Analysis of deformation coupled surface remodeling in porous biomaterials

Surface remodeling of biological tissues through tissue growth or dissolution is deemed critical to their proper functioning, and is influenced by the deformation of the tissues during physiological activities. The present work attempts to develop a constitutive framework for deformation modulated surface remodeling of biological tissues. The framework is developed assuming finite deformation of the tissue, and the effect of deformation on the driving force for surface remodeling is determined from thermodynamic principles. The microscopic trends are upscaled to yield the remodeling-induced change in a macroscopic porous tissue. By way of application, the effect of deformation on the remodeling kinetics is determined for an incompressible elastic tissue. Depending on the ratio of the specific elastic stiffness and the specific Gibbs energy variation induced by the cell, the effect of deformation on the remodeling kinetics can be significant. It is found that both tensile and compressive deformation aid tissue dissolution (and dissuade growth). However, the magnitude of the effect is found to be different under tensile and compressive loadings, and critically depends on the reference frame used for the strain measurements. For Lagrangian strain measures (e.g., stretch, engineering strain), the increase in the dissolution kinetics per unit strain is higher under compressive loadings. On the other hand, for Eulerian strain measures (e.g., logarithmic or true strain), the effect of tensile loading on the dissolution kinetics is higher. This reinforces the need for proper reference frame definition for experimental strain measurements.