Dose-time relationships in fractionated radiotherapy for cancer

$Page 1: Dose-time relationships in fractionated radiotherapy for cancer$
Rev Oncol 2003;5(1):49-54 49

SECCIÓN DOCENTE

Dose-time relationships in fractionatedradiotherapy for cancerVicente Pedraza Muriel

Department of Radiation Oncology. University Hospital. Granada.

INTRODUCTION

For decades, the irradiation schedules used in the treat-ment of cancer were based on empirical grounds. InParis (Coutard, 1932/Baclesse, 1958), the standard the-rapeutic method used until 1960 consisted of the admi-nistration over 5-7 weeks of total doses between 50 and70 Gy at 2 Gy per fraction, five fractions per week. InManchester (Paterson, 1963), the therapeutic approachwas based on the use of high doses per fraction (3.4 Gy)and short irradiation times (16 fractions in 21 days, i.e.,54.4 Gy in three weeks). It is now easy to understandthe success of these two regimens. The time periodused in the Paris regimen allows the development ofcell proliferation in early responding normal tissuesand reduces undesirable acute reactions. In contrast,the clinical utility of the Manchester approach is basedon the hypothesis of a marked degree of proliferation ofirradiated tumours that must be countered by reducingthe irradiation time.Unlike 40 years ago, the principles that underlie theresponse of tumours and normal tissues to radiationare now well known. The present analysis aimed todescribe the influence of two factors, the irradiation timeand the dose per fraction, on the final effect produced in each tissue type.

OVERALL TREATMENT TIME AND TUMOUR CONTROL

Late reactions produced by radiation occur in tissueswith cell populations that proliferate slowly. Becauseirradiated cells die in the course of cell division or divi-sions immediately after irradiation, the compensatoryproliferation mechanism of these tissues is not obser-ved during the irradiation time but rather some monthsafter the treatment. The practical consequences for radiotherapy of this effect are of key importance, becauseif the total administered dose is not modified, its effecton normal slow-responding tissue will not change, regardless of any increase or reduction in the total irra-diation time. On the contrary, the severity of acute reac-

tions in early-responding normal tissues and tumourscan be limited by prolonging treatment time, which enhances the proliferative response of surviving cells tothe irradiation. The problem is that prolongation of theirradiation time in order to limit the appearance of acutereactions has two drawbacks: a) it does not avoid lateeffects of the total administered dose; b) the lengtheningof treatment may lead to a fall in tumour control rates.In patients who undergo irradiation as the sole treatmentof squamous cell carcinoma of head and neck, local con-trol of the disease is significantly reduced if the irradia-tion time is excessively prolonged. The poor outcomesobtained with split irradiation regimens and the resultsof various retrospective studies have demonstrated thatwhen the treatment is excessively lengthened, an increa-se in the dose is required to maintain the same levels oflocal control of the disease. This phenomenon has beenlargely attributed to the accelerated regeneration of sur-viving tumour clonogens during the course of fractio-nated irradiation.

ISOEFFECT

Isoeffect and irradiation time

The concept of isoeffect (same level of biological damage)has been widely used throughout the history of ra-diotherapy to compare between different fractionationregimens. One of the first attempts to define the iso-effect was made by Strandqvist (1944). Based on obser-vations of tumour recurrence and skin responses afterthe irradiation of patients with cancer of skin and lip, herepresented as lines of equal effect the doses and irra-diation times required for: a) the cure of skin cancer; b) the induction of skin necrosis; c) the genesis of skinerythema and dry or moist desquamation (fig. 1).In the above figure, the slope of the isoeffect lines is approximately 0.22. It can therefore be affirmed that thetotal dose (TD) necessary to produce a given effect canbe derived from the relationship TD = K.T0.22 (K: singleisoeffect dose; T: total irradiation time). Thus, for irra-diation times of 10, 20, 30 and 40 days, the total dosesrequired to produce the isoeffect defined by line B (cureof skin cancer) are 4,150, 4,830, 5,280 and 5,630 cGy, res-pectively (the single-dose equivalent to the above frac-tionated doses is approximately 2,500 cGy).The time-dose isoeffect lines are of great importance inradiotherapy. Their utilisation allows the identification

Correspondence: Prof. V. Pedraza Muriel.Departament of Radiation Oncology. University Hospital.Avda. Dr. Olóriz, s/n.18012 Granada. E-mail: [email protected]

PEDRAZA MURIEL V. DOSE-TIME RELATIONSHIPS IN FRACTIONATED RADIOTHERAPY FOR CANCER

50 Rev Oncol 2003;5(1):49-54

of irradiation schemes characterised by the same effect.They also unequivocally demonstrate that when theirradiation time is prolonged, the total dose must be increased to maintain the isoeffect.

