Modelling of metastatic cure after radionuclide therapy: influence of tumor distribution, cross-irradiation, and variable activity concentration.

The objective was to study the influence of tumor number and size, cross-irradiation from normal tissue, and of variable activity concentration on metastatic cure after radionuclide therapy. A model to calculate the metastatic cure probability (MCP) was developed, in which it was assumed that the tumor response was an exponential function of the absorbed dose. All calculations were performed for monoenergetic electron emitters with different energies (10-1000 keV). The influence of tumor size and number of tumors were investigated with different log uniform distributions; the basic tumor distribution consisted of tumors with 1, 10, ..., 10(11) cells. The influence of cross-irradiation was assessed by calculating MCP for various tumor-to-normal tissue activity concentration ratios (TNC). The influence of variable activity concentration between tumors was calculated by assuming that the activity concentration in tumors was an inverse power law function of tumor mass. The required activity concentration (C0.9) and absorbed dose (D0.9) to obtain MCP=0.9 was calculated in the different models. The C0.9 and D0.9 needed to obtain MCP were very high; more than 25 MBq/g and 80 Gy, respectively. The lowest C0.9 and D0.9 for equal activity concentration in the different tumor sizes were obtained for electron energies less than 80 keV. For higher energies the low absorbed energy fraction in small tumors will increase the required C0.9 and D0.9 markedly. Cross-irradiation from normal cells surrounding the tumor will cause sterilization of the smallest tumors and decrease the required C0.9 and D0.9 for higher electron energies. Assuming that the activity concentration decreased with increased tumor mass caused a marked increase in C0.9 and D0.9 in favor of higher electron energies. With the MCP model we demonstrated significant influence of the number of tumors, their size, TNC and variable activity concentration on MCP. The results are valuable when evaluating optimal choices for radionuclides for internal-emitter therapy.