Traction force microscopy for linear and nonlinear elastic materials as a parameter identification inverse problem

TL;DR

This paper investigates the inverse problem of traction force microscopy for both linear and nonlinear elastic materials, analyzing models and operators, and validating with numerical experiments on simulated and real data.

Contribution

It introduces a unified approach to model and analyze linear and nonlinear elastic traction force microscopy as a parameter identification problem.

Findings

Analysis of forward operators for linear and nonlinear models

Numerical experiments demonstrate method effectiveness

Application to simulated and experimental data

Abstract

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.