*3.8. Radiation-Absorbed Dose Calculation*

For the calculation of the total number of nuclear transformations (N)(Bq. s) that occurred in the cytoplasm of the PC-3, HEP-G2, and fibroblast cells at different times, the mathematical integration of the activity (225Ac) in the cytoplasm (*A<sup>h</sup>* ), as a function of time (*N* = R *<sup>t</sup>*=<sup>2</sup> *t*=1 *Ah*(*t*)*dt*), was performed. The absorbed dose was calculated by multiplying N by the value of the dose factor (DF)(Gy/Bq. s). The DF value (from the cytoplasm to the nucleus) was calculated by using the MIRDcellV2.1 software, considering cells with a diameter of 20 µm, a nucleus radius of 3 µm, and a density of 1 mg/mL. For the dose calculation, the progeny of <sup>225</sup>Ac with significant decay yield (225Ac, <sup>221</sup>Fr, <sup>217</sup>At, <sup>213</sup>Bi, <sup>213</sup>Po, <sup>209</sup>Tl, <sup>209</sup>Pb) was considered, as expressed in Equation (1):

$$\overline{D}\_{225Ac\gets rHDL\ (n\gets\mathbb{C}y)} = \sum\_{j=1} N\_{(\mathbb{C}y)} \sum\_{k} b\_{k} D F\_{k}^{\mathbb{R}}{}\_{(n\gets\mathbb{C}y)} + \sum\_{j=1} N\_{(\mathbb{C}y)} \sum\_{k} b\_{k} D F\_{k}^{\varepsilon\_{\!\!r\!}p\!\!h}{}\_{(n\gets\mathbb{C}y)} \tag{1}$$

*<sup>D</sup>*225*Ac*−*rHDL* (*n*←*Cy*) = radiation-absorbed dose (Gy) to the cell nucleus.

*b<sup>k</sup>* = branching fraction for daughter *k.*

*DF<sup>α</sup> <sup>k</sup>* (*n*←*Cy*) = absorbed dose to the cell nucleus from *<sup>α</sup>* emission per nuclear transformation (Gy/Bq·s) from decay of daughter radionuclide "k" originated in the cytoplasm.

*DFe*, *ph k* = absorbed dose to the cell nucleus from electron (e) and photon (ph) emission per nuclear transformation (Gy/Bq·s) from decay of daughter radionuclide "k" originated in the cytoplasm.

*N*(*Cy*) = total number of nuclear transformations from each daughter radionuclide "k" in the cytoplasm.
