Oxygen distribution in channeled cardiac constructs perfused with oxygen carrier supplemented culture medium

Introduction: In vascularized tissues, such as myocardium, oxygen is supplied by convection of blood through a capillary network and diffusion into the tissue space surrounding each capillary, with the total oxygen content of blood increased by the presence of a natural oxygen carrier, hemoglobin. Most of the current tissue culture systems are limited by diffusional supply of oxygen from the surface of the tissue construct to the center. We developed a biomimetic tissue culture system in which neonatal rat heart cells were co-cultured on an elastic, highly porous scaffold with a parallel array of channels, to mimic the role of capillary network. To mimic the role of blood the channel array was perfused with culture medium supplemented with a synthetic oxygen carrier (Oxygent, perfluorocarbon emulsion). The main objective of this paper was to develop a mathematical model of oxygen distribution in a channeled cardiac construct that can be utilized to optimize channel geometry and culture conditions for cultivation of clinically thick (0.5cm) cardiac constructs of physiologically high cell density (10cells/cm). A steady state mathematical model of oxygen distribution within the cardiac tissue construct was derived as a function of culture medium flow rate, fraction of perfluorocarbon (PFC) emulsion, array geometry, cell density and inlet oxygen concentration. The model was solved using finite element method. Governing equations: The construct was divided into an array of cubic domains with a channel in the center and the tissue space surrounding the channel. Assuming constant density and diffusivity in each region, uniform oxygen concentration within the PFC droplets, local equilibrium between aqueous and PFC phases as well as low hydraulic permeability the governing equation for oxygen concentration in the channel lumen is: (1)