Microfluidic hydraulic permeability measurements

To measure hydraulic permeability, a rhodamine-bovine serum albumin (rhodamine-BSA) (Molecular Probes) was flowed through the microfluidic device. Flow was established by applying a fluidic height difference (2–2.4 cm) between the ports using cell culture medium, measured for each sample. After establishing flow, 4–8μL of rhodamine-BSA was injected into the tip and was transported by the flow through the microdevice. Timelapse microscopy experiments were recorded with an epifluorescence Nikon TS-100F microscope equipped with a Q-Imaging QIClick camera. Images were acquired every 15 s for 20–30 min. These images were then used to quantify the average velocity of the dye through the collagen/fibroblast matrix by tracking the position of the bulk of the dye as it flowed through the microdevice using FIJI. Hydraulic permeability was then calculated by using Darcy's Law for flow through porous medium as follows:

where μ is the viscosity of the cell culture medium (approximated using water), v is the average fluid velocity, ΔL is the length of the channel, and ΔP is the pressure difference across the channel due to the fluidic height difference and is given by the following equation:

where ρ is the density of the cell culture medium (approximated using water), g is the acceleration due to gravity (9.81 m/s²), and h is the fluidic height difference between ports.