Angiogenesis, the formation of new bloods vessels from the existing vasculature, is a process that is essential during development and regeneration of tissues, and that plays a major role in diseases like cancer. Computational models have been designed to obtain a better understanding of the mechanisms behind angiogenesis. In this paper we review computational models of sprouting angiogenesis. These models can be subdivided into three categories: models that mainly focus on tip cell migration, models that make a distinction between the role of tip cells and stalk cells, and models that consider cell shape dynamics. Many models combine discrete modeling of individual cells with continuous modeling of the extracellular matrix (ECM) and diffusing solutes, in this way resulting in a hybrid model. We discuss their merits in unraveling the role of certain factors for vascular network formation, such as the role of (chemotactic, haptotactic, contact) guidance cues in the dynamics and morphology of vascular network formation, and the role of cell-cell interactions that govern tip cell selection and phenotypic changes in general. At the same time, we identify a need for the inclusion of cell mechanical principles in models of angiogenesis, in particular for the description of cell migration, cell-matrix and cell-cell interaction, as the generation of cellular forces is key to cell migration. To further underline this we review models of single cell migration that incorporate such principles, which could be the starting point for formulating novel models of angiogenesis that respect the fundamental laws of classical mechanics at the cell level. As the generation of cellular forces is strongly mediated by pro-angiogenic signals, such models must couple cell mechanical principles to molecular signaling into multiscale mechanochemical models of angiogenesis. Finally, a tight coupling between models and experiments will be required to facilitate model improvements and the generation of novel insights on the regulation of angiogenesis.

for cell culture tips and techniques. We thank Evan Claes and Tobie Martens for their contributions to the experimental microscopy set-up and the live imaging.

To advance our current understanding of cell-matrix mechanics and its importance for biomaterials development, advanced three-dimensional (3D) measurement techniques are necessary. Cell-induced deformations of the surrounding matrix are commonly derived from the displacement of embedded fiducial markers, as part of traction force microscopy (TFM) procedures. However, these fluorescent markers may alter the mechanical properties of the matrix or can be taken up by the embedded cells, and therefore influence cellular behavior and fate. In addition, the currently developed methods for calculating cell-induced deformations are generally limited to relatively small deformations, with displacement magnitudes and strains typically of the order of a few microns and less than 10% respectively. Yet, large, complex deformation fields can be expected from cells exerting tractions in fibrillar biomaterials, like collagen. To circumvent these hurdles, we present a technique for the 3D full-field quantification of large cell-generated deformations in collagen, without the need of fiducial markers. We applied non-rigid, Free Form Deformation (FFD)-based image registration to compute full-field displacements induced by MRC-5 human lung fibroblasts in a collagen type I hydrogel by solely relying on second harmonic generation (SHG) from the collagen fibrils. By executing comparative experiments, we show that comparable displacement fields can be derived from both fibrils and fluorescent beads. SHG-based fibril imaging can circumvent all described disadvantages of using fiducial markers. This approach allows measuring 3D full-field deformations under large displacement (of the order of 10 μm) and strain regimes (up to 40%). As such, it holds great promise for the study of large cell-induced deformations as an inherent component of cell-biomaterial interactions and cell-mediated biomaterial remodeling.

Cells interplay with their environment through mechanical and chemical interactions. To characterize this interplay, endothelial cells were cultured on polyacrylamide hydrogels of varying stiffness, coated with either fibronectin or collagen. We developed a novel analysis technique, complementary to traction force microscopy, to characterize the spatiotemporal evolution of cellular tractions: We identified subpopulations of tractions, termed traction foci, and tracked their magnitude and lifetime. Each focus consists of tractions associated with a local single peak of maximal traction. Individual foci were spread over a larger area in cells cultured on collagen relative to those on fibronectin and exerted higher tractions on stiffer hydrogels. We found that the trends with which forces increased with increasing hydrogel stiffness were different for foci and whole-cell measurements. These differences were explained by the number of foci and their average strength. While on fibronectin multiple short-lived weak foci contributed up to 30% to the total traction on hydrogels with intermediate stiffness, short-lived foci in such a number were not observed on collagen despite the higher tractions. Our approach allows for the use of existing traction force microscopy data to gain insight at the subcellular scale without molecular probes or spatial constraining of cellular tractions. KEY TERMS cell mechanics; traction force microscopy; endothelial cell; ECM protein MATERIALS AND METHODS Polyacrylamide hydrogel preparation and functionalization Polyacrylamide (PA) hydrogels were prepared as described by Tse et al. (22). To obtain the desired stiffness values (1.4, 2.7, and 4.5 kPa), hydrogels were prepared by mixing different volumes of 40% acrylamide, 2% bis-acrylamide (Bio-Rad, Hercules, California) with distilled water. Stiffness of the gels was corroborated using Atomic Force Microscopy (AFM) (see Supplemental Materials for details). As fiducial markers for TFM, 200 nm carboxylate-modified microspheres (FluoSpheres®, ThermoFisher Scientific, Waltham, MA) were added to the mixture at a 1:60 ratio. Hydrogels were functionalized with either 5 μg/ml of human fibronectin (Sigma-Aldrich, St. Louis, MO) or 100 μg/ml rat tail collagen I (BD bioscience, San Jose, CA). Even though the ECM protein concentrations used are different, in both situations the gels are saturated with the ECM protein, meaning the entire surface of the gel is covered by the coating molecule without any gaps of the order of magnitude of the traction foci (Figure S1 in Supplemental Materials). For a more detailed description of the hydrogel preparation and functionalization processes, see Supplemental Materials. Cell culture Green fluorescence protein (GFP)-expressing human umbilical vein endothelial cells (HUVECs) (Angioproteomie, Boston, MA), were seeded at low density on polyacrylamide hydrogels with desired stiffness. Cells were allowed to attach and spread overnight before imaging. For a more detailed description of the culture setup, see Supplemental...

In order to unravel rapid mechano-chemical feedback mechanisms in sprouting angiogenesis, we combine selective plane illumination microscopy (SPIM) and tailored image registration algorithms -further referred to as SPIM-based displacement microscopy -with an in vitro model of angiogenesis. SPIM successfully tackles the problem of imaging large volumes while upholding the spatial resolution required for the analysis of matrix displacements at a subcellular level. Applied to in vitro angiogenic sprouts, this unique methodological combination relates subcellular activity -minute to second time scale growing and retracting of protrusions -of a multicellular systems to the surrounding matrix deformations with an exceptional temporal resolution of 1 minute for a stack with multiple sprouts simultaneously or every 4 seconds for a single sprout, which is 20 times faster than with a conventional confocal setup. Our study reveals collective but non-synchronised, non-continuous activity of adjacent sprouting cells along with correlations between matrix deformations and protrusion dynamics. OPEN ACCESS Citation: Steuwe C, Vaeyens M-M, Jorge-Peñas A, Cokelaere C, Hofkens J, Roeffaers MBJ, et al. (2020) Fast quantitative time lapse displacement imaging of endothelial cell invasion. PLoS ONE 15 (1): e0227286. https://doi.org/10.