Radiotherapy treatment interruptions during the Covid-19 pandemic: The UK experience and implications for radiobiology training

Unintended treatment interruptions during a course of radiotherapy can lead to extended overall treatment times which can allow increased tumour cell repopulation to occur. Extra dose may therefore be required to offset any loss of tumour control. However, the manner in which the extra dose is delivered requires careful consideration in order to avoid the risk of increased normal tissue toxicity. Radiobiological modelling techniques can allow quantitative examination of such problems and may be used to derive revised pattens of radiation delivery which can help restore a degree of tumour control whilst limiting the likelihood of excess normal tissue morbidity. Unintended treatment interruptions can occur in any radiotherapy department but the rapid spread of the Covid-19 pandemic caused a major increase in the frequency of such interruptions due to staff and patient illness and the consequent self-isolation requirements. This article summarises the radiobiological considerations and caveats involved in assessing treatment interruptions and outlines the UK experience of dealing with the new challenges posed by Covid-19. The world-wide need for more education programmes in cancer radiobiology is highlighted.

Clinical and practical considerations in the design of appropriate compensation schedules following treatment interruptions

Compensatory dose calculations to mitigate the deleterious effect of unscheduled treatment interruptions remain important. They may be increasingly required during and after epidemics, as with the present Covid-19 virus. The information presented to those involved in the actual dose estimations is often limited, thereby increasing the likelihood of confusion, further time delays and possibly incorrect decisions. This article sets out what aspects need to be considered by the Clinical Oncologist (or Radiation Oncologist), and the reasons why, in order to provide greater clarity. The key issues are: (a) the biological nature of the tumour (and hence its repopulation potential), (b) patient age and pre-existing medical risk factors that influence radiation tolerance, the use of chemotherapy, surgery etc, (c) the acceptable dose limits of the relevant normal tissues at risk and (d) consideration of the possibility of further field size adjustments, a change in treatment plan or acceptance of a greater role for alternative forms of radiation treatment (e.g. brachytherapy, electron boosts, etc.) or reliance on radical surgery. Only then can a compensatory schedule be more safely estimated.

The evolution of practical radiobiological modelling

A summary of the key aspects of radiobiological modelling is provided, based on the theoretical and practical concepts of the linear quadratic model, which gradually replaced other numerical approaches. The closely related biological effective dose concept is useful in many clinical applications. Biological effective dose formulations in conventional photon-based radiotherapy continue to be developed, and can be extended to the now increasingly used proton and ion-beam therapy, to very low or high dose ranges, the dose rate effect, hypoxia and repopulation. Such established and new research developments will be of interest to clinicians, physicists and biologists to better understand the processes underlying radiotherapy and assist their collaborative efforts to make radiotherapy safer and more effective.

Theoretical implications of incorporating relative biological effectiveness into radiobiological equivalence relationships

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.

The potential impact of relative biological effectiveness uncertainty on charged particle treatment prescriptions

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.

Fast neutron relative biological effects and implications for charged particle therapy

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 (RBE(max)), while the minimum relative biological effect (RBE(min)) is linearly related to the square root of the low-LET α/β ratio. RBE(max) 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. RBE(min) 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 RBE(max) and RBE(min, )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.

Repair kinetic considerations in particle beam radiotherapy

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.

Pulsed brachytherapy: a modelled consideration of repair parameter uncertainties and their influence on treatment duration extension and daytime-only "block-schemes"

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.

Why more needs to be known about RBE effects in modern radiotherapy

Radiation therapy remains a very effective tool in the clinical management and cure of cancer and new techniques of radiation delivery continue to be developed. Of particular note is the growing world-wide interest in particle beam therapy (PBT) using protons or light ions. Such beams (particularly light ions) are associated with an increased relative biological effectiveness (RBE) which, when viewed alongside the more favourable physical distributions of radiation dose available with all forms of particle beams, makes them especially attractive for treating tumours which are associated with disappointing outcomes following conventional X-ray therapy. Although the large body of clinical experience already gained with conventional X-ray therapy will be of paramount importance in guiding the development of treatment programmes using particle beams, understanding and quantification of the RBE effects which are unique to the latter will also be essential. This is because the magnitude of RBE effect is not fixed for any one radiation/tissue combination but is subject to a number of other radiobiological influences. Such relationships may be quantified within the linear-quadratic radiobiological model, within which the associated concept of biologically effective dose (BED) provides a way of inter-comparing the overall biological impact of existing and projected treatments. This paper summarises the main features of RBE and BED, discusses the main quantitative implications for PBT and highlights why clear understanding of RBE effects will be essential to make best use of PBT. It also summarises other clinical applications where knowledge of and allowance for RBE effects is important and suggests that more needs to be done to allow safer practical applications.

