A process for making nanoparticles of biocompatible materials is described, wherein an aqueous reaction mixture comprising cerous ion, malic acid, an oxidant, and water, is provided along with temperature conditions to directly form within the reaction mixture, a stable dispersion of nanoceria particles. Biocompatible nanoparticles comprised of ceria and malic acid are described. A reduction in cell death in a murine model of ischemic stroke utilizing intact brain slices is demonstrated by a prophylactic treatment of ceria nanoparticles prepared with malic acid.