Accelerating frequency-domain numerical methods for weakly nonlinear focused ultrasound using nested meshes.

The numerical simulation of weakly nonlinear ultrasound is important in treatment planning for focused ultrasound (FUS) therapies. However, the large domain sizes and generation of higher harmonics at the focus make these problems extremely computationally demanding. Numerical methods typically employ a uniform mesh fine enough to resolve the highest harmonic present in the problem, leading to a very large number of degrees of freedom. This paper proposes a more efficient strategy in which each harmonic is approximated on a separate mesh, the size of which is proportional to the wavelength of the harmonic. The increase in resolution required to resolve a smaller wavelength is balanced by a reduction in the domain size. This nested meshing is feasible owing to the increasingly localised nature of higher harmonics near the focus. Numerical experiments are performed for FUS transducers in homogeneous media to determine the size of the meshes required to accurately represent the harmonics. In particular, a fast volume potential approach is proposed and employed to perform convergence experiments as the computation domain size is modified. This approach allows each harmonic to be computed via the evaluation of an integral over the domain. Discretising this integral using the midpoint rule allows the computations to be performed rapidly with the FFT. It is shown that at least an order of magnitude reduction in memory consumption and computation time can be achieved with nested meshing. Finally, it is demonstrated how to generalise this approach to inhomogeneous propagation domains.

Unmyelinated Peripheral Nerves Can Be Stimulated in Vitro Using Pulsed Ultrasound.

Appreciation for the medical and research potential of ultrasound neuromodulation is growing rapidly, with potential applications in non-invasive treatment of neurodegenerative disease and functional brain mapping spurring recent progress. However, little progress has been made in our understanding of the ultrasound-tissue interaction. The current study tackles this issue by measuring compound action potentials (CAPs) from an ex vivo crab walking leg nerve bundle and analysing the acoustic nature of successful stimuli using a passive cavitation detector (PCD). An unimpeded ultrasound path, new acoustic analysis techniques and simple biological targets are used to detect different modes of cavitation and narrow down the candidate biological effectors with high sensitivity. In the present case, the constituents of unmyelinated axonal tissue alone are found to be sufficient to generate de novo action potentials under ultrasound, the stimulation of which is significantly correlated to the presence of inertial cavitation and is never observed in its absence.