the hazard of accelerated tumor clonogen number re population during radiotherapy

8/2/2019 The Hazard of Accelerated Tumor Clonogen Number Re Population During Radiotherapy

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Acta Oncologica 27 (1988)F a s c . 2FROM THE DEPARTMENT OF R ADIATION ONC OLOGY, THE J ONSSON C OMPR EHENSIVE C ANC ER C ENTE R , ANDTHE DIVISION O F BIOSTATICS, SCHOOL OF PUB LIC HEALTH, UC LA, LOS ANGELES, USA AND THE C ENTR E O F

ONCOLOGY, GLIVICE, POLAND.

T H E H A Z A R D OF A C C E L E R A T E D T U MO R C L O N O G E N R E P O P U L A T I O NDURING RADIOTHERAPY

H . R. WITHERS.. M . G . TAYLORnd B. MACIEJEWSKI

AbstractWhen analysis of results of radiotherapy f or nearly 500 patientswith oropharyngeal cancer showed evidence for rapid tumorregrowth during extensions of treatment from about 5 weeks toabout 8 weeks, we searched the literature on radiotherapy forhead and neck cancer to determine whether it revealed similarevidence of accelerated tumor regrowth. Estimates of doses toachieve local control in 50% of cases (TCDSo)were made frompublished local control rates, and th e depend ence of these d oseson overall treatment duration was evaluated. In parallel, pub-lished scattergrams were analyzed to estimate the rate of tumorregrowth over the period of 4-10 weeks from initiation of thera-

py. Both analyses suggested that, on average, clonogen repopula-tion in squamous cell carcinomas of the head and neck acceler-ates only after a lag period of the order of 4+ 1 weeks afterinitiation of radiotherapy and that a dose increment of about 0 .6Gy per day is required to compensate for this repopulation. Sucha dose increment is consistent with a 4-day clonogen doublingrate, compared with a median of about 60 days in publishedreports of unperturbed tumor growth rates. Th e values presentedhere are average values for a large number of patients: it isnecessary, not only to verify the results of these retrospectiveanalyses in prospective studies, but also to develop methods topredict the time of onset and rate of accelerated tum or clonogenrepopulation in the individual patient.Key words: Therapeutic radiology; tumor growth kinetics, ad-juvant chemotherapy, head and neck cancer, dose fractionation,

isoeffect cu rves, tumor biology, hypoxic cell sensitizers, logisticregression, repopulation, radiation d ose responses for tumors.

A clonogen is a cell capable of indefinite reproductionand capable, there fore, of causing a recurren ce: it is to bedistinguished from the majority of cells in a tumor whichhave a limited lifetime.

The purpose of this paper is to analyze the effect ofaccelerated repopulation of tumor clonogens during acourse of radiotherapy on the probability of treatment

success: it is not addressed to the effect of unperturbedtumor growth on the probability of cure. It is not con-cerned with that small proportion of rapidly-growing car-cinomas, sarcomas and lymphomas which manifest de-tectable growth during workup, or in the early stages oftreatmen t, and w hich esca pe when th erapy is given at astandard rate. It is concerned with the insidious threat totreatment success from the accelerated growth of tumorclonogens during treatment in that great proportion oftumors which show no evidence of rapid growth at thetime treatment is initiated.By the time human tumors reach a clinically-detectablesize, most of them are growing fairly slowly, doubling involume at rates which vary from patient to patient, butwith a median time of abo ut 2 months (9, 62). The kineticparameters of tumors (cell loss factor, growth fraction,cell cycle time) do not change significantly over one ortwo doublings of tumor volume. There fore, the m edian of2 months required for a doubling in tumor volume is alsothe median doubling time for m alignant clonogen nu mbe r.Of course, the malignant clonogens cycle more quickly,e.g. every 2-4 days (62), but their rate of increase isslowed by the loss from the clonogenic pool of a largeproportion of the daughter cells through one or moremechanisms (e.g. differentiation, apoptosis, necrosis, ex-foliation, invasion into the lymphatic or blood vascularsystem). If malignant clono gens were t o co ntinue growingwith an unchanged 2 month median doubling timethroughout a 6-8 weeks course of radiotherapy, theirgrowth would not materially affect the c han ce of cure: forexample, if treatm ent lasted 2 months, the median incre-ment in dose to balance tumor growth would be that

Accepted for publication 17 September 1987.13 1


2/16

132 H. R. WITHERS, J . M. G . TAYLOR AND B. MACIEJEWSKIrequired t o reduce tumo r cell survival to one half. Fromclinical and laboratory (76, 78) da ta, th e halving dose canbe estimated to be between 2 and 3 Gy. (See Footn ote.) Iftreatment lasted only 6 weeks, the counterbalancing dosewould be about 1.4 to 2.1 Gy. Such a small influence ofgrowth on the d ose required for tum or control would beundetectable in a clinical study . Con verse ly, if there w erean easily detected increment in th e total dose necessaryfor a certain rate of tumor con trol as a function of increas-ing overall treatment time, or any decrement from short-ening it, accelerated clonogen growth is the most likelycause, and its rate can be estimated from the m agnitude ofthe change in dose.

A change in the d ose for a fixed rate of tumor controlwith change in treatment duration is, in fact, the only wayaccelerated repopulation can be detected. Measu rementsof cell cycle parameters are of no value because, with alogarithmic decrease in cell survival with inc rease in dos e,the majority of cells are dead after only a few treatments.Furthermore, even if clonogenic cells were identifiablefrom their more numerous nonclonogenic brethren, theirrate of increase would be modified by the unpredictableclonogenicity of their offspring. Clinically detectablegrowth of a tumor during treatment can signal a rapidlygrowing tumor but lack of detectable growth does notdenote a lack of clonogen repopulation. Accelerated repo-pulation late in treatment involves only a small absolutenumber of surviving cells and he nce their growth do es notcontribute to a detectable chan ge in tumor volume. (If theeffective Do for the survival curve for tumor clonogensexposed to a series of 2 Gy fractions was 3.5 Gy (76, 78),and accelerated repopulation by tumor clonogens beganafter delivery of 20 fractions of 2 Gy, the fraction ofclonogens retaining the potential for indefinite growthafter a 4-week treatm ent would b e e-403.s, that is, ab out 1in 100000. Thus, if the tumor originally contained 10malignant clonogenic ce lls, the abso lute surviving numberwould be abo ut 1000 and rapid repopulation by so fewcells would not be d etectab le as a change in volume of thetotal tumor mass.) Furthermore, the gross tumor mass,Footnote. If there were 10 tumor clonogens in a 1 cm diametertumor deposit, and if 64 Gy in 2 Gy fractions resulted in about50% (specifically 63%) chance of sterilizing the mass, and if itwere assumed there were no growth during treatment, the dose( D 3 to reduce cell survival by 1 logarithm to lo%, would be64/8=8Gy. Since DIo= 2.3 xD 0, he effective Do for 2 Gy frac-tions, i.e. the dose in 2 Gy fractions necessary to reduce survivalby e-, to 37%, would be U2.3 G y=3.5 Gy. The dose required toreduce survival to 50 % would be In ( 0 . 5 ) ~ 3 . 5 y = 2 .4 G y . Th us ,2.4 Gy of a 2 Gy per fraction regimen would counteract the effectof 1 doubling in clonogenic cell number. This value is consistentwith cell survival curves d etermined from multifraction experi-ments in mice (76) and man (4) using 2 G y per fraction. How ever,the estimated effective Do value would be less than 3 .5 Gy if a 1cm diameter mass w ere assumed to contain more than 10 malig-nant clonogens, or if a lower dose than 64 Gy in 2 Gy fractionswas necessary for 63% chance of cure, or if there were tumorgrowth during treatment.

being com pos ed mainly of sterilized cells, is most likely tobe seen regressing at a time when surviving clonogens areregrowing rapidly, as has been demonstrated in experi-mental animals (27, 35). Thus, the lack of visible growthof a tumor, or even more misleadingly its continuingregression, may conceal a rapid repopulation response ina previously slowly-growing tumor.