Isoeffect, irradiation time and number of fractions

After Puck (1956) cloned mammalian cells in vitro, itwas possible to determine radiation dose-survivalcurves. They showed an initial shoulder preceding alogarithmic decline at high doses. Elkind and Sutton(1959) demonstrated that when a dose was dividedinto two or more fractions, the survival curve for thesecond dose regained, within a few hours, a similarshoulder to that for the first exposure. These effectswere due to the repair of sublethal injury, leading tothe need for an increased total dose for a constant level of cell survival. This radiobiological observationled radiation oncologists to realize that the total dosefor an isoeffect should be plotted as a function of thenumber of fractions into which the total dose is divi-ded, rather than the overall time taken to deliver thedose. Based on this hypothesis, the Nominal StandardDose (NSD) concept was introduced (Ellis, 1969), bywhich the tolerance dose of normal tissues (TD) is related to the total irradiation time (T) and the num-ber of fractions (N), according to the equation

DT = NSD . T0.11 . N0.24 (Eqn. 1)

This equation can be used to compare the biologicaleffects produced by different regimens and to selectthe most appropriate approach in a given clinical si-tuation (the NSD parameter represents the isoeffectproduced by the total administered dose). Never-theless, as the isoeffect defined by the NSD concept isnot related to the cure of the irradiated tumours butrather to the tolerance of acutely responding tissues,the equation should not be used to define therapeuticregimens aimed to obtain a given level of tumourcontrol. On the other hand, the NSD equation under-values the incidence of late effects induced by the

high doses per fraction (which are more marked thancan be predicted by considering the acute effects oftreatment). Finally, the reliability of the T0.11 and N0.24

factors of the equation have been partially invalidated(Joiner, 1997) (indeed, the T0.11 parameter suggeststhat the proliferation of acutely responding tissues isdependent on the entire irradiation time rather thanon only the last part of it, which is the true situation).All of the above explains why the NSD is no longer inuse, and why it should not be employed to predict theisoeffect.

Isoeffect and dose per fraction. The linear-quadratic model

According to the linear-quadratic model of survival, theeffect E of an irradiation regimen based on the adminis-tration of «n» fractions of dose «d» (n. d = total dose) isgiven by the relationships:

S = e-E = e-(αd + βd2)n (Eqn. 2)E = -LS = nd (α + βd) (Eqn. 3)

S: survival fraction; E: effect of treatment (lethal dama-ge of irradiated cells); α, β: dose-effect parameters re-presenting the linear and quadratic components of thecell killing, respectively (α: lethal damage/Gy; β: lethaldamage/Gy2).In tumours and normal acutely responding tissues (α/βratio = 10-25), the influence of the α-parameter on the final radio-induced effect is much greater than that of βwhen low doses per fraction (≤ 2 Gy) are used. Underthese conditions, equation 3 can be reduced to the ex-pression E = n . d .α. Thus, in these tissues, the effect ofthe treatment depends on the total administered doseand the value of α. According to this hypothesis, in aconventional fractionated irradiation regimen (d=2 Gy),each fraction of the dose produces an effect equal to E = 2 . α. If α is considered as the standard mean valueof 0.35±0.1 Gy-1 (characteristic of epithelial tumours), itis clear that a dose of 2 Gy would produce an effect E = 2 × 0.35 = 0.70 lethal lesions per irradiated cell. The

1.000

2.000

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Fig. 1. Isoeffect curves re-lating the total dose to ove-rall treatment time for skinnecrosis (A), cure of skincarcinoma (B), moist des-quamation of skin (C), drydesquamation of skin (D)and skin erithema (E).Adapted from Strandqvist M.Acta Radiol 1944;55 (Suppl):1-300.


survival fraction defined by this effect would be S = e–E =e–0.70 = 0.5 = 50%. If it is assumed that tumour repopulation is absentduring radiotherapy and that fractions are adequatelyspaced to allow full repair of sublethal radiation damage, the survival fraction obtained with a standardirradiation regimen of 30 or 35 fractions of 2 Gy (60 Gy/6 w - 70 Gy/7 w) would be S60 Gy = 0.530 = 9.3 ×10–10

and S70 Gy = 0.535 = 2.9 × 10–11, respectively. This ele-mentary reasoning unequivocally shows that the pa-rameter with decisive influence on the achievementof a given effect is the dose per fraction rather thanthe number of fractions or the overall treatment time.