Radiotherapy treatment delays and their influence on tumour control achieved by various fractionation schedules

There is often a considerable delay from initial tumour diagnosis to the start of radiotherapy treatment. This paper extends the calculations of a previous paper on the effects of delays before the initiation of radiotherapy treatment to include results from a variety of practical fractionation regimes for three different types of tumour: squamous cell carcinoma (head and neck), breast and prostate. The linear quadratic model of radiation effect, logarithmic tumour growth (coupled with delay times where relevant) and the Poisson model for tumour control probability (TCP) are used to calculate the change in TCP for delays between diagnosis and treatment. Within the limitations of radiobiological modelling, these data can be used to tentatively assess the interactions between delays, dose fractionation and TCP. The results show that delays in the start of radiotherapy treatment do have an adverse effect on tumour control for fast-growing tumours. For example, calculations predict a reduction in local tumour control of up to 1.5% per week's delay for head and neck cancers treated following surgery. In addition, there may be a variety of fractionation regimes that will yield very similar clinical results for each tumour type. It is shown theoretically that, for the tumour types considered here, it is possible to increase the dose per fraction and decrease the number of fractions while maintaining or increasing TCP relative to standard 2 Gy fractionation regimes, although there may be some advantage to using hyperfractionated regimes for head and neck cancers in order to reduce normal tissue effects.

Radiobiological compensation of treatment errors in radiotherapy

The linear quadratic model of radiation effect and the biologically effective dose concept can sometimes be used to provide radiobiological compensation for errors that have occurred in radiotherapy dose delivery. The associated mathematics is not complex, but there are important subtleties, which can lead to misunderstanding and erroneous corrections if the processes involved are not properly understood. Unfortunately, training in this area is, at best, patchy. In this article, several worked examples are used to demonstrate the principles involved in establishing error compensations, including cases in which dose distribution is itself changed as a result of the error. Compromise solutions are sometimes necessary, and close liaison between the clinician, physicist and (where possible) radiobiologist is necessary to obtain the best (and safest) compensation.

The Radiobiology of Papillon-type Treatments

The dominant influence in all types of contact therapy is physical rather than radiobiological in nature and is associated with the rapid fall-off of dose with increasing depth in tissue. Even at a depth of only 20 mm the dose has typically fallen to around 15% of the surface dose, meaning that the deeper (and, potentially, dose-limiting) structures are physically spared. Papillon treatments therefore owe their clinical success largely to this simple characteristic and the radiobiological issues, although of interest, might be dismissed as being of secondary importance. However, consideration of the associated radiobiology is useful as it provides a deeper insight into why Papillon-type treatments are effective and also helps to identify the circumstances in which more careful planning of treatment might be required. Some of the most relevant issues are discussed in this paper. The essential points are introduced in a qualitative manner and then followed by some quantitative assessments.

Results of a UK survey on methods for compensating for unscheduled treatment interruptions and errors in treatment delivery

In order to obtain a preliminary overview of the current national status regarding the management of both unintentional interruptions to radiotherapy treatments and inadvertent errors in treatment delivery, a short questionnaire was sent to 60 UK radiotherapy departments, of which 35 (58%) responded. The study was initiated by the authors and was not commissioned by any professional body. Amongst the centres which responded the majority (86%) currently have standardized protocols in place for dealing with treatment interruptions and many have extended the enactment of compensation methods to cover a wider range of tumour types than are encompassed within the Royal College of Radiologists (RCR)-defined Categories 1 and 2. Fewer of the respondents (60%) have standardized methods for dealing with treatment errors. Given that 42% of centres did not respond it is difficult to assess the fuller national picture. Some smaller departments may seek protocols or advice from larger adjacent centres, but the overall percentage of centres with systems in place may be lower than indicated from the survey results. The desirability of providing training in the radiobiological methods pertaining to treatment compensation was raised by a number of respondents.

A theoretical investigation into post-operative, intracavitary beta therapy of high-grade glioblastomas using yttrium-90

Beta therapy with yttrium-90 (90Y) has recently been introduced as a post-operative intra-cavitary treatment for malignant glioblastoma, a generally radioresistant tumour for which cure rates with conventional radiotherapy are usually very disappointing. This short theoretical study investigates the conditions under which 90Y treatment might be most effective and assesses the likely amounts of activity which must be infused in order to successfully cope with the low radiosensitivities which characterize such tumours. The radiobiological and physical analysis is investigated using the linear quadratic (LQ) model and a range of possible scenarios for the distribution and density of the tumour cells surrounding the surgically formed cavities are considered. The results suggest that, in the absence of diffusion of 90Y from the cavity, the activity typically required for 50% tumour cure is well over 40 mCi (1480 MBq), this being considerably more than the clinically determined activities which may be tolerated. Suggestions are provided for improving the versatility of the model.

Radiobiological modelling of dose-gradient effects in low dose rate, high dose rate and pulsed brachytherapy

This paper presents a generalization of a previously published methodology which quantified the radiobiological consequences of dose-gradient effects in brachytherapy applications. The methodology uses the linear-quadratic (LQ) formulation to identify an equivalent biologically effective dose (BED(eq)) which, if applied uniformly to a specified tissue volume, would produce the same net cell survival as that achieved by a given non-uniform brachytherapy application. Multiplying factors (MFs), which enable the equivalent BED for an enclosed volume to be estimated from the BED calculated at the dose reference surface, have been calculated and tabulated for both spherical and cylindrical geometries. The main types of brachytherapy (high dose rate (HDR), low dose rate (LDR) and pulsed (PB)) have been examined for a range of radiobiological parameters/dimensions. Equivalent BEDs are consistently higher than the BEDs calculated at the reference surface by an amount which depends on the treatment prescription (magnitude of the prescribed dose) at the reference point. MFs are closely related to the numerical BED values, irrespective of how the original BED was attained (e.g., via HDR, LDR or PB). Thus, an average MF can be used for a given prescribed BED as it will be largely independent of the assumed radiobiological parameters (radiosensitivity and alpha/beta) and standardized look-up tables may be applicable to all types of brachytherapy treatment. This analysis opens the way to more systematic approaches for correlating physical and biological effects in several types of brachytherapy and for the improved quantitative assessment and ranking of clinical treatments which involve a brachytherapy component.

