Do you have access to electron paramagnetic resonance (EPR) spectroscopy instrument facility? If so, you can use spin probes such as CMH to measure the superoxide radical generation from the stem cells.
Like Ajit said you maybe able to detect cellular ROS easier than media ROS. We also looked as ROS in this paper attached (http://www.nature.com/cddis/journal/v7/n3/full/cddis2015409a.html OR https://www.researchgate.net/publication/296698867_Dengue-induced_autophagy_virus_replication_and_protection_from_cell_death_require_ER_stress_PERK_pathway_activation).
I'm not sure what is the half life of ROS in media but maybe you can calibrate your method. Even if you freeze the media, if the ROS scavenging in the media is fast it would be pointless. I don't know if you can concentrate your media through lyophilization, give it a shot and see if you can see ROS better? I would be surprised if this works! if it does please let me know! Best wishes!
-ED
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