Technical note: Errors introduced when using Dose Voxel Kernels for estimating absorbed dose from radiopharmaceutical therapies involving alpha emitters

Background: In radiopharmaceutical therapies (RPT) involving beta emitters, absorbed dose (D-abs) calculations often employ the use of dose voxel kernels (DVK). Such methods are faster and easier to implement than Monte Carlo (MC) simulations. Using DVK methods implies a non-stochastic distribution of particles. This is a valid assumption for betas where thousands to tens of thousands of particles traversing the cell nucleus are required to achieve cell kill. However, alpha particles have linear energy transfers (LET) that are similar to 500 times higher than LETs of betas. This results in a significant probability of killing a cell from even a single traversal through its nucleus. Consequently, the activity used for therapy involving alphas is very low, and the use of DVKs for estimating D-abs will generate results that may be erroneous. Purpose: This work aims at illustrating how use of DVKs affect the resulting D-abs in small tumors when irradiated with clinically relevant amounts of beta- and alpha-emitters. The results are compared with those from using a Monte Carlo method where the energy deposition from individual tracks is simulated. Methods: To illustrate the issues associated with DVK for alpha radiopharmaceutical therapies at the microscale, a tumor cluster model was used to compare beta (Lu-177) and alphas (At-211, Ac-225, and Th-227) irradiations. We used 103 beta particles and 20 alpha particles per cell, which is within the range of the required number of particle traversals through its nucleus to sterilize a cell. Results from using both methods were presented with D-abs histograms, dose volume histograms, and D-abs error maps. Results: For beta-emitter (Lu-177) irradiating the modeled tumor cluster, resulting D-abs was similar for both DVK and MC methods. For all alpha emitters, the use of DVK led to an overestimation of D-abs when compared to results generated using a MC approach. Conclusions: Our results demonstrate that the use of DVK methods for alpha emitters can lead to an overestimation in the calculated D-abs. The use of DVKs for therapies involving alpha emitters may therefore not be appropriate when only referring to the mean D-abs metric.