Application of the linear-quadratic model to combined modality radiotherapy

Abstract

Purpose: Methods of performing dosimetry for a combined modality radiotherapy (CMRT) consisting of a targeted radionuclide therapy (TRT) and separately delivered external beam therapy (EBT) have been established using the biologically effective dose (BED). However, a concurrent delivery of the two therapies may influence the radiobiologic effect of the treatment resulting from interaction between the therapies, and this situation has been modeled to assess the likely consequences of this regime.

Methods and materials: A general form of the linear-quadratic model with a dose protraction factor was applied to concurrent delivery of EBT and TRT. Contributions to total BED from intra- and intermodality effects were calculated, and parameter values varied to determine conditions under which the intermodality contributions were likely to be most significant. A Poisson model of tumor control probability (TCP) was used to assess the predicted effect of concurrent delivery on treatment outcome.

Results: In general, over a wide range of parameter values, the effect of intermodality interactions in CMRT is small, increasing total BED delivered to tumor by approximately 1%, and producing a negligible increase in TCP. Synergistic effects could be greater in normal tissues if high doses were received from both therapies, with intermodality terms increasing total BED delivered by approximately 6% in the general case, and by approximately 18% for the case of slow repair in the spinal cord. A significant synergistic effect was predicted between EBT and I-125 seed therapy of the prostate when values of alpha/beta = 1.2 Gy, alpha = 0.026 Gy, mu = 0.36 h(-1) and N(0) = 138 clonogens were used, with TCP increasing from approximately 0.5 to 0.6.

Conclusions: Under most clinical conditions, the relative temporal delivery of these two therapies is unlikely to significantly influence the overall radiobiologic effect to tumor at the cellular level. Synergistic effects may, however, be more significant in normal tissues and for tumors with low values of alpha/beta and alpha.