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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.

Hyperfractionated regimes are being used more frequently; this has created a clinical need for more sophisticated biologically effective dose (BED) calculations. A formula is given for calculating BED assuming reciprocal repair in the case of changing dose per fraction and changing interfraction interval. Example applications are given for hyperfractionated schedules. It is shown that the formula is useful for calculating isoeffective schedules for a treatment with unplanned gaps and for comparing regimes in trial design. This work should be of value for comparing risk across accelerated schedules when an organ of the central nervous system is at risk. Uncertainties in choice of parameter and model are discussed: the bi-exponential model of repair is invoked for this purpose.

Purpose: This paper considers why the proton therapy relative biological effect (RBE) should be variable rather than constant. Methods: The reasons for a variable proton RBE are enumerated, with qualitative and quantitative arguments. The heterogenous data sets collated by Pagenetti et al and the more homogenous data of Britten et al are further analysed using linear regression fitting and RBE-inclusive adaptations of the linear quadratic (LQ) radiation model. Results: The in vitro data show RBE increasing as dose per fraction is lowered. In the Paganetti et al (2002) data sets, the differences between observed and expected effects are smaller when the linear quadratic model is used, but with such data heterogeneity firm statistical conclusions cannot be obtained. The more homogeneous data set shows an unequivocal variation in RBE with dose per faction. The in vivo data are inappropriate for assessments of late normal tissue effects in radiotherapy. Also, if there is the same degree of uncertainty in an RBE of 1.1 or in an RBE of 2-3 for C ions, the fractional and biological effective doses (BED) can vary considerably and be greater in the proton case. So, errors in RBE assignment are important for protons, just as with C ions. Conclusions: Further experimental programmes are proposed, including late normal tissue endpoints. Better RBE allocations might further improve proton therapy outcomes. Advances in Knowledge: This study provides a rigorous critique of the 1.1 RBE used for protons, from theoretical and practical standpoints. The data analysis shows that the linear quadratic model is more appropriate than simple linear regression. Comprehensive research programmes are suggested.

It is unclear whether radiosensitization is beneficial when radiotherapy is administered at a high dose per fraction. The aim of this study was to assess the impact of radiation dose on the effectiveness of a broad range of radiosensitizers.We analyzed 653 pairs of clonogenic survival curves in 285 published articles, in which modifications of radiosensitivity were studied using the colony-forming assay. The modifications of radiosensitivity were arbitrarily classified into 20 classes. The survival curves were fitted to two biomathematical models: the linear-quadratic model and the repair-misrepair (RMR) model.We found that radiosensitization was predominantly characterized by an increase of the α value (α-sensitization) without an increase of the β value (β-sensitization). A subset analysis revealed that all 20 classes showed significant α-sensitization. In contrast, only oxygen/hypoxic sensitizers (oxygen) and poly(adenosine diphosphate-ribose) polymerase inhibition (PARPi) exhibited β-sensitization. An analysis using the RMR model revealed two major sources of radiosensitization: an increased residual DNA lesion through repair inhibition and a shift from linear repairs to quadratic misrepairs, leading to enhanced lethal chromosomal aberrations.Oxygen and PARPi were found to show β-sensitization, which was favourable for eliciting a comparable degree of sensitization in the higher dose range. Reduced fidelity of the repair was suggested to be a possible mechanism of β-sensitization. Further study targeting β-sensitization is needed to develop a novel combined modality therapy with high-dose-per-fraction radiotherapy.Radiosensitization can be classified into two groups, α- and β-sensitizations. These two phenomena may stem from distinct underlying mechanisms.

