Biomathematical model for simulating abnormal orifice patterns in colonic crypts

Colonic polyps, which are abnormal growths in the colon, are a major concern in colon cancer diagnosis and prevention. Medical studies evidence that there is a correlation between histopathology and the shapes of the orifices in colonic crypts. We propose a biomathematical model for simulating the appearance of anomalous shapes for the orifices of colonic crypts, associated to an abnormal cell proliferation. It couples a mechanical model that is a mixed elastic/viscoelastic quasi-static model describing the deformation of the crypt orifice, with a convection-diffusion model that simulates the crypt cell dynamics in space and time. The coupling resides in the variation of pressure generated by abnormal proliferative cells that induce a mechanical force and originate the change in shape of the crypt orifice. Furthermore the model is formulated in a two-dimensional setting, for emulating the top view of the colonic mucosa, observed in vivo in colonoscopy images. The primary focus of this study is on the modeling of this complex biological phenomenon, by defining an appropriate reduced biomathematical model. Additionally, a numerical procedure to determine its solution is also addressed. The overall numerical simulations indicate that an excess of cell proliferation, in different crypt locations, creates some of the anomalous patterns of the colonic crypt orifices, observed in vivo in medical images.