Modelling perspectives on the intestinal crypt, a canonical system for growth, mechanics, and remodelling

The intestinal epithelium is crucial to maintaining a healthy gut. Central to this are the crypts of Lieberkühn, which coordinate the rapid self-renewal of the epithelium to protect the small intestine and colon during digestion. Further, mutations in crypt cells may initiate colorectal cancer. It is, therefore, important to understand how crypts function during homeostasis and disease. Mathematical and computational modeling has contributed to increasing our understanding of crypt dynamics. However, many open questions remain to be addressed, particularly regarding the role of mechanics in intestinal crypt dynamics. In this article, we review the state-of-the-art in crypt modeling and explain why further progress requires the integration of new theory from continuum mechanics with cell-based computational models and experimental data.