DOSE-RESPONSE RELATIONSHIPS FOREARLY AND LATE RESPONDING TISSUES

Clinical and laboratory data suggest that there is aconsistent difference between early and late respon-ding tissues in their responses to changing fractiona-tion patterns. Thus, if fewer and larger dose fractionsare given, late reactions are more severe, even whenearly reactions are matched by an appropriate adjust-ment in the total dose. Figure 2 exhibits isoeffect cur-ves in which the total dose necessary to produce acertain effect in various tissues is plotted as a functionof the dose per fraction (under conditions in whichcell proliferation is negligible). As indicated on thegraph, the isoeffect curves for late responding normal

tissues (solid lines) tend to be steeper than those forearly responding normal tissues or tumours (dashedlines). This finding suggests that, for the same totaldose, late reactions can be spared by decreasing thesize of the dose per fraction used. It also follows thatby using smaller-sized dose fractions, a higher totaldose could be given for the same probability of a latereaction, i.e., a greater likelihood of tumour control.The difference in shape of the dose-response relations-hip for early and late-responding tissues leads to an im-portant axiom (Hall, 2000): «fraction size is the domi-nant factor in determining late effects (overall treatmenttime has little influence on this effect); by contrast, frac-tion size and overall treatment time both determine theresponse of acutely responding normal tissues and ma-lignant tumours to irradiation». Surpris-ingly, neitherclinical radiation oncologists nor experimental radiobio-logists recognized these facts before the mid-1980s. Itwas Withers (1985) who most clearly perceived the es-sential difference in the fractionation response (at cons-tant overall time) of late and early radiation reactions.

BIOLOGICALLY EFFECTIVE DOSE

One of the most important recent developments in ra-diobiology in this context has been the use of the line-ar-quadratic survival cell model to describe the rela-tionships between the total isoeffective dose and doseper fraction in fractionated radiotherapy. Thus, if thetwo terms of equation 3 are divided by α, E/α =nd(1+d[α/β]) is obtained. The parameter E/α has the dimen-sions of dose. It is known as extrapolated tolerance do-se (ETD) (Barendsen, 1982) or biologically effectivedose (BED) (Fowler, 1989). The factor in parenthesis(1 + d/[α/β]) is known as relative effectiveness (RE).Therefore, it can be written that

Biologically effective dose = total physical dose ×relative effectiveness

BED = E/α = n . d(1+d [α/β]) (Eqn. 4)

Equation 4 shows that the response to radiation is a func-tion of the α/β ratio of the irradiated tissue and the dose perfraction. In the clinical setting, it is common to assume anα/β value of 10 Gy for tumours and acutely respondingnormal tissues, and of 3 Gy for slowly responding normaltissues. In the former, radiation produces a high propor-tion of single-hit (α-type) non-repairable events, an effectthat is not dependent upon fraction size. In contrast, slowlyresponding tissues are more susceptible to interactive mul-ti-hit (β-type) ionization lesions. For this reason, slowlyresponding tissues are more damaged as d is increasedand more spared as d is reduced (Withers/Mc Bride, 1999).

Overall treatment time and biologically efective dose

Unlike the models proposed by Strandqvist and Ellis,the isoeffect BED equation does not include the irradia-

Rev Oncol 2003;5(1):49-54 51

Fig. 2. Isoeffect curves in which the total dose necessary for acertain effect in various tissues is plotted as a function of thedose per fraction. Late effets are plotted with solid lines andacute effects with dashed lines. The main point of the date isthat the isodoses for late effects increase more rapidly with adecrease in the dose per fraction that those for acute effects.From Withers HR. Cancer 1985;55:2086-95, with permission.

