Application of the linear-quadratic model with incomplete repair to radionuclide directed therapy.

The linear-quadratic (LQ) model for fractionated external beam therapy has been modified by previous authors to include the effects due to an exponentially decaying dose rate. However, the LQ model has now been extended to include a general time varying dose rate profile, and the equations can be readily evaluated if an exponential radiation damage repair process is assumed. These equations are applicable to radionuclide directed therapy, including brachytherapy. Kinetic uptake data obtained during radionuclide directed therapy may therefore be used to determine the radiobiological dosimetry of the target and non-target tissues. Also, preliminary tracer studies may be used to pre-plan the radionuclide directed therapy, provided that tracer and therapeutic amounts of the radionuclide carrier are identically processed by the tissues. It is also shown that continuous radionuclide therapy will induce less damage in late-responding tissues than 2 Gy/fraction external beam therapy if the ratio of the maximum dose rate and the sublethal damage repair half-life in the tissue is less than 1.0 Gy. Similar inequalities may be derived for beta-particle radionuclide directed therapy. For example, it can be shown that radionuclide directed therapy will induce less damage to slowly repopulating tissue than 2 Gy/fraction external beam therapy for the same total dose if the maximum percentage initial uptake in tissue is less than 0.046%/g or 0.23%/g for an injected activity of 50 mCi of 90Y or 131I, respectively.