A four-dimensional computer simulation model of the in vivo response to radiotherapy of glioblastoma multiforme: studies on the effect of clonogenic cell density

Tumours behave as complex, self-organizing, opportunistic dynamic systems. In an attempt to better understand and describe the highly complicated tumour behaviour, a novel four-dimensional simulation model of in vivo tumour growth and response to radiotherapy has been developed. This paper presents the latest improvements to the model as well as a parametric validation of it. Improvements include an advanced algorithm leading to conformal tumour shrinkage, a quantitative consideration of the influence of oxygenation on radiosensitivity and a more realistic, imaging based description of the neovasculature distribution. The tumours selected for the validation of the model are a wild type and a mutated p53 gene glioblastomas multiforme. According to the model predictions, a whole tumour with larger cell cycle duration tends to repopulate more slowly. A lower oxygen enhancement ratio value leads to a more radiosensitive whole tumour. Higher clonogenic cell density (CCD) produces a higher number of proliferating tumour cells and, therefore, a more difficult tumour to treat. Simulation predictions agree at least semi-quantitatively with clinical experience, and particularly with the outcome of the Radiation Therapy Oncology Group (RTOG) Study 83-02. It is stressed that the model allows a quantitative study of the interrelationship between the competing influences in a complex, dynamic tumour environment. Therefore, the model can already be useful as an educational tool with which to study, understand and demonstrate the role of various parameters in tumour growth and response to irradiation. A long term quantitative clinical adaptation and validation of the model aiming at its integration into the treatment planning procedure is in progress.

Calculation of high-LET radiotherapy dose required for compensation of overall treatment time extensions

A method is presented that allows biological effective dose (BED) equations to be used to calculate compensatory doses for treatment time extensions when high-LET (linear energy transfer) radiotherapy schedules are used. The principles involved are the same as those for low-LET radiations, but incorporate two relative biological effectiveness (RBE) factors, RBE(max) and RBE(min), which represent the RBE at very low and very high fraction doses, respectively, with the actual RBE changing between these extremes. The method has the advantage that low-LET alpha/beta ratios and low-LET daily dose-equivalent repopulation factors are used in the calculations. The daily dose repopulation equivalents and increments in dose per fraction in the case of high LET radiotherapy are smaller than those for low LET.

The potential for mathematical modelling in the assessment of the radiation dose equivalent of cytotoxic chemotherapy given concomitantly with radiotherapy

The linear quadratic (LQ) concept of biological effective dose (BED) is used with Poisson statistics to estimate the radiation equivalent BED of cytotoxic chemotherapy (CBED) that would provide improvements in tumour control probability (TCP) typically achieved in randomized clinical trials of chemoradiation. The concepts of pure radio-sensitization and independent chemotherapy cell kill are represented by mathematical equations. Small values of sensitizer enhancement ratios (s) can provide modest increases in TCP when large numbers of radiotherapy fractions are sensitized; larger s values are required if only a small number of radiotherapy fractions are sensitized. Independent chemotherapy induced cell kill is sufficient to explain the benefits achieved with concomitant chemoradiotherapy in situations where a sufficiently high chemotherapy dose intensity is used (i.e. the dose-time intensity of cytotoxic chemotherapy without radiation is considered to be sufficient to cause significant tumour regression although not cure). Care is required in the use of the Poisson cure probability model because of the associated steep dose-response curves that may underestimate both s and the CBED. By use of random sampling methods and estimation over a theoretical population of different tumours, more robust results are obtained with dose-response curves that correspond better to those in clinical data sets. These predict a 2-4 Gy(10) equivalent for each pulse of chemotherapy such as single agent Cis-Platinum when used weekly during radiotherapy for a maximum of 4 cycles. This preliminary paper does not consider normal tissue complication probabilities, of which there are relatively few mature results for modern chemoradiotherapy. The BED concept can be used to estimate the equivalent dose of radiotherapy that will achieve the same cell kill as concomitant cytotoxic chemotherapy. Relatively simple radiobiological modelling can be used to guide decision-making regarding the assessment of the most appropriate combined modality schedules, and has important implications in the design of clinical trials.

