Energy deposition and receptor saturation set a tumour size threshold for radiopharmaceutical therapy: insights from a pharmacokinetic-tumour dynamics model

Abstract

Radiopharmaceutical therapies (RPTs) offer targeted radiation delivery to tumour cells, yet treatment outcomes vary substantially across patients while dosing protocols remain largely uniform. Translating mechanistic insight into improved protocols requires models that couple radioligand (RL) pharmacokinetics, spatial tumour biology, and radiation response -- a combination that existing models have not yet fully achieved. We coupled a cellular automaton for spatially resolved tumour dynamics to a pharma-cokinetic compartment model that tracks RL from injection through receptor binding and internalization. We estimate the energy deposited by radiation emitted from RL within the tumour and use a linear-quadratic radiobiological survival probability to determine the impact of the treatment. Simulating heterogeneous tumours across a range of conditions, we find that treatment outcome is governed primarily by tumour size and receptor expression levels and is relatively insensitive to the injected amount per cycle but highly dependent on inter-injection time intervals. The models uniform RL delivery separates radiobiological resistance from delivery effects -- two mechanisms that are spatially correlated in real tumours -- and the simulations suggest that compromised RL delivery may play a larger role in hypoxic treatment failure than radioresistance alone. These findings provide a mechanistic basis for patient stratification by receptor expression, yield a new size-based rationale for multi-injection protocols, and demonstrate that spatially resolved modelling can reveal treatment principles inaccessible to non-spatial approaches.