Pattern formation in a nonlinear membrane model for epithelial morphogenesis
Acta Biotheoretica 48 (1) (2000)
| 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. | |||||||||
| Keywords | No keywords specified (fix it) | |||||||||
| Categories | ||||||||||
| Options |
|
|||||||||
Download options| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,875 |
| External links |
 |
| Through your library | Configure |
Similar books and articlesMalcolm Maden (1993). The Effect of Vitamin a (Retinoids) on Pattern Formation Implies a Uniformity of Developmental Mechanisms Throughout the Animal Kingdom. Acta Biotheoretica 41 (4).
Rosine Chandebois (1977). Cell Sociology and the Problem of Position Effect: Pattern Formation, Origin and Role of Gradients. Acta Biotheoretica 26 (4).
Alexander Egoyan, Elastic Membrane Based Model of Human Perception. Toward a Science of Consciousness.
Hisao Honda, Masaharu Tanemura & Akihiro Yoshida (2000). Differentiation of Wing Epidermal Scale Cells in a Butterfly Under the Lateral Inhibition Model - Appearance of Large Cells in a Polygonal Pattern. Acta Biotheoretica 48 (2).
Paco Lorente, Carmen Delgado, Mario Delmar & Jose Jalife (1992). Analytical Modeling of the Hysteresis Phenomenon in Guinea Pig Ventricular Myocytes. Acta Biotheoretica 40 (2-3).
M. A. J. Chaplain (1995). The Mathematical Modelling of Tumour Angiogenesis and Invasion. Acta Biotheoretica 43 (4).
Loïc Forest & Jacques Demongeot (forthcoming). A General Formalism for Tissue Morphogenesis Based on Cellular Dynamics and Control System Interactions. Acta Biotheoretica.
Analytics
Monthly downloads |
Added to index2009-01-28Total downloads5 ( #162,017 of 556,888 )Recent downloads (6 months)1 ( #64,931 of 556,888 )How can I increase my downloads? |
My notes
Discussion
