| Summary: | <p>The intestinal epithelium exhibits remarkable rates of self-renewal to protect the small intestine and colon from damage during digestion and facilitate nutrient absorption. This monolayer of epithelial cells is maintained by the crypts of Liehberkühn, test-tube-shaped glands that are robust in morphology and structure, undergoing significantly large deformations, despite comprising a heterogeneous composition of cells with varying proliferative capacities and mechanical properties. While the genetic and molecular processes governing crypt morphogenesis have been studied in detail, there is a lack of understanding regarding the evident contribution of biomechanical factors, leading to a poor understanding of crypt morphogenesis as a whole. Additionally, it is not known how the crypt's unique, yet incredibly robust, proliferation structure arises. However, morphoelastic rod theory allows one to consider the interplay between growth and tissue mechanics in a unified framework, where we can exploit the slenderness aspect of the crypt and model the tissue as a growing, elastic rod. </p> <p>In this thesis, we use the framework of morphoelastic rods, which extends the classical Kirchhoff rod theory to account for local tissue growth, to explore various aspects of morphogenesis, growth, and homeostasis that are motivated by the crypt. We restrict ourselves to a planar geometry to model the transverse deformations of the crypt epithelium. Morphogenesis is modelled by the buckling and subsequent deformation of an elastic rod tethered to an underlying foundation, representing the crypt and the supporting extracellular matrix and stroma.</p> <p>First, we consider an abstracted model of the crypt, a morphoelastic rod supported by an elastic foundation. We consider crypt morphogenesis in the context of buckling, exploring how growth and spatial heterogeneous properties-two key aspects of the crypt-impact mechanical pattern formation. We investigate the buckling and post-buckling behaviour of the simplified crypt model, extending previous linear stability analyses with a weakly nonlinear analysis and complementing the analysis with numerical continuation of the full nonlinear system. We analyse how incorporating spatial heterogeneity in growth, rod and foundation stiffness affects the underlying bifurcation structure. </p> <p>Then, we specialise the framework to simulate tissue morphogenesis more realistically. We develop different models for the processes that are believed to play a role in crypt morphogenesis, but were not previously included, such as tissue relaxation, chemical signalling, self-contact, and so on. We use simulation results to determine which of these models contribute most significantly to a realistic crypt morphology. By combining several of these processes, we show that a realistic crypt morphology, which is highly-invaginated but narrow in structure, can be generated.</p> <p>To close, we consider a simplified 1D geometry to analyse how the unique growth structure of the crypt rises in development and subsequently is maintained in homeostasis. We develop a minimal mechanochemical model for tissue growth that captures the proliferation structure observed in the crypt, where proliferation activity is maximal away from the crypt base and the crypt top and is thus bimodal in shape. We finish by identifying the necessary conditions for dynamic tissue homeostasis, in which the proliferation structure is fixed with respect to the observable reference frame, but there is a continuous flux of tissue material due to the balance between growth and cell death, modelled through the sloughing of material.</p>
|
|---|