Validation of an analytical expression for the absorbed dose from a spherical beta source geometry and its application to micrometastatic radionuclide therapy.

The purpose of this study was to validate an analytical expression for the absorbed-dose calculation from the spherical source of beta-emitting radionuclides and to apply it to micrometastases treated with radiolabeled monoclonal antibodies. The self-absorbed fractions from I-131 and P-32 uniform spherical sources were calculated using the analytical expression introduced by P. K. Leichner (J. Nucl. Med., 35: 1721-1729, 1994). The calculated absorbed fractions were compared with previously reported values and were found to be in reasonable agreement, with a maximum difference of 15% for smaller masses and a long-range beta emitter. The expression was subsequently applied to estimate the absorbed dose within spheroid models with nonuniform penetration of radiolabeled antibody. The corresponding absorbed dose for I-131 was compared with reported micro-thermoluminescence dosimeter measurements and found to be in good agreement. This work has independently substantiated the methodology outlined by Leichner and may be reliably incorporated into new software developments for radionuclide dosimetry treatment planning.