  Colorectal cancers are the third most common type of cancer. They originate
from intestinal crypts, glands that descend from the intestinal lumen into the
underlying connective tissue. Normal crypts are thought to exist in a dynamic
equilibrium where the rate of cell production at the base of a crypt is matched
by that of loss at the top. Understanding how genetic alterations accumulate
and proceed to disrupt this dynamic equilibrium is fundamental to understanding
the origins of colorectal cancer. Colorectal cancer emerges from the
interaction of biological processes that span several spatial scales, from
mutations that cause inappropriate intracellular responses to changes at the
cell/tissue level, such as uncontrolled proliferation and altered motility and
adhesion. Multiscale mathematical modelling can provide insight into the
spatiotemporal organisation of such a complex, highly regulated and dynamic
system. Moreover, the aforementioned challenges are inherent to the multiscale
modelling of biological tissue more generally. In this review we describe the
mathematical approaches that have been applied to investigate multiscale
aspects of crypt behaviour, highlighting a number of model predictions that
have since been validated experimentally. We also discuss some of the key
mathematical and computational challenges associated with the multiscale
modelling approach. We conclude by discussing recent efforts to derive
coarse-grained descriptions of such models, which may offer one way of reducing
the computational cost of simulation by leveraging well-established tools of
mathematical analysis to address key problems in multiscale modelling.
