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

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 developed a hybrid discrete-continuous model coupling a cellular automaton for spatially resolved tumour dynamics to a pharmacokinetic compartment model tracking RL from injection to tumour-cell receptor binding and internalization, linked to an energy deposition and linear-quadratic radiobiological model. Simulating treatment of 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. By decoupling radiobiological resistance from RL delivery effects --- which are spatially correlated in real tumours but separated in our model --- we show that hypoxic radioresistance alone is insufficient to prevent cure, identifying compromised RL delivery, rather than intrinsic radioresistance, as the dominant mechanism of hypoxic treatment failure. 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.