The subject was covered more widely than the terse title suggests. One might say that radiobiological treatment planning involves most of radiobiology and all of radiation pathology. There was much of interest from seven excellent speakers. Modelling is now entirely respectable scientifically, being used in economic and weather forecasting, climate, voting predictions and cosmology. For radiotherapy, modelling is highly practical and is necessary in optimization of treatment plans and in any new modality being developed. The first speaker, Prof. Bleddyn Jones (Birmingham), spoke on ‘‘The clinical aspects, what should modelling provide?’’ The answer was greater confidence in clinical decision making, especially now, when new treatments are breaching standard methods. Intensity-modulated radiation therapy (IMRT ) involves essentially ‘‘simultaneous boost in a field’’ and so depends on non-standard dose per fraction for selected subvolumes. We need to know how much improvement in tumour control probability (TCP) might be expected, and how much increase or decrease in normal tissue complication probability (NTCP). Although absolute values of these in percentage points cannot be predicted accurately, their ranking order can be helpful in optimization of treatment planning already. He pointed out that tumour cure statistics have provided much of the data for modelling, but that tumour regrowth delay data can be useful too. His list of practical current uses for modelling with BED (biologically effective dose) included the following ‘‘bullets’’: treatment gap compensation; correction of treatment dose delivery errors; choice of dose per fraction in altered radiotolerance; comparative assessments of dose–time fractionation schedules; assessment of new techniques; analysis of optimum dose per fraction; dose rate compensations; and high linear energy transfer (LET) compensations. All these are now being aided by active modelling. Dr Danielle Powers (Hammersmith Hospital) gave a beautifully illustrated presentation on ‘‘The clinical perspective of radiobiological modelling’’. She described the recent technological developments in radiotherapy (imaging, positioning devices, forward and inverse planning programmes, tumour tracking and real-time dose recording) and listed seven ‘‘bullets’’ of modern treatment delivery: 3D conformal RT; intensity-modulated RT; brachytherapy at HDR (high dose rate); respiratory gating; stereotactic bodyframe RT; proton beam (and heavy-ion) RT; and 4D RT (tumour size tracking). She emphasized the potential advantages but the present uncertainties of predicting individual patient’s radiosensitivities. Her final emphasis was on the necessity for further accurate data collection. An interinstitutional data bank of treatment protocols and outcomes was needed, for which the Academic Clinical Oncology and Radiobiology Research Network (ACORRN) could be helpful. Prof. John Hopewell (Oxford) showed that revisiting old (30 years) radiobiological experimental animal data (from the acknowledged peacefulness of partial retirement) could lead to fresh insights. His special contribution had been to show that repair of radiobiological damage after irradiation is not monoexponential but consists of two (or more) rates of repair, most simply one of 5–15 min and a slow one of 3–5 h. It was not allowing for these which has led to much confusion about repair. Prof. Alan Nahum (Clatterbridge) described assumptions involved in calculating TCP and NTCP for various radiotherapy situations. He mentioned the BIOPLAN programme (published by himself and Beatriz SanchezNieta), which they generously offer from alan.nahum@ccotrust.nhs.uk and which the present reporter has used successfully for clinical cases. He mentioned that hypofractionation (fewer and larger fractions) is appropriate in certain limited circumstances and can save resources. Address correspondence to: Jack F Fowler, University of Wisconsin Medical School, Madison, USA. E-mail: jackfowler@btinternet.com The British Journal of Radiology, 81 (2008), 89–90

The purpose of this study was to seek radiation dose responses separately for primary hepatocellular carcinoma (HCC) and metastatic (MET) colorectal liver tumours to establish tumour control probabilities (TCPs) for radiotherapy (RT) of liver tumours.The records of 36 HCC and 26 MET colorectal liver tumour patients were reviewed. The median dose per fraction and total dose were 4 Gy (2-10 Gy) and 52 Gy (29-83 Gy) for the HCC group and 3.6 Gy (2.0-13.0 Gy) and 55 Gy (30-80 Gy) for the MET group, respectively. Median tumour diameter was 6.6 cm (3.0-18.0 cm) and 5.0 cm (1.0-13.0 cm) for the HCC and MET groups, respectively. A logistic TCP model was fitted to the response data for each group using the maximum likelihood method.50% and 90% probabilities of 6-month local control were estimated to be achievable by 2 Gy per fraction equivalent doses (α/β=10 Gy) of 53 Gy and 84 Gy for the HCC group and 70 Gy and 95 Gy for the MET group, respectively. Actuarial 1-year local control for the HCC and MET groups was 65% (45-85%) and 32% (6-58%), respectively, whereas median time to failure was 543 days (374-711 days) and 183 days (72-294 days), respectively.Dose-response relationships were found and modelled for the HCC and MET patient groups, with a higher dose required to control MET tumours. RT offers better local control for HCC than for MET colorectal liver tumours at our institution.An improved understanding of radiation dose-response relationships for primary and MET colorectal liver tumours will help inform future dose prescriptions.

