A finite element method for growth in biological development

  • Received: 01 May 2006 Accepted: 29 June 2018 Published: 01 February 2007
  • MSC : 65M60, 76Z05.

  • 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.

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

    Related Papers:

  • 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.


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  • © 2007 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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