Cells interact mechanically with their surroundings by exerting and sensing forces. Traction force microscopy (TFM), purported to map cell-generated forces or stresses, represents an important tool that has powered the rapid advances in mechanobiology. However, to solve the ill-posed mathematical problem, conventional TFM involved compromises in accuracy and/or resolution. Here, we applied neural network-based deep learning as an alternative approach for TFM. We modified a neural network designed for image processing to predict the vector field of stress from displacements. Furthermore, we adapted a mathematical model for cell migration to generate large sets of simulated stresses and displacements for training and testing the neural network. We found that deep learning-based TFM yielded results that resemble those using conventional TFM but at a higher accuracy than several conventional implementations tested. In addition, a trained neural network is appliable to a wide range of conditions, including cell size, shape, substrate stiffness, and traction output. The performance of deep learning-based TFM makes it an appealing alternative to conventional methods for characterizing mechanical interactions between adherent cells and the environment.
Six different algorithms (Single Differencing, Double Differencing, Linear Interpolated Differencing, Parabolic Interpolated Differencing, Spatial Differencing and Spatial Filtering) are investigated to judge their ability to track subpixel targets in moving background and additive noise. This investigation used a set of computer generated imagery for the targets, background and the additive noise. Based on this extensive simulation study, guidelines are provided about the selection of the algorithms.
Cells interact mechanically with their surrounding by exerting forces and sensing forces or forceinduced displacements. Traction force microscopy (TFM), purported to map cell-generated forces or stresses, represents an important tool that has powered the rapid advances in mechanobiology. However, to solve the ill-posted mathematical problem, its implementation has involved regularization and the associated compromises in accuracy and resolution. Here we applied neural network-based deep learning as a novel approach for TFM. We modified a network for processing images to process vector fields of stress and strain. Furthermore, we adapted a mathematical model for cell migration to generate large sets of simulated stresses and strains for training the network. We found that deep learning-based TFM yielded results qualitatively similar to those from conventional methods but at a higher accuracy and resolution. The speed and performance of deep learning TFM make it an appealing alternative to conventional methods for characterizing mechanical interactions between cells and the environment. Statement of SignificanceTraction Force Microscopy has served as a fundamental driving force for mechanobiology. However, its nature as an ill-posed inverse problem has posed serious challenges for conventional mathematical approaches. The present study, facilitated by large sets of simulated stresses and strains, describes a novel approach using deep learning for the calculation of traction stress distribution. By adapting the UNet neural network for handling vector fields, we show that deep learning is able to minimize much of the limitations of conventional approaches to generate results with speed, accuracy, and resolution.
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