The effects of delays in radiotherapy treatment on tumour control

There is often a considerable delay from initial tumour diagnosis to the start of radiotherapy treatment, which may be due to factors such as waiting lists and referral delays. This paper uses widely published models and clinical parameters to calculate the effect of delays in treatment on local tumour control for four different types of tumour-squamous cell carcinoma (head and neck), breast, cervix and prostate. The Poisson model for tumour control probability (TCP), an exponential function for tumour growth and the linear quadratic model of cell kill are used to calculate the change in TCP for delays between diagnosis and treatment of up to 100 days. Typical values of the clinical parameters have been taken from the literature; these include alpha and beta, sigma(alpha), tumour size at diagnosis, pre-treatment doubling time, delay in onset of accelerated repopulation and doubling time during treatment. It is acknowledged that there are limitations in the reliability of these data for predicting absolute values of tumour control, but models are still useful for predicting how changes in treatment parameters are likely to affect the outcome. It is shown that for fast-growing tumours a delay of 1-2 months can have a significant adverse effect on the outcome, whereas for slow-growing tumours such as Ca prostate a delay of a few months does not significantly reduce the probability of tumour control. These calculations show the importance of ensuring that delays from diagnosis through to treatment are minimized, especially for patients with rapidly proliferating tumours.

Practical methods for compensating for missed treatment days in radiotherapy, with particular reference to head and neck schedules

Unscheduled interruption of a radiotherapy treatment can lead to significant loss in local tumour control, particularly in tumours that repopulate rapidly. General guidelines for dealing with such treatment gaps have been issued by the Royal College of Radiologists and more specific advice on the use of compensation methods has been published previously [Hendry et al., Clin Oncol 1996;8:297-307; Slevin et al., Radiother Oncol 1992;24:215-220]. This article further elaborates on the practical application of these methods. It sets out the main considerations arising in the especially critical case of head and neck treatments and simple calculations are used to illustrate the approaches which may be adapted for particular situations. Radiobiological parameter values are suggested for use in the calculations, but these may require modification in the light of further research in this important area.

A theoretical investigation into the role of tumour radiosensitivity, clonogen repopulation, tumour shrinkage and radionuclide RBE in permanent brachytherapy implants of 125I and 103Pd

There is growing clinical interest in the use of 125I (half-life 59.4 days) and 103Pd (half-life 16.97 days) for permanent brachytherapy implants. These radionuclides pose interesting radiobiological challenges because, even with slowly growing tumours, significant tumour cell repopulation may occur during the long period taken to deliver the full radiation dose. This results in a considerable amount of the prescribed dose being wasted. There may also be changes in the tumour volume during treatment (due to oedema and/or shrinkage), thus altering the relative geometry of the implanted seeds and causing additional dose rate variations. This assessment examines the interaction between the above effects and additionally includes allowance for the influence of the relative biological effectiveness (RBE) of the radiations emitted by the two radionuclides. The results are presented in terms of the biologically effective doses (BEDs) and likely tumour control probabilities (TCPs) associated with the various parameter combinations. The overall BED enhancement due to the RBE effect is shown always to be greater than the RBE itself and is greatest in tumours which are radio-resistive and/or fast growing. The biological dose uncertainties are found to be less with 103Pd and the TCPs associated with this radionuclide are expected to be significantly higher in the treatment of some 'difficult' tumours. Using typically prescribed doses 125i appears to be better for treating radiosensitive tumours with long doubling times and which shrink fairly rapidly. However, unless 125I doses are reduced, this advantage may well be offset by the greatly enhanced biological doses delivered to adjacent normal structures.

The role of biologically effective dose (BED) in clinical oncology

There are many clinical situations in which radiobiological considerations can be usefully applied and all clinicians should be aware of the potential benefits of developing a quantitative radiobiological approach to their practice. The concept of biologically effective dose (BED) in particular is useful for quantifying treatment expectations, but clinical oncologists should recognize that careful interpretation of modelling results is required before clinical decisions can be made and that there is a lack of reliable human parameters for application in some situations. Correct use of the BED concept will, in more complex treatment situations, sometimes involve the use of multiple parameters and BED calculations. Examples include: 1. Where the dose per fraction is being altered and it is possible that normal tissue tolerance may be compromised, calculations should include two or more alpha/beta ratio values, some being less than 3 Gy, in order to estimate the 'worst case scenario'. 2. A single one-point BED calculation will not be representative of the biological effect throughout a large planning target volume where there are significant 'hot spots'. Multiple BED evaluations are then indicated. 3. Where there are combinations of radiotherapy treatments or phases of treatments, these can be quantitatively assessed by the addition of BEDs, although the volume of tissue is not inherently included in the BED calculation and any high-dose region needs to be separately assessed as in point 2. 4. Allowance for tumour clonogen repopulation during therapy is required for some tumour types. 5. Different histological classes of cancers require the use of different alpha/beta ratios. Where there is reasonable doubt regarding this parameter, a suitable range should be used. The principles involved are illustrated by worked examples. Attention to detail and the examination of ranges of possible results should offer a safer guide to alternative dose fractionation schedules, although the ultimate choice will be tempered by clinical circumstances.

Estimation of optimum dose per fraction for high LET radiations: implications for proton radiotherapy

PURPOSE

For high linear energy transfer (LET) radiations, the relative biologic effect (RBE) changes with dose per fraction. Methods for calculating the optimum dose per fraction for high LET radiations should therefore include an allowance for RBE.

