Oxygen Transport in Bioreactors for Engineered Vascular Tissues - Computational Modeling in Tissue Engineering - page 280

Fig. 1 Illustration of domain
for DO transport problem of
tubular tissue constructs
cultured statically around a
glass mandrel in a culture
dish (not to scale). Schematic
represents the symmetric
domain as it was entered into
COMSOL Multiphysics with
two subdomains, which
consisted of culture medium
surrounding the DO-
consuming engineered tissue

C O 2 j y ¼ 0 ¼ a P 1 ð 2 : 3 Þ

r ¼ R i

o C O 2
or

¼ 0 ð 2 : 4 Þ

J O 2 ; tissue r ¼ R o ¼ J O 2 ; fluid r ¼ R o

ð 2 : 5 Þ

The problem was further simplified by implementation of a symmetry plane at
x = 0.
DO profiles were modeled using the finite element method (FEM) software
package COMSOL Multiphysics (version 3.5a, COMSOL, Inc.). The model was
solved using the UMFPACK stationary solver with a convergence tolerance of
10 -6 and a minimum damping factor of 10 -4 . Numerical values used in this and
subsequent models are shown in Table 1 .
In order to provide values for V max and K m , the oxygen consumption rate (OCR)
was measured for neonatal human dermal fibroblasts (nhDFs) using a stirred
microchamber and an oxygen monitoring system as described in Bjork and
Tranquillo [ 23 ]. Measurements provided by this system provided changes in DO
due to metabolic oxygen consumption inside an impermeable microchamber. V max
was determined on a per-cell basis by Eq. 2.6 [ 27 ]:

V max ¼ V ch a
N cell

Dp O 2
Dt

ð 2 : 6 Þ

where V ch is the volume of the microchamber, a is the Bunsen solubility coefficient
(1.27 nmol/cm 3 /mmHg at 37C[ 28 ]), and N cell is the number of cells in the sample
as determined by DNA quantification and a cell viability assessment. Dp O 2 = Dt is
the slope of the linear portion of the curve obtained from the oxygen monitoring
data. The OCR data obtained with the microchamber was used to determine K m by
plotting OCR versus the oxygen concentration. The concentration at which the
OCR was one-half V max was taken as K m .