*3.4. Preparation of <sup>225</sup>Ac-rHDL*

To 1 mL of the previously prepared rHDL, 200 µL of <sup>225</sup>Ac-DOTA-benzene-p-SCN (12 MBq) were added, and the mixture was incubated at 37 ◦C for 1 h to obtain the <sup>225</sup>AcrHDL nanosystem.

The labeling efficiency of <sup>225</sup>Ac-rHDL was evaluated by ultracentrifugation (2500 g for 0.5 h; MWCO 30-kDa filter units, Amicon Ultra, Millipore, MilliporeSigma, Burlington, MA, USA). The fraction that is not retained in the membrane was considered as the radioactivity associated with <sup>225</sup>Ac-DOTA-benzene-p-SCN and <sup>225</sup>Ac3+ that was not bound to rHDL, while the fraction that remained in the membrane represents the <sup>225</sup>Ac-rHDL system. Both fractions were counted in a well-type scintillation NaI(Tl) detector to evaluate the labeling efficiency. The radioactive sample that remained in the filter membrane was resuspended in 10 mL of acetate buffer (pH 5.0)/0.1% ascorbic acid. Finally, a sample of the final solution (100 µL; activity measured in a well-type scintillation NaI(Tl) detector) was centrifuged again under the same conditions (2500× *g* for 0.5 h; MWCO 30-kDa filter units) to verify the radiochemical purity (RP) (RP = (activity remained in the filter membrane/total activity) × 100).