This paper will survey the literature for evidence ofchanges in dose required for a constant rate of tumorcontrol as a function of differences in overall treatmentduration, making adjustments in the total biologically-effective dose, when necessary, to a ccount fo r variationsin size of dose fractions. The analysis is confined tosquamous cell carcinomas of the head and neck ( 5 , 7, 8 ,54-56, 58-61, 64, 65, 67 , 71-73, 80).12, 15-17, 19-26, 28, 30-32, 34, 37-4 6, 48, 49, 51, 52,

Material and M ethodsTCDSOAnalysis. Results which permitted a reason-

ably accurate assessment of local control rate, dose perfraction, total dose and overall treatment duration weretaken from the literature. Approximate median values fortotal dose, dose per fraction and overall treatment timewere used to determine the effect of treatment time onlocal tumor con trol for 59 sets of data. A follow-up time ofat least 2 years was usually required but in some instances(e.g. 22) results from shorter follow-up were included.Some tumor control rates were d etermined actuarially andsome were absolute rates. Some data were read fromfigures with the attendant possibility of errors. Groupingsof data (e.g. for stage of diseas e) were those of the variousauthors, although, in some instances, we sub-groupeddata sets from within one publication. When possible,carcinoma of vocal cord was considered separately fromsupraglottic tumors. To minimize errors in extrapolatingdoses from the median dose actually used to the doseestimated to control 50% of the tumors (TC D~ O), fewreports of very high or very low control rates were ex-cluded. However, high (max. 0.86) or low (min. 0.18)rates were accepted from treatment schemes for whichalternative data were not plentiful (22, 51, 72). Manypapers were excluded because it was impossible to recon-struct treatment parameters from doses expressed afterconversion to a single number using the NSD concept(14), or one of its derivatives, TDF (47) or CR E (33).Since it is rare, even in protocol studies, for all patients,even with the same stage of disease, to receive exactly thesame dose regimen, some liberty was taken in assigningmedian do ses and treatment times (Table 1, Fig. 1) wheretreatments were not uniform b ut wh ere the autho r impliedthat deviations from th e usual routine were minor and/orrelatively infrequent. No attempt was made to allow forvariations in dosimetry methods (e.g. calibration, dosespecification). When kilovoltage x-rays had been used(37-391, do se s were incr eas ed by an RBE factor of 1.15.


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TUMOR CLONOGEN REPOPULATION DURING RADIOTHERAPY 133

I10 20 30 40 50 60

T R E A T M E N T DURATION (Days)

Fig. 1 . TCDSoas a function of overall treatment time for squa-mous cell carcinomas of head and neck (Table 1 ) . Data relate toT2 (O),T3 ( 0 ) r a combination of more than 2 stages (A). otaldoses are normalized to the dose equivalent to that from aregimen of 2 Gy fractions usin g an a@value of 25 Gy. D ose s andtimes are best estimates of median values. The dose and controlrate reported in the literatu re from which the T CD50 value wascalculated is presented (0 ) o show the extent of the extrapola-tion. Rate of increase in TCDJo redicted from a 2 month clono-gen doubling rate. (---). Estimated increase in TCD50 withtime for 'T3' (U) and mixed T stages (A) from independentscattergram analy ses (Tables 2, 3) involving different data setsfrom those presented in this figure.

Normalizing total doses for influence of fraction size.MACIEJEWSIUt al. (38, 39) have previously analyzed datafrom nearly 500 pat ients with oro-pharyngeal cancerstreated in Gliwice, Poland , and c orrelated the influence oftotal dose, dose per fraction and overall treatment timewith the probability of control of the primary lesion. Byparametric and nonparametric analyses, it was deter-mined that the effectiveness of a total dose in obtainingtumor control was not very sensitive to cha nge in dose perfraction between about 1.8 Gy and 3.5 Gy. The bestestimate for the alp ratio in the linear-qua dratic isoeffectformula (79) was 25 Gy. Therefore, in the present analy-sis, total doses were normalized t o that w hich would havebeen isoeffective if given in 2 Gy fractions using theformula (79)

where D ~ Qnd D, are total dose s in fractions of 2 Gy or xGy, and alp was taken a s 25 Gy. To check the importanceof the assumed alp rat io to the conclusions drawn, analternative series of calculations was made using an alpvalue of 10 Gy, a value within a range commonly foundfor acutely-responding normal tissues in e xperim ental ani-mals (18, 74, 76). Relative to a value of 25 Gy, an alp ratio

of 10 Gy slightly increases the adjustment made to th etotal dose.

Calculating TCDsO values. To intercompare data inwhich control rates were usually different from 50%,TCDJ,, values were calculated based on Poisson assump-tions regarding cell killing (57) in which the slope of thedose resp onse cu rve reflected an effective Do value of 5

Change in dose to achieve P,,,, o f 0 . 5 = n x e f f D o = n x 5GY.Gy where n=ln ( n Pobserved 1.The value of 5 Gy, rather than a lower value, e.g. 3.5Gy, which would be more relevant to clonogenic cellsurvival, was chosen on the presu mption that there wouldbe heterogeneity of tumor and treatment characteristicsaffecting the slope of tumor control probability curves(78). However, choosing values different from 5 Gy wouldhave little influence on the analysis because extrapola-tions were limited by selecting repor ts where control rate swere not greatly different from 50%: 40159 data sets hadlocal control rates between 30 and 70%, and 51159 werebetween 25 and 75%.

Analysis of scattergrams. Published scattergramsshowing the total do se, treatm ent time an d result of treat-ment (control or failure) for a specific tumor site and stage(Tables 2, 3) were analyzed. Data points on the scatter-grams at extremes of treatment time and dose were ex-cluded because the assumptions of our model may not beappropriate t o such extrem es and , furthermore, they areof little relevance to the clinical problem of treatment ofsquamous cell carcinoma of the head and neck. Thus,total doses less than 45 Gy , and overall times sh orter than10 days, or longer than 70 days, were not considered.Other reasons for excluding results at the extremes ofoverall time were that no information on variations infraction size was given on the sca ttergram s, and low totaldoses in short overall times may have involved th e use ofa few large dose fractions; also treatm ent times larger than70 days were infrequent and it is reasonable to supposethat they were associated with individual disruptions oftreatment not described in the text. Since the point ofinterest was not the overall control rate fo r each da ta set,but rather the control rate for specific treatme nt regim ens,no information was lost through excluding uninterestingdata at the extremes. In a summary of the scat tergramdata used in the a nalysis (Table 2 ) the limits of each dataset were indicated by the 10-90 percent i le ranges for doseand time.