METHODS AND MATERIALS

The linear-quadratic (LQ) model, and the associated biologic effective dose (BED) concept, has previously been extended to incorporate the RBE effect. Differential calculus is now used to calculate the optimum dose per fraction (z), when high-LET radiation is used, which is given by the solution for z of (g - LATE(alpha/beta)(L)/TUM(alpha/beta)L . RBE(M( z(2))) - 2 . f . g . K . z - (LATE)(alpha/beta)(L) . f . K . RBE(M) = 0 where g is the normal tissue sparing factor, RBE(M) is the maximum RBE value, f the mean interfraction interval, K the daily low-LET BED equivalent dose for clonogen repopulation and (LATE)(alpha/beta)(L) and (TUM)(alpha/beta)(L) are the respective late reacting normal tissue and tumor fractionation sensitivities for low-LET radiation.

RESULTS

The optimum dose per fraction for proton therapy is generally lower than that calculated for photons but there is not a simple relationship between the magnitude of the reduction and the assumed value of RBE(M.) Thus(,) generic values of RBE(M) cannot always be used in such calculations. In some cases, where tumor alpha/beta ratios are low (around 5-6 Gy) and where there is good normal tissue sparing, the optimum dose per fraction is relatively large, typically 4-8 Gy.

CONCLUSION

BED equations that include the RBE parameter, together with low-LET alpha/beta ratios and repopulation dose equivalents, constitute a rational model of high-LET radiotherapy. In the case of proton beam therapy, a wide range of optimum dose per fraction is predicted.

Radiobiological modeling and clinical trials

PURPOSE

Standard clinical trial designs can lead to restrictive conclusions: the "best recommended treatments" based on trial results, although generally applicable to patient populations, do not necessarily apply to individual patients. In theory, radiobiological modeling, coupled with reliable predictive assays, can be used to rationalize the selection of patients for particular schedules in trials.

MATERIALS AND METHODS

Linear-quadratic modeling of radiotherapy can be used to simulate a clinical trial. This is achieved by random sampling techniques where the key radiobiological parameters (alpha, beta, T(pot) and clonogen number) are selected from known or expected ranges. Clinical trial design in radiotherapy may be improved by formal radiobiological assessment designed to estimate the likely changes in tumor cure probability (TCP) and the likely normal tissue biologically effective dose (BED). Modeling may also be used to rationalize the allocation of patients to a test or standard schedule or for individual optimization of a treatment schedule. Such approaches depend on there being reliable predictive assays of the radiobiological parameters in individual patients. The influence of variations in predictive assay accuracy on the improved outcomes are assessed.

RESULTS

Clinical trials, which have been preceded by modeling simulation, offer potentially substantial improvements in the results of cancer treatment by radiotherapy. These exceed the usual gains found in standard clinical trials.

CONCLUSION

Future preclinical trial design should include modeling assessments that indicate how best to structure the trial.

Dose equivalents of tumour repopulation during radiotherapy: the potential for confusion

When employing linear quadratic equations to calculate compensation for changes in overall treatment time, a potential confusion exists regarding use of the parameter commonly described as the dose equivalent of tumour repopulation. The more correct term for this factor is the biologically effective dose equivalent of tumour repopulation. The distinction between the two concepts is discussed and the potential errors arising from their confusion are illustrated by means of an example.

Biological equivalent dose assessment of the consequences of hypofractionated radiotherapy

PURPOSE

To investigate the changes in biological effective dose (BED) that occur in high-dose regions within a target volume when radiotherapy is hypofractionated.

METHODS AND MATERIALS

By comparing a standard prescription of 2 Gy per fraction that is matched to give the same BED as a hypofractionated schedule at a standard intersectional prescription point, the BED increments for late-tissue effects at a higher dose region within the planning target volume (PTV) are compared. The alternative approach of BED matching between a conventional and hypofractionated schedule at the high-dose region is also considered. The results are presented as a sequence of calculations that can be understood by practicing radiation oncologists and in graphical form.

RESULTS

The BED increment at the high-dose region is marginally increased by hypofractionation, although the latter effect is relatively small: up to 5% additional BED due to hypofractionation for a 20% increase in physical dose when the prescribed fraction size is 6-7 Gy. BED matching for late effects between a conventional and hypofractionated schedule at the high-dose region produces lower BED values throughout the remaining PTV, but at the expense of a reduced tumor control BED.

CONCLUSION

Clinical trials that use BED isoeffect matching for late reacting tissue effects to design a hypofractioned test schedule should include comprehensive calculations of the likely BED in high-dose regions.

Mathematical models of tumour and normal tissue response

The historical application of mathematics in the natural sciences and in radiotherapy is compared. The various forms of mathematical models and their limitations are discussed. The Linear Quadratic (LQ) model can be modified to include (i) radiobiological parameter changes that occur during fractionated radiotherapy, (ii) situations such as focal forms of radiotherapy, (iii) normal tissue responses, and (iv) to allow for the process of optimization. The inclusion of a variable cell loss factor in the LQ model repopulation term produces a more flexible clonogenic doubling time, which can simulate the phenomenon of 'accelerated repopulation'. Differential calculus can be applied to the LQ model after elimination of the fraction number integers. The optimum dose per fraction (maximum cell kill relative to a given normal tissue fractionation sensitivity) is then estimated from the clonogen doubling times and the radiosensitivity parameters (or alpha/beta ratios). Economic treatment optimization is described. Tumour volume studies during or following teletherapy are used to optimize brachytherapy. The radiation responses of both individual tumours and tumour populations (by random sampling 'Monte-Carlo' techniques from statistical ranges of radiobiological and physical parameters) can be estimated. Computerized preclinical trials can be used to guide choice of dose fractionation scheduling in clinical trials. The potential impact of gene and other biological therapies on the results of radical radiotherapy are testable. New and experimentally testable hypotheses are generated from limited clinical data by exploratory modelling exercises.

