Department of Biomedical Engineering, Columbia University, NY 10023, New York, United States of America.
Thayer School of Engineering, Dartmouth College, Hanover NH 03755, United States of America.
Phys Med Biol. 2021 Apr 6;66(7). doi: 10.1088/1361-6560/abddd1.
The majority of disease processes involves changes in the micro-structure of the affected tissue, which can translate to changes in the mechanical properties of the corresponding tissue. Harmonic motion imaging (HMI) is an elasticity imaging technique that allows the study of the mechanical parameters of tissue by detecting the tissue response by a harmonic motion field, which is generated by oscillatory acoustic radiation force. HMI has been demonstrated in tumor detection and characterization as well as monitoring of ablation procedures. In this study, an analytical HMI model is demonstrated and compared with a finite element model (FEM), allowing rapid and accurate computation of the displacement, strain, and shear wave velocity (SWV) at any location in a homogenous linear elastic material. Average absolute differences between the analytical model and the FEM were respectively 1.2% for the displacements and 0.5% for the strains for 41 940 force voxels at 0.22 s per displacement evaluation. A convergence study showed that the average difference could be further decreased to 1.0% and 0.15% for the displacements and strains, respectively, if force resolution is increased. SWV fields, as calculated with the FEM and the analytical model, have regional differences in velocities up to 0.57 m swith an average absolute difference of 0.11 ± 0.07 m s, primarily due to imperfections in the non-reflecting FEM boundary conditions. The apparent SWV differed from the commonly used plane-wave approximation by up to 1.2 m sdue to near and intermediate field effects. Maximum displacement amplitudes for a model with an inclusion stabilize within 10% of the homogenous model at an inclusion radius of 10 mm while the maximum strain reacts faster, stabilizing at an inclusion radius of 3 mm. In conclusion, an analytical model for HMI stiffness estimation is presented in this paper. The analytical model has advantages over FEM as the full-field displacements do not need to be calculated to evaluate the model at a single measurement point. This advantage, together with the computational speed, makes the analytical model useful for real-time imaging applications. However, the analytical model was found to have restrictive assumptions on tissue homogeneity and infinite dimensions, while the FEM approaches were shown adaptable to variable geometry and non-homogenous properties.
大多数疾病过程都涉及受影响组织的微观结构变化，这可能导致相应组织的机械性能发生变化。谐波运动成像（HMI）是一种弹性成像技术，通过检测组织对谐波运动场的响应来研究组织的力学参数，该运动场是由振荡声辐射力产生的。HMI 已在肿瘤检测和特征描述以及消融过程监测中得到证实。在这项研究中，展示了一种分析 HMI 模型，并将其与有限元模型（FEM）进行了比较，允许在均匀线性弹性材料中的任何位置快速准确地计算位移、应变和剪切波速度（SWV）。在 0.22 秒的每个位移评估中，对于 41940 个力体素，分析模型和 FEM 之间的平均绝对差异分别为位移的 1.2%和应变的 0.5%。收敛性研究表明，如果增加力分辨率，位移和应变的平均差异可以分别进一步减小到 1.0%和 0.15%。根据 FEM 和分析模型计算的 SWV 场在速度上存在区域差异，最大可达 0.57 m s，平均绝对差异为 0.11±0.07 m s，主要是由于 FEM 边界条件不反射的不完善造成的。由于近场和中场效应，表观 SWV 与常用的平面波逼近相差高达 1.2 m s。在包含体半径为 10 mm 时，模型的最大位移幅度在 10%以内稳定在均匀模型上，而最大应变的反应更快，在包含体半径为 3 mm 时稳定。总之，本文提出了一种用于 HMI 刚度估计的分析模型。与 FEM 相比，分析模型具有优势，因为不需要计算全场位移来评估单点的模型。该优势以及计算速度使得分析模型适用于实时成像应用。然而，分析模型被发现对组织均匀性和无限维度有严格的假设，而 FEM 方法则被证明适用于可变几何形状和非均匀特性。
