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1.  The BJR and progress in radiobiological modelling 
The British Journal of Radiology  2010;83(991):544-545.
doi:10.1259/bjr/52885245
PMCID: PMC3473673  PMID: 20603406
2.  Theoretical implications of incorporating relative biological effectiveness into radiobiological equivalence relationships 
The British Journal of Radiology  2013;86(1022):20120417.
Objective:
Earlier radiobiological equivalence relationships as derived for low-linear energy transfer (LET) radiations are revisited in the light of newer radiobiological models that incorporate an allowance for relative biological effectiveness (RBE).
Methods:
Linear-quadratic (LQ) radiobiological equations for calculating biologically effective dose at both low- and high-LET radiations are used to derive new conditions of equivalence between a variety of radiation delivery techniques. The theoretical implications are discussed.
Results:
The original (pre-LQ) concept of equivalence between fractionated and continuous radiotherapy schedules, in which the same physical dose is delivered in each schedule, inherently assumed that low-LET radiation would be used in both schedules. LQ-based equivalence relationships that allow for RBE and are derived assuming equal total physical dose between schedules are shown to be valid only in limited circumstances. Removing the constraint of equality of total physical dose allows the identification of more general (and more practical) relationships.
Conclusion:
If the respective schedules under consideration for equivalence both involve radiations of identical LET, then the original equivalence relationships remain valid. However, if the compared schedules involve radiations of differing LET, then new (and more restrictive) equivalence relationships are found to apply.
Advances in knowledge:
Theoretically derived equivalence relationships based on the LQ model provide a framework for the design and intercomparison of a wide range of clinical techniques including those involving high- and/or low-LET radiations. They also provide a means of testing for the validity of variously assumed tissue repair kinetics.
doi:10.1259/bjr.20120417
PMCID: PMC3608045  PMID: 23385996
3.  Fast neutron relative biological effects and implications for charged particle therapy 
The British Journal of Radiology  2011;84(Spec Iss 1):S011-S018.
In two fast neutron data sets, comprising in vitro and in vivo experiments, an inverse relationship is found between the low-linear energy transfer (LET) α/β ratio and the maximum value of relative biological effect (RBEmax), while the minimum relative biological effect (RBEmin) is linearly related to the square root of the low-LET α/β ratio. RBEmax is the RBE at near zero dose and can be represented by the ratio of the α parameters at high- and low-LET radiation exposures. RBEmin is the RBE at very high dose and can be represented by the ratio of the square roots of the β parameters at high- and low-LET radiation exposures. In principle, it may be possible to use the low-LET α/β ratio to predict RBEmax and RBEmin, providing that other LET-related parameters, which reflect intercept and slopes of these relationships, are used. These two limits of RBE determine the intermediate values of RBE at any dose per fraction; therefore, it is possible to find the RBE at any dose per fraction. Although these results are obtained from fast neutron experiments, there are implications for charged particle therapy using protons (when RBE is scaled downwards) and for heavier ion beams (where the magnitude of RBE is similar to that for fast neutrons). In the case of fast neutrons, late reacting normal tissue systems and very slow growing tumours, which have the smallest values of the low-LET α/β ratio, are predicted to have the highest RBE values at low fractional doses, but the lowest values of RBE at higher doses when they are compared with early reacting tissues and fast growing tumour systems that have the largest low-LET α/β ratios.
doi:10.1259/bjr/67509851
PMCID: PMC3473886  PMID: 22374547
4.  The potential impact of relative biological effectiveness uncertainty on charged particle treatment prescriptions 
The British Journal of Radiology  2011;84(Spec Iss 1):S061-S069.
