br The human prostate cancer LNCaP cells
The human prostate cancer LNCaP cells (PSMA-positive; ATCC®, USA) were cultured in RPMI-1640 supplemented with o-Phenanthroline (pe-nicillin and streptomycin, 100 μg/mL) and fetal bovine serum to a final concentration of 15%, using a humidified atmosphere, CO2 at 5% and incubated at 37 °C.
2.5. Cell uptake and internalization assay
LNCaP cells were diluted to 2 × 106 cells/tube (PBS, 0.5 mL) and incubated with 177Lu-iPSMA (37 kBq; 0.5 nmol of peptide, n = 3) for 3, 6, 24, 48, 72 or 96 h at 37 °C. After centrifugation for 3 min at 500 g, the tubes were washed with PBS. Then, the cell pellet activity was mea-sured in a NaI(Tl) detector (cell uptake). After treated with a solution of 50 mM glycine HCl/100 mM NaCl, the tubes were again centrifuged and the cell pellet activity was measured in a NaI(Tl) detector (cell internalization). An aliquot of the initial activity was considered to represent 100%, and the percentage of internalization and cell uptake was calculated considering this value. r> 2.6. In vitro biokinetic model
The activity percentages in the membrane (cell uptake) and cyto-plasm (cell internalization) of cancer cells were used to obtain 177Lu time–activity curves (A(t)) for each subcellular compartment. Data corrected by decay and fitted to three exponential terms was estab-lished as the biological biokinetic model (BBM) for the target-specific iPSMA molecule in LNCaP prostate cancer cells. The experimental 177Lu-iPSMA radio-biokinetic model was obtained by adding the decay constant (λR) to the exponential terms of the BBM as follows (eq. (1)):
daughter radionuclides was added to the BBM, as in the case of 177Lu. In this way, a model for each radionuclide was established. Activity, as the number of disintegrations per unit time and integrated over time (from t = 0 to t = ∞), yielded the total number of nuclear transformations or disintegrations (N) in the membrane or cytoplasm expressed per unit of initial activity in the cancer cells (Eq. (2)).
The radionuclide chain analysis of 225Ac and 223Ra was simplified by calculating the activity as secular equilibrium between the final decay products and their parents, while the initial condition of activity was considered as 1 Bq.
the pharmacokinetic data reported by Yoshida et al. (2016) in six pa-tients receiving radium-223 dichloride. The 223RaCl2 bone uptake data at diﬀerent times was divided between the trabecular and the cortical bone at a ratio of 0.62:0.38, in accordance with the recommendations of the ICRP (1995).
2.7. Monte Carlo simulations with the MCNPX code
The deposited energy and the absorbed dose per disintegration or dose factor (DF = Gy/Bq.s) of Ac-225, Ra-223 (considering each one of their respective daughter radionuclides) and Lu-177 to the cell nucleus of cancer cells embedded in a simplified model of bone was calculated with the MCNPX transport simulation code. For the decay chain of Ac-225 and Ra-223, DF values for alpha emissions were first calculated and
Fig. 1. Illustration of the computer-simplified bone model composed of 7 spheres (LNCaP cancer cells) of 18 μm in diameter, immersed in a cylinder of r = 90 μm and h = 90 μm, representing the trabecular bone environment em-bedded in a sphere of 250 μm, with a cortical bone composition.
Fig. 2. Experimental biokinetic model of 177Lu-iPSMA in human prostate LNCaP cells.
bone was embedded in a larger sphere of r = 250 μm with the cortical bone composition (density of 1.85 g/cm3), where the osteocytes were placed (Fig. 1). 177Lu and 225Ac were located at the cancer cell surface (CS, membrane) and in the cytoplasm (Cy), while 223Ra was distributed in the trabecular (62%) and cortical bone (38%). In all cases, at least 1 × 106 initial particles for the monoenergetic and radionuclide sources in the cancer cells nuclei were simulated to obtain uncertainties lower than 1%. Those electron and photon emissions with energies lower than 1 keV and emission probability under 1% were not simulated, but their energy was considered to be deposited locally. The deposited energy (MeV) per nuclear transformation and per gram of cell nucleus was converted to grays (J/kg) per disintegration (Gy/Bq.s).
2.8. Radiation absorbed dose calculation
The nuclear-absorbed doses from 225Ac and 223Ra were calculated by multiplying the DF (Gy/Bqs) values by the total number of disin-tegrations (N) per radioactivity unit (Bq), based on the experimental biokinetic results described above, as follows:
Dnf = Radiation absorbed dose (Gy) to the cell nuclei "f" (f = 7 cells) RBEα = Relative biological eﬀectiveness for the α-particle emitters. In this research, the RBE factor is only indicated to be considered in the discussion section but is not considered in the absorbed dose values reported in the results section.