A finite element method for growth in biological development
Cornel M. Murea H. G. E. Hentschel
Mathematical Biosciences & Engineering 2007, 4(2): 339-353 doi: 10.3934/mbe.2007.4.339
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.
keywords: finite element algorithms. Stokes flow with surface tension biological development
Biological computing with diffusion and excitable calcium stores
H. G. E. Hentschel Alan Fine C. S. Pencea
Mathematical Biosciences & Engineering 2004, 1(1): 147-159 doi: 10.3934/mbe.2004.1.147
Intracellular signaling often employs excitable stores of calcium coupled by diffusion. We investigate the ability of various geometric configurations of such excitable stores to generate a complete set of logic gates for computation. We also describe how the mechanism of excitable calcium-induced calcium release can be used for constructing coincidence detectors for biological signals.
keywords: Biological Signaling. Diffusion Logic Gates Computation Calcium-Induced Calcium Release

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