We report how cell rheology measurements can be performed by monitoring the deformation of a cell in a microfluidic constriction, provided that friction and fluid leaks effects between the cell and the walls of the microchannels are correctly taken into account. Indeed, the mismatch between the rounded shapes of cells and the angular cross-section of standard microfluidic channels hampers efficient obstruction of the channel by an incoming cell. Moreover, friction forces between a cell and channels walls have never been characterized. Both effects impede a quantitative determination of forces experienced by cells in a constriction. Our study is based on a new microfluidic device composed of two successive constrictions, combined with optical interference microscopy measurements to characterize the contact zone between the cell and the walls of the channel. A cell squeezed in a first constriction obstructs most of the channel cross-section, which strongly limits leaks around cells. The rheological properties of the cell are subsequently probed during its entry in a second narrower constriction. The pressure force is determined from the pressure drop across the device, the cell velocity, and the width of the gutters formed between the cell and the corners of the channel. The additional friction force, which has never been analyzed for moving and constrained cells before, is found to involve both hydrodynamic lubrication and surface forces. This friction results in the existence of a threshold for moving the cells and leads to a non-linear behavior at low velocity. The friction force can nevertheless be assessed in the linear regime. Finally, an apparent viscosity of single cells can be estimated from a numerical prediction of the viscous dissipation induced by a small step in the channel. A preliminary application of our method yields an apparent loss modulus on the order of 100 Pa s for leukocytes THP-1 cells, in agreement with the literature data.
The authors are grateful to P. Bongrand, F. Gallet, A. Asnacios, and M. Sokol for helpful discussions. They also thank Rhodia Company (LOF, Pessac, France), as well as I. Ozerov and F. Bedu from Cinam (CNRS, Marseilles, France) for technical support with microfabrication. P.P.'s Ph.D. grant was supported by Région PACA and the company CAPSUM-SAS.
II. MATERIAL AND METHODS
B. Cell preparation
C. Microscopy setup
D. Reflection interference contrast microscopy modeling
III. EXPERIMENTAL DEVICE
A. Device rationale of the double constriction device
B. Setup used for single cell experiment
C. The double constriction
IV. RESULTS AND DISCUSSION
A. Cell entry in a rectangular constriction with reduced leakages around the cell
B. Quantitative force vs. deformation experiment
C. Cell-channel interface: Lubrication film and “gutters” in channel corners
D. Effect of cell size on the passage through the constriction
E. Pressure force in the presence of gutters
F. Friction force and lubrication film
G. Small deformation and steady state regime
H. Apparent cell loss modulus
I. Non-linear friction vs. velocity
J. Final protocol to measure cell loss modulus with a double constriction
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