Material Forces in the Context of Biotissue Remodelling

Abstract

Remodelling of biological tissue, due to changes in microstructure, is treated in the continuum mechanical setting. Microstructural change is expressed as an evolution of the reference configuration. This evolution is expressed as a point-to-point map from the reference configuration to a remodelled configuration. A "preferred" change in configuration is considered in the form of a globally incompatible tangent map. This field could be experimentally determined, or specified from other insight. Issues of global compatibility and evolution equations for the resulting configurations are addressed. It is hypothesized that the tissue reaches local equilibrium with respect to changes in microstructure. A governing differential equation and boundary conditions are obtained for the microstructural changes by posing the problem in a variational setting. The Eshelby stress tensor, a separate configurational stress, and thermodynamic driving (material) forces arise in this formulation, which is recognized as describing a process of self-assembly. An example is presented to illustrate the theoretical framework.

Computational modeling of healing: an application of the material force method

“…A monolithic incremental iterative Newton-Raphson solution strategy is suggested for the solution of the discrete residual statements [17]. The corresponding consistent linearization defines the following iteration scheme,…”

“…Residual stresses as well as anisotropic growth, which are neglected by the model proposed herein, are thus incorporated in a straightforward way. See also Cowin [7], Humphrey [30], or Ambrosi and Mollica [1] for the additional information on the original approach or the recent work Garikipati [17] for a slightly modified realization of the multiplicative decomposition. Moreover, soft tissues generally exhibit a highly nonlinear and typically anisotropic behavior, see Holzapfel et al [26,27], Lubarda and Hoger [42], or the collective special volume by Cowin and Humphrey [9].…”

A theoretical model of the endothelial cell morphology due to different waveforms

“…The WLC was used in DNA modeling by [8]. Recently it was used by [24], [39] and [2], among others, to model the behavior of biological tissue, as an extension of the WLC molecular model to approach continuum tissue.…”

Review: Rheological properties of biological materials

“…The multiplicative decomposition of the deformation gradient has been used in several applications, in particular, heart mechanics [164,165], aneurism formation [158], remodelling of arteries [166,167,159,163], and soft tissues in general [168,112].…”