2002 co practical methods for compensating for missed treatment days in radiotherapy, with...

8/20/2019 2002 CO Practical Methods for Compensating for Missed Treatment Days in Radiotherapy, With Particular Referen…

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Clinical Oncology (2002) 14: 382–393doi:10.1053/clon.2002.0111, available online at http://www.idealibrary.com on

Original Article

Practical Methods for Compensating for Missed TreatmentDays in Radiotherapy, with Particular Reference to Head

and Neck Schedules

R. G. Dale*, J. H. Hendry†, B. Jones*, A. G. Robertson‡, C. Deehan§,J. A. Sinclair*

*Hammersmith Hospitals NHS Trust/Imperial College School of Medicine, London, U.K.; †Paterson Institute forCancer Research, Christie Hospital NHS Trust, Manchester, U.K.; ‡Beatson Oncology Centre, Western Infirmary,

Glasgow, U.K.; §Department of Medical Physics, Leicester Royal Infirmary, Leicester, U.K.

ABSTRACT:Unscheduled interruption of a radiotherapy treatment can lead to significant loss in local tumour control, particularly in tumoursthat 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 thesemethods. It sets out the main considerations arising in the especially critical case of head and neck treatments and simplecalculations are used to illustrate the approaches which may be adapted for particular situations. Radiobiological parameter valuesare suggested for use in the calculations, but these may require modification in the light of further research in this important area.Dale, R. G. et al . (2002). Clinical Oncology 14, 382–393

2002 The Royal College of Radiologists. Published by Elsevier Science Ltd. All rights reserved.

Key words: Cancer, cell kinetics, fractionation, overall time, radiotherapy, time factors in radiotherapy, treatment interruptions

Received: 5 July 2001 Accepted: 2 May 2002

Introduction

Local tumour control can be adversely aff ected byprolongation of overall treatment time in radiotherapy.A number of studies have highlighted that tumour cellrepopulation can produce losses in local control which,particularly for squamous cell cancers of the head andneck region, may amount to 1–2% per day of treatmentprolongation [1,2]. Similarly, recent studies on non-small cell lung cancer and cervix carcinoma have indi-cated respectively 1.6% and 0.8% loss of local controlper day of treatment extension [3,4]. Adherence to

radiotherapy schedules is therefore important if individ-ual treatments are not to be compromised. However,there are occasions when unforeseen interruptionsoccur, prime causes being equipment breakdown orunwell patients and the Royal College of Radiologists(RCR) in 1996 issued guidelines for dealing withunscheduled treatment interruptions [5]. In parallel withthese guidelines a more detailed review of the evidencefor the deleterious eff ects of treatment prolongation was

published, together with a comparative assessment of the methods available for the compensation of missedtreatment days [1].

Many U.K. departments have since implementedmeasures for handling unscheduled treatment interrup-tions and the evolving experience has highlighted thatsome difficulties remain, particularly with respect toterminology and in relation to how to use the variousradiobiological parameter values. This article reiteratessome of the points previously discussed [1], but inaddition it specifically elaborates on the practical issues

which arise when devising compensations for inter-rupted treatments. Although some methods of treatmentcompensation are clearly preferable to others, practicalfactors (machine availability, ability of centres to workextended hours and/or weekends, ability of an unwellpatient to undergo the full compensation, etc.) alsoinfluence the decision regarding which form of compen-sation to adopt. It is therefore of some importance(particularly in more difficult cases) to examine two orthree possible solutions in order to identify a compro-mise scheme which helps the patient without causingsevere disruption to local service arrangements. Themethods described below are those to be considered

Author for correspondence: Dr R. G. Dale, Radiation, Physics &Radiobiology, Charing Cross Hospital, London W6 8RF, U.K.E-mail: [email protected]

0936–6555/02/040382+ 12 $35.00/0 2002 The Royal College of Radiologists. Published by Elsevier Science Ltd. All rights reserved.


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when technical failures have caused the interruption.For gaps resulting from adverse clinical reactions themethodology is the same but the condition of the patientmay mean that it is not always possible to compensate tothe same extent. Although this paper concentrates onhead and neck squamous cell cancer, the methodologyis applicable to other sites provided appropriatealternative parameter values are used.

Influence of unscheduled treatment interruptions on tumour

repopulationFigure 1 is a simplified diagram showing how the total(physical) dose for a given tumour response (e.g. 50%tumour control probability when the dose is delivered in2 Gy fractions) is assumed to vary with treatment time.If the treatment is completed before the initiation of accelerated repopulation (denoted by the rising linebeginning at time T delay) then the dose required in thisregion is fixed and is independent of the treatment timeused. If, however, the treatment is of duration greaterthan T delay days, the iso-eff ect dose increases in order tocompensate for the consequent tumour repopulation,the dose in this region now being time-dependent. The

dose prescribed in schedules which extend beyond T delaydays will inherently include extra dose to compensate forthe repopulation eff ect.

Figure 2 illustrates a prescribed treatment which isscheduled to be completed at time T . If there occurs anunscheduled interruption of duration t days during thetreatment, and no allowance is immediately made forthis, then the treatment will need to be extended byt days at the end of the prescribed schedule. To maintainthe tumour iso-eff ect would require the addition of extra dose, incurring an associated penalty (impairedTherapeutic Index) in terms of a higher normal tissuedose. To prevent overdosing of the normal tissue would

require that the supplementary tumour dose be reduced,also with detrimental eff ect.

If, however, the unscheduled interruption could becompensated for by delivering the ‘missing’ dose (byextra daily fractions, or weekend treatments), withoutextending thetreatment duration, no such penalty wouldbe incurred. This demonstrates an important point: it isthe likelihood of extension to the treatment time, ratherthan the gap per se, which is the main cause for concernwhen interruptions occur. A further point is thatunscheduled gaps occurring early in treatment (before

the onset of tumour repopulation), if they lead to atreatment extension, are assumed to be no less detrimen-tal (on current evidence) than those occurring later intreatment. The diff erence between an early- and late-interruption is practical rather than radiobiological:with the former more time remains within the prescribedschedule to eff ect a satisfactory compensation.

