Computational Modeling of Tissue Engineering Scaffolds as Delivery Devices for Mechanical and Mechanically Modulated Signals - Computational Modeling in Tissue Engineering - page 132

Fig. 9 CFD predictions compared to experimental measures (l-PIV) of velocity in the flow
chamber, in the absence of cells. Error bars report standard error (n = 5) at each data point. All
linear regressions show R 2 [ 0.8. The slopes of the linear regression lines represent the inverse of
strain rate. Adapted from [ 40 ], used with permission

Flow is calculated from the continuity Eq. ( 1 ) and Navier-Stokes Eq. ( 2 ) using
a second order upwind-discretization scheme in three dimensions. Wall shear
stress is calculated from the wall strain rate ( 3 ). Hence,

r v ¼ 0 ; ð 1 Þ

q ð v r v Þ D 2 v r P ; ð 2 Þ

s cell ¼ l o v
ox

ð 3 Þ

; cellheight

where v is the velocity vector, q is density, P is pressure, l is viscosity, s cell is the
shear stress at typical cell height, o v
ox

is the strain rate, and x is the height from

bottom of chamber. (Fig. 8 a).
CFD and microsphere displacement tracking enable the unprecedented pre-
diction, validation and spatiotemporal delivery of mechanical signals on cell
surfaces bordering other cells or the environment. This approach is rapidly
translatable to the design of geometries and surfaces for tissue engineering scaf-
folds as delivery devices for mechanical and biochemical signals to steer the fate
of cells seeded within.