The aim of the scattergra ms analysis was to quantify theeffect of overall treatment time o n the dose necessary toachieve a certain tumor co ntrol rate, expres sing the effectin terms of dose necessary to balance on e day's exte nsionof t reatment .The analysis is based on the s tat is t ical model

dose +A, x time(25)+A, X log(tu-1-Plog-= A,+ A ,X total


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134 H. R. WITHERS, J . M. G . TAYLOR AND B. MACIEJEWSKlTable 1

Data used to determine TCDSo alues as a function of overall treatment duration. Median values fo r dose s and times were estim ate d.NTD = normalized total dose = dose equivalent to that actually given if t had been given in 2 Gy fract ions , assuming un alp rutio of25 G yTumor No . Doselfx Total NTD Overall Local TCDSo Refere nceof Gy dose Median t ime control and No.pa ts. GY Med ian % alp = alp =

25 Gy 10GyOropharynx T3Larynx T 2 4 (excl. cord)Vocal cord T2Head & neck T4Larynx T2Larynx T 3Laryngo-pharynx T 2 4Oro, hypo, laryngo-pharynx T 2 4 HBOHead & neck-'notearly' misonidazole

136691441339848

21.6-2.32.01 .83. 73. 74. 54.5

48-5647-5547-535455554545

52 1 1 31 54 5452 11 33 54 5250 11 50 50 5054 12 66* 51 5058 20 77 53 5858 20 58 57 6249 22 28 52 5749 22 66 47 52

Peracchia et al. (54)Svoboda (65)Svoboda (65)Gonzales e t a l . (22) (6 m o)Stewart et al. (64)Stewart et al. (64)Henk et al . (26)Henk (25)162 4-4.5 4 M 5 46 22 32 49 53 MRC-Miso.working party (42)MRC-Miso.working party (42)

MRC-Neut. w. partyEdinb. photon (43)Harwood et al . (24) -Fig. 3Harwood e t al. (23) -Table 3

89 2.5-2.9 50-57 55 28 34 57 59Head & neck (excl. N-P)Glottis T4 (cartilage)Glottis T2 mobileGlottis T2 impairedHypopharynx T1-3 NOTonsil TI-2

T2-3

mobility

60 2.75 55 57 27 70 53 5523 2.2-2.5 50-55 53 29 61 51 52

121 86 46 4759 52 53

53 29.2-2.5 50-555533 2.2-2.5

2.2-2.54.5

50-5550-5545

53 29 33 55 56 Keane e t al . (32) -Garrett et al. (20) -Table 2Tables 3, 481Tonsil T3Head & neck st 2HBOst 3Head & neck T 3 4

6025 61 51 5249 31 72 45 51 Denham et a l . (12) Table 56594 34 51 5658 34 30 61 59 Denham et al. (12) Table 5Marcial et al. (41) -

Wang (72)Hjelm-Hansen (28) -Table 3Horiot et al. (30)Thames e t a l. (67)* Dose from isoeffectcurves fo r a 40 da ytreatment to yieldlocal control rateactually achieved.Henk (25)Henk (25)Marcial et al. (40) -Knee et al. (34)Fayos (15)Table 2 B

Fig. 2

Fig. 1

1.2 60Oropharynx T 3 4Larynx-all stagesOro, hypopharynx T3-4Pharyngeal wall T 3 4Tonsillar fossa T3-4Base of tongue T1-2Base of tongue T 3 4SupraglotticOral cav. oropharynxLaryngo, hypopharynxBase of tongue T3 - 4Head & neck T2-4Supraglottic larynx T2

larynx T2-3T2-4T2-4

2720897267798386269124

1.61. 92.01. 21 .12.02.02.02. 02.0

635760687465 *68 *66 *64*65*

40 83 56 5541 63 55 5541 74 56 5639 46 68 6545 65 72 6940 46 6640 63 6640 76 6140 59 6340 73 61

64576070766 56866646516 2.15 64 64 41 56 63 6433 2.15 64 64 41 41 65 6668782315

2.23.01.0-2.02

66606964

66 41 25 70 7162 48 35 64 6768 42 69 65 6464 43 74 60 60

Tonsil & base oftongue T2 NOT2 N1-3T3 NO-3Hypopharynx &larynx T2-3

414712040

2-2.52-2.52-2,51. 2

66666675

67 45 78 62 6267 45 47 67 6767 45 34 69 6973 45 12 69 67

Weller et al . (73) -Tables 6 & 9Parsons et a l . (52) -Table 4


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TUMOR CLONOGEN REPOPULATION DUR ING RADIOTHERAPY 135(Table 1 Continued)Tumor No. Doselfx Total NTD Overall Local TCDSo Referenceof Gy dose Median t ime control and No.pa ts. GY Me dian 7% alp = alp =

25 G y 1 0 G yHypopharynx T3Oral cavity T3Glottis-all stagesSupraglottis-all stagesPharynx-all stagesTonsil T2-3Head & neck T 3 4Tonsil T 2 4An t 213 tongue T3Floor of mouth T3RMT & ant fauc pillPharyngeal wall T 3 4Supragl larynx T3Vocal cord T2Base of tongue T2Tonsil-stage 3 4Glottis-all stagesPharynx-all stages

T2-3

71 132

36 421 431 72693951725

16 4I0823

I7 53553

12015 7

1.8-2.0 662.1 632.0 64

1.8 621.9 701.8-2.0 701.8-2.0 701.8-2.0 701.8-2.0 751.8 751.8-2.0 752.0 701.8 721.8-2.0 682.0k4.13

666364

637070707075747570726867

47594545

465154545457575748565966

711844704738582970416482518374465 55636

6271646164666273677167687468667361

6669

6271646164666273677167687468667467

Parsons et al . (51)-Sealy et al . (58) -Overgaard et al. (50) -

Table 3Table 5Fig. 2

Perez et al . (55) -Fig. 3Marcia1 et al. (41)Fig. 2Wong et al . (80) -Table 5Fletcher (16)Table 3-16Fletcher (16)Table 3-17Fletcher (16)Table 3-20Fletcher (16)Table 3-21Fletcher (16)Table 3-27Fletcher (16)Table 3-22Housset et al . (31) -Table 3Nussbaum et al. (46) -Table 3Overgaard et al. (50)Fig. 4D A H A N C A I1

mor volume) where P is probability of cure, time (25)=maximum of time (time -25) and zero, and the tumorvolume is calculated based o n an average diameter of 1.5,3,4.5 and 5 . 5 cm for T1, T 2, T3 and T 4 tumors respective-ly. A justification for this model is given elsewhere (38).The term for tumor volume was incorporated into themodel to permit an analysis of data combined from var-ious authors, the results of which are not presented here.The number of clonogenic cells in these (primary) tumorswas assumed t o be proportional t o (diameter),rather than (diameter), but thi s assump tion had no effecton the final estimates unless there were at least 3 T-stagesrepresented separately by the same author. The square ofthe diameter, rather than th e cube , was used on the prem-ise that primary tumors in head and neck are generallymore flat than spherical. When data were presented for amultiplicity of stages by on e aut hor , the use of the term A,introduced the requirement that the rate of increase inisoeffect dose with time (the slope of th e isoeffect curve)be assumed to be the same for all T-stages, but allowedthe TCD, values to be different for different T-stages.

Thus, although an authors data for each stage were ana-lyzed separately, the curves fitted to them by logisticregression were forced to a common slope. In otherwords, it was assumed that when a small number ofsurviving clonogens accelerated their repopulation rate,that rate was unaffected by the pretreatment volume (T-stage) of the tumor. Th is justified the form of the model inwhich T-stage affected only th e A, term . If 2 stages weregrouped in a scattergram, a diameter equal to the weight-ed average of the T -stage specific diameters was used incalculating the tumo r volume. Th e weights for the se aver-ages were chosen to be equal to the fraction of patientswith the particular T-stage. Wh en the TCDso value wasestimated for a 4. 5 cm diam eter tumor based o n interpola-tion from 2 or more T-stages, th e result was described asthat for a T3 tumor (Tables 2, 3).The maximum likelihood method (1 1) was used to esti-mate the parameters Ao,A ,, A2 an d A3. Time(25) definesthe time during which regeneration can oc cur. S ince near-ly all patients were treated in overall times longer than 25days, and since a separ ate analysis showed TCDso values


