Growth and morphogenesis of an everted tubular biological tissue

Eversion, a ubiquitous phenomenon in living organisms, significantly contributes to the growth and morphogenesis of soft biological tissues and organs. In this study, we examine the role of elasticity and geometry in the morphogenesis of everted tubular biological tissues, both theoretically and experimentally. Our findings demonstrate that the morphogenesis of an everted tubular tissue is primarily influenced by its elasticity and geometry. Through linear stability analysis, we show that an everted bilayer tubular tissue, with isotropic differential growth, can generate a circumferential or two-dimensional pattern, but fails to produce an axial pattern, which distinguishes it from a bilayer tubular tissue without eversion. Furthermore, as the modulus ratio and layer thicknesses increase, the surface instability pattern transitions from a two-dimensional pattern to a circumferential pattern. Notably, when the modulus ratio or layer thickness reaches sufficiently high values, spontaneous instabilities emerge on the inner surface of the everted bilayer tubular tissues pre-growth. To investigate the morphological instability of everted bilayer tubes, we perform a series of quantificational finite-element simulations and swelling experiments. The results of both numerical simulations and experimental observations align well with our theoretical analysis. This study not only enhances our comprehension of everted tubular tissue morphogenesis but also offers valuable insights for biomedical engineering and growth self-assembly applications.