We present a simple but accurate algorithm to calculate the flow and shear rate profile of shear thinning fluids, as typically used in biofabrication applications, with an arbitrary viscosity-shear rate relationship in a cylindrical nozzle. By interpolating the viscosity with a set of power-law functions, we obtain a mathematically exact piecewise solution to the incompressible Navier-Stokes equation. The algorithm is validated with known solutions for a simplified Carreau-Yasuda fluid, full numerical simulations for a realistic chitosan hydrogel as well as experimental velocity profiles of alginate and chitosan solutions in a microfluidic channel. We implement the algorithm in an easy-to-use Python tool, included as Supplementary Material, to calculate the velocity and shear rate profile during the printing process, depending on the shear thinning behavior of the bioink and printing parameters such as pressure and nozzle size. We confirm that the shear stress varies in an exactly linear fashion, starting from zero at the nozzle center to the maximum shear stress at the wall, independent of the shear thinning properties of the bioink. Finally, we demonstrate how our method can be inverted to obtain rheological bioink parameters in-situ directly before or even during printing from experimentally measured flow rate versus pressure data.

Numerous cell functions are accompanied by phenotypic changes in viscoelastic properties, and measuring them can help elucidate higher-level cellular functions in health and disease. We present a high-throughput, simple and low-cost microfluidic method for quantitatively measuring the elastic (storage) and viscous (loss) modulus of individual cells. Cells are suspended in a high-viscosity fluid and are pumped with high pressure through a 5.8 cm long and 200 μm wide microfluidic channel. The fluid shear stress induces large, near ellipsoidal cell deformations. In addition, the flow profile in the channel causes the cells to rotate in a tank-treading manner. From the cell deformation and tank treading frequency, we extract the frequency-dependent viscoelastic cell properties based on a theoretical framework developed by R. Roscoe that describes the deformation of a viscoelastic sphere in a viscous fluid under steady laminar flow. We confirm the accuracy of the method using atomic force microscopy-calibrated polyacrylamide beads and cells. Our measurements demonstrate that suspended cells exhibit power-law, soft glassy rheological behavior that is cell cycle-dependent and mediated by the physical interplay between the actin filament and intermediate filament networks.

Numerous cell functions are accompanied by phenotypic changes in viscoelastic properties, and measuring them can help elucidate higher-level cellular functions in health and disease. We present a high-throughput, simple and low-cost microfluidic method for quantitatively measuring the elastic (storage) and viscous (loss) modulus of individual cells. Cells are suspended in a high-viscosity fluid and are pumped with high pressure through a 5.8 cm long and 200 μm wide microfluidic channel. The fluid shear stress induces large, near ellipsoidal cell deformations. In addition, the flow profile in the channel causes the cells to rotate in a tank-treading manner. From the cell deformation and tank treading frequency, we extract the frequency-dependent viscoelastic cell properties based on a theoretical framework developed by R. Roscoe that describes the deformation of a viscoelastic sphere in a viscous fluid under steady laminar flow. We confirm the accuracy of the method using atomic force microscopy-calibrated polyacrylamide beads and cells. Our measurements demonstrate that suspended cells exhibit power-law, soft glassy rheological behavior that is cell cycle-dependent and mediated by the physical interplay between the actin filament and intermediate filament networks.

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