Acoustic radiation force for analyzing the mechanical stress in ultrasound neuromodulation

Objective. Although recent studies have shown that mechanical stress plays an important role in ultrasound neuromodulation, the magnitude and distribution of the mechanical stress generated in tissues by focused ultrasound transducers have not been adequately examined. Various acoustic radiation force (ARF) equations used in previous studies have been evaluated based on the tissue displacement results and are suitable for estimating the displacement. However, it is unclear whether mechanical stress can be accurately determined. This study evaluates the mechanical stress predicted by various AFR equations and suggests the optimal equation for estimating the mechanical stress in the brain tissue. Approach. In this paper, brain tissue responses are compared through numerical finite element simulations by applying the three most used ARF equations-Reynolds stress force ((RSF)), momentum flux density tensor force, and attenuation force. Three ARF fields obtained from the same pressure field were applied to the linear elastic model to calculate the displacement, mechanical stress, and mean pressure generated inside the tissue. Both the simple pressure field using a single transducer and the complex standing wave pressure field using two transducers were simulated. Main results. For the case using a single transducer, all three ARFs showed similar displacement. However, when comparing the mechanical stress results, only the results using the RSF showed a strong stress tensor at the focal point. For the case of using two transducers, the displacement and stress tensor field of the pattern related to the standing wave were calculated only from the results using the RSF. Significance. The model using RSF equation allows accurate analysis on stress tensor inside the tissue for ultrasound neuromodulation.