Three-Dimensional Traction Microscopy with a Fiber-Based Constitutive Model.
Three-Dimensional Traction Microscopy with a Fiber-Based Constitutive Model.
复制标题
具有基于纤维的本构模型的三维牵引显微镜。
DOI：
10.1016/j.cma.2019.112579
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发表时间：
2019
影响因子：
7.2
通讯作者：
Oberai,AssadA
中科院分区：
文献类型：
--
作者：
Song,Dawei;Hugenberg,Nicholas;Oberai,AssadA
细胞对其周围环境施加的牵引力在许多生物学过程中起重要作用，包括干细胞分化、肿瘤发生、细胞迁移、癌症转移和血管生成。量化这些牵引力的能力对于理解和操纵这些过程非常重要。三维牵引力显微镜（3DTFM）提供了可靠的手段来评估细胞牵引力，首先测量荧光珠的位移响应于这些牵引力在周围的矩阵，然后使用此测量来计算牵引力。然而，3DTFM的大多数应用假定周围的细胞外基质（ECM）是非纤维的，尽管事实上在许多天然和合成环境中ECM含有显著比例的纤维组分。出于这一动机，我们开发了一种计算方法来确定牵引力，同时占纤维性质的ECM。特别是，我们利用基于纤维的本构模型，其中的应力包含来自非线性弹性纤维和超弹性矩阵的分布的贡献。我们解决了一个反问题的牵引矢量的节点值作为未知数，并最大限度地减少预测的位移场之间的差异，通过求解与基于纤维的本构模型的平衡方程，并在珠的位置测得的位移场。我们采用基于梯度的最小化方法来解决这个问题，并通过求解适当的伴随场来有效地确定梯度。我们将此算法应用于实验观察到的细胞几何形状和合成的问题，虽然现实，牵引场来衡量其对噪声的敏感性，并量化使用不正确的本构模型的影响：所谓的模型误差。我们的结论是，该方法是强大的噪声，产生约10%的误差牵引5%的位移噪声。我们还得出结论，模型误差的影响是显着的，其中使用非线性指数超弹性模型，而不是基于纤维的模型，可能会导致超过100%的误差在牵引领域。这些结果强调了在3DTFM中使用适当的组成模型的重要性，特别是在纤维ECM构建体中。
Tractions exerted by cells on their surroundings play an important role in many biological processes including stem cell differentiation, tumorigenesis, cell migration, cancer metastasis, and angiogenesis. The ability to quantify these tractions is important in understanding and manipulating these processes. Three-dimensional traction force microscopy (3DTFM) provides reliable means of evaluating cellular tractions by first measuring the displacement of fluorescent beads in response to these tractions in the surrounding matrix, and then using this measurement to compute the tractions. However, most applications of 3DTFM assume that the surrounding extra-cellular matrix (ECM) is non-fibrous, despite the fact that in many natural and synthetic environments the ECM contains a significant proportion of fibrous components. Motivated by this, we develop a computational approach for determining tractions, while accounting for the fibrous nature of the ECM. In particular, we make use of a fiber-based constitutive model in which the stress contains contributions from a distribution of nonlinear elastic fibers and a hyperelastic matrix. We solve an inverse problem with the nodal values of the traction vector as unknowns, and minimize the difference between a predicted displacement field, obtained by solving the equations of equilibrium in conjunction with the fiber-based constitutive model, and the measured displacement field at the bead locations. We employ a gradient-based minimization method to solve this problem and determine the gradient efficiently by solving for the appropriate adjoint field. We apply this algorithm to problems with experimentally observed cell geometries and synthetic, albeit realistic, traction fields to gauge its sensitivity to noise, and quantify the impact of using an incorrect constitutive model: the so-called model error. We conclude that the approach is robust to noise, yielding about 10% error in tractions for 5% displacement noise. We also conclude that the impact of model error is significant, where using a nonlinear exponential hyperelastic model instead of the fiber-based model, can lead to more than 100% error in the traction field. These results underline the importance of using appropriate constitutive models in 3DTFM, especially in fibrous ECM constructs.