Creation of a New Tumor Retention Constant: A New Physical Parameter Derived from the Classical Radioactive Decay Equation for the Mathematical Modeling of 177Lu-DOTATATE Therapyin Neuroendocrine Tumors

Abstract

The quantitative characterization of radiopharmaceutical retention within tumors remains one of the major challenges in Peptide Receptor Radionuclide Therapy (PRRT), as current mathematical models primarily describe physical radioactive decay while biological tumor retention is represented only indirectly through dosimetric quantities and time–activity curves. In this study, we propose a novel mathematical framework by introducing the Tumor Retention Constant (τT ), an analytical parameter incorporated into the classical radioactive decay equation to explicitly describe the biological permanence of 177Lu-DOTATATE within neuroendocrine tumors. A complete mathematical derivation was developed, resulting in an explicit closed-form equation in which the proposed constant is analytically isolated and can be directly estimated from radioactive activity measurements. The proposed formulation was subsequently evaluated through six independent numerical simulations implemented in Python, investigating temporal activity evolution, three-dimensional spatial distribution, functional heat maps, analytical validation, sensitivity analysis, and the global response surface of the model. The numerical results demonstrated excellent mathematical consistency, analytical stability, and coherent behavior across all investigated retention scenarios, confirming the feasibility of the proposed formulation and highlighting the influence of biological retention on radiopharmaceutical kinetics. Unlike conventional dosimetric approaches, the proposed framework provides a new quantitative descriptor capable of separating biological tumor retention from intrinsic radioactive decay while preserving the physical properties of the radionuclide. The proposed Tumor Retention Constant establishes a new theoretical perspective for mathematical modeling in Nuclear Medicine and may provide the foundation for future developments in individualized dosimetry, quantitative molecular imaging, computational oncology, and precision radionuclide therapy.