Technical Note: Impact of cell repopulation and radionuclide uptake phase on cell survival.

Abstract

To study theoretically the impact on cell survival of the radionuclide uptake rate inside tumor cells for a single administration of a radiopharmaceutical. The instantaneous-uptake model of O'Donoghue ["The impact of tumor cell proliferation in radioimmunotherapy," Cancer 73, 974-980 (1994)] for a proliferating cell population irradiated by an exponentially decreasing dose-rate is here extended to allow for the monoexponential uptake of the radiopharmaceutical by the targeted cells. The time derivative of the survival curve is studied in detail deducing an expression for the minimum of the surviving fraction and the biologically effective dose (BED). Surviving fractions are calculated over a parameter range that is clinically relevant and broad enough to establish general trends. Specifically, results are presented for the therapy radionuclides Y-90, I-131, and P-32, assuming uptake half-times 1-24 h, extrapolated initial dose-rates 0.5-1 Gy h(-1), and a biological clearance half-life of seven days. Representative radiobiological parameters for radiosensitive and rapidly proliferating tumor cells are used, with cell doubling time equal to 2 days and α-coefficient equal to 0.3 and 0.5 Gy(-1). It is shown that neglecting the uptake phase of the radiopharmaceutical (i.e., assuming instantaneous-uptake) results in a sizeable over-estimation of cell-kill (i.e., under-estimation of cell survival) even for uptake half-times of only a few hours. The differences between the exponential-uptake model and the instantaneous-uptake model become larger for high peak dose-rates, slow uptakes, and (slightly) for long-lived radionuclides. Moreover, the sensitivity of the survival curve on the uptake model was found to be higher for the tumor cells with the larger α-coefficient. The exponential-uptake rate of the radiopharmaceutical inside targeted cells appears to have a considerable effect on the survival of a proliferating cell population and might need to be considered in radiobiological models of tumor cell-kill in radionuclide therapy.