Research on Nonlinear Acoustic Fields in Multi-layer Biological Tissue with Ribs as Strong Acoustic Absorbers

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During the treatment of subcostal lesions with high intensity focused ultrasound (HIFU), the obstruction by the ribs significantly affects the therapeutic effect, an impact that can be assessed through numerical calculations. In existing studies, ribs are typically regarded as perfect acoustic absorbers, even this assumption could reveal the impact of the ribs on the acoustic field to some extent, it might still underestimate the energy behind the rib cage. To address the shortcomings of current work, this paper proposes an innovative numerical calculation method refraining from regarding ribs as perfect acoustic absorbers. Subsequently, experiments are conducted using ABS plastic rib cage mimic to compare the effectiveness of the two methods, demonstrating that the method proposed in this paper, which avoids the assumption of considering ribs as perfect acoustic absorbers, could better reveal the impacts caused by ribs, and further studies are carried out on the impact of ribs in a multi-layered medium model. In response to the numerical oscillation issues encountered in existing work when dealing with media with high acoustic attenuation coefficients, this paper employs the operator splitting method to enhance the stability of numerical calculations. Furthermore, to tackle the challenges posed by asymmetric acoustic fields in numerical computations, this paper introduces matrix vectorization techniques and achieves stable solutions for the acoustic field under the backward implicit difference scheme. Additionally, a gradual maximum number of harmonics is employed to reduce the computational load when considering nonlinear effects. These improvements in both the numerical calculation model and the corresponding algorithm not only enhance the precision of numerical computations, but also reveal the underestimation of energy behind the ribs due to the assumption of perfect acoustic absorbers, which is significant for optimizing HIFU treatment strategies.