Background: Human induced pluripotent stem cells (hiPSCs) can form any tissue found in the body, making them attractive for regenerative medicine applications. Seeding hiPSC aggregates into biomaterial scaffolds can control their differentiation into specific tissue types. Here we develop and analyze a mathematical model of hiPSC aggregate behavior when seeded on melt electrospun scaffolds with defined topography. Results: We used ordinary differential equations to model the different cellular populations (stem, progenitor, differentiated) present in our scaffolds based on experimental results and published literature. Our model successfully captures qualitative features of the cellular dynamics observed experimentally. We determined the optimal parameter sets to maximize specific cellular populations experimentally, showing that a physiologic oxygen level (similar to 5%) increases the number of neural progenitors and differentiated neurons compared to atmospheric oxygen levels (similar to 21%) and a scaffold porosity of similar to 63% maximizes aggregate size. Conclusions: Our mathematical model determined the key factors controlling hiPSC behavior on melt electrospun scaffolds, enabling optimization of experimental parameters.