We report an experimental and theoretical investigation of the entry and passage behaviour of biological cells (HeLa and MDA-MB-231) in a constricted compliant microchannel. Entry of a cell into a micro-constriction takes place in three successive regimes: protrusion and contact (cell protrudes its leading edge and makes a contact with the channel wall), squeeze (cell deforms to enter into the constriction) and release (cell starts moving forward). While the protrusion and contact regime is insensitive to the flexibility of the channel, the squeeze zone is significantly smaller in the case of a more compliant channel. Similarly, in the release zone, the acceleration of the cells into the microconstriction is higher in the case of a more compliant channel. The results showed that for a fixed size ratio ρ and E _(c) , the extension ratio λ decreases and transit velocity U _(c) increases with increase in the compliance parameter f _(p) . The variation in the cell velocity is governed by force due to the cell stiffness F _(s) as well as that due to the viscous dampening F _(d) , explained using the Kelvin–Voigt viscoelastic model. The entry time t _(e) = m ( ρ ) ~( k _(1) ) (1 + f _(p) ) ~( k _(2) ) ( E _(c) ) ~( k _(3) ) and induced hydrodynamic resistance of a cell Δ R _(c) / R = k ( ρ ) ~( a ) (1 + k _(f) f _(p) ) ~( b ) ( k _(E) E _(c) ) ~( c ) were correlated with cell size ratio ρ , Young's modulus E _(c) and compliance parameter f _(p) , which showed that both entry time t _(e) and the induced hydrodynamic resistance Δ R _(c) are most sensitive to the change in the compliance parameter f _(p) . This study provides understanding of the passage of cells in compliant micro-confinements that can have significant impact on mechanophenotyping of single cells.
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