Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089.
Walker Department of Mechanical Engineering, Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, TX 78712.
J Biomech Eng. 2020 Aug 1;142(8). doi: 10.1115/1.4046974.
Cell-generated tractions play an important role in various physiological and pathological processes such as stem-cell differentiation, cell migration, wound healing, and cancer metastasis. Traction force microscopy (TFM) is a technique for quantifying cellular tractions during cell-matrix interactions. Most applications of this technique have heretofore assumed that the matrix surrounding the cells is linear elastic and undergoes infinitesimal strains, but recent experiments have shown that the traction-induced strains can be large (e.g., more than 50%). In this paper, we propose a novel three-dimensional (3D) TFM approach that consistently accounts for both the geometric nonlinearity introduced by large strains in the matrix, and the material nonlinearity due to strain-stiffening of the matrix. In particular, we pose the TFM problem as a nonlinear inverse hyperelasticity problem in the stressed configuration of the matrix, with the objective of determining the cellular tractions that are consistent with the measured displacement field in the matrix. We formulate the inverse problem as a constrained minimization problem and develop an efficient adjoint-based minimization procedure to solve it. We first validate our approach using simulated data, and quantify its sensitivity to noise. We then employ the new approach to recover tractions exerted by NIH 3T3 cells fully encapsulated in hydrogel matrices of varying stiffness. We find that neglecting nonlinear effects can induce significant errors in traction reconstructions. We also find that cellular tractions roughly increase with gel stiffness, while the strain energy appears to saturate.
细胞产生的牵引力在各种生理和病理过程中起着重要作用，例如干细胞分化、细胞迁移、伤口愈合和癌症转移。牵引力显微镜（TFM）是一种量化细胞与基质相互作用过程中细胞牵引力的技术。该技术的大多数应用都假设包围细胞的基质是线弹性的，并发生无穷小应变，但最近的实验表明，牵引力引起的应变可以很大（例如，超过 50%）。在本文中，我们提出了一种新的三维（3D）TFM 方法，该方法一致考虑了大应变引起的基质几何非线性，以及由于基质的应变硬化引起的材料非线性。特别是，我们将 TFM 问题作为基质受力构型中的非线性逆超弹性问题，目的是确定与基质中测量的位移场一致的细胞牵引力。我们将反问题表述为一个约束最小化问题，并开发了一种有效的基于伴随的最小化程序来解决它。我们首先使用模拟数据验证我们的方法，并量化其对噪声的敏感性。然后，我们使用新方法恢复完全封装在不同刚度水凝胶基质中的 NIH 3T3 细胞施加的牵引力。我们发现忽略非线性效应会导致牵引力重建中产生显著误差。我们还发现细胞牵引力大致随凝胶刚度增加而增加，而应变能似乎趋于饱和。
