Deep-learning-based 3D cellular force reconstruction directly from volumetric images.

The forces exerted by single cells in the three-dimensional (3D) environments play a crucial role in modulating cellular functions and behaviors closely related to physiological and pathological processes. Cellular force microscopy (CFM) provides a feasible solution for quantifying mechanical interactions, which usually regains cellular forces from deformation information of extracellular matrices embedded with fluorescent beads. Owing to computational complexity, traditional 3D-CFM is usually extremely time consuming, which makes it challenging for efficient force recovery and large-scale sample analysis. With the aid of deep neural networks, this study puts forward a novel, data-driven 3D-CFM to reconstruct 3D cellular force fields directly from volumetric images with random fluorescence patterns. The deep-learning-based network is established through stacking deep convolutional neural networks (DCNN) and specific function layers. Some necessary physical information associated with constitutive relation of extracellular matrix material is coupled to the data-driven network. The mini-batch stochastic-gradient-descent and back-propagation algorithms are introduced to ensure its convergence and training efficiency. The networks not only have good generalization ability and robustness but also can recover 3D cellular forces directly from the input fluorescence image pairs. Particularly, the computational efficiency of the deep-learning-based network is at least one to two orders of magnitude higher than that of traditional 3D-CFM. This study provides a novel scheme for developing high-performance 3D-CFM to quantitatively characterize mechanical interactions between single cells and surrounding extracellular matrices, which is of vital importance for quantitative investigations in biomechanics and mechanobiology.