More detailed schematics illustrating the problems of treatment interruptions have been published elsewhere[6 – 8].

Equations

The biologically eff ective dose (BED) received bya uniformly irradiated tissue which is concurrentlyrepopulating is calculated as:

where n is the number of fractions, d is the dose perfraction, T is the overall treatment time. T delay is thedelay time (from the beginning of treatment) before theonset of significant repopulation [9]. / (in units of Gy)is the fractionation factor and K (in units of Gy day1)is the biological dose per day required to compensate for

Fig. 1 – Schematic showing how the total dose required for a given tumour control probability (TCP) changes with increasingtreatment duration. The horizontal and sloped lines demonstrate how the dose rises steadily after an initial delay period.

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on-going tumour cell repopulation. K is the BED-equivalent of 1 days worth of repopulation [9]. Theexpression in square brackets in Eqn (1) is termed theRelative Eff ectiveness factor (RE).

Both / and K are tissue-specific and appropriatevalues must be selected for each when calculating

tumour BEDs.As applied to a tumour, Eqn (1) may be rememberedin words as:

BED=Total physical dose RE–Repopulation Factor(RF)

For most late-responding normal tissues the prolifer-ation rate is usually so small (except in cases whereconsequential late reactions are dose-limiting [10])that K can be neglected, i.e. K =0 and RF=0 in suchcases.

It has become conventional practice to place the / value used in the BED calculation as a subscript to both,

the BED symbol and its associated numerical value. Forexample, a stated BED3 of 100 Gy3 indicates that/ =3 Gy was used in calculating that particular biologi-cal dose. The use of the subscript reinforces the pointthat biological dose is conceptually diff erent to physicaldose, even though both are in similar dimensions. Bio-logical doses expressed in (for example) Gy10 can beadded to other Gy10 values to provide a measureof resultant eff ect, but it is not permissible to add (say)Gy3 values to Gy10 values.

Eqn (1) is valid in cases where the fractions arerelatively well-spaced. When two or more fractions aredelivered per day there may be incomplete repair of

sub-lethal damage between successive fractions, leadingto increased biological damage [11]. This is particularlyso withregard to late reactions. In such cases Eqn (1) ischanged to:

Factor h in Eqn (4) reflects the increased damage causedby incomplete repair. It is complex in form and isdependent on the inter-fraction intervals (which are notusually the same between all fractions) and the repairkinetics. The derivation of the h factor is discussed in theAppendix. There may be occasions when compensationfor unscheduled treatment gaps will involve the use of many relatively close fractions (less than 8 h betweenfractions) and, in such cases, the eff ects of incompleterepair should be borne in mind. If there is to be morethan one day on which twice-or thrice daily fraction-

ation is required then, where possible, such days shouldnot be consecutive. It is recommended that allowancesfor incomplete-repair should always be included whenthe use of four or more closely-spaced fractions isunavoidable. A later example (Example 5) will illustratesome of the issues involved.

Eqns (1) and (2) provide the basis for devising com-pensation for unscheduled treatment interruptions, butthere are many instances where they need to be utilizedin a slightly diff erent form. Rather than list a family of related equations, the methodology appropriate to par-ticular circumstances will be explained in the workedexamples.

Fig. 2 – Showing the eff ect of a treatment extension, caused by an earlier unscheduled gap. If the treatment extends into the timeperiod where steady tumour repopulation is occurring, extra dose (X) is required to compensate for this. It should be noted that thiswill be the case even if, as here, the unscheduled gap occurred during the period prior to the initiation of tumour repopulation.

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Recommended values of /, K and Tdelay

The range of / values usually considered for head andneck cancers is around 10–20 Gy [12]. A preliminaryanalysis of the recently reported RTOG9003 head andneck trial indicates a value just below the bottom end of

this range [13]. We therefore suggest that a generic / value of 10 Gy be used for head and neck cancers, butthis figure should be kept under review.

For late-responding normal tissues a generic / of 3 Gy is generally recommended. The important excep-tions to this are brain and spinal cord, for each of whichan / value of 2 Gy should be used, reduced furtherto 1.5 Gy when fraction sizes greater than 2 Gy areemployed. A reduced / of 2.5 Gy may also be prefer-able for normal tissues in cases where there are concernsthat tolerance may be clinically compromised [11]. Acomprehensive tabulation of / values for various nor-mal tissue and tumours can be found in the chapter by

Joiner and van der Kogel in reference [14].The data reviewed for the previous Clinical Oncologyarticle on gap compensation [1] indicated that head andneck K factors were in the range 0.5–0.74 Gy day1. Sincethen more sophisticated analyses of multi-centre data haveshown that K values are likely to be higher than originallybelieved. Roberts and Hendry [15] have conducted a meta-analysis of larynx treatment results from Edinburgh,Glasgow, Manchester and Toronto, leading to an upwardlyrevised K estimate of 1.2 (95% CL 0.8–2.2) Gy day1. Theresults of the RTOG9003 head and neck trial [16] alsolend support to the likelihood of higher K values withearly analyses of those data suggesting K values of 0.94–0.99 Gy day1 [13,17].

The head and neck tumour control data collated byWithers et al . [12] demonstrated a ‘dog-leg’ eff ect of the type illustrated in Fig. 1 and have been analysed indetail by Hendry and Roberts [18], who found therepopulation delay time (T delay) to be 29 (95% CL17–31) days. For the shorter Manchester treatmentregimes the delay time was established as 26 (95% CL19–33) days.

On the basis of the above, and bearing in mind therelatively large confidence intervals and the fact that thefitted values of K and T delay must be used together, wesuggest that respective working values of 0.9 Gy day1

and 28 days be adopted for head and neck cancers. It is

stressed that neither of these recommended values canyet be considered as definitive and that they must bereviewed in the light of continuing research.

