  The Starling principle describes exchanges in tissues based on the balance of
hydrostatic and osmotic flows. This balance neglects the coupling between
mechanics and hydrodynamics, a questionable assumption in strained elastic
tissues due to intravascular pressure. Here, we measure the elasticity and
permeability of collagen gels under tensile and compressive stress via the
comparison of the temporal evolution of pressure in an air cavity sealed at the
outlet of a collagen slab with an analytical kinetic model. We observe a drop
in the permeability and enhanced strain-stiffening of native collagen gels
under compression, both effects being essentially lost after chemical
cross-linking. Further, we prove that this asymmetric response accounts for the
accumulation of compressive stress upon sinusoidal fluid injection, which
modulates the material's permeability. Our results thus show that the
properties of collagen gels regulate molecular exchanges and could help
understand drug transport in tissues.