A new incomplete-repair model based on a 'reciprocal-time' pattern of sublethal damage repair

A radiobiological model for closely spaced non-instantaneous radiation fractions is presented, based on the premise that the time process of sublethal damage (SLD) repair is 'reciprocal-time' (second order), rather than exponential (first order), in form. The initial clinical implications of such an incomplete-repair model are assessed. A previously derived linear-quadratic-based model was revised to take account of the possibility that SLD may repair with time such that the fraction of an element of initial damage remaining at time t is given as 1/(1 + zt), where z is an appropriate rate constant; z is the reciprocal of the first half-time (tau) of repair. The general equation so derived for incomplete repair is applicable to all types of radiotherapy delivered at high, low and medium dose-rate in fractions delivered at regular time intervals. The model allows both the fraction duration and interfraction intervals to vary between zero and infinity. For any given value of z, reciprocal repair is associated with an apparent 'slowing-down' in the SLD repair rate as treatment proceeds. The instantaneous repair rates are not directly governed by total dose or dose per fraction, but are influenced by the treatment duration and individual fraction duration. Instantaneous repair rates of SLD appear to be slower towards the end of a continuous treatment, and are also slower following 'long' fractions than they are following 'short' fractions. The new model, with its single repair-rate parameter, is shown to be capable of providing a degree of quantitative explanation for some enigmas that have been encountered in clinical studies. A single-component reciprocal repair process provides an alternative explanation for the apparent existence of a range of repair rates in human tissues, and which have hitherto been explained by postulating the existence of a multi-exponential repair process. The build-up of SLD over extended treatments is greater than would be inferred using a single-exponential repair model and this has important implications in several areas of radiotherapy.

Inclusion of molecular biotherapies with radical radiotherapy: modeling of combined modality treatment schedules

PURPOSE

The use of molecular biology based therapies concurrently with radical radiotherapy is likely to offer potential benefits, but there is relatively little use of classical radiobiology in the rationale for such applications. The biological mechanisms that govern the outcomes of radiotherapy need to be completely understood before rational application and optimization of such adjuvant biotherapies with radiotherapy.

METHODS AND MATERIALS

Existing biomathematical models of radiotherapy can be used to explore the possible impact of biotherapies that modify tumor proliferation rates and/or radiosensitivity parameters during radiotherapy. Equations that show how to incorporate biotherapies with the linear-quadratic model of radiation cell kill are presented. Also considered are changes in tumor physiology, such as improved blood flow with enhanced delivery of biotherapy to the tumor cells and accelerated clonogen repopulation during radiotherapy. Monte Carlo random sampling methods are used to simulate these effects in heterogenous tumor populations with variation in radiosensitivities, clonogen numbers, and doubling times, as well as variations in repopulation onset rates and in vascular perfusion rates with time.

RESULTS

The time onset and duration of exposure of each type of biotherapy during radical radiotherapy can influence the predicted tumor cure probabilities in subtle ways. In general, the efficacy of biotherapies that radiosensitize will depend upon the number of radiotherapy fractions that are sensitized and the change in blood flow with time during radiotherapy. Biotherapies that control repopulation will depend not only on the duration of exposure but also, where accelerated repopulation occurs, on the time at which biotherapy is initiated during radiotherapy. From the ranges of radiobiological parameters and biotherapy efficacies assumed for exploratory examples, large changes of tumor control probability (TCP) are encountered in individual tumors from the application of cytostatic therapy. There are predictions of smaller increments in TCP in heterogenous tumor populations from the application of cytostatic and radiosensitizing biotherapies in combination.

CONCLUSIONS

The exercises show how the scheduling of biotherapies may critically influence tumor cure probabilities in subtle ways and give considerable insight into the interacting biological mechanisms that influence these changes. Future therapeutic developments should be guided by these principles.

BED-time charts and their application to the problems of interruptions in external beam radiotherapy treatments

PURPOSE

The use of radiobiological modelling to examine the likely consequences of interruptions to radiotherapy schedules and to assess various compensatory measures.

METHODS AND MATERIALS

An effect-time graphical display, the BED-time chart, has been developed using the linear-quadratic (LQ) model. This is used to examine the effects on tumour and normal tissues of treatment interruption scenarios representative of clinical situations. The mathematical criteria governing successful salvage have also been drafted and applied to typical situations.

RESULTS

The successful salvage of an interrupted treatment is dependent on a number of interacting factors and the method presented here can be used to examine the trade-offs that exist. Although the mathematics may be complex, it is shown that the dilemmas posed by an interrupted treatment may be more easily appreciated with reference to BED-time charts. These may therefore have a useful role as a teaching aid for portraying a wider variety of radiotherapy problems and also in the documentation of interruptions to treatment and the measures taken to compensate for them.

