Traction force microscopy is a method widely used in biophysics and cell biology to determine forces that biological cells apply to their environment. In the experiment, the cells adhere to a soft elastic substrate, which is then deformed in response to cellular traction forces. The inverse problem consists in computing the traction stress applied by the cell from microscopy measurements of the substrate deformations. In this work, we consider a linear model, in which 3D forces are applied at a 2D interface, called 2.5D traction force microscopy, and a nonlinear pure 2D model, from which we directly obtain a linear pure 2D model. All models lead to a linear resp. nonlinear parameter identification problem for a boundary value problem of elasticity. We analyze the respective forward operators and conclude with some numerical experiments for simulated and experimental data.

翻译：牵引力显微术是生物物理学与细胞生物学中广泛用于测定生物细胞施加于其环境作用力的方法。实验中，细胞黏附于柔软弹性基底上，基底因细胞牵引力作用而发生形变。该反问题在于根据基底形变的显微测量数据计算细胞施加的牵引应力。本文研究线性模型（三维力作用于二维界面，称为2.5维牵引力显微术）与非线性纯二维模型（由此可直接导出线性纯二维模型）。所有模型均转化为弹性力学边值问题的线性或非线性参数辨识问题。我们分析了各正演算子，并通过模拟与实验数据的数值实验进行验证。