Partial Differential Equations - Modelling and ... - ResearchGate

210 J. Hao et al.
due to shear flow and lubrication forces are small, the cells can be treated as
rigid. The Newtonian incompressible viscous flow is modeled by the Navier–
Stokes equations since the inertial effect is crucial for the lift-off of the cells;
in most studies of cell adhesion, the Stokes flow is considered since the rolling
of cells on the surface and then the capture of cells, like white blood cells, are
the main interest, e.g., see [KS06, KH01, SZD03].
2 Model for Cell Adhesion
Cell adhesion to the extracellular matrix (ECM) plays key roles in the assembly
of cells into functional multicellular organisms. Chondrocytes produce
collagen type-II and other important extracellular matrix constituents; this
allows them to adhere strongly to the artificial surfaces. Chondrocyte cells are
responsible for the synthesis and maintenance of a viable ECM which is suitably
adapted to cope with the physical pressures of its environment. On the
lined surface of LVAD, a monolayer of cells formed on the surface was reported
in [SBBR + 02]. Adhesive interactions between chondrocytes and ECM occur
via a variety of molecular systems (e.g., see discussion for cell-matrix adhesion
in [ZBCAG04]). Zaidel et al. have shown in [ZBCAG04] that cell-associated
hyaluronan plays a central role in mediating early stages in the attachment of
chondrocytes to the surfaces. Their results indicate that chondrocytes establish,
initially, “soft contact” to the surface through a hyaluronan-based coat.
The surface adhesion, mediated by the hyaluronan coat, occurs within seconds
after the cell first encounters the surface. Then within a few tens of secondsto-minutes,
the hyaluronan-mediated adhesion is replaced by integrin-based
interactions which is actually a sequential formation starting from dot-shaped
focal complexes (FXs), then changing to focal adhesions (FAs) and finally
becoming fibrillar adhesions (FBs).
In [ZBCAG04] chondrocytes were allowed to adhere to a serum coated glass
coverslip for 10–25 minutes and exposed to shear flow, they drifted under
flow for quite a distance (compared to their diameters) before detachment
from the surface. In [SKE + 99] chondrocytes were seeded on the surface of a
piece of articular cartilage for specific durations (5–40 minutes) and then were
exposed to shear flow in a flow chamber. It was observed that the increase
in resistance to shear stress-induced cell detachment with increasing seeding
duration. But in [SBBR + 02], chondrocytes were allowed to have 24 hours for
seeding process on the luminal surfaces of LVADs and then 4 days in incubator
for promoting ECM synthesis to maximize the adherence of cells. When using
flow loop to precondition seeded cells in order to promote good cell adherence,
the cell loss during the process did not exceed 12%. The results in [SKE + 99]
suggest that chondrocytes adhere to the surface mainly via hyaluronan gel
and the numbers of integrin-based interactions are not high enough since the
durations are comparable to the one used in [ZBCAG04]. But in [SBBR + 02],
the results indicate that adhesions are mainly integrin-mediated interactions