Oxygen Transport in Bioreactors for Engineered Vascular Tissues - Computational Modeling in Tissue Engineering - page 293

Assumptions used to allow for symmetry simplifications could have precluded
identification of more complex flows, such as the development of secondary flows
crossing symmetry planes. However, the symmetric model demonstrates sub-
stantial mixing below the lower manifold, which provides a uniform DO con-
centration in this region prior to reaching the tissue in the outlet flow. Since there
was little DO depletion axially in the construct lumen and the chamber was a well-
mixed, comparatively large volume reservoir, the lumenal and ablumenal surfaces
had reasonably close DO concentrations, as was measured with DO sensors.
Uniformity of the computed DO, which agreed with measurements taken at three
levels within the chamber at the high flow rates being used (data not shown),
allowed the mass transport model to be simplified to a 1D problem. The output of
the flow problem, namely the transmural flow velocity v r , was then used as an
input to the mass transport problem to determine the effects of O 2 diffusion,
convection and consumption on DO profiles within the tissue.
The model was extended to scenarios beyond the current capability of the bioreactor
since it was designed for 0.5-1.0 Hz pulse frequencies and the stroke volume was
limited by the allowable construct distension. Though frequency had minimal impact on
DO profiles, the stroke volume was found to help improve uniformity due to greater
transmural flow resulting from the higher lumenal pressure. Larger pulse pressures
would induce greater transmural flow but also greater distension of the construct.
Distensions above 10-15% have proven to have detrimental effects on tissue strength
and stiffness [ 9 , 14 ]. Pressures of approximately 25 mmHg have been shown to induce
10% strain in tubular tissue constructs [ 24 ]. The constructs also stiffen with time due to
cellular deposition of collagen, thus greater pressures could be exerted without
imparting detrimental strain levels assuming that L p remains constant. Values of L p have
been measured out to 2 weeks of culture; however, the values could fluctuate depending
on the rate of collagen deposition compared to the rate of fibrin degradation. This has not
been fully investigated, thus the values of L p wereassumedtoremainconstantinthis
study. The pressures examined by the model are relevant since they could be achievable
for bioreactor operation. The results in Fig. 10 were obtained with an L p of
1 9 10 -6 cm/s/Pa. A more porous construct could achieve higher transmural flows
with lower pressures. For example, increasing L p by an order of magnitude would cause
the 100 mmHg pulse to look like a 10 mmHg pulse according to Fig. 10 since L p , h v r i ,
and P are all linearly related. Likewise, decreasing L p by an order of magnitude would
have the opposite effect. In this case a 10 mmHg pulse would appear as the 100 mmHg
pulse in Fig. 10 . While this impacts DO uniformity, Fig. 10 b shows that there is still
notable improvement over a diffusion-only transport system for glucose.
Interstitial shear stress effects due to transmural flow should also be considered. At
a peak pressure of 10 mmHg and L p of 1 9 10 -6 cm/s/Pa, an interstitial shear stress
of 0.9 dyne/cm 2 is experienced by the cells based on Eq. 3.7 [ 26 ]. As with transmural
flow velocity, higher pressures would increase the shear stresses in a linear fashion,
but a decreasing L p increases the shear stress in a non-linear manner.
The DO analysis showed that high stroke volumes, yielding high transmural
flows, would be required to increase the uniformity of the DO profile. When
the analysis was extended to glucose, small stroke volumes were predicted to