Extracting permeability model parameters for skin tissue from injection experiments

Hollow microneedles are medical devices used to inject fluid, such as vaccines, into the skin. As the fluid flows into the skin, a soft porous medium, it deforms the porous matrix. The fluid flow and solid deformation are coupled -- the flow-induced deformation changes the porosity and permeability of the tissue, which in turn affects fluid flow. In our experiments, we injected water into excised porcine skin, while recording fluid flow-rate and visualizing the tissue cross-section in real time using optical coherence tomography (OCT). We performed digital image correlation on the OCT images to generate strain maps for quantifying tissue deformation. We used a spherical model of tissue expansion and a two-parameter exponential relationship between permeability and volumetric strain in tissue. Applying Darcy's law to the measured fluid flow-rate and the strain maps over time yields the two parameters through an optimization algorithm. The fluid flow estimated from the optimized permeability model matched closely with the recorded flow-rate. The permeability-strain relationship can help improve the efficiency of fluid injections into the skin.