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| The colon's epithelial lining exhibits a number of invaginations into the underlying tissue, called the crypts of Lieberk\"uhn. Housing stem cells at their bases, these crypts play an essential role in the maintenance of the epithelium, facilitating a complete renewal every 5--6 days. Disruptions to the healthy crypt shape and cellular dynamics are strongly linked to the onset of colorectal cancer.
Formation of the crypts is known to occur approximately seven days after birth in mice; prior to this the intestinal wall is smooth. However, the processes that underlie colorectal crypt formation are not conclusively understood. This study investigates one potential mechanism for crypt formation: that in the developing intestine, proliferation and growth of epithelial cells generate compressive stresses within the epithelium, resulting in buckling instabilities, which initiate crypt formation.
We present a simple cell culture experiment to validate the proposed mechanism, and describe associated biomechanical models for epithelial buckling based upon Euler--Bernoulli beam theory (in 1D) or von K\'arm\'an plate theory (in 2D). We demonstrate the range of attainable buckling patterns in each model, and show how these are affected by varying adhesion to underlying tissue, the mechanical properties of the epithelium, and patterning of cellular growth. |
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