The dynamic nature of in vitro drug metabolism models demands reliable numerical tools to determine key design parameter values towards high-fidelity cell-based platforms of in vivo drug metabolism. This paper represents the first of a two-part model-based investigation of a 3D dynamic microorgan device (DMD). The prescribed tissue model in this paper is precisely embedded within a DMD by 3D bioprinting hydrogel encapsulated liver cells into a patterned array of microchannels. A perfusing drug substrate is biotransformed by liver cells encapsulated within porous hydrogel walls. Therefore, the free and porous flow regime equations are first solved in tandem to derive the laminar velocity profile and wall shear stresses in the entire shear-mediated flow regime. These equations are then coupled with a convection-diffusion equation and Michaelis-Menten reaction terms, resulting in an effective convection-diffusion-cell kinetics model. A key consideration addressed herein is mechanotransduction where shear stresses on the encapsulated cells alter subcellular liver enzyme reaction rates. Cells are incorporated into the geometric model implicitly (macroscale) as enzyme reaction structures uniformly distributed throughout the DMD length. Transient simulations enable effluent drug metabolite profile determination wherein the proposed macroscale modeling approach is validated with an experimental drug flow study. Biotechnol. Bioeng. 2016;113: 612-622. (c) 2015 Wiley Periodicals, Inc.