Free boundary morphogenesis in living matter

Pasquale Ciarletta 1
1 MPIA - Modélisation, Propagation et Imagerie Acoustique
DALEMBERT - Institut Jean Le Rond d'Alembert
Abstract : Morphogenetic theories investigate the creation and the emergence of form in living organisms. A novel approach for studying free boundary problems during morphogenesis is proposed in this work. The presence of mass fluxes inside a biological system is coupled with the local gradient of diffusing morphogens. The contour stability of a growing material is studied using a two-dimensional system model with a rectilinear free border inside a Hele-Shaw cell. Modeling mass transport during morphogenesis allows fixing the velocity at the traveling wave solution as a function of one-dimensionless parameter. Performing a perturbation of the free boundary, the dispersion relation is derived in an implicit form. Although both the velocity of the moving front and the surface tension act as stabilizing effects at small wavelengths, the dispersion diagrams show that the rectilinear border is always unstable at large wavelengths. Further applications of this model can help give insights into a number of free boundary problems in biological systems.
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European Biophysics Journal, Springer Verlag (Germany), 2012, 41 (8), pp.681 - 686. 〈10.1007/s00249-012-0833-5〉
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Soumis le : mercredi 13 septembre 2017 - 15:42:29
Dernière modification le : jeudi 11 janvier 2018 - 06:27:14

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Pasquale Ciarletta. Free boundary morphogenesis in living matter. European Biophysics Journal, Springer Verlag (Germany), 2012, 41 (8), pp.681 - 686. 〈10.1007/s00249-012-0833-5〉. 〈hal-01587049〉

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