6/16

136 H . R. WITHERS, J . M. G . TAYLOR AND B . MACIEJEWSKITable 2

Data derived from published scattergrams fo r head and neck cancer was used to c alculate the increment in dose per day necessary tocompensate fo r accelerated tumor clonogen repopulation beyond 25 days from the start of radiotherapy. The range of dos es and overalltreatment times to which the data relate are indicated by the 10-90 percentile limitsReference Site of T No. of % Average Dose range Average Range of times

primary stage patients cured dose 10th-90th time 10th-90thGy percentile percentile

Maciejewski et al. (38)Maciejewski et al. (38)Maciejewski et al. (38)Maciejewski et al. (38)Maciejewski et al. (38)Maciejewski et al. (38)Maciejewski et al. (38)Maciejewski et al. (38)Maciejewski et al. (37)Shukovsky et al. (59)Shukovsky et al. (60)Shukovsky et al . (60)Shukovsky et al . (60)Spanos et al. (61)Spanos et al. (61)Spanos et al. (61)Spanos et al. (61)Ghossein et al. (21)Ghossein et al. (21)Million et al. (45)Million et al. (45)Million et al. (45)Million et al. (45)Million et al. (45)Million et al. (45)Million et al. (45)Million et al. (45)Million et al. (45)Million et al. (45)Million et al. (45)Vikram et al. (71)Vikram et al. (71)Barker et al. ( 5 )Meoz-Mendez et al. (44)Budihna et al. (7)Budihna et al. (7)Cardinale et al. (8)Gardner et al. (19)Gardner et al. (19)Gardner et al. (19)

Oral cavityOral cavityOral cavityTongueTongueTongueTonsilTonsilLarynxGlossopalatinesulcusTonsil

TonsilTonsilTongueTongueTongueTongueSupraglotticlarynxSupraglotticlarynxLarynxSoft palate

Pharyngeal wallPyriform sinusBase of tongueTonsilVocal cordVocal cordFloor of mouthOral tongueOral tongueNasopharynxNasopharynxRetromolarPharyngeal wallLarynxLarynxTonsilBase of tongueBase of tongueBase of tongue

Ant tonsil pillar

123I23233, 42, 3123, 412341 , 23, 42, 32, 32, 32, 32, 3212, 33231, 241 , 2, 32, 312212, 34

106312043312826463 1044I 128422637471980

104211918152215856118221535281329029152163518

904834100583381445073

1008267886270327356676344607367956650684769548364834757678022

616262646261616163 *67616465646768647475686469666763616571707266666668666462667072

48-6556-6557-6562-6560-6554-6557-6557-6561-68*60-7354-6660-7060-7360-7060-7 153-8063-8163-86

61-74

61-7456-7363-7554-7564-7 157-7057-6461-7064-7958-8 169-8760-7 160-7559-7360-7460-7657-6855-7862-7065-7666-78

37454449444541454343364140394245424445575054545444374450414457553945514750575657

2 2 4 835-5535-5545-5433-5835-5636-5033-5633-5735-522 4 4 73 1 4 83 0 4 82 8 4 734-4935-5632-5540-5 139-5 149-6533-6543-6644-6444-6734-5033-3837-5 128-6818-6728-5648-6642-6930-4737-5335-683 1-6743-6249-6445-6650-66* Adjusted for RBEdd, f I . I5 for %o and 200 kVp x-rays.

that were relatively constant over a period of approxi-mately 20-30 days (see later ), we assumed repopulationbegan at 25 days after the initiation of treatment: that is,the back-extrapolation of the cur ves (Fig. 1) was stoppedat 25 days. Thus, selecting a starting time less than 25days would not affect the slope of the curves tracing theincrease in dose per day, but only the estimate of theTCD5o value in the absence of repopulation. With this

balance an extra day's extension in treatment duration.Approximate standard errors were calculated from theasym ptotic information m atrix (1 1) .

ResultsTCD5,,estimates. The da ta analyzed, and the best est i -mates obtained for TCD50, are shown in Table 1 , togethermodel, A2/A1 is an es timate of the dose necessa ry to with the intermediate steps in the calculations.


7/16

TUMOR CLONOGEN REPOPULATION DURIN G RADIOTHERAPY 137Table 3

Analysis of scat tergrams. Doses to balance 1 day s extension of treatment time (beyond 25 days ) and the TCDjo or a T3 tumor treatedin 45 days calculated from the total data set l for all s ta ges) at that s i te . When mult iple s tages were presented in separate scat tergrams,they were analyzed separately, but the dose to balance I days extension of treatment t ime was forced to a commo n value. Whenmult iple s tages were presented in one sca ttergra m, the TCD,o is fo r the combination of stagesReference Site Dose to balance 1 day TCDS, (+S .E. ) (Gy)extra beyond 25 days for time =4 5 days

stage == T3GY (S.E .) or other (* )Maciejewski et al . (38)Maciejewski et al. (38)Maciejewski et al. (38)Maciejewski et al. (37)Shukovsky et al. (59)Shukovsky et al. (60)Spanos et al. (61)Ghossein et al. (21)Million et al. (45)Million et al. (45)Million et al. (45)Million et al. (45)Million et al . (45)Million et al. (45)Million et al. (45)Million et al. (45)Million et al. (45)Vikram et al. (71)Barker et al. (5)Meoz-Mendez et al. (44)Budihna et al. (7)Cardinale et a l. (8)Gardner et al. (19)

Oral cavityTongueTonsilLarynxGlossopalatine sulcusTonsilTongueSupraglottic larynxVocal cordSoft palateBase of tonguePharyngeal wallTonsilPyriform sinusLarynxOral tongueFloor of mouthNasopharynxRetromolar trigonePharyngeal wallLarynxTonsilBase of tongue

* Denotes stages other than T3, i .e . 4 .5 cm t u m o rs ; see Table 2 .* * Adjusted for RB E 1.15.

The values for TCDso, obtained using an alp ratio of 25Gy, are plotted against overall treatment duration in Fig.1 . Comparable estimates using an alp ratio of 10 Gy areshown in Table 1, but not in Fig. 1 .

Several features of Fig. 1 should be noted:1) The da ta show a non-linear, two-component relation-

ship between TCDS0 and overall treatm ent time, th erebeing no consistent change in TCDso between overalltimes of about 1 1 t o 30 days but a steep rate of increasethereafter.

2) The dashed line, originating arbitrarily at 50 G y ,traces the increase in TCDso which would result fromunperturbed tum or growth at a rate that would double thenumber of clonogens every 2 months, i .e. assuming noaccelerated growth of tumo r clonogens. (Its slope is basedon an effective Do of 3.5 Gy f or a 2-G y per frac tionregimen.)

3) TCDSovalues do not increase consistently between10 an d 30 days, suggesting no change in tum or clonogengrowth rate during approximately the first 4 weeks oftreatment . By contrast , T C D ~ Oalues for a 6-week treat-ment are consistently greater than those for a 4-weektreatment, implying a rapid repopulation by surviving tu-

0.640.720.670.56**1.330.540.651.432.39-0.28-0.90-2.09- I .052.900.58

1.150.091.031.360.740.880.34

-0.04

(0.07)(0.09)(0.13)(0.06)(0.42)(0.30)(0.29)(0.86)(2.15)(0.54)(0.97)(6.45)(4.64)(4.48)(0.15)(1.50)(0.32)(0.27)(0.25)(1.32)(0.38)(1.24)(1.13)

65.9 (0.8)65.1 (0.6)61.5 (1.0)65.0* (0.3)**63.5* (2.4)62.6 (3.3)64.2 (3.0)87.2 (12.7)80.8 (21.4)70.1* (6.2)81.4* (8.9)77.6* (30.6)70.6* (16.9)33.5* (53.4)59.3 (2.3)82.3 (15.8)71.2 (4.6)68.0 (5.6)63.4* (2.4)55.1* (15.4)63.2* (5.0)54.2* (12.2)77.3 (10.0)

mor clonogens between 4 and 6 weeks. By 7 weeks theTCDso values a re all greater th an 60 G y. T he solid lines inFig. 1 are not fitted to the d ata but ar e calculated from theseparate analysis of scattergram data (see below).

