A model for 3D deformation and reconstruction of contractile microtissues

Tissue morphogenesis and regeneration are essentially mechanical processes that involve coordination of cellular forces, production and structural remodeling of extracellular matrix (ECM), and cell migration. Discovering the principles of cell-ECM interactions and tissue-scale deformation in mechanically-loaded tissues is instrumental to the development of novel regenerative therapies. The combination of high-throughput three-dimensional (3D) culture systems and experimentally-validated computational models accelerate the study of these principles. In our previous work [E. Mailand, et al., Biophys. J., 2019, 117, 975-986], we showed that prominent surface stresses emerge in constrained fibroblast-populated collagen gels, driving the morphogenesis of fibrous microtissues. Here, we introduce an active material model that allows the embodiment of surface and bulk contractile stresses while maintaining the passive elasticity of the ECM in a 3D setting. Unlike existing models, the stresses are driven by mechanosensing and not by an externally applied signal. The mechanosensing component is incorporated in the model through a direct coupling of the local deformation state with the associated contractile force generation. Further, we propose a finite element implementation to account for large deformations, nonlinear active material response, and surface effects. Simulation results quantitatively capture complex shape changes during tissue formation and as a response to surgical disruption of tissue boundaries, allowing precise calibration of the parameters of the 3D model. The results of this study imply that the organization of the extracellular matrix in the bulk of the tissue may not be a major factor behind the morphogenesis of fibrous tissues at sub-millimeter length scales.