We have extended our previous multiple irradiations of mouse lung from 20 to 40 fractions of both X-ray and neutron radiation in order to test whether the repair parameters previously derived will hold for lower doses per fraction, down to 1.1 Gy of X rays and 0.18 Gy of 3 MeV neutrons per fraction. Repair parameters were calculated from measurements of breathing rate and lethality at monthly intervals up to 17 months after irradiation with 1, 10, 20 or 40 equal fractions. Sparing of neutron damage was negligible when the neutron dose was divided into multiple fractions, but progressively greater repair of lung damage was seen after increasing numbers of X-ray fractions. A significant increase in the iso-effect dose for 40 fractions of X rays was found compared with 20 fractions, even when two fractions per day were given at intervals of about 6 hours, as was the case in the 40 fraction experiment. The data were well fitted by the linear quadratic formula for response vs. dose per fraction and the ratio alpha/beta yielded values of approximately 3 Gy after X rays and 30 to 40 Gy after neutron irradiation; these values are not different from alpha/beta ratios found for up to 20 fractions. The single dose RBE was less than 2, increasing to about 6 at the lowest dose per fraction measured, in agreement with previous results. The ratio of the alpha component for neutrons to that for X rays was about 8, which is therefore the limiting RBE predicted for infinitely small doses per fraction.

The capacity for repair of sublethal damage during fractionated irradiation of the mouse bladder has been measured. Graded doses of electrons were given as 1, 2 or 5 equal daily fractions. Two functional end points were used to assess bladder damage: a) increased urination frequency and b) decreased bladder capacity. Repair of sublethal injury within 24 hours was found to be similar using both assays for bladder damage and was greater than the repair observed in mouse skin for a given dose per fraction. The possibility of a slower repair process occurring in bladder was investigated by giving two fractions in increasing overall times (from 24 hours to one month). No increased repair was observed with the longer time intervals; hence there was no evidence for slow repair in the bladder.

Clinical gains have been reported from the use of nonstandard fractionation schedules planned with a radiobiological basis. Hyperfractionation provides the leading example, as described below, with accelerated fractionation being developed more recently. Although examples of almost every kind of fractionated schedule can be found in the literature over the past 90 years, it is only within the last decade that the biological factors concerning overall time and delayed proliferation after irradiation, and the effect of dose per fraction, have been understood. Both these factors operate differently on late- and early-reacting tissues, because cell proliferation in late-reacting tissues is slow or absent, but early reacting tissues and tumours depend upon cells that proliferate rapidly. This basic knowledge is still diffusing through the radiotherapy community and I hope this review will help the diffusion process. The biological factors concerning fractionation seem to apply to the majority of tissues and tu...

Computer simulations have been made of four radiotherapy fractionation regimes either in current use or proposed for clinical trials of misonidazole. A variety of cell-survival parameters and reoxygenation patterns have been used. The models allow the relative importance of repair capacity, reoxygenation rate, and dose per fraction to be assessed for these four schedules in the presence or absence of misonidazole. Unlike hyperbaric oxygen, the dose of misonidazole and the fractionation scheme to be used are critically interdependent, because the total drug dose is limited to 12 g/m2 by its neurotoxicity, regardless of the extent to which it is fractionated. The largest sensitizing effect is always demonstrated with six fractions, each given with 2 g/m2 of misonidazole. In the absence of reoxygenation a sensitizer enhancement ratio of 1.7 is predicted, but this falls to 1.1--1.2 if extensive reoxy-generation occurs. Less sensitization is observed with 30 fractions, each with 0.4 g/m2 of drug. However, for clinical use, the important question is which treatment kills the maximum number of tumour cells. Many of the simulations predict a marked disadvantage of reducing the fraction number for X rays alone. The circumstances in which this disadvantage is offset by the large SER values with a six-fraction schedule are few. The model calculations suggest that many small fractions, each with a low drug dose, are safest unless the clinician has some prior knowledge that a change in fraction number is not disadvantageous.

In the use of multifraction microcolony assays to infer the low-dose response of in situ renewal systems such as intestinal crypts, the assumption of equal effect per dose fraction is required. Moreover, the construction of a cellsurvival curve requires knowledge of the initial count of cells capable of repopulating each renewal structure. We describe a method of designing fractionation protocols which provides a regression estimate of the initial number of clonogens per renewal structure and a test of the hypothesis of equal effect per fraction. The essential factor in the experimental design is the use of common dose fractions (use of the same dose per fraction in series with different numbers of fractions). Applications of the method to data for which the assumption of equal effect per fraction holds (four-hour fractionation interval testis study) and does not hold (one-hour fractionation interval jejunal crypt study) are presented.

