Mathematical Modeling of Preclinical Alpha-Emitter Radiopharmaceutical Therapy

Preclinical studies, in vivo, and in vitro studies, in combination with mathematical modeling can help optimize and guide the design of clinical trials. The design and optimization of alpha-particle emitter radiopharmaceutical therapy (αRPT) is especially important as αRPT has the potential for high efficacy but also high toxicity. We have developed a mathematical model that may be used to identify trial design parameters that will have the greatest impact on outcome. The model combines Gompertzian tumor growth with antibody-mediated pharmacokinetics and radiation-induced cell killing. It was validated using preclinical experimental data of antibody-mediated ²¹³Bi and ²²⁵Ac delivery in a metastatic transgenic breast cancer model. In modeling simulations, tumor cell doubling time, administered antibody, antibody specific-activity, and antigen-site density most impacted median survival. The model was also used to investigate treatment fractionation. Depending upon the time-interval between injections, increasing the number of injections increased survival time. For example, two administrations of 200 nCi, ²²⁵Ac-labeled antibody, separated by 30 days, resulted in a simulated 31% increase in median survival over a single 400 nCi administration. If the time interval was 7 days or less, however, there was no improvement in survival; a one-day interval between injections led to a 10% reduction in median survival. Further model development and validation including the incorporation of normal tissue toxicity is necessary to properly balance efficacy with toxicity. The current model is, however, useful in helping understand preclinical results and in guiding preclinical and clinical trial design towards approaches that have the greatest likelihood of success. SIGNIFICANCE: Modeling is used to optimize αRPT.