Quantitative elasticity imaging seeks to retrieve spatial maps of elastic moduli of tissue. Unlike strain, which is commonly imaged in compression elastography, elastic moduli are intrinsic properties of tissue and so this approach reconstructs images that are largely operator and system independent, enabling objective, longitudinal and multi-site diagnoses. Recently, novel quantitative elasticity imaging approaches to compression elastography have been developed. These methods use a calibration layer with known mechanical properties to sense the stress at the tissue surface, which combined with strain, is used to estimate the tissue's elastic moduli by assuming homogeneity in the stress field. However, this assumption is violated in mechanically heterogeneous samples. We present a more general approach to quantitative elasticity imaging that overcomes this limitation through an efficient iterative solution of the inverse elasticity problem using adjoint elasticity equations. We present solutions for linear elastic, isotropic and incompressible solids; however, this method can be employed for more complex mechanical models. We retrieve the spatial

Angiogenic sprouting is a critical process involved in vascular network formation within tissues. During sprouting, tip cells and ensuing stalk cells migrate collectively into the extracellular matrix while preserving cell–cell junctions, forming patent structures that support blood flow. Although several signaling pathways have been identified as controlling sprouting, it remains unclear to what extent this process is mechanoregulated. To address this question, we investigated the role of cellular contractility in sprout morphogenesis, using a biomimetic model of angiogenesis. Three-dimensional maps of mechanical deformations generated by sprouts revealed that mainly leader cells, not stalk cells, exert contractile forces on the surrounding matrix. Surprisingly, inhibiting cellular contractility with blebbistatin did not affect the extent of cellular invasion but resulted in cell–cell dissociation primarily between tip and stalk cells. Closer examination of cell–cell junctions revealed that blebbistatin impaired adherens-junction organization, particularly between tip and stalk cells. Using CRISPR/Cas9-mediated gene editing, we further identified NMIIA as the major isoform responsible for regulating multicellularity and cell contractility during sprouting. Together, these studies reveal a critical role for NMIIA-mediated contractile forces in maintaining multicellularity during sprouting and highlight the central role of forces in regulating cell–cell adhesions during collective motility.

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Abstract Cell-generated tractions play an important role in various physiological and pathological processes such as stem-cell differentiation, cell migration, wound healing, and cancer metastasis. Traction force microscopy (TFM) is a technique for quantifying cellular tractions during cell–matrix interactions. Most applications of this technique have heretofore assumed that the matrix surrounding the cells is linear elastic and undergoes infinitesimal strains, but recent experiments have shown that the traction-induced strains can be large (e.g., more than 50%). In this paper, we propose a novel three-dimensional (3D) TFM approach that consistently accounts for both the geometric nonlinearity introduced by large strains in the matrix, and the material nonlinearity due to strain-stiffening of the matrix. In particular, we pose the TFM problem as a nonlinear inverse hyperelasticity problem in the stressed configuration of the matrix, with the objective of determining the cellular tractions that are consistent with the measured displacement field in the matrix. We formulate the inverse problem as a constrained minimization problem and develop an efficient adjoint-based minimization procedure to solve it. We first validate our approach using simulated data, and quantify its sensitivity to noise. We then employ the new approach to recover tractions exerted by NIH 3T3 cells fully encapsulated in hydrogel matrices of varying stiffness. We find that neglecting nonlinear effects can induce significant errors in traction reconstructions. We also find that cellular tractions roughly increase with gel stiffness, while the strain energy appears to saturate.