Cross-fire doses from β-emitting radionuclides in targeted radiotherapy. A theoretical study based on experimentally measured tumor characteristics

A mathematical model based upon histological findings of cell cluster distributions in primary breast cancers and lymph node metastases was developed. The model is unique because it accounts for tumor cell cluster formations within both primary tumors and metastases. The importance of inter-cell cluster cross-fire radiation dose for β-emitting radionuclides of different energies was studied. The cell clusters were simulated as spheres with 15, 25 and 50 µm radii having a homogeneous radioactivity distribution. The self-dose as well as the dose distribution around the spheres was calculated for seven radionuclides, 90Y, 188Re, 32P, 186Re, 159Gd, 131I and 177Lu using the GEANT4 Monte Carlo code. Generally, the self-dose was decreasing with increasing energy of the emitted beta particles. An exception was 188Re which, compared to 32P, had higher beta energy as well as higher self-dose. This was due to the higher emission of conversion and Auger electrons in the 188Re-decay. When the cell clusters had a mean distance that was shorter than the maximum range of β-particles, then the inter-cluster cross-fire radiation contributed significantly to the absorbed dose. Thus, high-energy β-particles may, in spite of a low self-dose to single clusters, still be favorable to use due to the contribution of inter-cluster cross-fire radiation.