The recommended K value of 0.9 Gy day1 repre-sents the BED required each day (after T delay has beenpassed) to off set repopulation. If / for tumours istaken as 10 Gy then, more specifically, K is the BED-equivalent of repopulation in units of Gy10 per day. Thismeans that, when 2 Gy fractions are being used, thedaily physical dose required to off set the repopulationafter time T delay is K /[1+2/10]=0.75 Gy day

1, i.e. foreach 2 Gy fraction delivered, (0.75/2)100=38% iswasted in combating repopulation.

Values of K and T delay are derived on the basis thatthere is an intrinsic pairing between them. This arisesbecause there is an a priori assumption that there is zeropopulation in the period up to T delay, meaning that thepaired parameter values provide the best fit to theobserved increases in dose over the whole range of

treatment times studied.The data relating to time factors and the eff ects of

gaps for head and neck treatments were reviewed up to1996 in the previous article [1]. That review discussed thefact that the time factor was approximately the sameduring protracted treatments as in split-course treat-ments and that there were contradictory suggestionsregarding the relative importance of gaps early or late inthe schedule. Since 1996 the importance of treatmentinterruptions in radiotherapy for oropharyngeal carci-nomas has been highlighted [19]. Evidence has alsoemerged that the position of the gap is not importantand that the loss of tumour control following each day

of interruption of a head and neck treatment is aboutthe same as occurs when conventional schedules areprotracted [20,21]. The latter feature was confirmed in ahuman xenograft tumour model in mice [22]. In con-trast, in rat tumours it has been shown that the positionof the gap does matter [23]. Regarding the combinationof chemotherapy and radiotherapy, there are reports of a lack of a time factor in alternating chemoradiotherapyfor advanced head and neck squamous cell carcinoma[24]. Long gaps were found to be detrimental to localcontrol in anal canal carcinoma treated by split-courseradiotherapy and concomitant chemotherapy [25].

As discussed earlier, the assumptions in the head andneck data fitting exercises inherently excluded the possi-

bility of there being any repopulation in the period up tothe T delay time point, but that does not mean thatrepopulation does not occur in that time. Indeed, otheranalyses suggest that repopulation does occur from thebeginning of treatment [26]. There thus arises the ques-tion of what K factor should be used in interruptedtreatments for which the final overall time is less thanT delay. Withers et al . [12] suggested that the repopulationrate during the early part of treatment reflected thepre-treatment tumour growth-rate. Examination of theslopes before and after the delay time suggests they arein the approximate ratio 1:10, i.e. that the K value to use prior to T delay is one-tenth that used after the delay

point. For head and neck treatments we therefore rec-ommend K =0.1 Gy day1 and T delay=0 in cases wherethe final overall times are less that 28 days. It isemphasized that these values are suggested on the basisof the evidence currently available; they cannot beregarded as being definitive.

Although the methodology described in this paper ismore widely applicable, there is at present very little datarelating to K and T delay factors for other tumour types.For non-small-cell lung tumours there is evidence thatthe loss of local control per day towards the end of treatment is about the same as that for head and neckcancers [3,27]. For cervix tumours the time factors are

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probably around half those for head and neck tumours,i.e. 0.5 Gy day1 [1]. For breast tumours the K fac-tors are likely to be around 0.3 Gy day1 while forprostate tumours they are likely to be in the region0.1–0.3 Gy day1, or even lower [28 – 30]. Little isknown about the corresponding values of T delay.

Calculation process

The table below (based on reference [1]) identifies themain methods for compensation and the associatedbenefits and difficulties.

Interrupted treatments need to be evaluated on anindividual basis and there is no universal method fortackling all problems. However, most examples willinvolve a series of general steps which may besummarized as follows:

Once an unscheduled gap has occurred, first determine

the remaining treatment time and the number of frac-tions still to be delivered. Determine if there are ways of delivering these fractions to allow the originally pre-scribed treatment time to be maintained, e.g. by treatingat weekends or by giving all or part of the remainingtreatment twice-daily. If this is possible then furtherradiobiological calculations may not be necessary. (Ex-amples 1 and 2 below relate to such a case). If thisoption is not feasible (i.e. it is not possible to completetreatment within the prescribed treatment time) then:

(1) First calculate the tumour and normal tissueBEDs for the prescribed schedule. Both BEDs are

calculated via Eqn (1) but, for the late-reactingnormal tissue, K is set to zero.

(2) Determine the overall time until the beginning of the unscheduled gap and, hence, the respectivepre-gap BEDs.

(3) Determine the late-normal BED ‘still to give’ (the

post-gap BED).(4) Review the various treatment options (e.g.

twice-daily fractionation and hyperfractionation,increased fraction sizes, etc.) to ascertain which willbe likely to produce the minimum extension to thetreatment time, then calculate the required dose per

fraction to achieve the required late-normal BEDvalue. Calculate the resulting tumour BED for thisoption, remembering to make allowance for theextended time (Example 3–6 below demonstratevarious versions of this scenario).

(5) Review the final tumour and normal tissue BEDswhich will result from the preferred compensation

option. If the tumour BED is significantly smallerthan that originally prescribed a degree of clinical judgement may be required in order to ‘fine tune’the compensation in order to arrive at a reasonablecompromise. (Examples 4–6 illustrate the dilemmaswhich may be involved in such cases).

It is stressed that these are general steps. For example, if the favoured compensation option involves closely-spaced fractions after the gap, the modified BED for-mula [Eqn (2)] must be used to determine the possibleenhancement to normal tissue toxicity as a consequenceof incomplete-repair. It is suggested that if a total of four

Method Benefit Difficulty

(1a) Retain overall time and dose per fractionby treating on weekend days as necessary.

Overall time, fraction size, inter-fractioninterval and Therapeutic Index maintained.

