Department of Mechanical Engineering, University of Zaragoza, Zaragoza, Spain.
University Center for Defense, Zaragoza, Spain.
PLoS One. 2021 Apr 14;16(4):e0249018. doi: 10.1371/journal.pone.0249018. eCollection 2021.
Advances in methods for determining the forces exerted by cells while they migrate are essential for attempting to understand important pathological processes, such as cancer or angiogenesis, among others. Precise data from three-dimensional conditions are both difficult to obtain and manipulate. For this purpose, it is critical to develop workflows in which the experiments are closely linked to the subsequent computational postprocessing. The work presented here starts from a traction force microscopy (TFM) experiment carried out on microfluidic chips, and this experiment is automatically joined to an inverse problem solver that allows us to extract the traction forces exerted by the cell from the displacements of fluorescent beads embedded in the extracellular matrix (ECM). Therefore, both the reconstruction of the cell geometry and the recovery of the ECM displacements are used to generate the inputs for the resolution of the inverse problem. The inverse problem is solved iteratively by using the finite element method under the hypothesis of finite deformations and nonlinear material formulation. Finally, after mathematical postprocessing is performed, the traction forces on the surface of the cell in the undeformed configuration are obtained. Therefore, in this work, we demonstrate the robustness of our computational-based methodology by testing it under different conditions in an extreme theoretical load problem and then by applying it to a real case based on experimental results. In summary, we have developed a new procedure that adds value to existing methodologies for solving inverse problems in 3D, mainly by allowing for large deformations and not being restricted to any particular material formulation. In addition, it automatically bridges the gap between experimental images and mechanical computations.
在细胞迁移过程中确定细胞所受外力的方法的进展对于尝试理解重要的病理过程至关重要，例如癌症或血管生成等。来自三维条件的精确数据既难以获得又难以处理。为此，必须开发将实验与后续计算后处理紧密结合的工作流程。本文从在微流控芯片上进行的牵引力显微镜（TFM）实验开始，该实验自动与反问题求解器结合，该求解器允许我们从嵌入细胞外基质（ECM）中的荧光珠的位移中提取细胞施加的牵引力。因此，细胞几何形状的重建和 ECM 位移的恢复都用于生成反问题的解的输入。反问题通过有限元法在有限变形和非线性材料公式的假设下迭代求解。最后，在进行数学后处理后，获得细胞在未变形配置中的表面上的牵引力。因此，在这项工作中，我们通过在极端理论负载问题下测试不同条件下测试我们基于计算的方法的稳健性，然后根据实验结果将其应用于实际情况，证明了我们的方法的稳健性。总之，我们开发了一种新程序，通过允许大变形并且不受任何特定材料公式的限制，为解决 3D 中的反问题的现有方法增加了价值。此外，它自动弥合了实验图像和力学计算之间的差距。
