Purpose: To use tumor growth kinetics and other biologic parameters in an extended version of the linear-quadratic (LQ) formulation to determine radiobiologically optimized half-lives of radionuclides which might be used in permanent brachytherapy implants.
Methods and materials: A version of the LQ model suitable for the analysis of permanent brachytherapy implants has been modified to investigate the radionuclide half-lives that will maximize the biologically effective dose (BED) delivered to tumors with repopulation rates (K values) in the range 0.01-1.1 Gyday(-1). The method assumes that part of the physical dose delivered to the tumor may be radiobiologically wasted because of the repopulation phenomenon, whereas adjacent normal tissues will exhibit little or no wastage. To perform the analysis, it is necessary to stipulate alpha/beta ratios and sublethal damage recovery rates together with the normal tissue tolerance BED. The analysis also takes into account a range of likely relative biological effectiveness (RBE) values.
Results: Rapidly growing tumors require the shortest radionuclide half-lives, but even slow-growing tumors such as prostate adenocarcinomas can be satisfactorily treated with radionuclides possessing half-lives substantially less than that associated with I(125). The likelihood that prostate tumors possess an alpha/beta value which is comparable with, or lower than, that associated with late-responding normal tissues would also mitigate against the use of long-lived radionuclides. Although a number of parameter assumptions are involved, the results suggest that, for a wide range of tumor types, shorter-lived radionuclides are more versatile for achieving reasonable clinical results. The theoretically derived optimum half-lives typically range from around 0-5 days for fast-repopulating tumors (K 1.1 Gyday(-1)) to approximately 14-50 days for slow-growing tumors (K approximately 0.1 Gyday(-1) or less). For prostate implantation, 103Pd is overall a better choice than 125I.
Conclusion: With so many variables and parameter uncertainties, it is not appropriate to attempt to define optimum radionuclide half-lives too closely. However, this study suggests that half-lives in the approximate range 4-17 days are likely to be significantly better for a wide range of tumor types for which the radiobiologic characteristics may not be precisely known in advance.