Traction force microscopy using temporal information

Traction force microscopy is a simple, non-invasive method that can quantify cellular contact forces at the cell-substrate interface. It solves an inverse problem of determining the force field from measured substrate deformation. Because this problem is ill-posed with a large condition number, it is necessary to suppress the amplification of measurement noise during inversion. Previous studies have employed algorithms such as regularization or filtering that utilize spatial information to discriminate noise and true signals. Here, we propose an alternative approach that utilizes temporal information of the system. This method employs Kalman filter, a simple data assimilation algorithm in time series analysis, to recover the force field. Using numerically generated data, we show that the method is more accurate than standard algorithms including L2-regularization and is effective at filtering out temporal noise. Using experimental data on locomoting cells, we demonstrate that the method can reliably infer time-varying cellular traction forces. We also demonstrate two extensions of the proposed method: incorporation of additional knowledge and direct inference of low-dimensional force characteristics. These practical advantages will motivate the use of proposed framework for analyzing dynamic cell mechanics.Author summary: Traction force microscopy (TFM) is a common experimental method to determine the interfacial forces at the boundary of cells and their environment. TFM involves a delicate computational process that solves an ill-posed inverse problem to determine the interfacial forces from measured substrate deformation. Whereas available force-recovery algorithms predominantly rely on spatial information on the system, cells are dynamic, and their dynamics must contain temporal information, which has rarely been utilized in the traction force recovery problem. In this study, we propose an approach that utilizes temporal information on the system. This method employs Kalman filter, a simple data assimilation algorithm in time series analysis, to recover the force field. Using synthetic and experimental data, we show that the method is more accurate than standard algorithms including L2-regularization and can reliably infer time-varying cellular traction forces. We also demonstrate two extensions of the proposed method: incorporation of additional knowledge as a prior and direct inference of low-dimensional force characteristics.