The influence of repopulation kinetics on isoeffect doses for permanent implants

Abstract

Purpose: Determination of isoeffect doses for permanent implants with different half-life times.

Method: To calculate the isoeffective doses a model is used which describes the number of clonogenic tumor cells as a function of time. The effective irradiation time for permanent implants depends on the half-life T1/2 of the used isotope. During the irradiation tumor cells may repopulate, an effect which is well known in fractionated radiotherapy. The longer the radiation treatment lasts the more dose will be needed to kill these repopulating tumor cells. A differential equation has been constructed where cell kill is determined by an alpha-beta term and cell proliferation by a constant tumor cell doubling time Tpot. The solution of the differential equation gives the number of clonogenic tumor cells as a function of time.

Results: For our model an analytic solution has been found. The number of repopulating tumor cells shows a minimum if the dose rate is sufficiently high. Otherwise cell kill by radiation is overcompensated by growing tumor cells. The minimum value Nmin of tumor cells depends on the initial cell number N0, the total dose Dtot, the half-life T1/2 of the implant, the half-life Tr for repair of the sublethal damage, the alpha and beta values of the tumor cells, and the effective clonogen doubling time Tpot of the tumor. Assuming that the tumor is cured if no clonogenic cell survives, the tumor control probability (TCP) is determined by the Poisson statistics TCP = exp(-Nmin). Isoeffective doses are doses with constant TCP. Isoeffective doses Dtot have been calculated for different Tpot as a function of the half-life T1/2 of the isotope.

Conclusions: The model allows the calculation of isoeffective doses for permanent implants. Care must be taken to use the results in clinical practice unless all of the radiobiological parameters are known for a specific tumor.