4) The full lines are based on independent data fromscattergrams (Tables 2, 3, Figs 2, 3). The weighted aver-age TCD5o at 45 days was calculated from the data pre-sented in Table 3 for T3 (4.5 cm) tum ors ( 1 1 sets of data)an d a mixture of T-stages, mainly T2 and T3 (12 sets ofdata). The values were 64.9 Gy for T3 and 62.7 Gy formixed stages. The lines shown are drawn through these45-day TCDso values with a slope reflecting a change inTCDso of 0.61 Gy per day (see scattergram analysis later).It is apparent that 2 independent analyses show that therate of change in estimated TCD50 values from percenttumor control analyse s (Table 1 , Fig. l ) , and of increase inisoeffect dose per day from scattergrams (Tables 2, 3,Figs 2, 3) are consis tent with one a nother.

5 ) The magnitude of the extrapolat ions to the TCDsofrom the dos es actually delivered in achieving th e range ofobserved control rates (Table 1) is represented by thelengths of the lines from the c losed c ircles (dose s actuallyused) to the open symb ols (estimated TCDso values).


8/16

138 H . R. WITHERS, J . M. G . TAYLOR AND B. MACIEJEWSKIGliwice M.D. Anderson Unive rsity of F l o r i d am - 1 1

M i l l i o n and Cassisi).

.-1

Overal l Time> 25 days

I

Fig. 2. Increment in dose per day for a constant (50%) probabilityof control of head and neck can cer with protraction of treatment,determined from logistic analysis of published scattergrams (Ta-bles 2 , 3) an d 3 data sets of Maciejewski (38). Three small datasets (for pharyngeal wall, tonsil, pyn form sinus) have 95 % confi-

6) In general, and in particular f or an individual investi-gator, TCDso values are lower for T2 tumors (circles),than for T3 and T4 tumors (squares), with the groupscontaining a range of T-stages (triangles), also showingvalues generally lower than those for T3 and T 4 tumo rs.7) To avoid overcrowding of d ata in Fig. 1, values werenot plotted for TCDso calculated using an a/P ratio of 10Gy (instead of 25 Gy). However, they are presented inTable 1 and it can be see n that they d o not affect in anysignificant way the conclusions drawn above. The maineffect of using the lower a//3 ratio was to raise the TCDsoestimates in regimens lasting 18-26 days. Th e cluste r ofdata at 30-32 days would not be grea tly affec ted, lyingbetween 47-56 Gy with a med ian value of about 52 Gy,not different from the median value of 51 Gy for TCDsovalues in treatments lasting 10-12 days.8) The predominant facto r determining th e variation inTCDso values for the various series of patients is not thestage of disease, nor the site of the tumor, nor the size ofdose per fraction, but rather, the overall duration of thera-PY.Scattergram analysis. Table 2 shows the characteristicsof the scattergram data se ts analyzed . Table 3 shows that,for most da ta sets, extending overall treatmen t time had astrong effect on the dose for a constant rate of tumorcontrol. The dose required to counterbalance one day's

f

1denc e limits exten ding beyond the grap h but are included fo rcompleteness. (---) a t 0.6 Gy is encompassed by 22/23 of th e95 % confidence intervals, implying that 0.6 G y per day is a goodestimate of the dos e to compensate for tumor clonogen repopula-tion in head and neck cancer at times beyond 25 days.

extension late in a treatment regimen, averaged (withweights inversely proportional to the variance) from 23data sets, was 0.61 (S.E.=0.22) Gy. Also shown in Table3 are TCDS0 values pr edicted fro m the scattergram s fortreatmen ts lasting 45 days, using th e maximum likelihoodlogit analysis, for 11 sets of 'T3' tumors, 10 data setscontaining multiple, but unidentified, stages, and twosmall sets of patients with T2 primary cance r of tonsillarfossa.

Fig. 2 plots the scat tergram data from Table 3 for theincrement in dose required for a constant tumor controlrate for each day's protraction of treatment. The 95%-confidence intervals include the average value (of 0.61Gy/day) in 22 of the 23 data sets for head and neck can cer,confirming that this value is not inconsistent with the datafrom nearly all the scattergrams.Fig. 3 plots curves relating the TCDso to overall treat-ment durat ion. Only those curves for which the standarderror for the daily increment in TCDso was less than 0.4Gy per day (Table 3) were plotted. The location of thecurves relative to the TCDso ordinate depends upon thestage of tumor. The curves shown are those derived froman analysis which included all the da ta from each au thor.When the scattergram included results for multiple T-stages, identified separately, one curve for a tumor ofaverage diame ter 4.5 cm ('T3') was plotted , but its posi-


9/16

TUMOR CLONOGEN REPOPULATION DURING RADIOTHERAPY 1398C

70

I.W- 60nVI-

50

Moc

/

Shukovsky-G lossopa la l ineBark er R efromolar tr igone

I I I I I i I I I30 40. .DAYS OF

50 60 70T R E A T ME NT

Fig. 3. Curves plotting the increase in dose for tumor control withincreasing overall treatment duration. The data were derivedfrom published scattergrams and from Maciejewski et al. (38) .Only data with a S . E . less than 0 .4 Gy/day were plotted (Table 3,

tion and slope were influenced by data for all stagesbecause the curves for all stages were forced t o a commonslope. When data for multiple stages were presented inone scattergram, but not identified sepa rately, the cu rve isfor the combination of stage s (see asterisks in Table 3).

It should be noted th at, in the analy sis of scattergram s,no account was taken of possible variations in fractionsize, excep t, perhaps, by the exclusion of extrem es. Withan alp ratio of 25 Gy , variations in fraction size within therange 1.8-2.5 Gy have little effect on th e tot al biological-ly-effective tumor dose. Even if 3 Gy fract ions wereused, the biologically equivalent dose given in 2-Gy frac-tions would be less than 4% higher. For the data of mostinterest, that is, those including treatme nts longer than 28days, the fraction size is presum ed to vary relatively little,requiring no significant corrections, and leaving time andtotal dose as the dominant factors determining c hange s intumor control probability. If there were a trend to the useof higher dose fractions in sh orter treatm ent regimens, itseffect would be to ren der our results a slight overestimateof the influence of repopulation.From Table 3 and Figs 2 an d 3 it is obvious that, in mostinstances, protraction of overall treatment time createdthe need for an increase in dose for a constant rate oftumor control. In general, those few examples in whichthis was not shown were also those having the largesterror bars (Fig. 2).

DiscussionPre-radiation tumor growth rate versus accelerated tu-

mor clonogen repopulation. Data collected from the lit-

Fig. 2) . The positions of the curves relative to the ordinate werefixed at the TCDSo or treatment of a T3 tumor, or when T-stages were not identified, merely as the combination of multiplestages (Table 3) .

erature from predominantly retrospective analyses of re-sults of treatment of head and neck ca ncer from a varietyof institutions a nd over the span of abo ut 2 dec ades is notthe stuff for drawing firm conclusions regarding the pre-cise time after initiation of treatment at which tumorsbegin an accelerated rate of clonogen repopulation.However, Fig. 1 suggests that there is a period of about4 f 1 weeks after the start of treatment during which thereis, on average, little change in the TCDSo, but that, there-after, this relationsh ip chang es quite dramatically. Thedashed line in Fig. 1 illustrates that there would be a slightbut undetectable increase in TCDso as a result of th etumor continuing at its preradiation growth rate (Td=60days). In co ntrast to this cons tant slow increa se in TCDsopredicted from a 2-month doubling time there is a sharpincrease in TCDso at overall times greater than about 30days. This is convincing evidence that tumor clonogensaccelerate their rate of increase after a lag period. Thisconclusion from non-scattergram estimates of TCDso isindependently corroborated by the analysis of scatter-grams . Th e location a nd slo pes of the solid lines in Fig. 1 ,which trace TCDso estimates from scattergram data pro-vide, by coincidence, a reasonable fit to the completelyunrelated non -scattergram da ta points. Until the questionis addressed prospe ctively, a very difficult undertaking , areasonable w orking hyp othesis is that ther e is a lag periodof about 4 weeks after the start of radiotherapy before theaverage squamous cell carcinoma of the head and neckbegins a burst of rapid repopulation.