CONCLUSIONS

Interruptions to radiotherapy regimes are undesirable and compensatory measures need to be initiated as soon as possible after the gap, with a view to completing the amended treatment within the originally prescribed treatment time. Adequate compensation is particularly difficult for long gaps and gaps which occur towards the end of the scheduled treatment. Modelling exercises can help establish guidelines on the available windows of opportunity.

Enhanced normal tissue doses caused by tumour shrinkage during brachytherapy

Published data concerning shrinkage rates of low-grade gliomas implanted with 125I seeds have been used to determine the likely influence of such shrinkage on normal tissue doses. It is demonstrated that a tumour volume shrinkage of 50% over 6 months can bring about a 30% increase in the dose delivered to tissues which shrink centripetally towards the implanted volume. The use of radionuclides with a half-life shorter than that of 125I would substantially reduce shrinkage-induced dose increments.

High dose rate brachytherapy practice for the treatment of gynaecological cancers in the UK

A summary of UK high dose rate brachytherapy practice in gynaecological cancer is presented. There appears to be relatively good uniformity in dose prescription and biological effective doses, which represents a considerable improvement from the findings of a previous report of UK low dose rate brachytherapy practice in 1991. Individual details of the dose schedules used at each treatment centre are presented.

The assessment of RBE effects using the concept of biologically effective dose

PURPOSE

To modify existing linear-quadratic (LQ) equations in order to take account of relative biological effectiveness (RBE) using the concept of biologically effective dose (BED).

METHODS AND MATERIALS

Clinically useful forms of the LQ model have been modified to incorporate RBE effects in such a way as to allow comparison between high- and low-LET (linear energy transfer) radiations in terms of similar biological dose units. The new parameter in the formulation is RBEM, the intrinsic (or maximum) RBE at zero dose. The principal assumption (following Kellerer and Rossi; ref. 1) is that high-LET radiation modifies the alpha-coefficient of damage while leaving the beta-coefficient unaltered.

RESULTS

The equations allow a quantitative estimation of how the apparent RBE will change with changes in dose/fraction or dose-rate and of how the magnitude and rate of change is governed by the low-LET alpha/beta ratio of the irradiated tissue. The modifications are applicable to all types of radiotherapy (fractionated, continuous low dose-rate, therapy with decaying sources, etc.). In cases where the normal tissue RBEM is greater than that for the tumor, the revised formulation helps explain why there will be situations where therapeutic index will be adversely affected by use of high-LET radiation. Such clinical advantages as have been observed are more likely to result from favorable geometrical sparing of critical normal tissues and/or the fact that slowly growing tumors may have alpha/beta values more typical of late-responding normal tissues.

CONCLUSIONS

The incorporation of RBE into existing LQ methodology allows quantitative assessment of clinical applications of high-LET radiations via an examination of the associated BEDs. On the basis of such assessments high-LET radiations are shown to confer few advantages.

Radiobiological prediction of normal tissue toxicities and tumour response in the radiotherapy of advanced non-small-cell lung cancer

A number of randomized studies have been carried out in the UK and USA to determine the optimal radiotherapy dose schedule for advanced non-small-cell lung cancer (NSCLC). We have examined eight radiotherapy regimens from data taken from four randomized phase III studies carried out in the UK (1264 patients): 10 Gy single fraction; 17 Gy in two fractions over 8 days; 30 Gy in ten fractions over 14 days; 22.5 Gy in five fractions in 5 days; 27 Gy in six fractions over 11 days; 30 Gy in six fractions over 11 days; 36 Gy in 12 fractions over 16 days; and 39 Gy in 13 fractions over 17 days. We compared the clinical results in palliation, toxicity and survival with four regimens taken from one randomized study from the USA (365 patients): 40 Gy in 20 fractions over 4 weeks; 40 Gy 'split course' in ten fractions in 4 weeks; 50 Gy in 25 fractions over 5 weeks; and 60 Gy in 30 fractions over 6 weeks. Using the linear-quadratic (LQ) radiobiological model, we have calculated the radiobiological equivalent dose (BED) for acute-reacting tissues (BED10), late-reacting tissues (BED1.7) and tumour (BED25), and related the predicted response to the observed response in each tissue. There was a good correlation between the predicted response and the reported response in the case of late-reacting tissue toxicity and tumour response. The model confirmed that, in good performance status patients, a higher value for BED25 correlated with a higher degree of local control and survival and that radiotherapy regimens with a higher value for BED1.7 were associated with five cases of cord myelopathy, if the spinal cord was not shielded. In poor performance status patients the model suggested that the optimal regimen was a single fraction of 10 Gy because this resulted in an equivalent degree of symptom control as other regimens, needed only one hospital visit and was less likely to result in cord damage, thus, allowing for the possibility of retreatment at a later date.