The linear-quadratic (LQ) dose-effect formalism is currently providing new perspectives into the ways in which alterations in the dose per fraction in conventional radiotherapy may be used to bring about improved results with respect to early or late normal tissue reactions. In this paper, using a model initially developed by Roesch, the LQ equations are explored further in terms of dose-rate rather than dose. By the incorporation of one other parameter, mu, which relates to the rate of repair of sub-lethal radiation damage, a more general formalism is obtained. In particular, equations are derived which can be used to examine the relative effectiveness of different treatment regimes, including those involving decaying sources. Such equations are of wider applicability than other LQ derivations which relate only to dose-response relationships. The extended equations, which are fully consistent with the existing LQ method, are also shown to lead directly to other independently established, relationships for protracted irradiation. The nature of the link between high and low dose-rate treatments is discussed, and some worked examples provide indications of how the new equations may be used to assess further the potential clinical benefits of low dose-rate treatments and permanent implants.

The term “relative biological effectiveness” (RBE) is in almost universal use for comparing effects of radiations of different quality. The accepted definition (Storer et al., 1957), “Inverse of the ratio of doses to give the same effect” might, perhaps, suggest that it is a single valued parameter. However, it is now generally realized that in the comparison of radiations of different quality given as single doses the RBE usually depends on the level of effect under consideration and the state of oxygenation of the irradiated material; also, in some instances, on the dose-rate. When a fractionated scheme is used, the size and number of dose fractions also affect the RBE. It has been pointed out that for a given system the RBE depends on the dose per fraction when all fractions in a treatment are of equal size (Fowler and Morgan, 1963; Field, 1969). This is true, of course, only if the effect of any fraction does not in itself change the nature of the response to a subsequent one. Comparing observations m...

Experiments on fibroblasts in vitro were carried out to find the influence of dosage-rate on radiation effect. With a constant overall time the lethal effect of irradiation at a high dosage-rate, but highly fractionated, was found to be the same as that of low dosage continuous irradiation. However, the effect of highly fractionated high dosage-rate irradiation was less than that of irradiation given at the same dosage-rate in fewer fractions but with an interval of over 40 hours. Dosage-rate as such is, therefore, of less importance than the dose per fraction or the intervals between fractions, and it may be concluded that, in comparisons between high dosage-rate irradiation given over a short time and that at low dosage-rate continued over a longer period, the operative factor is the overall time.

Armstrong (1974) recently described a technique for computing NSDs by a most elegant graphical method. Since this method is based on the NSD (and not the partial tolerance) equation, it can be used only for calculations on treatment regimes in which the dose per fraction remains constant and in which the time between fractions is relatively invariable. For all other calculations, either the partial tolerance equations (Dixon, 1972) or time, dose, and fractionation (TDF) factors (Orton and Ellis, 1973) should be used.

If a radiotherapy treatment is increased in duration keeping the number of fractions constant, additional dose is required to sterilize the cells produced by proliferation during this extra time. The extent of proliferation is often expressed in terms of “rads per day” (Cohen, 1968; Liversage, 1971). However, the extra dose required to compensate for a given degree of repopulation will in general depend on the size of the dose per fraction, being independent only if the cell survival curve is a pure exponential or if the individual doses given are sufficiently large that the exponential region of the survival curve is reached. In practice these conditions are rarely met, the dose per fraction given usually being in the region where the slope of the survival curve is changing.

In a recent article published in your Journal, Orton and Ellis (1973) introduced an interesting simplification in the use of the NSD concept in practical radiotherapy. The method described involves the use of what are called the time, dose and fractionation factors (TDF). The TDF has been defined as where n is the number of fractions, d the dose per fraction, and x a constant whose value depends on the number of fractions/week.

According to the NSD Concept (Ellis, 1966, 1971) it is possible to determine the dose per fraction for a given number of fractions in a given time for a certain biological effect on the normal connective tissue. In many human neoplasms, apart from certain radiosensitive ones such as Hodgkin's disease, it is only possible to achieve tumour tolerance (i.e., local cure) by reaching or exceeding normal tissue (i.e., connective tissue) tolerance. Certain neoplasms are acknowledged to be “radioresistant” to the conventional schedules of radiotherapy. Using the NSD formula it is possible to decide on other schedules the effects of which lie within normal tissue tolerance.