In vivo validation of kinematic relationships for epithelial morphogenesis

Tissue growth and deformation result from the combined effects of various cellular events, including cell shape change, cell rearrangement, cell division, and cell death. Resolving and integrating these cellular events is essential for understanding the coordination of tissue-scale growth and deformation by individual cellular behaviors that are critical for morphogenesis, wound healing, and other collective cellular phenomena. For epithelial tissues composed of tightly connected cells, the texture tensor method provides a unified framework for quantifying tissue and cell strains by tracking individual cells in live imaging data. The corresponding kinematic relationships have been introduced in a continuum model that we previously reported. In this study, we validated the kinematic equations proposed in the continuum model using experimental data from a growing Drosophila wing. To accomplish this, we introduced modified definitions of the texture tensor and validated that one of these modifications more accurately represents approximated cellular shapes without relying on ad hoc scaling factors. By utilizing the modified tensor, we demonstrated the compatibility of the strain rate tensors and validated both the kinematic and cell number density equations. These results crossvalidate the modified texture analysis and continuum model. Further, the precision in the kinematic relationships achieved in this study provide a robust and solid foundation for more advanced integration of modeling and experiments.