Point/Counterpoint. The linear-quadratic model is inappropriate to model high dose per fraction effects in radiosurgery

Department of Radiation Oncology, Duke University Medical Center, Durham, North Carolina 27710, USA.
Medical Physics (Impact Factor: 2.64). 08/2009; 36(8):3381-4. DOI: 10.1118/1.3157095
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Available from: Colin G Orton, Sep 29, 2015
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    • "Cell response to the treatment was calculated using two different cell survival models, the linear-quadratic (LQ) model [22] and the universal survival curve (USC) model [23]. There is an on-going debate on whether the well-established LQ model overestimates the cell-kill for the high doses per fraction typically employed in SBRT [24]. The universal survival curve model, which is an empirical joining of the LQ model at low doses and the single-hit multi-target (SHMT) model at higher doses causing an exponential fall-off in survival as opposed to the continuously bending LQ-curve, has been proposed as an alternative. "
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    ABSTRACT: Background Stereotactic body radiotherapy (SBRT) for non-small-cell lung cancer (NSCLC) has led to promising local control and overall survival for fractionation schemes with increasingly high fractional doses. A point has however been reached where the number of fractions used might be too low to allow efficient local inter-fraction reoxygenation of the hypoxic cells residing in the tumour. It was therefore the purpose of this study to investigate the impact of hypoxia and extreme hypofractionation on the tumour control probability (TCP) from SBRT. Methods A three-dimensional model of tumour oxygenation able to simulate oxygenation changes on the microscale was used. The TCP was determined for clinically relevant SBRT fractionation schedules of 1, 3 and 5 fractions assuming either static tumour oxygenation or that the oxygenation changes locally between fractions due to fast reoxygenation of acute hypoxia without an overall reduction in chronic hypoxia. Results For the schedules applying three or five fractions the doses required to achieve satisfying levels of TCP were considerably lower when local oxygenation changes were assumed compared to the case of static oxygenation; a decrease in D50 of 17.7 Gy was observed for a five-fractions schedule applied to a 20% hypoxic tumour when fast reoxygenation was modelled. Assuming local oxygenation changes, the total doses required for a tumor control probability of 50% were of similar size for one, three and five fractions. Conclusions Although attractive from a practical point of view, extreme hypofractionation using just one single fraction may result in impaired local control of hypoxic tumours, as it eliminates the possibility for any kind of reoxygenation.
    Radiation Oncology 06/2014; 9:149. DOI:10.1186/1748-717X-9-149 · 2.55 Impact Factor
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    • "For the investigation of ion dose responses in the PIDE, we calculated RBE values from the LQ parameters. Note that these may deviate from directly measured RBE values (i.e. the ratio of doses needed for a fixed effect), in particular for higher doses where it is under discussion as to whether the LQ model is valid any more [15, 16]. To investigate the impact of LET on radio-sensitivity we show the RBE plotted against LET for different particle species in Fig. 4. We restricted the analysis to the RBEα and RBE10 corresponding to the initial slope (upper row) and 10% survival level (lower row), respectively. "
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    ABSTRACT: For tumor therapy with light ions and for experimental aspects in particle radiobiology the relative biological effectiveness (RBE) is an important quantity to describe the increased effectiveness of particle radiation. By establishing and analysing a database of ion and photon cell survival data, some remarkable properties of RBE-related quantities were observed. The database consists of 855 in vitro cell survival experiments after ion and photon irradiation. The experiments comprise curves obtained in different labs, using different ion species, different irradiation modalities, the whole range of accessible energies and linear energy transfers (LETs) and various cell types. Each survival curve has been parameterized using the linear-quadratic (LQ) model. The photon parameters, α and β, appear to be slightly anti-correlated, which might point toward an underlying biological mechanism. The RBE values derived from the survival curves support the known dependence of RBE on LET, on particle species and dose. A positive correlation of RBE with the ratio α/β of the photon LQ parameters is found at low doses, which unexpectedly changes to a negative correlation at high doses. Furthermore, we investigated the course of the β coefficient of the LQ model with increasing LET, finding typically a slight initial increase and a final falloff to zero. The observed fluctuations in RBE values of comparable experiments resemble overall RBE uncertainties, which is of relevance for treatment planning. The database can also be used for extensive testing of RBE models. We thus compare simulations with the local effect model to achieve this goal.
    Journal of Radiation Research 12/2012; 54(3). DOI:10.1093/jrr/rrs114 · 1.80 Impact Factor
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    • "Firstly the methods and models employed to generate much of the data in this paper (e.g., Figures 4, 5 and 6) are either directly, in the case of the Marsden TCP model [18, 21, 22, 31], or indirectly, in the case of Lyman-Kutcher-Burman NTCP model [18, 23, 24], based on the linear-quadratic expression linking (cell) surviving fraction and absorbed dose [41, 45–50, 88]. At doses per fraction above ≈10 Gy, however, the so-called generalized linear quadratic model proposed by Wang et al. [89] and by Carlone et al. [90] may be more correct, though this is by no means universally accepted [91]. Whatever the “truth” eventually turns out to be, if the LQ model does overpredict cell killing at very large fraction sizes then at such doses per fraction LQ-based radiobiological models will result in an overprediction of NTCP but an underprediction of TCP. "
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    ABSTRACT: "Biological optimization" (BIOP) means planning treatments using (radio)biological criteria and models, that is, tumour control probability and normal-tissue complication probability. Four different levels of BIOP are identified: Level I is "isotoxic" individualization of prescription dose D(presc) at fixed fraction number. D(presc) is varied to keep the NTCP of the organ at risk constant. Significant improvements in local control are expected for non-small-cell lung tumours. Level II involves the determination of an individualized isotoxic combination of D(presc) and fractionation scheme. This approach is appropriate for "parallel" OARs (lung, parotids). Examples are given using our BioSuite software. Hypofractionated SABR for early-stage NSCLC is effectively Level-II BIOP. Level-III BIOP uses radiobiological functions as part of the inverse planning of IMRT, for example, maximizing TCP whilst not exceeding a given NTCP. This results in non-uniform target doses. The NTCP model parameters (reflecting tissue "architecture") drive the optimizer to emphasize different regions of the DVH, for example, penalising high doses for quasi-serial OARs such as rectum. Level-IV BIOP adds functional imaging information, for example, hypoxia or clonogen location, to Level III; examples are given of our prostate "dose painting" protocol, BioProp. The limitations of and uncertainties inherent in the radiobiological models are emphasized.
    Computational and Mathematical Methods in Medicine 11/2012; 2012(2):329214. DOI:10.1155/2012/329214 · 0.77 Impact Factor
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