  Recent advancements in the ability to construct three-dimensional (3D)
tissues and organoids from stem cells and biomaterials have not only opened
abundant new research avenues in disease modeling and regenerative medicine but
also have ignited investigation into important aspects of molecular diffusion
in 3D cellular architectures. This paper describes fundamental mechanics of
diffusion with equations for modeling these dynamic processes under a variety
of scenarios in 3D cellular tissue constructs. The effects of these diffusion
processes and resultant concentration gradients are described in the context of
the major molecular signaling pathways in stem cells that both mediate and are
influenced by gas and nutrient concentrations, including how diffusion
phenomena can affect stem cell state, cell differentiation, and metabolic
states of the cell. The application of these diffusion models and pathways is
of vital importance for future studies of developmental processes, disease
modeling, and tissue regeneration.
