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

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Computing and Visualization in Science

Abstract

It is generally accepted that colorectal cancer is initiated in the small pits, called crypts, that line the colon. Normal crypts exhibit a regular pit pattern, similar in two-dimensions to a U-shape, but aberrant crypts display different patterns, and in some cases show bifurcation. According to several medical articles, there is an interest in correlating pit patterns and the cellular kinetics, namely of proliferative and apoptotic cells, in colonic crypts. This paper proposes and implements a hybrid convection-diffusion-shape model for simulating and predicting what has been validated medically, with respect to some aberrant colonic crypt morphogenesis. The model demonstrates crypt fission, in which a single crypt starts dividing into two crypts, when there is an increase of proliferative cells. The overall model couples the cell movement and proliferation equations with the crypt geometry. It relies on classical continuum transport/mass conservation laws and the changes in the crypt shape are driven by the pressure exerted by the cells on the crypt wall. This pressure is related to the cell velocity by a Darcy-type law. Numerical simulations are conducted and comparisons with the medical results are shown.

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Authors and Affiliations

  1. CMUC, Department of Mathematics, University of Coimbra, 3001-454, Coimbra, Portugal

    Isabel N. Figueiredo, Carlos Leal & Giuseppe Romanazzi

  2. Department of Mathematics, University of Texas at Austin, Austin, TX, 78712, USA

    Bjorn Engquist

  3. Faculty of Medicine, University of Coimbra, 3004-504, Coimbra, Portugal

    Pedro N. Figueiredo

  4. Department of Gastroenterology, University Hospital of Coimbra, 3000-075, Coimbra, Portugal

    Pedro N. Figueiredo

Authors
  1. Isabel N. Figueiredo
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  2. Carlos Leal
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  3. Giuseppe Romanazzi
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  4. Bjorn Engquist
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  5. Pedro N. Figueiredo
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Correspondence to Isabel N. Figueiredo.

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Communicated by Gabriel Wittum.

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Figueiredo, I.N., Leal, C., Romanazzi, G. et al. A convection-diffusion-shape model for aberrant colonic crypt morphogenesis. Comput. Visual Sci. 14, 157–166 (2011). https://doi.org/10.1007/s00791-012-0170-3

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  • DOI: https://doi.org/10.1007/s00791-012-0170-3

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