We present a 3-D extension of the Autoprogressive Method (AutoP) for quantitative quasi-static ultrasonic elastography (QUSE) based on sparse sampling of force-displacement measurements. Compared to current model-based inverse methods, our approach requires neither geometric nor constitutive model assumptions. We build upon our previous report for 2-D QUSE [1] and demonstrate the feasibility of recovering the 3-D linear-elastic material property distribution of gelatin phantoms under compressive loads. Measurements of boundary geometry, applied surface forces, and axial displacements enter into AutoP where a Cartesian neural network constitutive model (CaNNCM) interacts with finite element analyses to learn physically consistent material properties with no prior constitutive model assumption. We introduce a new regularization term uniquely suited to AutoP that improves the ability of CaNNCMs to extract information about spatial stress distributions from measurement data. Results of our study demonstrate that acquiring multiple sets of force-displacement measurements by moving the US probe to different locations on the phantom surface not only provides AutoP with the necessary information for a CaNNCM to learn the 3-D material property distribution, but may significantly improve the accuracy of the Young's modulus estimates. Furthermore, we investigate the trade-offs of decreasing the contact area between the US transducer and phantom surface in an effort to increase sensitivity to surface force variations without additional instrumentation. Each of these modifications improves the ability of CaNNCMs trained in AutoP to learn the spatial distribution of Young's modulus from force-displacement measurements.

中文翻译：

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用于3D定量准静态弹性成像的物理指导机器学习。

我们基于力-位移测量的稀疏采样，提出了用于定量准静态超声弹性成像（QUSE）的Autoprogressive方法（AutoP）的3-D扩展。与当前基于模型的逆方法相比，我们的方法既不需要几何模型也不需要本构模型假设。我们以先前关于2-D QUSE的报告为基础[1]，并论证了在压缩载荷下恢复明胶模型的3-D线性弹性材料特性分布的可行性。边界几何形状，施加的表面力和轴向位移的测量值进入AutoP，在该位置中，笛卡尔神经网络本构模型（CaNNCM）与有限元分析相互作用，以学习物理上一致的材料属性，而无需先前的本构模型假设。我们引入了一个新的正则化术语，该术语专门适用于AutoP，可提高CaNNCM从测量数据中提取有关空间应力分布信息的能力。我们的研究结果表明，通过将US探针移动到幻像表面上的不同位置来获取多组力-位移测量值，不仅为AutoP提供了必要的信息，以使CaNNCM学习3-D材料的特性分布，而且可能提高了杨氏模量估计的准确性。此外，我们研究了减少US换能器与体模表面之间的接触面积的权衡，以努力提高对表面力变化的灵敏度，而无需其他仪器。