Characterization of the cell/gel constructs

The flow speed within the cell/gel construct was obtained by monitoring the intensity of fluorescent molecules traveling through the agarose gels during flow application. Alexa Fluor 594-conjugated bovine serum albumin (BSA-594; Thermo Fisher) was used. Before flow speed measurement, a standard curve of fluorescence intensity was created by measuring the average fluorescence intensity of a drop of different concentrations of BSA-594 on a coverslip. The solute concentration (50 μg/ml) used in this study was within the linear range of this curve (data not shown). The background fluorescence images were captured before the addition of fluorescent media and the time-lapse images were obtained every minute to monitor the perfusion of BSA-594. The maximum fluorescence images were captured after the imaging regions were uniformly perfused with BSA-594. Flow speed v was obtained using the following equation⁶⁹.

where L is the length of the measuring window, and I _b and I _max are background and maximum fluorescence intensity values, respectively. I ₁ and I ₂ are those taken at time t ₁ and t ₂, respectively.

Permeability of the agarose gel was measured using a dynamic mechanical analyzer (DMA, TA Instruments Q800) and post-analysis based on poroelastic theory as described previously⁷⁰. Briefly, samples were prepared in a disk shape (12 mm-diameter and a 3 mm-thickness) and subjected to compression in the DMA based on a strain ramp from 0 to 10% at a rate of 10%/min. The reaction force exerted by the specimen on the compression clamp was recorded as the specimen was maintained at compression with constant strain (10%) for 120 min. Approximating the agarose gel as a poroelastic material, its force-relaxation behavior during the unconfined compression could be described as a function of its poroelastic properties, including permeability and elastic modulus, using a previously reported analytical model⁷¹. The permeability of agarose gel was then estimated by fitting the model simulations to the time-dependent force measurements using a non-linear optimization routine developed in MATLAB.

The shear stress (τ) applied on the cell by interstitial fluid flow was estimated by the following equation assuming spherical cells^{72, 73}.

where μ is the viscosity of the fluid, Q is the volumetric flow rate, A is the cross-sectional area of the flow chamber, and k is the Darcy permeability.