Physical model of serum supplemented medium flow in organ-on-a-chip systems

Abstract

Creating a physiologically relevant shear stress in organ-on-a-chip (OOC) devices requires careful tailoring of microfluidic flow parameters. Currently, it is fairly common to use a simple approximation assuming constant viscosity, even for serum-based media. Here, we show that a popular nutrient solution (Dulbecco's Modified Eagle Medium supplemented with Fetal Bovine Serum) requires a more complex treatment (i.e., is a non-Newtonian fluid), with observed shear stress values significantly greater than reported in literature. We measure the rheology of the solutions and combine it with a 3-dimensional flow field measurement to derive shear stress at the channel surface. We verify the experiments with numerical simulations, finding good agreement and deriving flow properties. Finally, we provide relevant expressions for the shear stress approximation, suitable for development of OOC devices with various geometries.

Fig 1. Viscosity of the medium over the shear rate range relevant to cell growth.

The solid lines represent fits of experimental data to power law (5). Inset: Viscosity plots in log-log coordinates, showing the correspondence to the power law. Note that two additional measurements have been added to the DMEM + $10\%$ FBS data set, expanding the range of the data.

Fig 2

The experimental setup: (a) an array of channel pairs, the pair marked red has the inlet and outlet for one channel connected (the thicker, nutrient flow channel), and blocked for the other channel; (b) OOC device placed in a microscope; (c) the microscope with an OOC device and the syringe pump; (d) a schematic of the channel layout.

Fig 3. An example of a measured velocity field in the microchannel water at flow rate 4 μL/min).

Left: velocity distribution at a given z coordinate value ($z=0.5mm$). Right: a vector field $\overrightarrow{u}(x,y,z)$ assembled from a stack of plane measurements for the channel volume within the microscope field of view.

Fig 4. (a1), (b1), and (c1) – Flow velocity obtained using PIV; (a2), (b2) and (c2) – numerically calculated flow velocity using COMSOL.

(a1) and (a2) – water at room temperature T=20^∘C (n = 1); (b1) and (b2) – DMEM + 10% FBS at 37^∘C (n = 0.5); (c1) and (c2) – DMEM + 10% FBS at 20∘C(n = 0.32). Channel boundaries are indicated with red lines (zero velocity boundary condition). Here n is the flow index in the power law (5).Different channels were used for different mediums.

Fig 5. Velocity profiles obtained via PIV (dots) and COMSOL (solid lines) for 3 different fluids: water at room temperature T =20∘C (blue, n = 1), DMEM + 10% FBS at T =37∘C (red, n = 0.5), DMEM + 10% FBS at room temperature T =20∘C (green, n = 0.32), all at flow rate 4 μL/min.

The profiles are compared in the middle of the channel (a), 1/3 of the channel width (b), and 1/6 of the channel width (c). Shaded regions are 10% error margins for COMSOL. n is the flow index in the power law equation (5).

Fig 6. Shear stress at the membrane, which is the channel surface relevant for cell growth. Note the different color schemes in top and bottom rows, necessitated by the significant spread of of shear stress values.

Flow rate $4\mu \mathrm{L}/\mathrm{m}\mathrm{i}\mathrm{n}$ used in all measurements.

Fig 7. A schematic of the fluid flow in a rectangular channel with width w (y-axis), height h (z-axis) and length L (x-axis).