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52 Rev Oncol 2003;5(1):49-54

tion time. Because cell proliferation in late reacting tissues is slow or absent, the time factor for these tissuesis and should be zero. In contrast, because tumours andearly reacting tissues depend upon cells that proliferaterapidly, an exponential time factor (eγT) should be intro-duced into the isoeffect BED equation. This time factorworks in an inverse direction to the killing effect of ra-diation. Thus, for early-responding normal tissues andmalignant tumours, equations 2, 3 and 4 adopt the form

S = e–E = e-([αd + βd2] n + γT) (Eqn. 5)E = –LS = nd (α + βd) - γT (Eqn. 6)

BED = E/α = nd (1 + d/[α/β] - γ/α . T) (Eqn. 7)

In equation 7, T is the overall treatment time and γ isthe proliferation coefficient of the tumour or normal tissue. T can be replaced by T-Tx, where Tx is the timeat which proliferation begins after onset of irradiationand γ = L2/Tp, where Tp is the average doubling time ofthe tumour or normal tissue rescuing cells. In theseconditions, the isoeffect BED is given by

BED = E/α = (nd [1+d/[α/β]) - (L2 (T-Tx)/ αTp) (Eqn. 8)

This is the linear-quadratic equation with a time factorthat allows for proliferation. Examples of its use will begiven below.

Normalized total dose

A major benefit of using the linear-quadratic model toanalyse the response of tumours and normal tissues to radiation is that the effect of different fractionated regi-mens can be compared in terms of early or late reac-tions. For example, if two irradiation schedules with dif-ferent fractionation (n1d1 and n2d2) produce a similarlate response, we can write in accordance with equa-tion 3 that

E = n1d1 (α +βd1) = n2d2 (α +βd2) (Eqn. 9)E = n1d1 (α/β + d1) = n2d2 (α/β + d2) (Eqn. 10)

If we consider that d1 = 2 Gy (for a total dose [n1d1] of 70 Gy, n1 = 35), the total dose n2d2 is designated as nor-malised total dose (NTD). Thus, each total dose givenwith the dose per fraction d can be normalized to thetotal dose to which it would be biologically equivalent ifgiven in 2 Gy fractions. Under these conditions, we cantherefore write

NTD = total dose ([α/β] + d/[α/β] + 2) (Eqn. 11 )

According to this equation, if two tumours receive the sa-me NTD, they will be equally depleted of cells regardlessof the fraction dose used, all else being equal. Table 1shows the total doses that are biologically equivalent(in terms of late response) to the doses of 6,000 and 7,000cGy given at 2 Gy per fraction. As can be observed, thetotal dose required to maintain the isoeffect decreaseswith the increase in the dose per fraction.

Comparison between schedules. Early and late effects

The linear-quadratic model offers the possibility ofspecifying the effects of radiation on slowly respon-ding and acutely responding tissues (including malig-nant tumours), it enables identification of the irra-diation regimens that produce, in theory, the best tumour control rates and, finally, it can be used to determine the hypothetical therapeutic relationship (tumour control versus late complications) of irradia-tion regimens commonly used in cancer treatments.Examples of its utilisation are the following:

Early and late effects

The application of equation 4 to a standard irradiationregimen (60 Gy/6 w/5 ×2 Gy per week) yields a quanti-tative expression of the tissue response to treatment:early BED = 72 Gy10/late BED = 100 Gy3. In the sameway, the acute and late responses derived from a se-cond standard irradiation regimen of greater total dose(70 Gy/7 w/5 ×2 Gy per week) can be calculated: earlyBED = 84 G10/late BED = 117 Gy3. The subscripts 10and 3 are added to the dose values to indicate that thedoses administered are biological doses (α/β values of10 and 3 were assumed in the calculations for early andlate-responding normal tissues, respectively).

Comparison between regimens

A similar calculation method to the above demonstra-tes the greater therapeutic effectiveness (greater acuteresponse, lesser late reaction, better therapeutic rela-tionship) of a hyperfractionated irradiation regimen(80.5 Gy/7 w/ 2 ×1.15 Gy twice a day/5 days per week)in comparison with a standard high-dose schedule

TABLE 1. Radiotherapy schedules calculated to keep lateeffects constant as a function of dose per fraction (NTD at 2 Gy per fraction and α/β =3)

Dose per Total dose (cGy)

fraction (cGy)NTD 6,000 cGy NTD 7,000 cGy

120 7.140 8.330140 6.820 7.960160 6.520 7.610180 6.250 7.290200 6.000 7.000220 5.770 6.730240 5.560 6.480280 5.170 6.040300 5.000 5.830400 4.290 5.000500 3.750 4.380600 3.330 3.890

NTD: total dose ([ α/β] + d/[ α/β]+2).


