Identifying the spatial variation of stiffness properties in soft tissues nondestructively, with limited surface measurements, poses significant challenges. In this paper, we present a novel explicit inverse approach designed to characterize the nonhomogeneous elastic property distribution of soft tissues using only surface displacement datasets. In contrast to the prevalent implicit inverse approach, which focuses on optimizing the elastic properties of individual pixels, our proposed method optimizes the geometric parameters of deformable and movable components, as well as shear moduli of each component. As a result, the proposed approach requires far fewer optimization variables, streamlining the process. Numerical tests conducted in this study demonstrate the superiority of the explicit inverse method over the implicit inverse method, providing much-improved reconstructed results. In particular for a ring structure, while the average relative error of reconstruction using the implicit inverse method can exceed 40 %, the explicit inverse method achieves a remarkable average relative error of only 5 %. Given that surface displacements are easily measurable, the integration of our proposed explicit inverse method with low-cost imaging techniques shows great potential in accurately mapping the elastic property distribution of biological tissues.

中文翻译：

---

使用表面变形和显式逆方法无损地识别软组织的机械行为


通过有限的表面测量来非破坏性地识别软组织刚度特性的空间变化提出了重大挑战。在本文中，我们提出了一种新颖的显式逆方法，旨在仅使用表面位移数据集来表征软组织的非均匀弹性属性分布。与流行的隐式逆方法侧重于优化单个像素的弹性特性相比，我们提出的方法优化了可变形和可移动组件的几何参数以及每个组件的剪切模量。因此，所提出的方法需要更少的优化变量，从而简化了流程。本研究中进行的数值测试证明了显式逆方法相对于隐式逆方法的优越性，提供了大大改进的重建结果。特别是对于环形结构，虽然使用隐式逆方法重建的平均相对误差可以超过40％，但显式逆方法实现了仅5％的显着平均相对误差。鉴于表面位移很容易测量，我们提出的显式反演方法与低成本成像技术的集成在准确绘制生物组织的弹性分布方面显示出巨大的潜力。