There continues to be uncertainty regarding the relative biological effectiveness (RBE) values that should be used in charged particle radiotherapy (CPT) prescriptions using protons and heavier ions. This uncertainty could potentially offset the physical dose advantage gained by exploiting the Bragg peak effect and it needs to be clearly understood by clinicians and physicists. This paper introduces a combined radiobiological and physical sparing factor (S). This factor includes the ratio of the most relevant physical doses in tumour and normal tissues in combination with their respective RBE values and can be extended to contain the uncertainties in RBE. S factors can be used to study, in a simplified way for tentative modelling, those clinical situations in which high-linear energy transfer (LET) irradiations are likely to prove preferable over their low-LET counterparts for a matched tumour iso-effect. In cases where CPT achieves an excellent degree of normal tissue sparing, the radiobiological factors become less important and any uncertainties in the tumour and healthy tissue RBE values are correspondingly less problematic. When less normal tissue sparing can be achieved, however, the RBE uncertainties assume greater relevance and will affect the reliability of the dose-prescription methodology. More research is required to provide accurate RBE estimation, focusing attention on the associated statistical uncertainties and potential differences in RBE between different tissue types.
doi:10.1259/bjr/36792876
PMCID: PMC3473889  PMID: 22374549
5.  Repair kinetic considerations in particle beam radiotherapy 
The British Journal of Radiology  2011;84(1002):546-555.
Objectives
A second-order repair kinetics model is developed to predict damage repair rates following low or high linear energy transfer (LET) irradiations and to assess the amount of unrepairable damage produced by such radiations. The model is a further development of an earlier version designed to test if low-LET radiation repair processes could be quantified in terms of second-order kinetics. The newer version allows calculation of both the repair rate of the proportion of DNA damages that repair according to second-order kinetics and the proportion of DNA damages that do not repair.
Methods
The original and present models are intercompared in terms of their goodness-of-fit to a number of data sets obtained from different ion beams. The analysis demonstrates that the present model provides a better fit to the data in all cases studied.
Results
The proportions of unrepairable damage created by radiations of different LET predicted by the new model correspond well with previous studies on the increased effectiveness of high-LET radiations in inducing reproductive cell death. The results show that the original model may underestimate the proportion of unrepaired damage at any given time after its creation as well as failing to predict very slow or unrepairable damage components, which may result from high-LET irradiation.
Conclusion
It is suggested that the second-order model presented here offers a more realistic view of the patterns of repair in cell lines or tissues exposed to high-LET radiation.
doi:10.1259/bjr/19934996
PMCID: PMC3473638  PMID: 21266398
6.  Pulsed brachytherapy: a modelled consideration of repair parameter uncertainties and their influence on treatment duration extension and daytime-only “block-schemes” 
The British Journal of Radiology  2011;84(1001):449-456.
Objectives
The radiobiological modelling of all types of protracted brachytherapy is susceptible to uncertainties in the values of tissue repair parameters. Although this effect has been explored for many aspects of pulsed brachytherapy (PB), it is usually considered within the constraint of a fixed brachytherapy treatment time. Here the impact of repair parameter uncertainty is assessed for PB treatments of variable duration. The potential use of “block-schemes” (blocks of PB pulses separated by night-time gaps) is also investigated.
Methods
PB schedule constraints are based on the cervical cancer protocols of the Royal Marsden Hospital (RMH), but the methodology is applicable to any combination of starting schedule and treatment constraint. Calculations are performed using the biologically effective dose (BED) as a tissue-specific comparison metric. The ratio of normal tissue BED to tumour BED is considered for PB regimens with varying total pulse numbers and/or “block-schemes”.
Results
For matched brachytherapy duration, PB has a good “window of opportunity” relative to the existing RMH continuous low dose rate (CLDR) practice for all modelled repair half-times. The most clear-cut route to radiobiological optimisation of PB is via modest temporal extension of the PB regimen relative to the CLDR reference. This option may be practicable for those centres with scope to extend their relatively short CLDR treatment durations.
Conclusion
Although daytime-only “block-scheme” PB for cervical cancer has not yet been employed clinically, the possibilities appear to be theoretically promising, providing the overall (external beam plus brachytherapy) treatment duration is not extended relative to current practice, such that additional tumour repopulation becomes a concern.
doi:10.1259/bjr/58276427
PMCID: PMC3473649  PMID: 21266397

Results 1-6 (6)