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在使用高强度聚焦超声(High Intensity Focused Ultrasound)进行肋下病灶治疗的过程中, 肋骨的遮挡显著地影响了治疗的效果, 在先前的研究中, 肋骨通常被视作完美吸声体, 这一模型虽然能够在一定程度上体现肋骨造成的影响, 但也同样可能导致对肋后能量的低估. 为弥补现有工作的不足, 本文提出了一种将肋骨视作强吸声体、而非完美吸声体的数值计算方法, 并使用ABS塑料构建的仿肋模型进行了相关实验以比较两类方法的优劣, 此外本文还在多层介质模型中研究了肋骨对非线性声场造成的影响. 由于肋骨在新模型中具有较大的声衰减系数, 现有算法在计算过程中容易出现数值振荡问题, 为此本研究使用了算子分离法以提高数值计算的稳定性, 并进一步地通过矩阵向量化方法在后向隐式差分格式下实现了声场的稳定求解. 这些改进不仅提高了数值计算的准确性, 还揭示了完美吸声体模型造成的肋后能量低估问题, 对于优化临床治疗策略有重要意义.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.
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Keywords:
- high intensity focused ultrasound /
- operator separation method /
- asymmetry /
- matrix vectorization
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图 2 球面波区域与平面波区域划分示意图
Fig. 2. Illustration of the division between spherical wave region and plane wave region.
图 3 生物组织模型示意图 (a) 三维视图; (b) $ xz $截面图
Fig. 3. Schematic diagram of the biological tissue model: (a) 3D-view; (b) $ xz $-section.
图 4 实验环境示意图 (a) 声场扫描系统; (b) ABS塑料仿肋模型
Fig. 4. Schematic diagram of the experimental environment: (a) ultrasonic scanning system; (b) rib mimic made of ABS plastic.
图 5 焦平面内声压峰峰值分布图 (a) $ \mathrm{H_{FS} = 64\; mm} $; (b) $ \mathrm{H_{FS} = 74 \;mm} $; (c) $ \mathrm{H_{FS} = 84 \;mm} $; (d) $ \mathrm{H_{FS} = 94 \;mm} $
Fig. 5. Distribution of peak-to-peak pressure in the focal plane: (a) $ \mathrm{H_{FS} = 64\; mm} $; (b) $ \mathrm{H_{FS} = 74\; mm} $; (c) $ \mathrm{H_{FS} = 84\; mm} $; (d) $ \mathrm{H_{FS} = 94\; mm}. $
图 6 $ \mathrm{H_{FS} = 70\; mm} $时基波振幅沿z轴的分布
Fig. 6. Distribution of fundamental amplitude with $ \mathrm{H_{FS} = 70\; mm} $ along the z-axis.
图 7 $ \mathrm{H_{FS} = 70 \;mm} $时热沉积速率在截面$ \varphi = 0 $内的分布 (a) $ \mathrm{x_c = 0\; mm} $; (b) $ \mathrm{x_c = 5 \;mm} $; (c) $ \mathrm{x_c = 10\; mm} $; (d) $ \mathrm{x_c = 15 \;mm} $
Fig. 7. Distribution of heat deposition rate in the $ \varphi = 0 $ plane with $ \mathrm{H_{FS} = 70 \;mm} $: (a) $ \mathrm{x_c = 0 \;mm} $; (b) $ \mathrm{x_c = 5 \;mm} $; (c) $ \mathrm{x_c = 10\; mm} $; (d) $ \mathrm{x_c = 15\; mm} $.
图 8 $ \mathrm{H_{FS}} $对最大热沉积速率的影响 (a) 完美吸声体模型; (b) 强吸声体模型
Fig. 8. Maximum heat deposition rate corresponding to different $ \mathrm{H_{FS}} $: (a) perfect acoustic absorber model; (b) strong acoustic absorber model.
图 9 测温组织模型 (a) 定制容器; (b) 模型实物
Fig. 9. Temperature measurement tissue model: (a) customized container; (b) actual model.
图 10 焦域的归一化温升随时间的变化情况
Fig. 10. Normalized temperature variation in the focal region over time.
表 1 数值计算中使用的介质声参数
Table 1. Acoustic parameters of the medium used in numerical computation.
$ \rho/\left(\mathrm{kg \cdot m^{-3}} \right) $ $ c/\left(\mathrm{m\cdot s^{-1}} \right) $ $ \alpha/\left(\mathrm{Np\cdot {MHz}^{-\mu} \cdot m^{-1}} \right) $ μ β 水 1000 1500 0.025 2 3.5 脂肪 910 1430 9 1.15 10.5 肋骨 1450 2300 90 1 0 肝脏 1050 1596 6.69 1.13 6 
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表 2 $ \mathrm{H_{FS} = 70 \;mm} $时z轴上的声场参数
Table 2. Acoustic field's parameters along the z-axis with $ \mathrm{H_{FS} = 70 \;mm} $.
$ \mathrm{x_c/mm} $ Field Ref 0 5 10 15 $ \mathrm{A_1}/p_0 $ 49.09 27.43 27.75 29.07 29.73 $ \mathrm{A_2}/p_0 $ 26.02 10.21 10.13 10.22 10.26 $ \mathrm{A_3}/p_0 $ 14.96 3.82 3.71 3.59 3.53 $ \mathrm{z_1/mm} $ 179.60 180.99 180.90 179.42 179.37 $ \mathrm{z_2/mm} $ 180.09 180.54 180.36 179.78 179.46 $ \mathrm{z_3/mm} $ 180.32 180.90 180.68 179.96 179.60
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表 3 $ \mathrm{H_{FS} = 70 \;mm} $时平面$ \sigma = 0 $内的声场参数
Table 3. Acoustic field's parameters in the $ \sigma = 0 $ plane with $ \mathrm{H_{FS} = 70 \;mm} $.
$ \mathrm{x_c/mm} $ Field Ref 0 5 10 15 $ \mathrm{WX_{1, -3 dB}/mm} $ 3.22 3.39 3.21 2.86 2.71 $ \mathrm{WX_{2, -3 dB}/mm} $ 1.90 1.91 1.83 1.62 1.53 $ \mathrm{WX_{3, -3 dB}/mm} $ 1.46 1.40 1.36 1.23 1.18 $ \mathrm{WY_{1, -3 dB}/mm} $ 3.22 3.12 3.13 3.23 3.27 $ \mathrm{WY_{2, -3 dB}/mm} $ 1.90 1.80 1.80 1.84 1.86 $ \mathrm{WY_{3, -3 dB}/mm} $ 1.46 1.39 1.39 1.39 1.39
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