It should be emphasized that such data (Tables 1-3,Figs I-3), although very useful in designing general treat-


10/16

I40 H. R. WITHERS. J . M. G. TAYLOR AND B. MACIEJEWSKIment strategies, refer only to the average behavior: sincehuman tumors are known to differ widely in their pretrea t-ment growth rates (9, 62, 69), the average time of onsetand rate of accelerated growth during treatmen t may alsoconceal wide variations, and may be of limited value inindividualizing radiotherapy prescriptions.

Rate of accelerated repopulation. Rapid repopulation,at least at times beyond 25 days , leads t o a daily incre asein TCDJOof about 0.6 Gy, estimated from scattergramanalysis (Table 3, Figs 2, 3) . Little change in this value isfound by varying the possible day of ons et of regenerationbetween day 10 an d 28 because most scattergram datarelated to treatments lasting longer than 28 days. It isreiterated that the scattergram d ata sh ed little light on thetime of onset of the acc elerated tum or repopulation. T heeffect of tumor clonogen repopulation on the dose toachieve tumor c ontrol estimated he re from scattergram s issimilar to that estimated by BUDIHNAt al. (7) and OVER-GAARD et al. (50) from comparisons of continuous andsplit-course regimens. (Out method of analyzing the scat-tergram published by B UDIHN At al. (7) yielded a greaterincrement per day in the isoeffect dose than determinedby those au thors (Table 3 , Figs 2 , 3).)If it is assumed that it requires about 2.4 Gy in a 2-Gy/fraction regimen to compensate for each doubling inclonogen number, then a daily increment of 0.6 Gy inTCDJO is consisten t with a clonogen doubling ra te of2.4/0.6=4 days. Cell cycle times of 2 4 days are common-ly measured in unperturbed tumors (62), and, while thismay shorten, the mechanism likely to c ontribute most tothe reduction in clonogen doubling rate from 60 days to 4days is a change in cell loss factor such that most daugh-ters of a clonogenic cell division retain their clonogenicityinstead of leaving the clonogen pool (e.g. by differenti-ation, apoptos is, etc.).This result is not inconsistent with the slopes of exclu-sion lines drawn on scattergram s by previous a uthors (forreferences, see Table 2) . The difference is that, in thepresent analysis, the influence of fraction size, or number(except as the dete rminan t of total dose), was ignored andthe increase in isoeffect dose with time was attributedexclusively to repopulation. Also, we did not assume thatthe exclusion line needed to be straight in its extrapola-tion to very short overall treatment times. While the da tain the various scattergrams may have been derived from avariety of treatment regimens, the variation in fractionsize within each set was probably relatively small. Sincethe tumor responses are not very sensitive to change infraction size anyway (e.g. alp ratio 25 Gy), this variablewould have little influence on the slopes of exclusionlines of past au thors , or on the isoeffective dose (TCDSo)curves in our scattergram analyse s.

Accelerated tumor repopulation in the individual. Thepresent analysis of a spectrum of predominantly retro-spective studies provides an estimate of the average lagtime before accelerated clonogen growth reduces tumor

control probability. However, this average may reflect arange of repopulation rates (Fig. 4a ) or a range of times ofonset of accelerated growth (Fig. 4b), or both. Althoughthe implications of these different possibilities are thesame for the average patient they are clearly differentwhen the oncologist aims at individualizing treatment pre-scriptions. Predicting the lag time before the onset oftumor repopulation in each individual patient should be animportant aim of research. Meanwhile, even determiningaverage lag times and repopulation rates for tumors ofvarious histologies and sites would improve our ability todesign rational average treatme nt schem es.

Optimum overall treatment duration. Historically, ex-tending the overall treatm ent d uration was aimed at mini-mizing acute toxicity in normal tissues. In most acutely-responding normal tissues, a repopulation re sponse pro b-ably begins within ab out 2 week s from the start of radio-therapy (3 , 16,70 ,76). In oropharyngeal mucosa and skin,repopulation is rapid enough tha t during the latter part ofa 6- to 7-week treatment regimen, the severity of re-sponses to a 5-day per week regimen of 2 Gy p er fractionremains stable, or even decreases (16), with clonally de-rived foci of regenerated epithelium some times appearingwithin the irradiated area (4). Thus, repopulation by nor-mal epithelium can ba lance o r outstrip the cytotoxicity of10 Gy in 5 fract ions per week at a time when only 4-5 Gyper week would be necessary to balance tumor clonogenrepopulation in the average squamous cell carcinoma ofthe head and neck. Because of this, extension of treat-ment time provides a favorable differential between acute-ly-responding tissues and these tumor s. Th is is particular-ly true in the interval between the o nset of rnucosal repo-pulation a t about 2 weeks an d the o nset of tumo r clonogenrepopulation a t about 3 t o 5 weeks. Thus, shortening theoverall treatment time to less than 3 weeks, and perhapseven to less than 4 or 5 weeks, would be predicted toreduce the therape utic differential between normal e pithe-lial tissues and the tumor. These ideas are illustrated bytheoretical curv es in Fig. 5 , which plot the repopulationkinetics and therapeutic ratios for acutely- and slowly-responding tissues relative to an average squamous cellcarcinoma of the head and neck.

The therapeut ic advantage accruing to acutely-respond-ing normal tissues from rapid repopulation during an ex-tended treatment regimen would probably not be sharedby slowly-proliferating, late-responding normal tissues(because their repopulation response is slow to begin).There fore, the onset of tumor clonogen repopulation sig-nals a progressive decrease in therapeutic differentialbetween late responding tissues and the tumor (Fig. 5).For these tissues, a favorable therapeutic differential isderived only from differentials between their target cellsand tumor clonogens in their respective capacities forrepair of molecular injury. Su ch differentials a re enhan cedby using small doses per fraction, that is, by hyperfrac-tionation (75, 77). Henc e, the most favorable therapeut ic


11/16

141UMOR CLONOGEN REPOPULATION DURING RADIOTHERAPY

IT I ME T I ME

Fig. 4. Two generic repopulation responses that could yield thesame average rate of repopulation: a) a cons tant lag period withvariable regrowth ra tes (---) to yield an average rate defined bythe solid line: b) a variable lag period with constant regrowthrates (---) for the same average rate as in a). The two types ofresponse are not mutually exclusive.* n,,, I La te Normalw ,,,

Irumor I ,_ _ _ _ _ _ &>-

,T TIME ( W E E K S )

