Application of the linear-quadratic model to myelotoxicity associated with radioimmunotherapy

The purposes of this study were: (1) to use the linear-quadratic model to determine time-dependent biologically effective doses (BEDs) that were delivered to the bone marrow by multiple infusions of radiolabeled antibodies, and (2) to determine whether granulocyte and platelet counts correlate better with BED than administered radioactivity, which does not take stem cell repopulation, i.e., time, into consideration. Twenty patients with B-cell malignancies that had progressed despite intensive chemotherapy and who had a significant number of malignant cells in their bone marrow were treated with multiple 0.7-3.7 GBq/m2 (18-100 mCi/m2) intravenous infusions of Lym-1, a murine monoclonal antibody that binds to a tumour-associated antigen, labeled with iodine-131. Granulocyte and platelet counts were measured in order to assess bone marrow toxicity. BEDs were calculated according to the formula: BED=D(1+gD/(alpha/beta))-0.693(Tn-Tk)/alphaTp, where D represents the absorbed dose of radiation delivered to the red marrow by penetrating emissions of 131I throughout the whole body and nonpenetrating emissions of 131I in the blood and bone marrow, g is a factor that depends on the duration of irradiation relative to the repair half-life of human bone marrow, alpha is the coefficient of nonrepairable damage per Gy, beta is the coefficient of repairable damage per Gy2, Tn is the time required to reach the granulocyte or platelet count nadir after an 131I-Lym-1 infusion, Tk is the time at which bone marrow proliferation begins after the start of treatment and Tp is the doubling time of the bone marrow after the granulocyte or platelet count nadir has been reached. The cumulative 131I-Lym-1 radioactivity administered to each patient was calculated. Biologically effective doses from multiple 131I-Lym-1 infusions were summated in order to arrive at a total BED for each patient. There was a weak association between granulocyte and platelet counts and radioactivity (the correlation coefficients were -0.23 and -0.60, respectively). Likewise, there was a weak association between granulocyte and platelet counts and BED (the correlation coefficients were -0.27 and -0.40, respectively). The attempt to take bone marrow absorbed doses and overall treatment time into consideration with the linear-quadratic model did not produce a stronger association than was observed between peripheral blood counts and administered radioactivity. The association between granulocyte and platelet counts and BED may have been weakened by several factors, including variable bone marrow reserve at the start of 131I-Lym-1 therapy and the delivery of heterogeneous absorbed doses of radiation to the bone marrow.