Pattern Selection in Growing Tubular Tissues

Abstract

Tubular organs display a wide variety of surface morphologies including circumferential and longitudinal folds, square and hexagonal undulations, and finger-type protrusions. Surface morphology is closely correlated to tissue function and serves as a clinical indicator for physiological and pathological conditions, but the regulators of surface morphology remain poorly understood. Here, we explore the role of geometry and elasticity on the formation of surface patterns. We establish morphological phase diagrams for patterns selection and show that increasing the thickness or stiffness ratio between the outer and inner tubular layers induces a gradual transition from circumferential to longitudinal folding. Our results suggest that physical forces act as regulators during organogenesis and give rise to the characteristic circular folds in the esophagus, the longitudinal folds in the valves of Kerckring, the surface networks in villi, and the crypts in the large intestine.

Size and curvature regulate pattern selection in the mammalian brain

“…During development, the initially smooth outer cortex grows at a faster rate than the inner white matter core [14]. Differential growth gives rise to residual stresses that induce a mechanical instability, which results in surface buckling [15,16]. The stress patterns associated with differential growth theories agree well with physical stress measurements in the developing ferret brain [17].…”

Modulation of apical constriction by Wnt signaling is required for lung epithelial shape transition

“…With growing attention to the concept of mechanical deformation to explain a variety of morphogenetic events (Ciarletta et al, 2014;Drasdo, 2000;Savin et al, 2011;Takigawa-Imamura et al, 2015;Varner et al, 2015), branching formation based on physical buckling (Varner et al, 2015) and local apical constriction (Kim et al, 2013) have been proposed as mechanisms of bud formation. In our model, apical constriction was assumed to occur globally within the cyst, and uniformly sized buds emerge spontaneously without pre-patterning of protruding regions.…”

Mathematical Modeling of Morphogenesis in Living Materials

“…For example, it has been shown that both elastic properties and the geometry of the growing layers are key factors determining the pattern selection and the emergence of several functional structures on the epithelium of gastro-intestinal tissues [102,23]. In the following, we define a morpho-elastic model of a hyperelastic soft tissue made of two flat layers growing under a spatial constraint.…”