Towards a multiscale model of colorectal cancer

Abstract

Colorectal cancer (CRC) is one of the best characterised cancers, with extensive data documenting the sequential g e n e m u t a t i o n s t h a t u n d e r l i e i t s d e v e l o p m e n t . Complementary datasets are also being generated describing changes in protein and RNA expression, tumour biology and clinical outcome. Both the quantity and the variety of information are inexorably increasing and there is now an accompanying need to integrate these highly disparate datasets. In this article we aim to explain why we believe that mathematical modelling represents a natural tool or language with which to integrate these data and, in so doing, to provide insight into CRC.

Predictions of tumour morphological stability and evaluation against experimental observations

“…There has been extensive progress in employing mathematical modelling to study solid tumour growth over the past few decades, and this work has provided insight into the understanding of experimental and clinical data. Most models fall into two categories, discrete cell-based and continuum models (see recent reviews [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]). For example, models have been applied to brain cancer (e.g.…”

A convection-diffusion-shape model for aberrant colonic crypt morphogenesis

“…We refer, in particular, to [3,[6][7][8]13,19,23,31,44] for models concerning dynamics of cell populations, to [5,9,16,23,24,28,36,47] for papers reporting models related to colorectal cancer, to [1,2,15,26,29,32,34,35,39] for the mathematical modelling of tumor growth, and also [17,25], where the level set technique is used to model the tumor's boundary in time, and finally to [11,14,18,33,37,40,42] for some medical papers related to aberrant crypt foci and colorectal cancer. To the best of our knowledge, there are no mathematical models in the literature reporting the connection between cellular kinetics and colonic crypt patterns, as done here in this paper.…”

Chaste: A test-driven approach to software development for biological modelling

“…Colorectal cancer was originally chosen due to the availability of experimental data and because its biological understanding is sufficiently advanced to allow such a systems-level approach [14]. However, taking a systems, multi-scale approach means that the complexity of the resultant model is greatly increased, with a concomitant decrease in analytical tractability.…”

“…Our second exemplar is a tissue growth model that bridges across spatial and temporal scales within a single, generic modelling framework [13,14]. The main focus of this component of Chaste is the modelling of the initiation of colorectal cancer in intestinal crypts, although the software has developed into a general tissue modelling framework which has also been used to model the growth of tumour spheroids, a common in vitro experimental system that mimics the morphology and growth of avascular tumours in vivo.…”