Wan-Hsiang Liang1, Vijayakumar Janakiraman, Kamlesh Mathur2, and Harihara Baskaran3. (1) Chemical Engineering, Case Western Reserve University, Bingham #126, 10900 Euclid Avenue, Cleveland, OH 44106, (2) Operations Research, Case Western Reserve University, A.W.Smith Building, 10900 Euclid Avenue, Cleveland, OH 44106, (3) Chemical Engineering and Biomedical Engineering, Case Western Reserve University, A.W.Smith Building, 10900 Euclid Avenue, Cleveland, OH 44106
Nutrient mass transfer limitations pose a serious problem for current tissue-engineered (TE) products. Several strategies including porous matrices, hydrogels, and angiogenic factor delivery, have been employed to address the nutrient limitations. However these strategies fail to overcome the problem as mass transfer primarily occurs by passive diffusion until the product is vascularized
in vivo through angiogenesis. An ideal TE product will feature a built-in microvasculature, leading to convective delivery of nutrients, and will succeed in eliminating this mass transfer limitation. The primary goal of this research is to design capillary flow networks with optimal transport characteristics for developing a three dimensional microvascularized tissue-engineered product. Choosing skin as the tissue model and utilizing three dimensional quadruplicating flow networks as our basic design, we developed an approach to design optimal flow networks that have maximum mass transport efficiency and minimum pressure losses. In this work, we discuss the effect of network variables such as porosity and generations on the characteristics of the optimal designs.
For a cuboidal tissue section of given length, width and depth, the extent of branching depends on the number of generations. We assumed that there were 4i equidistant branches in the ith generation. The length of the vessel from one generation to another was reduced by a factor Y, which was the same for each generation. Likewise, the width of the vessel was reduced by a constant factor X. The arteriole and venule sections were assumed to be mirror images of one another. We used the cylindrical duct geometry as the flow model and the flow rate in each daughter vessel was assumed to be one quarter of that in the parent vessel. We assumed the surface area per unit volume in the tissue section to be an indicator for the mass transport efficiency of the section. An optimization model was developed and solved to maximize the surface area per volume for a particular generation and porosity. Results were tabulated for number of generations ranging from 1 to 6 and porosities ranging from 0.2 to 0.6. Finally, we compared the effectiveness of the three dimensional geometry with corresponding two dimensional designs.