High-resolution reconstruction of cellular traction-force distributions: the role of physically motivated constraints and compressive regularization

TL;DR

This paper introduces a novel method for high-resolution reconstruction of cellular traction forces from substrate displacement data, utilizing physically motivated regularization and convex optimization to accurately recover localized stress fields.

Contribution

The authors develop a new inverse problem framework with specialized regularization and constraints for reconstructing localized cellular forces from high-resolution displacement images.

Findings

Successfully reconstructs localized stress fields in simulated data.

Effectively applies to experimental substrate displacement measurements.

Enhances resolution and accuracy of cellular traction-force imaging.

Abstract

We develop a method to reconstruct, from measured displacements of an underlying elastic substrate, the spatially dependent forces that cells or tissues impart on it. Given newly available high-resolution images of substrate displacements, it is desirable to be able to reconstruct small scale, compactly supported focal adhesions which are often localized and exist only within the footprint of a cell. In addition to the standard quadratic data mismatch terms that define least-squares fitting, we motivate a regularization term in the objective function that penalizes vectorial invariants of the reconstructed surface stress while preserving boundaries. We solve this inverse problem by providing a numerical method for setting up a discretized inverse problem that is solvable by standard convex optimization techniques. By minimizing the objective function subject to a number of important physically motivated constraints, we are able to efficiently reconstruct stress fields with localized structure from simulated and experimental substrate displacements. Our method incorporates the exact solution for the stress tensor accurate to first-order finite-differences and motivates the use of distance-based cut-offs for data inclusion and problem sparsification.