Rev Oncol 2003;5(1):49-54 53

(70 Gy/7 w/5 × 2 Gy per week) (table 2). Comparisonof the Gy10 values for these two treatment schedulessuggests that the more highly fractionated scheduleshould result in a better tumour control, albeit at theexpense of a more vigorous early-responding tissuereaction (mucosal reaction in head and neck can-cers). The comparison of the Gy3 values for the tworegimens is of even greater interest. Late-respondingnormal tissue (spinal cord in head and neck cancer)would clearly benefit from the hyperfractionated regi-men and fewer complications could be expected. Clear-ly, the use of low doses per fraction offers an unde-niable advantage in the radiation treatment of cancer.

Effect of time on tumour proliferation

The BED concept can be used to quantify the influenceof cell regeneration on the effect produced by a givenfractionated irradiation regimen in a tumour or anyproliferative tissue. As irradiation decreases the survi-val of tumour cells, whereas tumour regeneration du-ring the irradiation time increases their number, thebiological effect on a malignant tumour of a fractiona-ted radiation dose (n.d) administered in a given periodof time (T) is given, in accordance with equation 7, assuming that tumour regeneration starts at a certaintime (Tx) after the onset of irradiation and is maintai-ned for time t (t= T-Tx), by the relationship:

BED = E/α = nd (1+d [α/β]) - L2/Tp. t/α (Eqn. 12)

Tp: effective tumour doubling time assuming that cellloss is zero.Assuming the standard value of α described above (α = 0.35 ± 0.1 Gy-1) and a mean Tp value of 4 days, it iseasy to demonstrate that the influence of tumour regene-ration during irradiation is equivalent to: a) 5.94 Gy10 for aconventional treatment schedule of 60 Gy/6 w, assumingthat tumour regeneration starts to be significant at four weeks after onset of irradiation (t = 40-28 = 12 days);b) 9.40 Gy10 for a regimen of 70 Gy/7 w, assuming a simi-lar regeneration process (t = 47-28 = 19 days) (Withers,1988). In both cases, the increase in total dose required tomaintain unchanged the likelihood of tumour control isapproximately 5.94/12=9.40/19= 0.5 Gy/day.

Because 2 Gy is the dose required to reduce tumour cellsurvival by a factor of 2 and the daily dose in conventio-nal radiation treatments is 2 Gy, the daily increase ofabout 0.5 Gy in the isocontrol dose can be interpreted asreflecting a doubling time of 4 days (2 Gy/ 0.5 Gy. day-1)for tumour clonogens. When compared with pre-treat-ment tumour volume-doubling times, which average 45-60 days, these data indicate that surviving tumour clono-gens can accelerate their growth to 10-15 fold pre-treatment rates. In head and neck cancer, carcinoma ofcervix, bladder cancer and lung cancer, the loss of tu-mour control derived from this effect is 0.5% to 3% foreach day the treatment is prolonged (Withers, 1999).The acceleration of tumour growth is presumably pro-duced as a response to the microenvironment sur-rounding tumour cells that survive to the irradiation(abundant cytokines, decreased ratio of tumour cellnumbers to vascular endothelial surface area, decrea-sed interstitial pressure, and an improved blood flowyielding better oxygenation and nutrition) and itsmost important clinical consequence is the avoidanceof any unnecessary protraction of standard therapy.Tumour control rates may be improved by intensifyingtreatment. This can be achieved by shortening theoverall time taken to complete a standard treatment,by adding concomitant chemotherapy without shorte-ning overall treatment duration, or by delivering hy-perfractionated doses in standard overall times. If thephysical dose is given in small fractions, the intensifi-cation of treatment translates a high biological doseto the tumour but not to the late-responding normaltissue. This is the reason for the success of therapeu-tic intensification in cancer treatment.

