Page 89 - Physico-Chemical Niche Conditions for Bone Cells

geometry was considered constant during the computational evaluation since PFF did not change the cell topography significantly during the modeling period (5 sec). The culture medium inside the chamber was considered as incompressible, and homogeneous Newtonian fluid. The effect of heat dissipation from the culture medium was neglected. Therefore, the culture medium specifications, such as dynamic viscosity and density, were assumed to be constant during the computational analysis.
Laminar fluid flow equations
Time dependent Navier-Stokes equations for incompressible fluid dynamics were used to model a fully developed and laminar flow as described earlier [14].
Initial and boundary conditions for fluid flow
The initial fluid velocity was set to zero in the simulation volume. The average pressure at the outlet surface of the parallel-plate flow chamber was set to zero as a boundary condition (Fig. 1C). No-slip boundary condition was applied to the inner surface of the parallel-plate flow chamber (Fig. 1C), while a slip-boundary condition was applied to the outer surface of the cell [15]. As inlet flow boundary condition, PFF (inlet flow rate, 3.5 ml/min (small chamber); amplitude, 1.0 Pa; frequency, 1 Hz) was chosen based on the PFF used in the experimental part of our study. The parameters and default values used in the simulation model were as follows: T = 37°C (operational temperature (experimental part of this study)), Qinlet = 3.5 ml/min´(sin(ω*t)+b) (ω= 2×π×f, f: frequency, t: time, b: amplitude; Qinlet: pulsating inlet flow rate), ρ = 893 kg.m-3 (culture medium density [16]), μ = 0.83 mPa.s (culture medium dynamic viscosity [16]), P = 1 atm (operation pressure (experimental part of this study)).
Mesh generation
For the generation of FE meshes, the “user controlled meshes” with normal element size (total elements: 649554, tetrahedra, 494820; triangles, 150873; edge elements, 3241; vertex elements: 620) was constructed using commercial finite element software. Average element quality was 0.68 measured by skewness, which is considered as good element quality. Maximum mesh element was 0.14 mm, minimum mesh element was 0.00432 mm, maximum element growth rate 1.5, curvature factor 0.6, and resolution of the narrow area 0.5 (Fig. 1C).
FE modeling
FE modeling was performed with a time-dependent Fully Coupled solver using a commercial FE software package (COMSOL Multiphysics v5.4, Stockholm, Sweden). An iterative method for the numerical solution of a non-symmetric system of linear equations (generalized minimal
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