Validation tool for traction force microscopy

Field Guide to Traction Force Microscopy

Introduction

Traction force microscopy (TFM) is a widely used technique to measure cell contractility on compliant substrates that mimic the stiffness of human tissues. For every step in a TFM workflow, users make choices which impact the quantitative results, yet many times the rationales and consequences for making these decisions are unclear. We have found few papers which show the complete experimental and mathematical steps of TFM, thus obfuscating the full effects of these decisions on the final output.

Methods

Therefore, we present this "Field Guide" with the goal to explain the mathematical basis of common TFM methods to practitioners in an accessible way. We specifically focus on how errors propagate in TFM workflows given specific experimental design and analytical choices.

Results

We cover important assumptions and considerations in TFM substrate manufacturing, substrate mechanical properties, imaging techniques, image processing methods, approaches and parameters used in calculating traction stress, and data-reporting strategies.

Conclusions

By presenting a conceptual review and analysis of TFM-focused research articles published over the last two decades, we provide researchers in the field with a better understanding of their options to make more informed choices when creating TFM workflows depending on the type of cell being studied. With this review, we aim to empower experimentalists to quantify cell contractility with confidence.

Supplementary Information

The online version contains supplementary material available at 10.1007/s12195-024-00801-6.

Simulation and evaluation of 3D traction force microscopy

Measuring cell-generated forces by Traction Force Microscopy (TFM) has become a standard tool in cell mechanobiology. Although widely used in two dimensional (2D) experiments, only a few methods exist to measure traction in three-dimensional (3D) cell culture, since 3D volumetric high-resolution microscopy and more demanding computational approaches are required. Although it is commonly known that the selected experimental and computational setup highly influence the quality and accuracy of the results, no existing methods can adequately assess the errors involved in this process. We present a fully integrated simulation and evaluation platform that allows one to simulate TFM images and quantify errors of an applied approach for traction stress reconstruction, in order to improve experiments that attempt to measure mechanical interaction in cellular systems. In this context, we show that a careful parameter selection can decrease the reconstructed traction error by up to 40%.

Full L1-regularized Traction Force Microscopy over whole cells

Background

Traction Force Microscopy (TFM) is a widespread technique to estimate the tractions that cells exert on the surrounding substrate. To recover the tractions, it is necessary to solve an inverse problem, which is ill-posed and needs regularization to make the solution stable. The typical regularization scheme is given by the minimization of a cost functional, which is divided in two terms: the error present in the data or data fidelity term; and the regularization or penalty term. The classical approach is to use zero-order Tikhonov or L₂-regularization, which uses the L₂-norm for both terms in the cost function. Recently, some studies have demonstrated an improved performance using L₁-regularization (L₁-norm in the penalty term) related to an increase in the spatial resolution and sensitivity of the recovered traction field. In this manuscript, we present a comparison between the previous two regularization schemes (relying in the L₂-norm for the data fidelity term) and the full L₁-regularization (using the L₁-norm for both terms in the cost function) for synthetic and real data.

Results

Our results reveal that L₁-regularizations give an improved spatial resolution (more important for full L₁-regularization) and a reduction in the background noise with respect to the classical zero-order Tikhonov regularization. In addition, we present an approximation, which makes feasible the recovery of cellular tractions over whole cells on typical full-size microscope images when working in the spatial domain.

Conclusions

The proposed full L₁-regularization improves the sensitivity to recover small stress footprints. Moreover, the proposed method has been validated to work on full-field microscopy images of real cells, what certainly demonstrates it is a promising tool for biological applications.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-017-1771-0) contains supplementary material, which is available to authorized users.

High-resolution traction force microscopy on small focal adhesions - improved accuracy through optimal marker distribution and optical flow tracking

The accurate determination of cellular forces using Traction Force Microscopy at increasingly small focal attachments to the extracellular environment presents an important yet substantial technical challenge. In these measurements, uncertainty regarding accuracy is prominent since experimental calibration frameworks at this size scale are fraught with errors – denying a gold standard against which accuracy of TFM methods can be judged. Therefore, we have developed a simulation platform for generating synthetic traction images that can be used as a benchmark to quantify the influence of critical experimental parameters and the associated errors. Using this approach, we show that TFM accuracy can be improved >35% compared to the standard approach by placing fluorescent beads as densely and closely as possible to the site of applied traction. Moreover, we use the platform to test tracking algorithms based on optical flow that measure deformation directly at the beads and show that these can dramatically outperform classical particle image velocimetry algorithms in terms of noise sensitivity and error. We then report how optimized experimental and numerical strategy can improve traction map accuracy, and further provide the best available benchmark to date for defining practical limits to TFM accuracy as a function of focal adhesion size.

Free Form Deformation-Based Image Registration Improves Accuracy of Traction Force Microscopy

Traction Force Microscopy (TFM) is a widespread method used to recover cellular tractions from the deformation that they cause in their surrounding substrate. Particle Image Velocimetry (PIV) is commonly used to quantify the substrate’s deformations, due to its simplicity and efficiency. However, PIV relies on a block-matching scheme that easily underestimates the deformations. This is especially relevant in the case of large, locally non-uniform deformations as those usually found in the vicinity of a cell’s adhesions to the substrate. To overcome these limitations, we formulate the calculation of the deformation of the substrate in TFM as a non-rigid image registration process that warps the image of the unstressed material to match the image of the stressed one. In particular, we propose to use a B-spline -based Free Form Deformation (FFD) algorithm that uses a connected deformable mesh to model a wide range of flexible deformations caused by cellular tractions. Our FFD approach is validated in 3D fields using synthetic (simulated) data as well as with experimental data obtained using isolated endothelial cells lying on a deformable, polyacrylamide substrate. Our results show that FFD outperforms PIV providing a deformation field that allows a better recovery of the magnitude and orientation of tractions. Together, these results demonstrate the added value of the FFD algorithm for improving the accuracy of traction recovery.