Fig. 5 . Hypothetical curves to illustrate time-related changes intherapeutic differential. Upper panel, changes in isoeffect doseswith time: lower panel, therapeutic differentials. Assumptionswere: all treatme nts given in 2 Gy fractions, tolerance =70 G yfor late responding tissues, 30 Gy for acutely-responding tissuesin the absence of repopulation, tumor control dose in absence ofclonogen repopulation during treatment =50 Gy, repopulationbegins at day 10 in acutely -respon ding normal tissues , day 28 fortumors and is faster in normal tissues. The therapeutic differen-tial between acutely-responding t issues and the tumor increasessteeply between 10 an d 28 days and then co ntinues more slowlyafter the beginning of accelerated tumor growth. The therapeu ticdifferential between late responding normal tissues a nd the tum orchanges only very little until tumor growth accelerates, afterwhich it declines. In summ ary, the maximum therapeutic differ-ential would be achieved at 4 weeks, but only if the acutely-responding normal tissue would tolerate such a quick treatment.At shorter t imes, acute responses would be more severe thannecessary and, at longer times, the differential between the lateresponding normal t issues and the tumor decreases. This modelis only an examp le of gene ral principles: quantitative values willvary for different tumor sites and for different patients. It shouldnot be interpreted a s advocating trea tmen t in 4 weeks.

differential between late responding normal tissues andthe tumor would be derived by using the smallest feasibledoses per fraction, fractionation intervals long enou gh forcomplete repair of cellular injury, and an overall time

equal to, or less than the time of onset of acceleratedtumor repopulation. In the average squa mou s cell carci-noma of head and n eck, the overall time fo r this particulartherapeu tic differential (late effects vs. tumor) should beless than abo ut 3 to 5 wee ks; but for individual patients, orin treating tumors of other sites and histologies, it may beshorter or longer. However, even for sq uamo us cell carci-nomas such rapid treatments may be suboptimal becausethe toxicity to ac utely-respo nding normal tissues, whichcan be greatly modified by repop ulation during more pro-tracted regimens, may limit the total dose that could begiven.

From consideration of both early and late respondingnormal tissues, and at least those tumors that show anearly response to radiotherapy, the greatest overall thera-peutic differential would be derived from using the small-est feasible dose per fraction and an overall treatmentduration as short as consistent with achieving acceptableacute normal tissue toxicity, without reduction in the totaldose , determined by the tolerance of critical late re-sponding tissue(s). The constraints on total dose, overalltreatment time and dose per fraction will vary with theclinical situation, being affected by such co nsiderations astumor type, location and growth rate, critical normal tis-sue tolerances, risk factors , etc. A lthough 5 fractions of 2Gy per week is an effective average treatment, there is noreason to consider it the optimum for all, or even themajority of clinical situations (75).

Strategies fo r accelerated treatment. As clearly illus-trated in Fig. 1 and 3 , it would be an advantage in thetreatment of head and neck c ancer, an d probably also incancers of other sites (1, 6, 10, 29 , 53 , 68, 69) if overalltreatment times were shorter than the 6 weeks or longercommonly employed. Th ere a re several metho ds of short-ening treatment duration (22, 54, 56, 64, 65, 68, 72, 75),and, if this can be achieved without reducing the pre-scribed tumor dose , and w ithout increasing seriou s toxic-ity, especially acute toxicity, a therapeutic advantageshould follow.

Initiation of radiotherapy. The influence of tumorgrowth during a delay in initiation of treatment on theprobability of achieving tumor control is, on average,slight (see dashed line, Fig. 1) . However, once t reatmenthas begun it is incum bent on th e oncologist to complete i tas quickly as possible since the clonogen doubling timemay shorten at some time during treatment, from anaverage of 60 days to an estima ted average of about 4 daysin head and neck cancer. If treatment delays can bepredicted (e.g. public holidays, machine maintenance), itis advisable to delay the start of treatment rather than tointroduce interru ptions in the trea tme nt after it has begun.Alternatively, lost days can be made up by treating morethan 5 times per week. Similarly, if a patient is scheduledto complete treatment on a Monday or a Tuesday, it maybe possible, depending upon the severity of the acuteresponses, to t reat 6 o r 7 times per week in the preceding


12/16

142 H . R. WITHERS, J . M. G. AYLOR A N D B . MACIEJEWSKIweek or weeks. (When more than 5 t reatments are to begiven in a Monday or Friday treatment week, 2 dosesmust be given on one o r more days. T o ensure completerepair of sublethal injury in slowly-responding tissues thefractionation interval should be as long as possible, pref-erably 6-8 h (2)).

Tumor regresssion and accelerated tumor growth.Clinically, most head and neck tumors are still regressing4 weeks after the initiation of treatment and continue todo so over the following weeks. Therefore, the presentanalysis indicates th at during the la ter stages of regressionof the visible tumor mass there is a concomitant rapid, butsubclinical, increase in tumor clonogens. This has beenquantified previously in animal tumor systems (27, 35,69). Thus, clinical observation of regression of a tumor islikely to be a snare and a delusion concealing an insidiousand rapid subclinical repopulation by tumor clonogensequivalent, on ave rage, to a loss of an average of at least 4Gy per week in the biologically effective tumo r dose in thecase of head and neck cancer.

Chemotherapy before radiothe rapy. Rapid repopulationby surviving tumo r clonogens r esul ts from killing of tumo rcells: it is not a specific response to x-irradiation. It isreasonable to expe ct that if chem otherapy w ere effectivein killing cells and producing partial or complete tumorregression it would also lead to an ac cele rate d regrowth ofsurviving clonogens similar to that occurring after irradia-tion (63). Since cell death after exposure to chem otherap yagents may be more rapid than after irradiation, the timeof onset of such a regenerative response is unlikely to belater than tha t which follows rad iotherapy , especially re-peated daily radiation exposures which slow the rate ofrepopulation (3) . Clinical experience, especially in ran-domized trials, has found that chemotherapy that hasresulted in complete or partial regression of squamous cellcarcinomas of head and neck has not improved controlrates over those achieved with radiotherapy alone (36,66). A likely cause for this unexpected lack of improve-ment is accelerated clonogen regrowth as a result of thechemotherapy (631, a reflection once again of the decep-tiveness of tumor regression as an indicator of subclinicaltumor behavior.

The use of 2 or 3 courses of chemotherapy prior to theinitiation of radiotherapy was developed empirically andshould be reco nsidered. If the 2 modalities ar e combine d,radiotherapy should begin as soon as possible after asingle dose of che mothe rapy or the cy totoxic drug shouldbe delivered as soon after completion of radiotherapy ascompatible with acce ptab le muco sal reactions. (An addi-tional potential advan tage of this latter scheduling is that agreater proportion of the viable tumo r clonogens would belikely to be in active cycle).

Hypoxic cell sensitizers. Hypoxic cell sensitizers havebeen too toxic to administer in adequ ate doses with ea chradiation dose fraction. In the past, conflicting argumentsregarding the scheduling of a less-frequent drug schedule

have been tha t the sensitizer should be given early in thetreatment regimen w hile the tumor w as large and hypoxiccells numero us, or late when those tumors that reoxygen-ated poorly would have an enhanced ratio of hypoxic toeuoxic cells. Our present analysis suggests that, in th eaverage squam ous cell carcinom a of head and nec k, clon-ogens surviving after 4 weeks of radiotherapy are suffi-ciently well nourished to re populate rapidly an d that theyare probably euoxic. Therefore, hypoxic cell sensitizersmay be more likely to be beneficial if used early in acourse of radiotherapy. It is interesting that the onlyclinical trial to have shown an advantage from the adju-vant use of misonidazole used the drug during only thefirst part of a spli t-cou rse regimen (48).