Unsocial hours and associated costs. May notbe appropriate for gaps occurring near the

end of a schedule.(1b) Retain overall time and dose per fractionby treating twice-daily as necessary.

Overall time and fraction size maintained. Possible loss of late-normal tissue tolerancewhen several fractions have to be delivered at6–8 h inter-fraction intervals. Schedulingdifficulties.

(2a) Retain overall time by increasing doseper fraction for same number of post-gapdays as there were gap days.

Overall time retained by accepting reducednumber of fractions. Still one fraction on eachtreatment day.

Not suitable for schedules which already usehigh dose per fraction. Therapeutic Indexadversely aff ected: Seeking equivalence fortumour control gives increase in latereactions. Seeking equivalence forlate-reactions leads to tumour under-dosage.

(2b) Retain overall time by using smallernumber of larger fractions after the gap.

Overall time retained. Still one fraction perday.

As above.

(3a) Accept that treatment extension isunavoidable and deliver extra fractions, using

increased dose per fraction to minimize theextension duration.

Allows at least partial restoration of theprescribed schedule.

Therapeutic Index adversely aff ected. Mightrequire acceptance of both reduced tumour

control and increased late-eff ects.

(3b) As for 3(a) but use twice-daily fractionsand a slightly reduced treatment extension.

As above. As for 3(a), but deterioration in TherapeuticIndex is not so marked.

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fractions or more are to be given at twice-daily intervals(or more frequently) then the eff ects of incomplete repairshould always be considered.

Worked examples

Worked examples 1–3 each consider the handling of 5-day gaps. In practice the majority of unscheduledinterruptions involve interruptions of 5 days or less andare relatively easy to deal with. With a gap of just 1 or2 days diff erent policies may apply in diff erent centres.

Examples 1–5 involve a reference schedule of 70 Gydelivered in 35 fractions over 46 days, typically used forCategory 1 head and neck tumours. The overall time of 46 days corresponds to a treatment beginning on aMonday, continues with daily-fractionation for 7 weekswith no treatment at weekends and finishes on a Friday.For a similar 35 fraction schedule which begins mid-week the treatment time will be longer (because the

treatment will extend into an eighth week) and specificcalculations should allow for this.For other schedules, e.g. the commonly used 4-week

treatments, the principle involved in determining amethod of compensation is exactly the same as set out inthe 7-week treatments used here. In such cases, however,there is more concern about b.i.d treatments if the doseper fraction is already significantly larger than 2 Gy,because of the greater potential for incomplete repair.Example 6 elaborates on this and also discusses atreatment which does not begin on a Monday.

In all the examples requiring calculations, the processhere has been to devise a compensation scheme tomaintain the desired late-reacting BED and then, as

necessary, to consider alternatives in the light of howmuch the resultant tumour BED is compromised. This isdone because late morbidity is often the most criticalconcern in radiotherapy and some normal tissue para-meter values are more reliably known than those fortumours. Also, because late-responding tissues areassociated with less heterogeneity than tumours theyoften exhibit steeper dose-response curves, i.e. anydeviations from the BEDs associated with the originalschedule will be more critical for the normal tissues.Notwithstanding this view, however, there may beinstances where clinicians decide from the outset toaccept the risk of an elevated late-normal BED in order

to maintain a desired tumour eff

ect.

Example 1. Loss of all of the third week (five fractions) of atreatment schedule of 70 Gy/35 fractions/46 days.

Assuming the treatment began on a Monday, theintended overall treatment time is 46 days. After the gap,treatment resumes on the Monday of the fourth week of the schedule. Ten fractions have been delivered; 25remain to be given. If treatment is to be completed onthe prescribed finishing date the available number of days (including weekends) is 26. Thus the missed dosein the gap can be compensated for by delivering the

remainder of the treatment on weekdays (20 fractions)and on five of the six remaining weekend days. Thisdoes not involve changing the fraction size and, asthe treatment is not extended, constitutes a ‘good’compensation.

If weekend treatments are not feasible a good com-

pensation is still possible if, on five of the 20 remainingtreatment days, two fractions are delivered instead of one. The important proviso is that the twice-daily frac-tions must be delivered with a minimum time gapbetween them of at least 6 h, preferably 8 h, in order tominimize any potential problems with incomplete repair[31]. It is further recommended that the days on whichtwice-daily treatments are delivered are not consecutive,but spaced throughout the available time period. In thisinstance Fridays are a good choice for delivery of someof the twice-daily fractions as there is a greater oppor-tunity for completion of repair before treatment resumesthe following week.

Example 2. Loss of all of the sixth week (five fractions) of atreatment schedule of 70 Gy/35 fractions/46 days.

After the gap, treatment resumes on the Monday of theseventh week of the schedule. Twenty-five fractions havebeen delivered; 10 remain to be given. Ideally these 10fractions should be delivered over the five remainingtreatment days. The missed dose can therefore becompensated for by delivering the remainder of thetreatment as twice-daily fractions in each weekdayof the final week. This does not involve changing thefraction size and, as the treatment is not extended,constitutes a good compensation. A better solution, if feasible, would be also to make use of the weekendbefore the final week of treatment, thus providing 7 dayswithin which 10 fractions have to be delivered. Bi-dailyfractionation could be used (for example) on Monday,Wednesday and Friday, single fractions on the other4 days. The advantage of the latter scheme is thatit reduces the likelihood of creating excess biologicaldamage if there is incomplete repair between fractions.

Examples 1 and 2 represent sound solutions fordealing with unscheduled interruptions; they do notinvolve changing fraction size or overall time and,provided there is reasonable spacing between treatmentdays on which bi-daily treatment is given, do not invoke

any quantitative evaluations or serious radiobio-logical dilemmas. The following examples illustrate thecompromises involved in more difficult cases.

Example 3. Loss of all of the seventh week (five fractions)of a treatment schedule of 70 Gy/35 fractions/46 days.

