Biomedical Engineering Reference
In-Depth Information
interstitial perfusion improved cell proliferation, nutrient delivery, and shear stress
[ 21 ].
The
perfusion
model
demonstrated
improvements
in
cell
proliferation
through the scaffold, uniformity, and enhanced nutrient delivery.
Interstitial (transmural) flow for vascular tissue engineering has been investi-
gated recently [ 22 - 24 ] as a means of improving uniformity and mechanical
properties for these types of tissues. Transmural flow bioreactors were imple-
mented to investigate controlled flow of culture medium to cells within the
engineered tissues, whereas axial perfusion bioreactors typically impart transmural
flow in an uncontrolled fashion [ 15 - 17 ]. Peclet numbers pertaining to these studies
ranged from just over 1 to approximately 170. In all cases, significant improve-
ments in uniformity were observed compared to diffusion alone. Models have also
been developed to predict how changes in interstitial flow affected cell prolifer-
ation [ 25 ], nutrient delivery, and shear stress [ 17 , 26 ]. Spatial and temporal control
of the DO concentration can be used to maintain cell function and uniformity,
which can ultimately improve tissue quality and mechanical properties [ 26 ].
In this work, an analysis of oxygen transport in engineered vascular tissues is
performed. First, a static culture model is examined which demonstrates DO
limitations that can arise in systems that depend only on diffusion. This is followed
by computational and experimental analysis of several different bioreactor designs
aimed at improving DO uniformity through implementation of convective trans-
port through the tissue interstitium.
2 Static Culture Model
The static culture model was developed to understand the severity of DO gradients
without any convection during incubation in a culture dish [ 23 ]. The general
species conservation equation for DO in tissue is shown in Eq. 2.1 :
o C O 2
ot
þ v r C O 2 ¼ D O 2 ; t r 2 C O 2 R O 2
ð 2 : 1 Þ
where D O 2 ; t is the diffusivity of oxygen in tissue, C O 2 is the DO concentration, v is
the velocity vector and R O 2 is the oxygen consumption term. Simplifying for
steady-state, diffusion-only DO transport, and substituting Michaelis-Menten
kinetics for oxygen consumption within the tissue yields Eq. 2.2 :
D O 2 ; t r 2 C O 2 ¼ q cell V O 2 max C O 2
K m þ C O 2
ð 2 : 2 Þ
where q cell is the cell density, and V O 2 max and K m are Michaelis-Menten param-
eters. The system consisted of two subdomains—the tissue and the culture medium
surrounding the tissue as illustrated in Fig. 1 . Equation 2.2 was solved with the
boundary conditions shown in Eq. 2.3 - 2.5 :
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