Microfluidic cell culture systems offer a convenient way to measure cell biophysical parameters in conditions close to the physiological environment. We demonstrate the application of a mathematical model describing the spatial distribution of nutrient and growth factor concentrations in inferring cellular oxygen uptake rates from experimental measurements. We use experimental measurements of oxygen concentrations in a poly(dimethylsiloxane) (PDMS) microreactor culturing human hepatocellular liver carcinoma cells (HepG2) to infer quantitative information on cellular oxygen uptake rates. We use a novel microchannel design to avoid the parameter correlation problem associated with simultaneous cellular uptake and diffusion of oxygen through the PDMS surface. We find that the cellular uptake of oxygen is dependent on the cell density and can be modeled using a logistic term in the Michaelis-Menten equation. Our results are significant not only for the development of novel assays to quantitatively infer cell response to stimuli, but also for the development, design, and optimization of novel in vitro systems for drug discovery and tissue engineering.