LIMITATIONS OF THE LINEAR-QUADRATIC MODEL

Even though the linear-quadratic model of analysis ismore robust and much better grounded in biologicalfacts than the NSD model, it remains a theoretical model.Its limitations include the following: a) no provision ismade for the influence of the cell cycle or of proliferativeor microenvironmental effects (especially hypoxia); b) itis not possible to account for differences in repair ratesbetween different tissues (important for fractionated the-rapy with short interfraction intervals and/or continuouslow-dose or pulsed high-dose brachytherapy); c) radia-tion volume effects are not considered, and d) there is lit-tle or no knowledge on its application to patients recei-ving both radiation and chemotherapy. Despite theselimitations, the contribution of the linear-quadratic mo-del to the development of the clinical radiotherapy ofcancer in the last few years can be considered decisive.

SUMMARY AND CONCLUSIONS

The irradiation time and the dose per fraction are twokey parameters in the fractionated therapy of patients

TABLE 2. Comparison between schedules. Early and late effects

Standard treatment (n = 35; d = 2 Gy)Early BED = E/ α = 70 (1 + 2/10) = 84 Gy 10Late BED = E/ α = 70 (1 + 2/3) = 116 Gy 3

Hyperfractionated treatment (n = 70; d = 1.15 Gy)Early BED = E/ α = 80.5 (1 + 1.15/10) = 90 Gy 10Late BED = E/ α = 80.5 (1 + 1.15/3) = 111 Gy 3

Tumour effect: 90/84: 107%Late response: 111/116: 95%Therapeutic gain: 1.07/0.95: 12%

BED: nd (1 + d/[ α/β]).


54 Rev Oncol 2003;5(1):49-54

with cancer. Reduction of the total treatment time andthe use of low doses per fraction lead to improve-ments in the therapeutic relationship in cancer of thehead and neck and at other tumour localisations ofepithelial origin. The introduction of the linear-qua-dratic model and the biologically effective dose con-cept into the clinical setting has enabled quantitativeanalysis of the biological effects of radiation on malig-nant tumours and on acutely and slowly respondingtissues, notably enhancing the perception of rela-tionships between basic phenomena and clinical data.As a result, new and better irradiation regimens havebeen developed for the treatment of patients with spe-cific tumours.

Recommended references

Baclesse F. Clinical experience with ultrafractionated radio-therapy. Progress in radiation therapy. New York: GruneStratton; 1958. p. 128-48.Barendsen GW. Dose fractionation, dose rate and isoeffectrelationships for normal tissue response. Int J Radiat OncolBiol Phys 1982;8:1982-97.Coutard H. Roentgentherapy of epitheliomas of the tonsillarregion, hypopharynx and larynx from 1920 to 1926. Am J Roentgenol 1932;28:313-31.

Elkind MM, Sutton H. X-ray damage and recovery in mam-malian cells in culture. Nature 1959;184:1293-5.Ellis F. Dose, time and fractionation. A clinical hypothesis.Clin Radiol 1969;20:1-7.Fowler JF. The linear-quadratic formula and progress infractionated radiotherapy. Br J Radiol 1989;62:679-84.Hall EJ. Time, dose and fractionation in radiotherapy. En:Hall EJ, editor. Radiobiology for the radiologist. 5.ª ed. Phila-delphia: Lippincott Williams Wilkins; 2000. p. 397-418.Joiner MC, van der Kogel AJ. The linear-quadratic approachto fractionation and calculation of isoeffect relationships. En:Steel GG, editor. Basic Clinical Radiobiology. London: Ar-nold; 1997. p. 106-22.Paterson R. The treatment of malignant disease by radiothe-rapy. Baltimore: Williams Wilkins; 1963.Puck TT, Markus PI. Actions of X-rays on mammalian cells.J Exp Med 1956;103(5):653-66.Strandqvist M. Studien uber die kumulative wirkung der roentgenstrahlen bei fractionierung. Acta Radiol (Stock-holm) 1944; Suppl 55:1-300.Withers HR. Biological basis for altered fractionation sche-dules. Cancer 1985;55:2086-95.Withers HR. Radiation biology and treatment options in ra-diation oncology. Cancer Res 1999;59:1676-84.Withers HR, McBride W. Radiation effects on normal tissues.Front Radiat Ther Oncol 1999;32:1-8.Withers HR, Taylor JMG, Maciejewski B. The hazard of ac-celerated tumour clonogen repopulation during radiothe-rapy. Acta Oncol 1988;27:131-46.

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Dose-time relationships in fractionated radiotherapy for cancer