Zsoeffect formu lae. Present knowledge regarding tumorbiology and radiobiology indicates that isoeffect form ulae,such as the NSD (14, 33, 47), have no biological validity(78). The effect on tumor control of change in fractionsize, assuming the overall treatment time is fixed, appearsto be less than previously considered, and may be mod-eled, at least over a modest dose range (e.g. 2-8 Gy perfraction) using a high value for the a//? atio in the linearquadratic isoeffect formu la (13, 18, 38, 74, 76, 79). Theremay be a spectrum of a/@ atios for different tumors orwithin similar tumors of different kinetic characteristics(13, 74). In general, however, a//? at ios for tumors arelikely to be high (38, 74) making the size of dose fraction srelatively unimportant in isoeffect relationships fo r tum orcontrol using doses pe r fraction of 3 Gy and less .

Likewise, the effect of overall treatment time on theprobability of tumor contro l is likely to vary among tumortypes and am ong individual tumo rs of a given type. How -ever, the pattern of accelerated repopulation beginningafter a lag per iod, as illustrated in this paper , is likely to beas generic for tum ors a s it is for normal tissue s (76). Thereare likely to be wide individual variations in tumor re-growth characteristics, not only among tumors of differ-ent sites but also within tum ors of the same site in differ-ent patients. The development of average models forcalculating isoeffect dose relationships is useful as a gen-eral guide to treatment strategy, but should not obscurethe need to develop methods for predicting the regrowthcharac teristics of individual tumors as a m eans of individ-ualizing therapy.

Shortcomings of the analysis . Th e results of analysis ofa variety of data sets from the literature, and MAC IEJEWSKIet al. (38) were combined. The comparability of suchdiverse data can be questioned. There could be manybetween-author differences, in particular; in definitions ofend-po ints, dosime try, staging criteria, schem es for in-cluding patients who were lost to follow-up, criteria fortreating with radiotherapy and for selecting fractionationparameters and total dose, ways of grouping tumor sites,etc. Also, our analyses grouped tumors from m any differ-ent sites in head and ne ck.

Anoth er caveat is that most of the data s ets were retro-


13/16

TUMOR CLONOGEN REPOPULATION DURING RADIOTHERAPY 143spective. This could bias the results if, for each patient,the choice of treatment regimen was influenced by prog-nostic factors (such a s node stage) which were not pub-lished and hence could not be controlled for in the analy-sis. For example, if within one T-stage, the more ad-vanced disease was routinely treated in a longer overalltime, then, for a given dose the probability of tumorcontrol from mo re prolonged treatm ents w ould be lower,giving an effect similar to th at from accelera ted repopula-tion. This is a consideration only for the scattergramanalyses: it would not a ffect the dog-leg da ta in Fig. I , inwhich a median time was plotted against total dose foreach independent da ta set.

Heterogeneity of tumor stage within a data set is asource of bias: it was common for 2 or more tumo r s tagesto be drawn on the sam e scattergram (Table 2) or groupedwhen presenting local tumor con trol rates (Table 1).

Another source of concern is publication bias, that is,the tendency to publish only results which show an effect.It is possible, although probably unlikely, that time-dosescattergrams were only published if there was clear evi-dence of an effect of protraction of overall time. This biaswould cause the effect of repopulation to be overestimat-ed .

There are various assumptions and approximations inthe statistical analysis which are worth reiterating. Theplacement of the TCD5o values in Fig. 1 was based on theassumption that an effective Do of 5 Gy appropriatelydefined a tumor control probability cu rve, and tha t an a/@ratio of 25 Gy was valid. However, other reasonablechoices for the effective Do, or an alp rat io greater than,say 8 Gy, would not qualitatively change the conclusionthat the time component is an important determinant ofthe radiation response beyond about 3 to 5 weeks.

In the scattergram analysis, the logistic model is as-sumed to hold for all data sets; but this model is certainlyonly an approximation to the reality. Th e main purpose ofthe model is as a means of assessing the relative impor-tance of time and dose: hence the form of the left handside of the equation is of little im portance . Calculations ofthe standard errors in Table 3 were based on the asymp-totic information matrix (1 1 ) and as su ch are only approxi-mate for small samples.

Although it is necessary to be aware of the limitationsof the analysis, they d o not introduc e large and/or system-at ic errors . For ex ample, assume that in one s tudy usedfor constructing Table 1 and Fig. 1 an actuarial localcontrol rate of 30% was reported, but that the absolutecontrol rate, if reported, would have been 60%. Even inthis extreme exam ple, the TCD so would be changed byonly 4.28 Gy by a change in the method of reporting localcontrol. Also, it should be remembered that some poten-t ial errors counterbalance one a nother, and that the TCDmvalues were obtained by extrapolations from doses thatgave both higher and lower control rates th an 50 %. Moreimportantly, the magnitude of the increase in dose for

tumor control with protraction of treatment time almostcertainly overwhelms minor unc ertainties in th e data andthe methods of their analysis. Also, given all these poten-tial or real differences, it is encouraging that the TCDsovalues (Fig. 1) and the dose to balance an extra day oftreatment (Figs 2 and 3 ) showed relative consistencyamong the broadly-derived data.

Thus, although there may be som e uncertainties regard-ing the precise averages for its time of onset and subse-quent rate, the phenomenon of accelerated repopulationby tumor clonogens is clearly established: Its occurrenceis usually u ndetec table in its early stages a nd, sinc e it mayoccur during treatment, is an important cause for failure.

Some ConclusionsSome implications of our findings are :1 ) Radiotherapy, at least for head and neck cancers ,

should be completed as soon as practical after it hasbegun: it is better to delay initiation of treatment than tointroduce delays during treatme nt.

2) Accelerated growth involves small absolute numbe rsof tumor clonogens an d, rath er than being de tectable clini-cally as tumor growth, occurs while the mass is stillregressing.

3) Administration of 2 or more course s of chemotherapybefore beginning radiothera py may pre cipitate a regenera-tive response in the tum or and prejudice local contro l byradiotherapy.

4) In view of the above, comp lete or partial regressionsshould not be a primary aim of curative treatment, andregression should not blind the radiation oncologist ormedical oncologist to the subclinical existence of acceler-ated repopulation, a potent ca use of treatment failure.5) Hypoxic cell sensitizers may be more useful if em-ployed early in a cou rse of treatment since rapid rep opula-tion late in treatment suggests that surviving clonogensare well-oxygenated.

6) A simple isoeffect formu la for change s in fractiona-tion pattern cannot ever be valid because normal tissuesand tumors var y, not only in their sensitivity to ch anges infraction size, but also in their repopulation k inetics. Fur -thermore, repopulation kinetics change during treatment.

7) The dose s necessary to achieve acceptable rates oflocal control in head and neck cancer vary widely amonginstitutions worldwide: the m ajor cau se fo r this variationis probably the variation in overall treatment durationwith resulting differences in extent of tumor clonogenrepopulation during therap y.These analyses and conclusions relate to the averagecance r of the head and n eck: prospec tive quantification ofthe likely time of onset and rate of accelerated tumorclonogen repopulation is required for optimizing treat-ment for individual patients with head and neck cancerand should be an impo rtant goal of resea rch. Th e findingsfor head and neck m ay be inappropriate to oth er sites: theeffects of overall treatment time on the local control of


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144 n. R. WITHERS, J . M . G. TAYLOR A N D B . MACIEJEWSKIcancers of other his to logies and s i t e s in the b o d y alsoneeds inves t iga t ion.

ACKNOWLEDGEMENTSKathy Mason reconstructed da ta from scattergrams and helpedwith various other aspects of the analyses. Jan Haas and CallyDavis helped with preparation of the manuscript. We are grateful

for their valuable contributions.This investigation was supported in part by U.S. PHS grantnumbers CA-31612, CA-29644 an d CA-16042 awarded by theNational Cancer Institute, DHHS.Request fo r reprints: Prof. H. Rodney Withers, Dep artment ofOncology, UCLA, Los Angeles, CA 90024, USA.

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the hazard of accelerated tumor clonogen number re population during radiotherapy

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