A. Cell motility

This research concerns the development of models for surface growth, as they apply to the motility of certain classes of biological cells, such as fish epidermal keratocytes. Surface growth occurs when material is added to or removed from the surface of the body. The theoretical challenges of surface growth stem from the fact that the resulting motion is generally non-material and needs to be tracked relative to an ever evolving reference configuration. Furthermore, one needs to track the dynamics of several motility-relevant protein species, which affects the stress, as well as the tractions developed between the cell and the substrate. On the computational side, finite element methods need to be suitably formulated to account for the growth and resorption at the surface.

The following image depicts the actin network (mesh) and the myosin-II (red dots) in a motile fish epidermal keratocyte.


Related Publications:

  • N. Hodge and P. Papadopoulos. ``Continuum Modeling and Numerical Simulation of Cell Motility'' , J. Math. Biology, 64, pp. 1253-1279, (2012).

  • P. Papadopoulos and N. Hodge. ``On Surface Growth of Actin Networks'' , Int. J. Engrg. Sci., 48, pp. 1498-1506, (2010).

  • N. Hodge and P. Papadopoulos. ``A Continuum Theory of Surface Growth'' , Proc. Royal Soc. London A., 466, pp. 3135-3152, (2010).

  • B. Bone strength

    This work, done jointly with Professor T.M. Keaveny, concerns the detailed modeling of bone structures, especially of trabecular type, and the estimation of strength from a combination of experimental measurement of the bone topology and computer simulation of the stress due to habitual or accidental loading. A further area of interest includes bone adaptation through stress- or strain-induced volumetric growth and resorption.

    The following image depicts a high-resolution finite element model of trabecular bone obtained by converting a CT-scan into a mesh of hexahedral elements.


    Related Publications:

  • C. Vignes and P. Papadopoulos. ``Material Growth in Thermoelastic Continua: Theory, Algorithmics, and Simulation'' , Comp. Meth. Appl. Mech. Engrg., 199, pp. 979-996, (2010).

  • A. Gupta, H.H. Bayraktar, J.C. Fox, T.M. Keaveny and P. Papadopoulos. ``Constitutive Modeling and Algorithmic Implementation of a Plasticity-like Model for Trabecular Bone Structures'', Comp. Mech., 40, pp. 61-72, (2007).

  • G. Bevill, S.K. Eswaran, A. Gupta, P. Papadopoulos and T.M. Keaveny. ``Influence of Bone Volume Fraction and Architecture on Computed Large Deformation Failure Mechanisms in Human Trabecular Bone'' , Bone, 39, pp. 1218-1225, (2006).

  • M.F. Adams, H.H. Bayraktar, T.M. Keaveny and P. Papadopoulos. ``Ultrascalable Implicit Finite Element Analyses in Solid Mechanics with over Half a Billion Degrees of Freedom'' , ACM/IEEE Proceedings of SC2004: High Performance Networking and Computing.