Morphing of growing sheets via active contractions of muscle cells

Morphological shape transformations in biological systems often arise from patterned biochemical processes, which can produce mechanical forces either actively via molecular motors or passively via differential growth of connected tissues. Both the active contractions and the growth mismatch between tissues produce internal stresses, which are released by shape transformations and mechanical instabilities. Such processes play important roles for shaping of brain, guts, lungs and other organs in developing organisms. Inspired by these biological systems, we investigate how growing epithelial sheets can be folded into complex structures by active contractions of neighbouring smooth muscle cells. To capture large deformations of soft tissues we developed a theoretical and computational framework based on the finite strain theory, where the total deformation gradient tensor was decomposed into one part due to growth/active contractions and another part due to elastic deformation. This framework was then used to predict folding of growing epithelium in response to patterned contractions of smooth muscle cells. These results help illuminate what kind of processes are needed to generate the complex architectures found within tissues in developing organisms.