Biomechanical Modelling of Colorectal Crypt Budding and Fission

Abstract

This paper presents a biomechanical model for the small pits, called crypts, that line the colon. A continuum approach is adopted, with the crypt epithelium modelled as a growing beam attached to the underlying lamina by cell bonds, which generate tension within the layer. These cell attachments are assumed to be viscoelastic thus allowing for cell progression along the crypt. It is shown that any combination of: an increase in net proliferation (i.e. cell production minus apoptosis), an enlargement of the proliferative compartment, an increase in the strength of the cellular attachment to the underlying lamina, or a change in the rate of cell growth or cell bonding may generate buckling of the tissue. These changes can all be generated by an activating mutation of the Wnt cascade, which is generally accepted to be the first genetic change in colorectal cancer, with subsequent deformation, budding, and crypt fission an observed feature of the adenomatous crypt.

Towards a multiscale model of colorectal cancer

“…These include stochastic models designed to investigate where in the crypt the second APC hit associated with CRC initiation is most likely to occur [18] , detailed models of Wnt signalling to enhance our understanding of the mechanisms of action of this pathway [36,37] and continuous models to explore the causes of crypt buckling and fission [43,44] . While useful, models that focus on a single time and length scale provide limited insight into crypt dynamics and CRC.…”

“…Multiscale mathematical models that account for subcellular, cellular and tissue scale phenomena represent a natural framework for integrating and exploiting these different datasets. As part of a UK government funded project in Integrative Biology [49] , we are using grid technology and high performance computing to perform multiscale simulations of cardiovascular disease [25,27] and cancer [12,37,44,50] . The protype multiscale model of a colonic crypt that we are developing uses a lattice-free model to describe epithelial cell movement and will incorporate subcellular, biochemical phenomena, such as the Wnt signalling pathway and detailed models of the cell cycle [51] .…”

“…By further extending our model to account for the attachment of epithelial cells to the underlying tissue stroma, it will be possible to see how increases in cell proliferation associated with CRC and changes in cell-stroma adhesion contribute to crypt fission. Finally, by upscaling or homogenising our celllevel models, we aim to derive tissue scale models similar in form to that of Edwards and Chapman [44] . In addition to per mitting the simulation of large tissue regions (and hence the colonisation of neighbouring crypts by malignant cells), this will enable us to relate tissue level parameters, associated with, for example, cell proliferation and adhesion to experimentally measurable quantities, such as nuclear β-catenin levels and extracellular concentrations of Wnt factors.…”

“…More recently Edwards and Chapman [44] have developed a biomechanical model of crypt budding and fission in which the epithelial cells are treated as a continuous tissue layer that is attached to a rigid basal lamina ( Figure 6). The model input parameters quantify cell proliferation, adhesion, movement and apoptosis, which are dependent on lower-scale effects.…”

“…It is noteworthy that metastatic deposits also contain stroma showing the importance of the relationship between the tumour epithelium and the tumour stroma. Cell proliferation generates stress Figure 6 Schematic of the biomechanical model developed in Edwards and Chapman [44] . Proliferation in the epithelium generates stress within the layer through cellular attachment to the underlying basal lamina.…”