For the prescribed treatment the normal tissue BED(BED3) is, from Eqn (1) with K=0:

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The tumour BED (BED10), also from Eqn (1) but withK =0.9 and T delay=28 days is:

In this example the unscheduled gap extends to the timewhen treatment should have finished and any form of compensation will therefore extend the treatment timebeyond the scheduled time.

We begin by assuming that the missing dose isreplaced by treating five 2 Gy fractions over a full extra(eighth) week, beginning on a Monday. On completion,the overall time is 7 days longer than scheduled. Witha daily BED-equivalent of tumour repopulation of 0.9 Gy day1 the tumour BED10 will be lower thanintended by an amount 70.9=6.3 Gy10. The late-normal BED3 will be as prescribed.

If, instead, the outstanding daily treatments are givenin the period Saturday–Wednesday, the net treatmentextension is 5 days, i.e. the tumour BED10 is low by asmaller factor of 50.9=4.5 Gy10. A further alternativeis to treat two fractions per day on Saturday andMonday with one fraction on Sunday, thus extendingtreatment by 3 days. In this case the tumour BED10 willbe low by an even smaller amount of 30.9=2.7 Gy10.In each of these instances the normal tissue BED3 will beas prescribed.

The dilemmas arise when attempts are made toincrease the total dose in order to restore the tumourBED10 to that originally prescribed; in this case it isimpossible to do that without increasing the normal

tissue BED3 [8]. Delivering extra dose by treating withextra fractions has the eff ect of further extending thetreatment time, which may compound the original prob-lem. Increasing the dose per fraction helps minimize thetreatment extension but, because of the greater sensitiv-ity of the late-responding critical tissue to changes indose per fractions, will increase the normal tissue bio-logical dose proportionately more than that for thetumour.

We next consider an instance where it is felt essentialto restore the tumour BED10 to what it should be,initially without regard for the eff ect on the normaltissue. We assume the option of treating additionallyover the weekend is to be adopted, i.e. the overall time is46+5=51 days.

The tumour BED10 of 67.8 Gy10 is to be maintained.Therefore, for the whole schedule (pre-gap plus post-gap):

BED10 (pre-gap)+BED10 (post-gap)–TumourRepopulation Factor=Required BED10

where d is the new value of dose per fraction to beutilized over the five fractions. The solution for d inthe above equation is d =2.62 Gy, i.e. 52.62 Gy willrestore the tumour BED10 to that initially prescribed.Again it should be noted that the required extra BED10of (50.9)=4.5 Gy10 cannot be added simply pro-rata

across the five 2 Gy fractions. The values of the biologi-cal Gy10 and the physical Gy units are diff erent and theycannot be added; to do so would lead to an even higherfraction dose of 2.9 Gy. This and other subtleties associ-ated with the use BED-equivalents has been discussed inmore depth elsewhere [9,11].

For the normal tissue, the compensated treatmentincreases the BED3 to:

BED3 (pre-gap)+BED3 (post-gap)

i.e.

Thus the revised treatment delivers a 6.7% excess innormal tissue BED3. To evaluate what this compensatedscheme would mean in terms of the equivalent dosein a schedule delivered with 2 Gy fractions we notethat, by re-arrangement of Eqn (1) and omitting therepopulation factor:

i.e. the total dose in 2 Gy fractions would be 74.7 Gy.Thus, the given normal tissue BED3 is approximatelyequivalent to 372 Gy fractions.

If the normal tissue dose is considered too high it ispossible to ‘split the diff erence’, i.e. aim to achieve atumour BED10 which is a little less than that prescribedwhilst accepting a small increase in normal tissue BED3.Such a result may be arrived at by trial and errorprocessing of diff erent values of dose per fraction. Forinstance, in the above example an intermediate dose perfraction of 2.3 Gy would deliver a total tumour BED10of:

BED10 (pre-gap)+BED10 (post-gap)–TumourRepopulation Factor

i.e.

The normal tissue BED is:


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i.e.

Thus, with 2.3 Gy fractions in the compensation, thetumour and normal tissue BEDs are respectively 3.5%lower and 3.1% higher than for the uninterrupted sched-ule. The eff ects of higher or lower values of dose perfraction could be tested, as appropriate, using the sameprocess. It is stressed that the process of hypofraction-ating treatment after the gap is not necessarily the bestoption: a better result is likely to be obtained if someextra fractions can be used (via bi-daily fractionation) inorder to further reduce fraction size.

Worked examples for more complex cases

Unscheduled interruptions of longer than 5 days aregenerally more difficult to deal with as there is lesschance of completing treatment without incurring asignificant extension of the treatment time. Thefollowing examples highlight such cases.

Example 4. Loss of all of the sixth and seventh weeks(10 fractions) of a treatment schedule of 70 Gy/35 fractions/ 46 days.

As in Example 3, the unscheduled gap runs right up to

the time when treatment should have finished. In thiscase however, a very significant part of the treatment hasyet to be delivered. In order to minimize the consequentextension to treatment time it is inevitable that anincreased dose per fraction will need to be considered if treatment is to be delivered in once-daily fractions.

We initially attempt to complete treatment in fivefractions delivered during the eighth week, i.e. thetreatment time is extended by 7 days to 53 days. We firstaim to match the prescribed late-normal tissue BED3(116.7 Gy3), i.e. the dose per fraction to use is d , where d is solved from:

BED3 (pre-gap)+BED3 (post-gap)=Required BED3.

i.e.

for which d =3.22 Gy.This same dose per fraction would produce a resultant

tumour BED10 of:


i.e.

