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Pattern Formation in a Nonlinear Membrane Model for Epithelial Morphogenesis

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Abstract

A theoretical model is presented for pattern formation in an epithelium. The epithelial model consists of a thin, incompressible, viscoelastic membrane on an elastic foundation (substrate), with the component cells assumed to have active contractile properties similar to those of smooth muscle. The analysis includes the effects of large strains and material nonlinearity, and the governing equations were solved using finite differences. Deformation patterns form when the cells activate while lying on the descending limb of their total (active + passive) stress-stretch curve. Various one-dimensional and two-dimensional simulations illustrate the effects of spatial and temporal variations in passive stiffness, as well as the effects of foundation stiffness and stretch activation. The model can be used to examine the mechanical aspects of pattern formation in morphogenetic processes such as angiogenesis and myocardial trabeculation.

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  1. Department of Biomedical Engineering, Washington University, Campus Box 1097, One Brookings Drive, St. Louis, MO, 63130, USA. Tel

    Larry A. Taber

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  1. Larry A. Taber
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Taber, L.A. Pattern Formation in a Nonlinear Membrane Model for Epithelial Morphogenesis. Acta Biotheor 48, 47–63 (2000). https://doi.org/10.1023/A:1002691300115

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