Extending the linear–quadratic model for large fraction doses pertinent to stereotactic radiotherapy

Abstract

Ongoing clinical trials designed to explore the use of extracranial stereotactic radiosurgery (ESR) for different tumour sites use large doses per fraction (15, 20, 30 Gy or even larger). The question of whether the linear-quadratic (LQ) model is appropriate to describe radiation response for such large fraction doses has been raised and has not been answered definitively. It has been proposed that mechanism-based models, such as the lethal-potentially lethal (LPL) model, could be more appropriate for such large fraction/acute doses. However, such models are not well characterized with clinical data and they are generally not easy to use. The purpose of this work is to modify the LQ model to more accurately describe radiation response for high fraction/acute doses. A new parameter is introduced in the modified LQ (MLQ) model. The new parameter introduced is characterized based both on in vitro cell survival data of several human tumour cell lines and in vivo animal iso-effect curves. The MLQ model produces a better fit to the iso-effect data than the LQ model. For a high single dose irradiation, the prediction of the MLQ is consistent with that from the LPL model. Unlike the LPL model, the MLQ model retains the simplicity of the LQ model and uses the well-characterized alpha and beta parameters. This work indicates that the standard LQ model can lead to erroneous results when used to calculate iso-effects with large fraction doses, such as those used for ESR. We present a solution to this problem.

Redefining Relative Biological Effectiveness in the Context of the EQDX Formalism: Implications for Alpha-Particle Emitter Therapy

“…While the LQ model is generally recognized as valid and forms the basis for much of the normal organ dose-toxicity thresholds that have been established, it is also generally recognized that high dose rates or fractions such as those present in high dose rate brachytherapy, hypofractionated therapy or stereotactic radiosurgery have cellular responses that can depart from the linear-quadratic model. Several supplementary or alternative models have been proposed to account for these high dose rates (37)(38)(39). To date none have commanded unequivocal consensus.…”

Therapeutic analysis of Intrabeam‐based intraoperative radiation therapy in the treatment of unicentric breast cancer lesions utilizing a spherical target volume model

“…Recently, the accuracy of the LQ model for survival rates at doses greater than 12 Gy has come into question,13, 14 due to clinical observations have found that the classical LQ model overestimated cell killing at high doses. For this reason, a modified linear quadratic model (MLQ), introduced by Guerrero and Li15 for describing large dose radioresponses, is used in this study to estimate survival fractions of cell lines after the IB‐IORT. The MLQ model can be expressed as$SFfalse(xfalse)=exp(-\mathit{\alpha }\bullet Dfalse(xfalse)-\mathit{\beta }\bullet Gfalse(\mathrm{italic\lambda }\bullet T+\mathrm{italic\delta }\bullet D(x)false)\bullet D{(x)}^2)$Where the dose protraction factor δD(x) was included.…”

“…All the MLQ parameters for the five modeled cells are shown in Table 1. A value of 0.15 for δ and 0.693 for λ was chosen for all normal tissues and cancer cells 15, 17…”

Hypofractionation for Prostate Cancer

“…Other analyses, however, suggest thatapplication of the model to larger fraction sizes could under predict the total dose required to produce a given effect. 16 , resulting in a less toxic but also less effective treatment. Other uncertainties cited above such as reoxygenation and redistribution are also particularly relevant as the total number of fractions in a treatment course diminishes.…”