A computational study on the scale-dependence of chemomechanical signals in soft collagenous tissues

Soft collagenous tissues have been shown to reduce their volume when subjected to tensile loads [1,2]. The drastic but reversible loss of volume is caused by the strong alignment of the collagen network and enabled by outflow of water. In particular, when the network compacts, gradients of the fluid chemical potential develop within the tissue and drive the fluid across the external boundaries [1]. Due to the presence of long proteoglycan macromolecules with negatively charged groups, this dehydration of the tissue leads to an increase of the osmotic pressure. Considering the high sensitivity of cells to changes in their environment within the tissue [3], a direct implication of this chemomechanical coupling resides in the potential cues for mechanotransduction stemming from the link between volumetric deformation and osmotic pressure changes [1]. In this contribution, we investigate these potential osmotic stimuli together with purely mechanical cues at different length-scales of the network. By means of multiscale simulations, we study the heterogeneity of these signals, arising from the non-affine motion of the fibre network, and from the coupling between collagen fibres and the chemo-responsive tissue constituents. For this purpose, a mixed continuumdiscrete approach is adopted that consists of a three-dimensional stochastic fibre network [1,4] combined with biphasic continuum elements [5]. The latter allow a lumped representation of interstitial fluid, proteoglycans and the other constituents of the extra-cellular matrix. Representative volume elements are generated, parameterised to be representative for skin tissue [2] and subjected to mechanical loads at their boundaries. While the homogenised response of the model is in excellent agreement with the test data on skin, the multiscale approach gives access to the osmotic and mechanical environments at lower scales, difficult to measure in experiments. The model predicts osmotic stresses in physiologically relevant order of magnitude and sheds light on the scale-dependence of the osmotic and mechanical stimuli.