Thus, despite using a relatively large dose per fractionfor the last five fractions, the resultant tumour BED10 is13.2% less than prescribed. If the weekend prior to theeighth treatment week is used for treatment then sevenfractions may be delivered, leading to a fractional doseof 2.57 Gy and a tumour BED10 of 60.1 Gy10. If 11fractions are distributed over the seven available treat-ment days (by treating bi-daily on four of them) therequired fractional dose drops to 1.87 Gy, the tumourBED10 then being 61.9 Gy10. This latter value is still8.7% short of the prescribed tumour BED10 (67.8 Gy10),thus some degree of compromise, achieved by increasingdose per fraction as illustrated in the previous example,might be considered. In extreme cases thrice-dailyfractionation could be considered, but only after care-ful consideration of the potential for detriment fromincomplete repair.

If weekend or twice-daily fractionation cannot beaccommodated then it might be considered to treat theremaining treatment over two full working weeks, i.e.extend treatment into an eighth and ninth week, makingthe overall treatment time 46+14=60 days. For this thedose per fraction (d) ideally required to maintain thetumour BED10 is obtained from:

BED10 (pre-gap)+BED10 (post-gap)–Tumour

Repopulation Factor

i.e.

for which d =2.85 Gy, leading to an associated BED3 of 138.9 Gy3, which is 19% higher than prescribed. Thisresult demonstrates the alternative dilemma associatedwith further extending the treatment in order to avoidweekend and twice-daily treatments: the total dose to be

delivered is again increased by the extension into theninth week, with a consequently incurred penalty toBED3.

Example 5. Loss of the final 13 fractions of a treatment schedule of 70 Gy/35 fractions/46 days.

This represents a very difficult case. As a compromisebetween minimizing the extension whilst at the sametime ensuring that a reasonable number of fractions areused we assume that 10 post-gap fractions will be given,twice daily from Saturday to Wednesday, extending the

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treatment to 46+5=51 days. We first consider that theeff ect of incomplete repair is negligible, i.e. that Eqn (1)remains valid. The relevant equation to determine thedose per fraction (d ) to maintain the prescribed normaltissue BED3 (116.7 Gy3) is:

BED3 (pre-gap)+BED3 (post-gap)=Required BED3

i.e.

For which d =2.41 Gy. The resultant tumour BED10would then be:


i.e.

To allow for the possibility of incomplete repair in thecritical normal tissue Eqn (2) is used for calculatingthe post-gap BED3. Eqn (2) requires prior evaluation of the h factor, which in turn requires an assumption to bemade about the nature of the repair kinetics. Mono-exponential repair half-times for late-normal tissues are

often assumed to be of the order of 1.5 h, but there isevidence that they may be longer for head and neckmorbidity. Bentzen et al . [31] investigated the repairhalf-times of three normal tissue end-points from ananalysis of the CHART head and neck data and foundthese to be in the range 3.8–4.9 h. Taking a mid-rangevalue of 4.5 h, this corresponds to an exponential repairrate () of 0.15 h1. (The repair rate is related to repairhalf-time via: =0.693/half-time). If the post-gap dailyfractions are 6 h apart and there is an 18-h overnightgap, it is easier to calculate h only for the shorter timeinterval between any two adjacent fractions. This isbecause the incomplete repair after the longer (18 h)gaps is relatively negligible compared with that following

each 6-h gap. Referring to the Appendix, and using Eqn(A1) with N=2, =6 h and =0.15 h1, h is calculatedto be 0.407. The normal tissue BED3 then becomes fromEqns (1) and (2) with K =0:


i.e.

This is 6.7% higher than the value calculated whenincomplete repair is ignored. If the twice-daily fractionswere to be spaced at 4-h intervals then the h factor is0.549 and BED3 increases further to 127.4 Gy3, 9.1%higher than when incomplete repair is ignored. (Becausethe h factors are based only on the shorter inter-fraction

intervals the consequent BED3 values are slightly under-estimated as there will be an additional amount of incomplete repair following the longer, overnight, inter-vals. This ‘overnight’ contribution will become moresignificant as the number of successive days on whichmultiple treatment is delivered is increased.)

It has been speculated [33,34] that the sub-lethaldamage repair may not be exponential in form (asconventionally assumed) but may proceed at a slowerrate than is predicted by a single exponential function. A‘reciprocal time’ model of repair, built on this supposi-tion, has been found to give an excellent fit a to a widerange of experimental repair data and, unlike models

based on the mono-exponential repair mechanism, helpsexplain the cases of radiation myelopathy observed inthe CHART trial [35]. The h factors in the reciprocaltime model may be calculated from Eqn (A2) in theAppendix and used directly in Eqn (4). Bi-phasic andother stretched functions have also been developed [36].

Example 6. A nominal 4-week schedule beginning on aWednesday is prescribed as 54 Gy/20 fractions/27days. As the

patient is too unwell for the last seven fractions to be treated on schedule their deferment extends eventual completion of treatment to 38 days.

This treatment began on a Wednesday and the expected

treatment time (with no treatment at weekends) is 27days, rather than 25 days if it had began on a Monday.

The prescribed normal tissue BED3 is:

Because the overall time is extended from 27 to 38 dayswe assume for calculation purposes that K is zero in thetime up to 28 days and 0.9 Gy day1 thereafter. Theprescribed tumour BED is therefore:

The interruption extends the overall time to 38 days. If the seven outstanding fractions were treated at theoriginal fraction size (2.8 Gy) the late-reaction normaltissue BED3 would be unaltered. However, the tumourBED10 will be compromised because the treatment hasextended beyond the 28 days at which time fastertumour repopulation is assumed to begin.

The tumour BED10 would then be calculated from:


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i.e.

a reduction of 13.1%.In short-duration treatments of this type the dose

per fraction is already relatively large and any furtherincrease (as may be required to strike a balance betweennormal tissue and tumour BEDs) should be consideredwith caution. As an example, to achieve a tumourBED10 with an intermediate value 65.0 Gy10 requires adose per fraction (d) which is obtained from:

BED10 (pre-gap)+BED10 (post-gap)–TumourRepopulation Factor=Required BED10

i.e.

i.e. d=3.19 Gy per fraction.Use of this fraction size for the deferred seven

treatments would increase the normal tissue BED3 to:


i.e.

which is still 10% more than that prescribed, eventhough the tumour BED10 has been deliberatelycompromised.

