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In a fully nonlinear model of wave propagation through bubbly media, computational complexity arises when the medium contains a polydisperse bubble population. This is because a nonlinear ordinary differential equation governing the bubble response must be solved for the current radius of each bubble size present at every spatial location and at every time step. In biomedical ultrasound imaging, commercial contrast agents typically possess a wide range of bubble sizes that exhibit a variety of differing behaviours at ultrasound frequencies of clinical interest. Despite the advent of supercomputing resources, the simulation of ultrasound propagation through microbubble populations still represents a formidable numerical task. Consequently, efficient computational algorithms that have the potential to be implemented in real time on clinical scanners remain highly desirable. In this work, a numerical approach is investigated that computes only a single ordinary differential equation at each spatial location which can potentially reduce significantly the computational effort. It is demonstrated that, under certain parameter regimes, the approach replicates the fully nonlinear model of an incident ultrasound pulse propagating through a polydisperse population of bubbles with a high degree of accuracy.

Original publication




Journal article


J acoust soc am

Publication Date