Estimation of tumour hypoxic fraction from clinical data sets compatible with accelerated repopulation

By extrapolation to zero time, the initial and final slopes of data sets which probably demonstrate the existence of accelerated repopulation during radiotherapy can be used to estimate the lower limits of the initial tumour hypoxic fraction. The slow repopulation phase (initial slope) is assumed to reflect treatment in mixed oxic and hypoxic conditions and the later fast repopulation (final slope) phase that of a well-oxygenated cell population. The method assumes that accelerated repopulation in tumours results from an improvement in oxygen status during radiotherapy, but quantitative knowledge of repopulation factors is not required in the calculations. Using the data of (a) Withers et al. (for head and neck squamous cell cancer) and (b) Maciejewski & Majewski (for bladder cancer), the lower limits of initial hypoxic fraction appear to be between 10 and 52%, the exact values depending on the value assumed for the oxygen-enhancement ratio (OER) of the hypoxic compartment. The analysis also suggests that the half-life of effective tumour reoxygenation is probably less than 5 days.

Radiobiologically based assessments of the net costs of fractionated focal radiotherapy

PURPOSE

To assess the potential changes in the net costs of focal radiotherapy techniques at differing doses per fraction and interfraction intervals.

METHODS

Linear quadratic radiobiological modeling is used with appropriate variations in the radiosensitivity and tumor cell proliferation parameters. The notional cost of treatment is calculated from the number of fractions, cost per fraction and the cost of treatment failure, which is itself related to (1-TCP) where TCP is the tumor cure probability. Additional Monte Carlo calculations from ranges of radiobiological parameters have been used to simulate the cost of treatment of tumor populations.

RESULTS

The optimum dose per fraction (and optimum overall cost) for conventional (nonfocal) radiotherapy is generally at low doses of around 2 Gy per fraction. The use of hyperfractionated and accelerated radiotherapy in addition to focal radiotherapy techniques appear to be indicated for more radioresistant tumors and if tumor proliferation is extremely rapid, but the need for treatment acceleration is much reduced where effective focal techniques are used.

CONCLUSIONS

Radiobiological and economic modeling can be used to guide clinical choices of dose fractionation techniques providing the key radiobiological parameters are known or if the ranges of likely parameters in a tumor population are known. Focal radiotherapy, by the introduction of changes in the physical dose distribution, produces an upward shift in the optimum dose per fraction and a reduced dependency on overall treatment time.

The clinical radiobiology of brachytherapy

The unique geometrical features of brachytherapy, together with the wide variety of temporal patterns of dose delivery, result in important interactions between physics and radiobiology. These interactions exert a major influence on the way in which brachytherapy treatments should be evaluated, both in absolute and comparative terms. This article reviews the main physical and radiobiological aspects of brachytherapy and considers examples of their influence on specific types of treatment. The issues relating to the optimization of high dose rate brachytherapy are presented, together with the implications of multiphasic repair kinetics for low dose-rate and pulsed high dose rate brachytherapy. The opportunities for application of radiobiological principles to improve various brachytherapy techniques, together with the integration of brachytherapy with teletherapy, are also outlined. Equations for the numerical evaluation of brachytherapy treatments are presented in the Appendices.

Calculation of integrated biological response in brachytherapy

PURPOSE

To present analytical methods for calculating or estimating the integrated biological response in brachytherapy applications, and which allow for the presence of dose gradients.

METHODS AND MATERIALS

The approach uses linear-quadratic (LQ) formulations to identify an equivalent biologically effective dose (BEDeq) which, if applied to a specified tissue volume, would produce the same biological effect as that achieved by a given brachytherapy application. For simple geometrical cases, BED multiplying factors have been derived which allow the equivalent BED for tumors to be estimated from a single BED value calculated at a dose reference point. For more complex brachytherapy applications a voxel-by-voxel determination of the equivalent BED will be more accurate. Equations are derived which when incorporated into brachytherapy software would facilitate such a process.

RESULTS

At both high and low dose rates, the BEDs calculated at the dose reference point are shown to be lower than the true values by an amount which depends primarily on the magnitude of the prescribed dose; the BED multiplying factors are higher for smaller prescribed doses. The multiplying factors are less dependent on the assumed radiobiological parameters. In most clinical applications involving multiple sources, particularly those in multiplanar arrays, the multiplying factors are likely to be smaller than those derived here for single sources. The overall suggestion is that the radiobiological consequences of dose gradients in well-designed brachytherapy treatments, although important, may be less significant than is sometimes supposed. The modeling exercise also demonstrates that the integrated biological effect associated with fractionated high-dose-rate (FHDR) brachytherapy will usually be different from that for an "equivalent" continuous low-dose-rate (CLDR) regime. For practical FHDR regimes involving relatively small numbers of fractions, the integrated biological effect to tissues close to the treatment sources will be higher with HDR than for LDR. Conversely, the integrated biological effect on structures more distant from the sources will be less with HDR. This provides quantitative confirmation of an idea proposed elsewhere, and suggests the existence of a potentially useful biological advantage for HDR brachytherapy delivered in relatively small fraction numbers and which is not apparent when considering radiobiological effect only at discrete reference points.

CONCLUSION

The estimation and direct calculation of integrated biological response in brachytherapy are both relatively straightforward. Although the tabular data presented here result from considering only simple geometrical cases, and may thus overestimate the consequences of dose gradients in multiplanar clinical applications, the methods described may open the way to the development of more realistic radiobiological software, and to more systematic approaches for correlating physical dose and biological effect in brachytherapy.