, using a skull that was not part of the optimization process, this model is also tested against a published homogeneous speed-of-sound model and shown to return an improved prediction of transcranial ultrasound propagation.