An anisotropic biphasic theory of tissue-equivalent mechanics: the interplay among cell traction, fibrillar network deformation, fibril alignment, and cell contact guidance.

We present a general mathematical theory for the mechanical interplay in tissue-equivalents (cell-populated collagen gels): Cell traction leads to compaction of the fibrillar collagen network, which for certain conditions such as a mechanical constraint or inhomogeneous cell distribution, can result in inhomogeneous compaction and consequently fibril alignment, leading to cell contact guidance, which affects the subsequent compaction. The theory accounts for the intrinsically biphasic nature of collagen gel, which is comprised of collagen network and interstitial solution. The theory also accounts for fibril alignment due to inhomogeneous network deformation, that is, anisotropic strain, and for cell alignment in response to fibril alignment. Cell alignment results in anisotropic migration and traction, as modeled by a cell orientation tensor that is a function of a fiber orientation tensor, which is defined by the network deformation tensor. Models for a variety of tissue-equivalents are shown to predict qualitatively the alignment that arises due to inhomogeneous compaction driven by cell traction.