Enhanced Mass Transport Through Permeable Polymer Microcirculatory Networks
Authors: Xia Chunguang , Fang Nicholas 
Published: April 2008

One of the obstacles of culturing functioning vital tissues in vitro is to obtain a substantial biomass at a physiological cell density (&gt;108cells/cm3). At this high density, the diffusion length of metabolites is limited to ~100um. As a matter of fact, in real tissue, almost all the cells are located within 100um distance from the capillaries [1]. Studies [2, 3] also confirmed that the cells in the artificial tissue cannot be properly cultured when they are further than 400um from the external nutrient source. Therefore, to culture three dimensional artificial tissue with substantial biomass, vascularization is necessary to enhance the metabolites transport. The short diffusion length of the metabolites requires high capillary density (&gt;100/mm2) in vascularization. To meet this need, we have developed a novel high resolution and high speed 3D microfabrication technique, the projection microstereolithography[4] to explore microcirculatory networks with high density (&gt;150/mm2). Using this technology we designed and fabricated the microreactors as shown in Figure 1. In our samples, 800um PEG microcapillaries with 20um inner radius and 40um outer radius with pitch of 96um are fabricated. Two rings as inlet and outlet are connected to external supply of culture medium. We designed the parameters of the vascularized microbioreactor based on the simulations of oxygen and carbon dioxide transport and metabolism in hepatocytes. As shown in Figure 2, the capillaries are arranged in a hexagonal way. According to the geometric symmetry, the final simulation domain is divided into 2 regions, the polymer capillary wall and the tissue. We assumed that a culture media with dissolved oxygen is pumped through the capillaries at 1.5mm/s rate and diffuses through the capillary wall, into the hepatocytes. The consumption of oxygen follows Michaelis-Menten kinetics [5, 6] and the metabolic rate of carbon dioxide is assumed to be proportional to that of oxygen by a fixed quotient (-0.81) which is addressed and studied by other groups [7]. The carbon dioxide diffuses into the capillaries and can be carried away through the flow of the culture medium. Our simulation indicates that the bottleneck of effective oxygen transport is the permeability of the polymer materials. The oxygen concentration drops off about 90% after diffusing through the capillary wall. It is predicted that the diffusion length at the inlet is 74um and 48um at the outlet; the rapid drop of carbon dioxide concentration also happens across the capillary wall. The predicted carbon dioxide concentration in the tissue is ~80nmol/cm3; this value is much smaller than the toxic value (100mmHg or 3umol/cm3) reported by David Gray and coworkers [8]. In Figure 2, we present the effect of the permeability of the capillary polymer materials on the diffusion length of oxygen and the concentration of carbon dioxide in the tissue. Our study indicates the existence of an optimal permeability for the capillary network, at which the overall diffusion length of oxygen is maximized. Interestingly, we also found a maximum concentration of carbon dioxide in the cultured tissue as the permeability of the polymer material changes. We attribute it to the competition between the tissue thickness and the permeability. Higher permeability increases the cultured tissue thickness, and also increases the ability of capillary to empty carbon dioxide. Not only is this model applicable for oxygen and carbon dioxide, but also for the transport of other metabolites. As an ongoing experimental effort, our fluorescent microscopy measurement validated the diffusion transport of fluorescent species from the capillary (Figure 3). Experiments are also in progress on the oxygen diffusion from the capillaries will cell cultures of high density on the PEG scaffold by introducing proper indicators. In summary, we have established a method to design and manufacture vascularized microcirculatory network to enhance the mass transport during the tissue culture. To ensure the effective nutrient delivery and wastes removal, our numerical simulation also confirms that it is essential to embed high density microcapillaries with optimal permeability.