A finite element method for growth in biological development - Cornel M. Murea; H. G. E. Hentschel (Mathematical Biosciences and Engineering)
We describe finite element simulations of limb growth based on Stokes flow models witha 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 limband 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 andthe 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 treatedby a Lagrange multiplier technique. Numerical results are presented.