Oxygen Transport in Bioreactors for Engineered Vascular Tissues - Computational Modeling in Tissue Engineering - page 290

Fig. 9 Solutions to 3D flow during peak flow of PFS bioreactor. a Streamlines show flow around
manifolds through the chamber interior. Streamline color indicates local stream velocity.
b Solution shown in a isolating the tissue to highlight transmural flow. c Surface plot showing
symmetry of flow and higher velocity around the manifolds. d Lower manifold outlet highlighting
the swirl flow as shown by the streamlines. e Top view showing the tubular tissue construct
surrounded by streamlines. Streamlines originating at the ablumenal surface are associated with
transmural flow

examine pulsatile or steady fluid flow, respectively, with a convergence tolerance
of 10 -6 and a minimum damping factor of 10 -4 . Solutions were typically found
after 200 iterations using a biconjugate gradient stabilized solver. The mesh was
refined until minimal variation in the solution was observed.
The output of the flow problem was coupled to the DO transport problem using
COMSOL in order to evaluate the effect of pulsatility and stroke volume on DO
profiles. Based on measurements showing no spatial variation in DO concentration
in the annular region of the jar and low curvature of the construct, the 3D model
was simplified to a 1D transport model as shown in Fig. 8 .
The DO transport problem required solution to the species balance equation as
shown in Eq. 2.1 . The flow velocity was determined from Darcy's Law and was
driven by a pulsatile waveform in the lumen, which was modeled by Eq. 4.1 :

(

ð Þ; ð Þ [ 0

P peak sin 2 pxt sin 2 pxt

P pulse ¼ ð 4 : 1 Þ

0 ; sin 2 pxt ð Þ 0

where P peak is the measured peak pressure and x is the frequency of pulsatility,
which results in the oscillatory pressure P pulse . The model pulsatile pressure
in Eq. 4.1 was compared to pressure monitoring data and found to match
with suitable accuracy. The transient model was solved in COMSOL using the