Assessment of Three Possible Criteria for Remodelling of Collagen Gels and Collagenous Tissues

Collagenous tissues are living structures, in which new material may be added and the structural organisation may change over time. The maintenance of the collagen matrix is accomplished by fibre-producing cells, such as fibroblasts. During maintenance, the extracellular matrix (ECM) influences the development, shape, migration, proliferation, survival, and function of the cells. The mobility of the fibroblasts and their ability to contract the ECM are important properties for a proper maintenance of the ECM [1,2]. The purpose of the present paper is to shed some more light on the interaction between the ECM and the fibre-producing cells. The fibroblasts remodel the collagen gel by reorienting the individual collagen fibres. This reorientation of fibres is described by an evolution law, which depends on a continuum mechanics entity. Three possible choices are assessed: reorientation towards increasing Cauchy stress, increasing elastic stretch, and increasing current stiffness of the material. The model is compared with experimental results, and the three different criteria are evaluated in terms of the predicted distribution of collagen fibres after remodeling and resulting stress-strain relations. Experimental results from tissue equivalents in the form of collagen gels are used when assessing the three criteria [3]. We consider a network of collagen fibres, where the fibres are embedded in a matrix fluid. The collagen fabric and the surrounding fluid are assumed to be the only load-carrying constituents in the material. Embedded in and attached to the collagen fabric is also a population of fibroblasts. The collagen fabric is composed of collagen fibres, which in turn are bundles of collagen fibrils. The deformation of a line element in the matrix is described by the deformation gradient F(X) = ∂x/∂X, which is decomposed according to F = F_elF_lfF_r, see Fig. 1. The fibroblasts’ remodelling of the collagen fabric results in a new matrix configuration Ω_r. This deformation of the matrix is described by F_r. The configuration Ω_r does not necessarily fulfill equilibrium, and the deformation gradient F_lf takes the matrix to the state Ω_lf, that fulfils global equilibrium with no external loads applied. Finally, if external loads are applied to the material, the configuration Ω_el is attained, and this deformation is described by the deformation gradient F_el.