Optimal planar flow network designs for tissue engineered constructs with built-in vasculature

Convective delivery of nutrients is important to enhance mass transport within tissue engineered (TE) products. Depending on the target tissue, an ideal TE product will have an integrated microvasculature that will eliminate mass transport limitations that can occur during product growth in vitro and integration in vivo. A synthetic approach to develop microvasculature involves development of network designs with efficient mass transfer characteristics. In this paper, utilizing a planar bifurcating network as a basis, we develop an approach to design optimal flow networks that have maximum mass transport efficiency for a given pressure drop. We formulated the optimization problem for a TE skin product, incorporating two types of duct flow, rectangular and square, and solved using a generalized reduced gradient algorithm. Under the conditions of this study, we found that rectangular ducts have superior mass transport characteristics than square ducts. Microvascular area per volume values obtained in this work are significantly greater than those reported in the literature. We discuss the effect of network variables such as porosity and generations on the optimal designs. This research forms the engineering basis for the rational development of TE products with built-in microvasculature and will pave the way to design complex flow networks with optimal mass transfer characteristics.