Organic tissues in rotating bioreactors: fluid-mechanical aspects, dynamic growth models, and morphological evolution.
This analysis deals with advances in tissue-engineering models and computational methods as well as with novel results on the relative importance of "controlling forces" in the growth of organic constructs. Specifically, attention is focused on the rotary culture system, because this technique has proven to be the most practical solution for providing a suitable culture environment supporting three-dimensional tissue assemblies. From a numerical point of view, the growing biological specimen gives rise to a moving boundary problem. A "volume-of-fraction" method is specifically and carefully developed according to the complex properties and mechanisms of organic tissue growth and, in particular, taking into account the sensitivity of the construct/liquid interface to the effect of the fluid-dynamic shear stress (it induces changes in tissue metabolism and function that elicit a physiological response from the biological cells). The present study uses available data to introduce a set of growth models. The surface conditions are coupled to the transfer of mass and momentum at the specimen/culture-medium interface and lead to the introduction of a group of differential equations for the nutrient concentration around the sample and for the evolution of tissue mass displacement. The models are then used to show how the proposed surface kinetic laws can predict (through sophisticated numerical simulations) many of the known characteristics of biological tissues grown using rotating-wall perfused vessel bioreactors. This procedure provides a validation of the models and associated numerical method and also gives insight into the mechanisms of the phenomena. The interplay between the increasing size of the tissue and the structure of the convective field is investigated. It is shown that this interaction is essential in determining the time evolution of the tissue shape. The size of the growing specimen plays a critical role with regard to the intensity of convection and the related shear stresses. Convective effects, in turn, are found to impact growth rates, tissue size, and morphology, as well as the mechanisms driving growth. The method exhibits novel capabilities to predict and elucidate experimental observations and to identify cause-and-effect relationships.