The biological effectiveness of targeted radionuclide therapy based on a whole-body pharmacokinetic model

Biologically effective dose (BED) may be more of a relevant quantity than absorbed dose for establishing tumour response relationships. By taking into account the dose rate and tissue-specific parameters such as repair and radiosensitivity, it is possible to compare the relative biological effects of different targeted radionuclide therapy (TRT) agents. The aim of this work was to develop an analytical tumour BED calculation for TRT that could predict a relative biological effect based on normal body and tumour pharmacokinetics. This work represents a step in the direction of establishing relative pharmacokinetic criteria of when the BED formalism is more applicable than absorbed dose for TRT. A previously established pharmacokinetic (PK) model for TRT was used and adapted into the BED formalism. An analytical equation for the protraction factor, which incorporates dose rate and repair rate, was derived. Dose rates within the normal body and tumour were related to the slopes of their time-activity curves which were determined by the ratios of their respective PK parameters. The relationships between the tumour influx-to-efflux ratio (k ₃₄:k₄₃), central compartment efflux-to-influx ratio (k₁₂:k₂₁), central elimination (k_el), and tumour repair rate (μ), and tumour BED were investigated. As the k ₃₄:k₄₃ ratio increases and the k₁₂:k ₂₁ ratio decreases, the difference between tumour BED and D increases. In contrast, as the k₃₄:k₄₃ ratios decrease and the k₁₂:k₂₁ ratios increase, the tumour BED approaches D. At large k₃₄:k₄₃ ratios, the difference between tumour BED and D increases to a maximum as k_el increases. At small k ₃₄:k₄₃ ratios, the tumour BED approaches D at very small k_el. At small μ and small k₃₄:k₄₃ ratios, the tumour BED approaches D. For large k₃₄:k₄₃ ratios, large μ values cause tumour BED to approach D. This work represents a step in the direction of establishing relative PK criteria of when the BED formalism is more applicable than absorbed dose for TRT. It also provides a framework by which the biological effects of different TRT agents can be compared in order to predict efficacy.