Advanced in silico validation framework forthree-dimensional Traction Force Microscopy andapplication to an in vitro model of sproutingangiogenesis

In the last decade, cellular forces in three-dimensional hydrogels that mimic the extracellular matrix have been calculated by means of Traction Force Microscopy (TFM). However, characterizing the accuracy limits of a traction recovery method is critical to avoid obscuring physiological information due to traction recovery errors. So far, 3D TFM algorithms have only been validated using simplified cell geometries, bypassing image processing steps or arbitrarily simulating focal adhesions. Moreover, it is still uncertain which of the two common traction recovery methods, i.e., forward and inverse, is more robust against the inherent challenges of 3D TFM. In this work, we established an advanced in silico validation framework that is applicable to any 3D TFM experimental setup and that can be used to correctly couple the experimental and computational aspects of 3D TFM. Advancements relate to the simultaneous incorporation of complex cell geometries, simulation of microscopy images of varying bead densities and different focal adhesion sizes and distributions. By measuring the traction recovery error with respect to ground truth solutions, we found that while highest traction recovery errors occur for cases with sparse and small focal adhesions, our implementation of the inverse method improves two-fold the accuracy with respect to the forward method (average error of 23% vs. 50%). This advantage was further supported by recovering cellular tractions around angiogenic sprouts in an in vitro model of angiogenesis. The inverse method recovered more realistic traction patterns than the forward method, showing higher traction peaks and a clearer pulling pattern at the sprout protrusion tips.