Computational Modeling of the Acoustic Radiation Force and Viscoelastic Displacement for Transcranial Focused Ultrasound Neuromodulation

Objective: In transcranial ultrasound neuromodulation (TUS), simulations of the harmonic pressure are often used for treatment planning. However, other mechanisms of energy transfer, such as acoustic radiation force (ARF) and the resulting tissue displacement, are reported less frequently. Furthermore, there is limited guidance on how these mechanisms should be simulated. This study evaluates the numerical convergence and accuracy of different ARF formulations and investigates the simulation of ultrasound-induced tissue displacement in the context of TUS. Approach: Two simulations steps are used in k-Wave to first simulate the first order acoustic pressure and velocity fields. Subsequently, these fields are used to calculate the ARF using the momentum-flux density tensor, Reynolds stress force, and attenuation force formulations. The ARF is then applied as input for a second viscoelastic simulation to estimate the tissue displacement induced by the ultrasound field. Numerical accuracy and convergence are quantified as functions of the various numerical choices and hyperparameters in the solvers. Main results: Among the investigated formulations, the attenuation-force approach proved to be the most robust and the least susceptible to numerical errors across variable medium types and transducer geometries. Within the parameter space relevant to TUS, it is a valid approximation of the momentum flux density tensor formulation. Similar tissue displacement distributions are found across the different ARF formulations. However, the accuracy of the displacement simulation decreases with increasing pulse duration. Finally, recommendations are formulated on the ARF calculation method and on the numerical hyperparameters for ARF and displacement simulations. Significance: This study offers guidelines for calculating the ARF and simulating tissue displacement. The proposed framework enables a more comprehensive characterization of ultrasound-mediated energy transfer in TUS.