Physiological tissue-on-a-chip technology is enabled by adapting microfluidics to create micro scale drug screening platforms that replicate the complex drug transport and reaction processes in the human liver. The ability to incorporate three-dimensional (3d) tissue models using layered fabrication approaches into devices that can be perfused with drugs offer an optimal analog of the in vivo scenario. The dynamic nature of such in vitro metabolism models demands reliable numerical tools to determine the optimum tissue fabrication process, flow, material, and geometric parameters for the most effective metabolic conversion of the perfused drug into the liver microenvironment. Thus, in this modeling-based study, the authors focus on modeling of in vitro 3d microfluidic microanalytical microorgan devices (3MD), where the human liver analog is replicated by 3d cell encapsulated alginate hydrogel based tissue-engineered constructs. These biopolymer constructs are hosted in the chamber of the 3MD device serving as walls of the microfluidic array of channels through which a fluorescent drug substrate is perfused into the microfluidic printed channel walls at a specified volumetric flow rate assuring Stokes flow conditions (Re1). Due to the porous nature of the hydrogel walls, a metabolized drug product is collected as an effluent stream at the outlet port. A rigorous modeling approached aimed to capture both the macro and micro scale transport phenomena is presented. Initially, the Stokes Flow Equations (free flow regime) are solved in combination with the Brinkman Equations (porous flow regime) for the laminar velocity profile and wall shear stresses in the whole shear mediated flow regime. These equations are then coupled with the Convection-Diffusion Equation to yield the drug concentration profile by incorporating a reaction term described by the Michael-Menten Kinetics model. This effectively yields a convection-diffusion-cell kinetics model (steady state and transient), where for the prescribed process and material parameters, the drug concentration profile throughout the flow channels can be predicted. A key consideration that is addressed in this paper is the effect of cell mechanotransduction, where shear stresses imposed on the encapsulated cells alter the functional ability of the liver cell enzymes to metabolize the drug. Different cases are presented, where cells are incorporated into the geometric model either as voids that experience wall shear stress (WSS) around their membrane boundaries or as solid materials, with linear elastic properties. As a last step, transient simulations are implemented showing that there exists a tradeoff with respect the drug metabolized effluent product between the shear stresses required and the residence time needed for drug diffusion.
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