A final difficulty with interrupted schedules whichalready employ large fraction sizes is that the scope forpost-gap acceleration using twice-daily treatments islimited on account of the large total daily doses whichwould result. In this particular example, bi-daily frac-

tionation would deliver a total daily dose of 22.7 Gy,corresponding to a BED3 delivery rate of 10.3 Gy3 perday. This is over 50% higher than the BED3 delivery rate(6.8 Gy3 per day) associated with the thrice-daily frac-tionation of CHART, which itself is very similar to22 Gy daily fractionation (6.7 Gy3 per day). Thesefigures take no account of incomplete repair, whichwould increment the BED3 associated with 22.7 Gyeven further. Even with well-spaced fractions somecaution would be required when contemplating dailybiological doses of this magnitude and the possibility of treating bi-daily with a significantly reduced fractionaldose should be explored.

Conclusion

This paper sets out the practical considerations involvedin calculating compensations once a treatment interrup-tion has occurred, but it is stressed that it is goodpractice to aim to avoid interruptions wherever possible.

A wealth of radiobiological and clinical evidence con-firms the seriousness of unnecessary treatment prolon-gation and unscheduled gaps, particularly those near theend of treatment, are especially problematic. Althoughit is impossible to pre-empt some interruptions, e.g.those resulting from machine breakdowns or bad clinicalresponse to treatment, those resulting form PublicHolidays and Statutory Days can be pre-planned. It isnot sufficient to devise ‘last-minute’ compensations forsuch interruptions and departmental policies shouldprohibit such practice. Rather, patients should be cat-egorized in advance according to RCR guidelines andtheir treatment schedules reviewed such that the pre-

dictable treatment gap is properly compensated by, if necessary, revision to the whole schedule.Extremely busy departments are clearly more likely to

be troubled by unscheduled gaps and will also find it lesseasy to timetable an eff ective compensation when suchgaps do occur. The permanent presence of spare treat-ment capacity (e.g. by provision of enough treatmentmachines within each department to allow the deliberateunder-usage of at least one of them) is an obviousmethod for anticipating and coping with unscheduledinterruptions. Such a policy has resource implications,but these need to be set against the fact that withtreatment interruptions, as in several other aspects of radiotherapy treatment delivery, there exists a likely

inverse relationship between pressurized workingconditions and treatment quality.

Radiobiological methods of compensation, when theyhave to be utilized, are better than none at all, but it isnevertheless essential to be aware of the potential down-side of invoking calculations which are themselves over-simplifications and which rely on parameter valueswhichsometimes are not accurately known. Three particularaspects of the calculation methods set out above shouldbe borne in mind.

Firstly (and as has been assumed in the calculationshere), although there is strong evidence for acceleratedrepopulation following an initial period of slower

repopulation, it is not clear whether or not the K factorvaries during treatment. There is the possibility thatchanging the dose per fraction, or the dose delivery rate,(as occurs in devising some gap compensations) mayitself alter K or the lag period.

Secondly, the sub-lethal damage repair mechanismsare not fully understood and there is a strong likeli-hood that repair is slow in some normal tissues.Hyperfractionated compensation schemes, involvingthe delivery of many closely-spaced fractions after theunscheduled gap, carry the risk of significantly increas-ing normal tissue morbidity, even in cases where theconsequences of incomplete repair potentially have been

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allowed for by the inclusion of a seemingly appropriate‘h’ factor in the calculations.

Finally, it should be remembered that BED calcula-tions take no account of the physiological factors whichmay influence radiation response throughout an irradi-ated volume. The response is essentially governed by the

integrated eff ect of the radiation, which in turn is relatedto the degree of dose uniformity and to the functionalcomplexity of the tissue or organ. Where there areunavoidable or deliberate dose gradients the response tothe gap compensation may diff er throughout the treat-ment volume. In such cases it is prudent to repeat thebiological assessments at the normal tissue ‘hot spots’[37]. Where tumour shrinkage is known to haveoccurred the clinician may feel that the use of reducedfield size during gap compensation may partially off setsome of the potential problems. The possibilities of thisand other safeguards (increased shielding, revised treat-ment plan, etc.) should always be considered alongside

the radiobiological aspects whenever the normal tissueBED is likely to increase as a result of treatmentprolongation.

Ongoing elucidation of radiobiological processes andparameters will inevitably mean that there will be arequirement to review and, in some cases, modify, therecommendations set out in this article. It is recom-mended that each radiotherapy centre identifies an indi-vidual (local or remote) who is in a position to keepabreast of unfolding developments and who can be theprime source of advice to that centre on how to devisetreatment compensations.

Acknowledgements. The authors wish to express their apprecia-tion to Drs Colligan (Inverness), Fowler (Wisconsin), Henk (London),Morgan (Nottingham), Roberts (Manchester), Slevin (Manchester)and Spittle (London), all of whom read the draft manuscript and madea number of useful and constructive comments.

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1 Hendry JH, Bentzen SM, Dale RG, et al . A modelled comparisonof the eff ect of using diff erent ways to compensate for missedtreatment days in radiotherapy. Clin Oncol 1996;8:297–307.

2 Slevin NJ, Hendry JH, Roberts SA, Agren-Cronqvist A. Theeff ects of increasing the treatment time beyond three weeks onthe control of T2 and T3 laryngeal cancer using radiotherapy.Radiother Oncol 1992;24:215–220.

3 Fowler JF, Chappell R. Non small cell lung tumours repopulaterapidly during radiation therapy. (Letter) . Int J Radiat Oncol Biol Phys 2000;46:516–517.

