Mathematic Modeling of Tumor Growth During [¹⁷⁷Lu]Lu-PSMA Therapy: Insights into Treatment Optimization

The treatment regimen for [¹⁷⁷Lu]Lu-prostate-specific membrane antigen (PSMA) 617 therapy follows that of chemotherapy: 6 administrations of a fixed activity, each separated by 6 wk. Mathematic modeling can be used to test the hypothesis that the current treatment regimen for a radiopharmaceutical modality is suboptimal. Methods: A mathematic model was developed to describe tumor growth during [¹⁷⁷Lu]Lu-PSMA therapy. The model examined alternative treatment schedules to maximize tumor mass reduction while still maintaining an acceptable biologically effective dose to kidneys. Median patients' pharmacokinetics from literature reports were used to obtain the dose rate over time. The model incorporates the Gompertz tumor growth and linear quadratic models to describe the effect of radiation-induced cell kill on tumor growth. For a fixed total activity of 44.4 GBq of [¹⁷⁷Lu]Lu-PSMA-617 and a 6-wk interval between cycles, the efficacy of the standard fractionation (6-cycle) treatment schedule was compared with different treatment regimens for a distribution of published tumor masses. A treatment schedule whereby 7.4 GBq are administered in the first cycle, and the remaining activity (37 GBq) in the second cycle (1-2-cycle treatment), was examined. Results: When tumor mass nadir was used as the optimization metric, a lower tumor burden (e.g., <4 g) was insensitive to the number of cycles; the 6-cycle treatment was equivalent to the 1-2-cycle treatment. For larger masses, fewer cycles yielded better results. For a 7-g tumor, the 5-cycle, 4-cycle, 3-cycle and 1-2-cycle schedules were 24%, 50%, 76%, and 84% more efficacious, respectively, than the 6-cycle schedule. The absorbed doses to kidneys, parotid glands, lacrimal glands, and red marrow were 23, 16, 70, and 1 Gy, respectively. In all fractionated schedules, the biologically effective dose to kidneys was within tolerance (<40 Gy). Conclusion: On the basis of model-derived simulations, treatment delivered in a 1-2-cycle schedule is recommended to achieve better outcomes for patients undergoing [¹⁷⁷Lu]Lu-PSMA therapy.