A Numerical Simulation for Aberrant Crypt Foci

A Numerical Simulation for Aberrant Crypt Foci

Romanazzi∗, G.; Figueiredo, I.N.; Leal, C.

Full Article:

It is generally accepted that colorectal cancer (CRC) occurs as a consequence of several genetic mutations in the colonic mucosa. The detection and assessment of aberrant crypt foci (ACF), which are clusters of abnormal colonic crypts and believed to be the precursors of CRC, is therefore of crucial importance. This paper models and describes the dynamics of abnormal cells in the colon epithelium, with the goal of simulating the appearance and evolution of ACF. The colon is represented by a rectangular periodic domain, consisting of small rectangles containing at their centers small circles (these symbolize the crypts) and the exterior of the circles represents the intercryptal regions. The dynamics of the abnormal cells is modeled by a convection-diffusion system (where the convective velocity is defined by a Darcy’s law), inside the crypt, and by a pure diffusive model in the intercryptal region. Moreover this model is coupled with a level set equation for tracking the boundary of the abnormal cell set. Numerical simulations are reported and discussed for the particular case of a periodic domain consisting only of two rectangles.

It is generally accepted that colorectal cancer (CRC) occurs as a consequence of several genetic mutations in the colonic mucosa. The detection and assessment of aberrant crypt foci (ACF), which are clusters of abnormal colonic crypts and believed to be the precursors of CRC, is therefore of crucial importance. This paper models and describes the dynamics of abnormal cells in the colon epithelium, with the goal of simulating the appearance and evolution of ACF. The colon is represented by a rectangular periodic domain, consisting of small rectangles containing at their centers small circles (these symbolize the crypts) and the exterior of the circles represents the intercryptal regions. The dynamics of the abnormal cells is modeled by a convection-diffusion system (where the convective velocity is defined by a Darcy’s law), inside the crypt, and by a pure diffusive model in the intercryptal region. Moreover this model is coupled with a level set equation for tracking the boundary of the abnormal cell set. Numerical simulations are reported and discussed for the particular case of a periodic domain consisting only of two rectangles.

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DOI: 10.5151/meceng-wccm2012-18318

Referências bibliográficas

• [1] Boyle, P. and LevinSteward, B.,”World Cancer Report”,IARC Press, Lyon, France 2008.
• [2] Figueiredo I.N., Leal C., Leonori T., Romanazzi G., Figueiredo P.N., Donato M.M., “A coupled convection-diffusion level set model for tracking epithelial cells in colonic crypts”. Procedia Computer Science 1, 955-963, 2010.
• [3] Figueiredo I.N., Leal C., Romanazzi G., Engquist B., Figueiredo P., “A convectiondiffusion- shape model for aberrant colonic crypt morphogenesis”. Computing and Visualization in Science 14(4), 157-166, 2011.
• [4] Holt P. R. et al., “Modulation of Abnormal Colonic Epithelial Cell Proliferation and Differentiation by Low-Fat Dairy Foods”. Journal of AmericanMedical Association 280(12), 1074-1079, 1998.
• [5] Osher S., Fedkiw R., “Level set methods and dynamic implicit surfaces”. Applied Mathematical Sciences 153, Springer-Verlag, New York, 2003.
• [6] Pina H., “M´etodos num´ericos”. McGraw-Hill, Lisboa, 1995.
• [7] Preston S. L. et al., “Bottom-up Histogenesis of Colorectal Adenomas: Origin in the Monocryptal Adenoma and Initial Expansion by Crypt Fission”. Cancer Research 63, 3819-3825, 2003.
• [8] Shih I. M. et al.,“Top-down morphogenesis of colorectal tumors”. Proceedings of the National Academy of Sciences of the United States 98(5), 2640-2645, 2001.
• [9] van Leeuwen I. M. M., Byrne H. M., Jensen O. E., King J. R., “Crypt dynamics and colorectal cancer: advances in mathematical modelling”, Cell Proliferation 39, 157-181, 2006.

Como citar:

Romanazzi∗, G.; Figueiredo, I.N.; Leal, C.; "A Numerical Simulation for Aberrant Crypt Foci", p-1271-1282. In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1]. São Paulo: Blucher, 2014.
ISSN 23580828, DOI 10.5151/meceng-wccm2012-18318