4 Fowler JF. Radiobiological modelling to compensate forunplanned gaps in radiation treatment. International Congressof Radiation Research, Dublin, July, 1999. In Radiation Research,Vol 2 Proceedings. Moriarty M, Mothersill C, Seymour C,Eddington M, Ward JF, Fry RJM, eds. Oak Brook, IL, U.S.A.:Int. Assoc. Rad. Res., pp. 653–659, 2000.

5 RCR Ref No BFCO (96) 4. Guidelines for the management of the unscheduled interruption or prolongation of a radical courseof radiotherapy. ISBN 1 872599 26 5. 1996; Royal College of Radiologists.

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Br J Radiol 1994;67:1001–1007.9 Dale RG, Jones B, Sinclair JA. Dose-equivalents of tumour

repopulation during radiotherapy: the potential for confusion. Br J Radiol 2000;73:892–894.

10 Doerr W, Hendry JH. Consequential late eff ects in normal tissues.Radiother Oncol 2001;61:223–231.

11 Jones B, Dale RG, Deehan C, et al . The role of biologicallyeff ective dose (BED) in clinical oncology. Clin Oncol 2001;13:71–81.

12 Withers HR, Taylor JMG, Maciejewski B. The hazard of acceler-ated tumour clonogen repopulation during radiotherapy. ActaOncol 1988;27:131–146.

13 Fowler JF, Harari PM. Confirmation of improved loco-regionalcontrol with altered fractionation in head and neck cancer. Int J Radiat Oncol Biol Phys 2000;48:3–6.

14 Steel GG. (ed.) Basic clinical radiobiology. London: Arnold, 1997.

15 Roberts SA, Hendry JH. Time factors in larynx tumour radio-therapy: Lag times and intertumour heterogeneity in clinical data-sets from four centres. Int J Radiat Oncol Biol Phys 1999;45:1247–1257.

16 Fu KK, Pajak TF, Trotti A, et al . A Radiation Therapy OncologyGroup (RTOG) Phase III randomised study to compare hyperfrac-tionation and two variants of accelerated fractionation to standardfractionation radiotherapy for head and neck squamous cell carci-nomas: first report of RTOG 9003. Int J Radiat Oncol Biol Phys2000;48:7–16.

17 Withers HR, Peters LJ. Transmutability of dose and time.Comments on the 1st report of RTOG 9003 (KK Fu et al) . Int J Radiat Oncol Biol Phys 2000;48:1–2.

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19 Allal AS, de Pree C, Dulguerov P, Bierei S, Maire D, Kurtz JM.Avoidance of treatment interruption: an unrecognised benefitof accelerated radiotherapy in oropharyngeal carcinomas? Int J Radiat Oncol Biol Phys 1999;45:41–45.

20 Robertson C, Robertson AG, Hendry JH, et al . Similar decreasesin local control are calculated for treatment protraction and forinterruptions in the radiotherapy of carcinoma of the larynx in fourcenters. Int J Radiat Oncol Biol Phys 1998;40:319–329.

21 Robertson AG, Robertson C, Perone C, et al . Eff ect of gaplength and position on results of treatment of cancer of thelarynx in Scotland by radiotherapy: a linear quadratic analysis.Radiother.Oncol 1998;48:165–173.

22 Baumann M, Petersen C, Wolf J, Schreiber A, Zips D. No evidencefor a diff erent magnitude of the time factor for continuouslyfractionated irradiation and protocols including gaps in twohuman squamous cell carcinoma in nude mice. Radiother Oncol

2001;59:187–194.23 Zieron JO, Omniczynski M, Raabe A, Beck-Bornholdt HP. Impact

of the position of a gap on the response of the RIH-tumour of therat on fractionated split-course radiotherapy. Strahlenther Onkol 2001;177:592–596.

24 Sanguineti G, Benasso M, Corvo R, et al . Lack of a time factor inalternating chemotherapy for advanced head and neck squamouscell carcinoma. Tumori 2001;87:10–13.

25 Weber DC, Kurtz JM, Allal AS. The impact of gap duration onlocal control in anal canal carcinoma treated by split-courseradiotherapy and concomitant chemotherapy. Int J Radiat Oncol Biol Phys 2001;50:675–680.

26 Bentzen SM, Thames HD. Overall treatment time and tumourcontrol dose for head and neck tumours: the dog leg revisited.Radiother Oncol 1992;25:143–144.

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28 Haustermans K, Fowler J, Geboes K, et al . Relationship betweenpotential doubling time (Tpot), labelling index and duration of DNA synthesis in 60 oesophageal and 35 breast tumours: is itworthwhile to measure Tpot? Radiother Oncol 1998;46:157–167.

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APPENDIX

Calculation of h values for closely-spaced fractions

For mono-exponential recovery kinetics h is calculatedfrom:

In Eqn (A1), N is the number of fractions in a ‘group’ of closely spaced fractions and =exp(x), where is the

exponential repair constant of sub-lethal damage and xis the average time interval (h) between these closely-spaced fractions. For late-responding normal tissues isoften assumed to have a generic value of 0.5 h1; forprediction of radiation myelopathy subsequent to headand neck radiotherapy a smaller value of around0.22 h1 is more appropriate [31,32].

For reciprocal-time repair kinetics h is calculatedfrom:

In this model z is the reciprocal-time repair constant of sub-lethal damage [34]. The myelopathies observed inthe CHART Trial [35] are consistent with a z value of 0.36 h1 [34].

Provided there are only a few consecutive days onwhich multiple daily fractions are delivered the calcula-tion of h using either Eqn (A1) or Eqn (A2) may besimplified by taking into account only the shortestinter-fraction intervals. For example, if twice-daily frac-tionation is being used with an interval of 6 h betweenfractions, followed by an longer overnight interval of 18 h, the values used to calculate h are N=2 and x=6.Allowance for the additional incomplete repair follow-

ing the longer overnight intervals may become necessaryif there are many successive days on which twice-dailyfractions is delivered. Reference [34] provides moredetails on this.

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