Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

A finite element method for growth in biological development

1. Laboratoire de Mathématiques, Informatique et Applications, Université de Haute-Alsace, 4, rue des Frères Lumière, 68093 MULHOUSE Cedex
2. Department of Physics, Emory University, Maths/Science Center, 400 Dowman Drive, Atlanta, GA 30322


We describe finite element simulations of limb growth based on Stokes flow models with a nonzero divergence representing growth due to nutrients in the early stages of limb bud development. We introduce a ''tissue pressure'' whose spatial derivatives yield the growth velocity in the limb and our explicit time advancing algorithm for such tissue flows is described in detail. The limb boundary is approached by spline functions to compute the curvature and the unit outward normal vector. At each time step, a mixed-hybrid finite element problem is solved, where the condition that the velocity is strictly normal to the limb boundary is treated by a Lagrange multiplier technique. Numerical results are presented.
  Article Metrics

Keywords finite element algorithms.; Stokes flow with surface tension; biological development

Citation: Cornel M. Murea, H. G. E. Hentschel. A finite element method for growth in biological development. Mathematical Biosciences and Engineering, 2007, 4(2): 339-353. doi: 10.3934/mbe.2007.4.339


This article has been cited by

  • 1. Yong-Tao Zhang, Mark S. Alber, Stuart A. Newman, Mathematical modeling of vertebrate limb development, Mathematical Biosciences, 2013, 243, 1, 1, 10.1016/j.mbs.2012.11.003
  • 2. Ricardo Ruiz-Baier, Primal-mixed formulations for reaction–diffusion systems on deforming domains, Journal of Computational Physics, 2015, 299, 320, 10.1016/j.jcp.2015.07.018
  • 3. Bernd Boehm, Henrik Westerberg, Gaja Lesnicar-Pucko, Sahdia Raja, Michael Rautschka, James Cotterell, Jim Swoger, James Sharpe, Alfonso Martinez Arias, The Role of Spatially Controlled Cell Proliferation in Limb Bud Morphogenesis, PLoS Biology, 2010, 8, 7, e1000420, 10.1371/journal.pbio.1000420
  • 4. C. M. Murea, Arbitrary Lagrangian Eulerian approximation with remeshing for Navier-Stokes equations, International Journal for Numerical Methods in Biomedical Engineering, 2010, 26, 11, 1435, 10.1002/cnm.1223
  • 5. Stuart A. Newman, Scott Christley, Tilmann Glimm, H.G.E. Hentschel, Bogdan Kazmierczak, Yong-Tao Zhang, Jianfeng Zhu, Mark Alber, , Multiscale Modeling of Developmental Systems, 2008, 311, 10.1016/S0070-2153(07)81011-8
  • 6. Paramita Chatterjee, Tilmann Glimm, Bogdan Kaźmierczak, Mathematical modeling of chondrogenic pattern formation during limb development: Recent advances in continuous models, Mathematical Biosciences, 2020, 108319, 10.1016/j.mbs.2020.108319

Reader Comments

your name: *   your email: *  

Copyright Info: 2007, , licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved