dose fractionation and regenration in readiotherapy for cancer of the oral cavity and oro pharynx...

In/ J Rod,o,,on 0ncolr1~1~ Bwl P/I,IY Vol. 16. pp. 831-843 Printed tn the U.S.A. All rights reserved.

0360-3016/89 $3.00 + .oO Copyright 0 1989 Pergamon Press plc

??Brief Communication

DOSE FRACTIONATION AND REGENERATION IN RADIOTHERAPY FOR CANCER OF THE ORAL CAVITY AND OROPHARYNX:

TUMOR DOSE-RESPONSE AND REPOPULATION

BOGUSLAW MACIEJEWSIU, M.D., 1,4 H. RODNEY WITHERS, M.D., D.Sc ., 1,3 JEREMY M. G. TAYLOR, PH.D. 1,2,3 AND ANDRZEJ HLINIAK, M.D.

Department of Radiation Oncology, Division of Biostatistics, School of Public Health, 3 Jonsson Comprehensive Cancer Center, UCLA Center for Health Sciences, Los Angeles, CA 90024, U.S.A.; 41nstitute of Oncology, Gliwice, Poland and Warsaw, Poland

In a retrospective study, local control of the primary tumor in 498 squamous cell carcinomas of the oral cavity and oropharynx was analyzed with respect to initial tumor volume, total dose after normalization for variations in fraction size, and to overall treatment time. Frimary tumors were grouped into 4 sites, tongue (175), oral cavity including floor of mouth, faucial pillar, soft and hard palate and gingiva (210), tonsil (72) and buccal mucosa (41). Total doses of 6oCo irradiation ranged from 30 Gy to 72 Gy, overall treatment times from 15 to 80 days and dose per fraction from 1.8 to 6 Gy. The large number of patients and diversity of dose fractionation patterns permitted assessment of the independent contributions to treatment outcome of stage, fraction size and overall treatment duration. The following conclusions were drawn: (1) Overall treatment time influenced strongly the probability of local tumor control. Over the interval of about 30-55 days used in treating most of this series of patients, an increase of 60 cGy per day, on average, was required for a constant control rate. (2) The increase in dose was attributed to accelerated tumor clonogen growth rate. Such accelerated growth could be a major determinant of failure in protracted regimens. (3) The accelerated rate of regrowth was similar for all tumor sites and stages. (4) The dose for tumor control was relatively independent of variations in fraction size within a range of about 1.6 Gy to 3 Gy: the alpha/beta value in the linear quadratic isoeffect equation was at least 15 Gy. (5) Local control at the primary site required an average of about 3 Gy more for each increase in T stage. This increase most likely reflected an increased number of tumor clonogens, not a decreased tumor cell radiosensitivity. (6) The probability of control at the primary site was less likely if lymph nodes were positive, but this association was only shown to be statistically significant for primaries classified here as oral cavity and oropharynx, not tonsil, toogoe or buccal mucosa. (7) After allowing for differences in treatment parameters, especially for heterogeneity in overall treatment times, tumor control probability increased steeply with increase in total dose. (8) A general prhtciple of radiotherapy, at least for squamous carcinomas of head and neck, should be to deliver the desired fractionated dose regimen without unnecessary interruptions and in the shortest time compatible with no reduction in dose below that tolerated by the late-responding normal tissues.

Head and neck cancer, Dose fractionation, Repopulation, Tumor control probability, Isoeffect curves, Radiotherapy.

INTRODU~ION

The response of a tumor to fractionated radiotherapy de- pends on tumor size and various radiobiological mecha- nisms, described as the four Rs (33 ). Of these, sublethal damage repair and reoxygenation have been studied ex- tensively in animals, and the effect of cell cycle related fluctuations in radiosensitivity has been investigated ex- tensively in vitro. Tumor repopulation is a time dependent process that has received much less attention, reflecting perhaps the clinical perception that it was not a problem with most human tumors.

Tumor regeneration has been studied in experimental animals by assaying the proportion of clonogenic tumor cells as a function of time after radiation exposure (12, 14)) and by measuring the increase in radiation dose necessary for tumor control with increasing fractionation interval (2 1, 27 ). Kummermehr et al. (14) found an un- expectedly high potential for repopulation even in a slowly-growing adenocarcinoma.

Very few clinical data on the importance of repopulation in human tumors are available. However, its importance can be inferred from a number of observations:

Reprint requests to H. R. Withers. FOS TW03565-01, awarded to B. Maciejewski by the Fogarty Acknowledgements-We would like to thank Ms. Jan Haas for Foundation, and by PHS grant numbers CA-3 16 12, CA-29644 her assistance in preparing this manuscript. and CA- 16042 awarded by the National Cancer Institute, DHHS.

This investigation was supported in part by MH grant number Accepted for publication 29 September 1988.

831

832 I. J. Radiation Oncology 0 Biology 0 Physics March 1989, Volume 16, Number 3

1. The probability of control of carcinomas of larynx and skin, and melanoma metastases decreased with protraction of overall treatment time in continuous ( 1,6, 13, 16, 19, 27, 28) or split course regimens (17).

2. The short recurrence time distributions for many human malignancies (11, 22) treated with radiotherapy for cure or palliation are not consistent with the median doubling time of about 2 months measured in unper- turbed tumors (2, 5,20,27, 30). These observations sug- gest that accelerated regeneration begins at some time after the start of irradiation but, unlike the studies showing a decline in control probability from a certain total dose, they do not establish that repopulation begins before completion of a regimen of fractionated irradiation.

Tumor repopulation and dose response relationships for various T and N stages are further studied in the present analysis of a large series (498 ) of squamous cell carcinomas of the oral cavity and oropharynx.

METHODS AND MATERIALS Total

This retrospective study involved 498 of 983 patients receiving radiotherapy for cancer of the oral cavity and oropharynx at the Institute of Oncology in Gliwice, Poland between 1970 and 1979.

* Floor of mouth, faucial pillar, hard and soft palate, gingiva.

Criteria for inclusion were: ( 1) Completed a prescribed course of external radiotherapy alone (i.e. no surgery, chemotherapy or brachytherapy); (2) Age less than 75 years; (3) Histologically-proven squamous cell carcinoma; (4) No distant metastases; (5) No prior treatment; (6) A minimum of 3 years available for follow-up.

Not included in the analysis were 165 cases with his- tology different from squamous cell carcinoma, 234 cases in which external radiotherapy was combined with surgery, brachytherapy or radiosensitizers, 46 cases in which treatment was incomplete and 40 cases where the patient never returned for follow-up. The exclusion of 40 patients lost to follow-up is not considered too damaging because the purpose of the analysis was not intercomparison with other series but merely the assessment of response of squamous cell carcinomas to external beam therapy as a function of treatment parameters. Similarly, patients who did not complete treatment would be outliers in a time dose scattergram and of little value to the type of analysis undertaken here.

eluded 133 cases with tumor of oral tongue and 42 cases with base of tongue. The distribution of cancers in the second group was 93 floor of mouth, 60 soft palate and faucial pillar, 25 hard palate and 32 upper or lower gingiva. Seventy-two cases of cancer of the tonsillar region and glossopalatine sulcus were included in the third group and 4 1 cases of buccal mucosa cancer were in the fourth group. Whereas these groupings may not have been optimal based on historical results of radiotherapy, the analyses, which accounted for variables in treatment parameters, yielded well-ordered responses. Because most of the patients who achieved local control and were not lost to follow-up survived at least 3 years (189/201), actuarial analysis was not used.

The distribution of TNM stages classified by the UICC system, 1984, is also shown in Table 1. There were only 15 T 1 tumors because, for most such cases, surgery and/ or interstitial brachytherapy were the primary treatment choices.

Treatment technique and dose There were 457 males and 41 females. Ages ranged

from 29 to 75 yrs, being on average 59.8 yrs. All results reported here relate only to control or failure

at the primary site. Response was scored as local control for 3 years = 1 or at last follow-up if death was from intercurrent disease in less than 3 years, recurrence = 2, persistence = 3. Of 201 patients achieving local control, 189 were alive at 3 years; 12 died free of local disease within 3 years. The response of regional nodes was not analyzed for this report.

All cases were treated with 6oCo gamma-rays usually through two opposed fields ranging in size from 6 X 8 cm to 12 X 15 cm. Primary tumor and regional metastatic lymph nodes were within the irradiated fields. Dose was specified at the midline. For a few patients with lateral lesions, wedged fields were used and the dose specified as a median value for a volume extending 1.5-2 cm beyond the tumor margin.

The cases were divided into four groups depending on site of the primary tumor (Table 1). The first group in-

A standard aim of curative treatment between 1970 and 1979 was to give a total dose of 65 Gy in 26 fractions in about 35-40 days. For many reasons, this aim was often not realized: severe mucosal response, advanced

Table 1. Distribution of patients according to the site of primary tumor and TNM stage-UICC, 1984

Primary site TNM stage No. of patients

Tongue (base and oral)

TINo.,Mo 4 TzNo. I .z.No 34 T3No.nNo 137

Total 175

Oral cavity and oropharynx*

TINo.,.~Mo 10 TzNo, I .~.&fo 65 TsNo.,mMo 135

Total 210

Tonsil TzNo. I .2,3MO 26 T3No. I .2.3Mo 46

Total 72

Buccal mucosa TlNoMo T2No.,Mo T3No. I .z.No

Total

9 31 41

498

Dose fractionation and regeneration 0 B. MACIEJEWSKI et al. 833

stage of disease, poor general condition of the patient, age, or holidays. Slowly-regressing tumors were sometimes given a boost dose of up to 5 Gy in 2 fractions. Otherwise, the treatment fields remained constant during a course of therapy and were similar for patients with the same site and stage of disease. Field size and primary tumor volume were not factors independently determining the original prescription of overall treatment duration, although there was a tendency to use fewer larger fractions for patients with advanced nodal disease. It was not usual to give elec- tive irradiation to lymph nodes in the lower neck.

In an individual patient, the dose per fraction was constant throughout treatment. Total doses ranged from 30 Gy to 72 Gy, dose per fraction from 1.8 Gy to 6.0 Gy and overall treatment time from 15 to 80 days. Figure 1 shows the distributions of total dose (D) , dose per fraction (d) and overall treatment time (t). Although there is a wide spectrum of treatment variables, more than 80% of patients received 57.5-67.5 Gy total dose in overall treatment times ranging between 35 and 60 days. In 70% of patients, dose per fraction ranged from 2.3 Gy to 2.7 Gy. The analysis may be influenced by systematic biases (e.g. protraction of treatment for more advanced stages because of severe acute morbidity) even though such bias was not a factor in the original treatment prescription. However, the influence of such biases is less critical than in other types of rectrospective analysis because there were fairly large numbers of patients in relatively homogeneous subgroups and, furthermore the analysis was not aimed at comparisons with other series.

Quantifying the influence offraction size: (Y/B ratio The influence of variations in fraction size on biological

response was quantified using a linear-quadratic survival and isoeffect model (4, 10, 26, 29, 35).

Surviving fraction = e-(0d+gd2).

Two methods were used, one parametric and the other non-parametric. The purpose of using two methods was to check that the results depended on the data, not the assumptions of the analysis.

Non-parametric method. The Spearmans correlation coefficient for tumor response and fraction size was calculated ( 15). Data were separated into groups in which the T and N stage and overall treatment time were similar but the total dose and dose per fraction varied. A data group was not helpful for this non-parametric analysis if it could give no information on the association between the 2 variables being correlated (tumor control and dose per fraction). Therefore, groups were excluded if there was only one patient or if the outcome was constant for example, all tumors controlled. For a given value of alpha/ beta, the Spearmans correlation coefficient (15, 23) between tumor response, measured as cure (l), recurrence (2) or persistence (3) and the form nd( cu//3 + d) was calculated. A value of + 1, ( - 1) for the correlation coef-

FREQUENCY

200--

160--

120--

60--

40--

O-- _&-L 30 35 40.45 Sri 5; so. 65 7d

TOTAL DOSE

OVERALL TREATMENT TIME

120 l-l

210 T I--l DOSE PER FRACTION

150

1

Fig. 1. Distribution of fractionation parameters in the treatment of 498 patients.

ficient indicates perfect positive (negative) association; zero indicates no association. Any value larger than 0.4 is usually considered a strong association. The average Spearmans correlation coefficient is given by

? = 2 (Ni - l)rJC (Ni - 1)

where ri is the correlation and Ni is the number of patients in group i. The form, nd(a/P + d), where n is the number of dose fractions and d is the dose per fraction, is a function of the biological dose if the given CY//~ value is correct. Eleven different values of (Y/B were tried, namely, 0, 1,2,8, 10, 15,20,25,35,50, and infinity, and then placed in order according to which gave the best fit to the analyzed data, that is according to the absolute value of the correlation coefficient. The value of a//3 which maximizes ? is the best overall estimate of cr/fi.

Parametric method. The second method was a logistic regression (25) using the model

log(p/(l - P))

= & + A,nd + A2nd2 + h(t - 14)+ + Fi

where Fi represents categorical variables which depend on

834 1. J. Radiation Oncology 0 Biology 0 Physics March 1989, Volume 16, Number 3

the tumor site and the T and N Stage, A,, AZ and h are parameters to be estimated, n is the number of fractions, d is the dose per fraction, and (t - 14)+ is the overall treatment time minus 14 days. (If treatment times less than 14 days would have been used, or when values oft less than 14 were tested, (t - 14)+ would be zero.) Implicit in this model is that accelerated repopulation by tumor clonogens did not begin within 14 days. The choice of 14 days was somewhat arbitrary: the likely time was unknown and there were few data for overall times less than 28 days that could help establish it. Values other than 14, from 7 to 2 1, were tested and gave similar results. The estimate of P/a is given by AZ/AI. (Using /3/u! is preferable to using (r/p in an analysis such as this because it avoids discontinuity when values of A2 are close to zero.)

Normalizing total doses for changes in fraction size Each total dose from fractionation schemes using a

spectrum of doses per fraction was normalized to the total dose to which it would be biologically equivalent if given in 2.5 Gy fractions, using the formula (35 ):

Normalized total dose (NTD) = Total Dose - aI@ + d (Y/fl + 2.5

where a/B is a characteristic of the tumor and d is dose per fraction. If two tumors received the same NTD, they would be equally depleted of cells regardless of the size of dose per fraction, other things being equal.

Total doses were normalized for 2.5 Gy fractions because most of the 498 patients were treated with 2.5 + 0.2 Gy per fraction (Fig. 1). For this reason, and because an CY/~ value of 25 Gy was ultimately used in normalizing the doses, the NTD values were not greatly different from the doses actually prescribed.

IdentifVing the eflect of overall treatment time The Spearmans correlation coefficient between tumor

response and overall time was calculated ( 15 ). The method (23) was the same as described earlier for quantifying the influence of fraction size except that when data were separated into groups, the T and N stage, total dose and dose per fraction were similar within each group, but the overall treatment time varied. To calculate the correlation coefficient, each group must contain some variation in response (cure, recurrence, persistence) and overall treatment time.

Quantifying the e#ect of changes in overall treatment duration

Differences in overall treatment duration were accounted for by an exponential factor operating after a certain time delay from the initiation of radiotherapy. The model used is closely related to other cell survival and repopulation models (4, 7, 20, 25, 26).

Let K denote the number of tumor cells, then from the

linear quadratic model, a single dose of radiation (d) re- duces this number to

K = Kee-(ad+Pd2) (1)

If a series of equal fractions produces an equal effect per fraction, then after n fractions, the number of surviving clonogenic tumor cells will be, on average,

K = K_e-(nc7d+n~d2) (2)

To model the effect of repopulation between dose fractions, let (t,, tZ, t3, * - - t,_,) denote the time intervals between fractions and assume a rapid exponential proliferation of tumor clonogens immediately after the first fraction. Just prior to the second fraction, the average number of surviving cells would be

K.e-c+Sd2 . eAt, (3)

and just prior to the third fraction would be

K e-2ad-2@d2 . eA(t,+tz) (4)

From Eqs. ( 3 ) and ( 4 ) , the average number of surviving tumor clonogens at the completion of treatment will be

K, = K.e-nad-nSd2 ,eXt,+. . .+1.-I)

= K.e- nad-n,3d2+ht (5)

where (t) is the overall treatment time. If tumor repopulation begins after some time delay (b), then the average number of surviving tumor clonogens after the completion of treatment will be

K = K e-nmd-nSd2+X(t-tr,)+ s . (6)

If overall treatment time, t, is equal to, or shorter than this time delay b, the value of (t - b) in equation (6) equals zero, and no correction for repopulation is needed.

Tumor control probability The probability of tumor cure (p) is the probability of

no surviving clonogenic cells per tumor which, assuming random killing, is given by

Prob (cure) = emKs (7)

Using equation (6), equation ( 7) becomes

log(-log(p)) = A,, - ncud - n/3d2 + X(t - to) (8)

in which & is log K. For convenience, a slight variation of this model

(equation 8) introduced, in which the logit transformation was used instead of the double log transformation, i.e.


WP/(l - P))

= Ac + Alnd + Aznd2 + x(t - to) (9)

&, A,, A2 and X are estimated in equation 9 by the method of maximum likelihood. Thus Al /A2 is an estimate of a/&

Quantifving the effect of tumor and node stage The model, log(p/(l - p)) = & + B(NTD) + C(t

- 14)+ + D(T stage) + E(N stage), was fitted for each tumor site, where A, B, C, D, and E are coefficients to be estimated, NTD is normalized total dose and (t - 14)+ is the extension of treatment time beyond 14 days. T- stage was given values of 1, 2, and 3, and N stage was given values of 0, 1,2,3. Then D/B and E/B are estimates of the extra dose needed for the same probability of local control for an increase of one in the T-stage or N-stage, respectively.

RESULTS

The sequential aims of the analysis were to:

a. Establish the importance of the T and N stage to treatment outcome.

b. Quantify the effect on tumor response of change in dose per fraction and to account for this in subsequent analyses.

c. Establish the importance of overall treatment time. d. Quantify the repopulation effect. e. Quantify the T and N stage effect.

1. Local control in relation to T and N stages Three-year local control rates for various stages of dis-

ease in four tumor sites in the oral cavity and oropharynx are shown in Table 2. This table groups the data from all 4 tumor sites and shows that local control depended strongly on T stage, being 3 times lower for advanced cases (33% for Tj) than for early stages (93% for T,).

There is a weak trend to a lower probability of local (primary tumor) control with increasing size of metastatic lymph nodes. Overall primary tumor control rates for No, NI,Nz,andN3stageswere98/191(51%),61/162(38%), 24/60 (40%), and 18/85 (21%). Table 2 also correlates the pattern of failure with stage of disease. Persistence, as distinct from recurrence, becomes more common with increase in both T and N stage but was determined more by N stage than by T stage. As will be discussed later, these results are partly a consequence of having treated patients with large nodes with regimens shown to be in- ferior to the regimens used for less advanced disease.

2. Fractionation response characteristics of tumors The influence of changes in fraction size on tumor re-

sponse was assessed using a non-parametric and a parametric method. The results are shown in Table 3 A and B. The non-parametric method (Table 3A) shows that

Table 2. Radiotherapy results for 498 patients treated for squamous cell carcinomas of the oral cavity and oropharynx

Failure Local

control* RCt PL-s

Stage No. % No. % No. %

T,No 10 91 1 9 0 0 T,NI 3 100 0 0 0 0 T,N2 1 100 0 0 0 0 Total T, 14 93 1 7 0 0

TzNo 39 60 17 26 9 14 TrN, 18 49 9 24 10 27 T2N2 9 50 4 22 5 28 TzN3 6 43 0 0 8 57 Total T2 72 54 30 22 32 24

T3No 49 43 31 27 35 30 T3Nr 40 33 19 16 63 51 T3Nz 14 34 5 12 22 54 T3N3 12 17 6 8 53 75 Total T3 115 33 61 17 173 50

Total 201 41 92 19 205 40

* 3 year in 189/201 patients. t Tumor recurrence. * Persistent tumor.

high a//3 values (15 Gy or more) give a better fit to the data than do low values ( 8 Gy and below).

Table 3B gives estimates of/3/s together with 95% confidence limits calculated by the parametric method. Also shown is the lowest possible value of a/B based on the 95% confidence limits. Pia ratios are near zero, indicating

Table 3. cu/@ values (Gy) and /3/ar values (Gy-) for four origins of squamous cell carcinoma of the oral

cavity and oropharynx

Site Order of (Y//I values from best to worst*

A. Non-parametric method

Tongue 25, (35, 30), 10, 20, 50, 15, 8, 03, 2,0 Oral cavity

oropharynx co, 50, 35, 30, 15, 20, 25, 10, 8, 2,0 Tonsil 20, (25, 30, 35, 50), 15, co, (10, 8), 2, 0 Buccal mucosa co, (50, 35, 30, 25, 20, 15, 10, 8), 2, 0

* Values within parentheses give equally good fit to the data.

Lower bound of 95% C.I. Site B/a value (&SE.) interval for (Y//I

B. Logistic regression

Tongue -0.107 (kO.021) co Oral cavity

oropharynx -0.07 1 (f0.022) Tonsil 0.138 (kO.069) 3; Buccal mucosa 0.15 1 (zkO.097) 2.9


large values for (Y/P, which is consistent with the results obtained using the non-parametric method of analysis.

In subsequent analyses, an a/B value of 25 Gy was used in the linear-quadratic isoeffect formula (26, 35) to normalize total doses to the equivalent dose given as 2.5 Gy fractions. Any value of 15 Gy or above would have been reasonable, and from a practical point of view, total doses are altered very little by selecting different (Y/B values above 15 Gy. This is especially so for that large proportion of treatments given in 2.3 to 2.7 Gy fractions.

Table 5. Correlation between local control (LC) and overall treatment time (t) for 4 origins of squamous cell

carcinoma of the oral cavitv and oronharvnx

Stage groups TR* Sample size

(# cases)

Tongue T,TzNo

TzN~2.3 3. Influence of overall treatment time on local control

a. Subgroups with similar dose regimens. To analyze the influence of overall treatment time on local control rate, using Spearmans correlation method, data for 345 patients were first stratified into 46 homogenous groups with respect to the tumor site, T and N stage, and total biologically effective dose (Tables 4 and 5). (The remaining 153 patients were excluded because they could not be placed within homogeneous groups or because the whole group showed an identical tumor response.) Thus, the only remaining variable influencing tumor response was overall treatment time, which ranged from 20 to 80 days. Within each of 46 subgroups, the correlation between local tumor control rate and overall treatment time was analyzed using Spearmans correlation ( 15 ) . Table 5 (A-D) shows the correlation coefficient for each of the subgroups. A positive correlation indicates that extension of the overall treatment time is detrimental to the chances of local control and a negative value indicates that it is beneficial. In 44 of the 46 subgroups, the correlation coefficient was positive, and in 4 1 of them it was higher than 0.5, with an overall p value of 0.000 1.

b. Quantijication of tumor clonogen regeneration. Data for all 498 patients were consolidated into 12 groups which were relatively homogeneous with respect to tumor site,

T3No

T~NI.z

T3N3

Fl 2 7

e 6 b : 2 :

e 4

: : : 7 5

e 11 b 4

: 20 11 e 12 b 7

f = 0.74 p = 0.0001~

T,TzNo

TzN~2.3

T,No

Oral cavity f 5 h 15 i 10 g 4 h 11 f 4 8

f 3 h 11 i 12

TJNI,? j f 2

T3N3 Table 4. Characteristics of fractionation regimens

TR* Range of total dose Range of dose per

(D) in Gy fraction (x) in Gy

: 46.0 < D < 62.0 56.0 < D 5 64.0

Fl 58.0 < D 5 64.0 64.0 < D 5 68.0

e 64.0 < D < 68.0 f 51.0 5 D < 59.0 g 58.0 5 D 5 65.0 h 59.0 < D < 65.0 i 65.0 5 D < 72.0 J 65.0 IS; D < 72.0 k 57.0 5 D < 65.0 1 59.0 < D 5 64.0 m 65.0 < D 5 68.0 n 52.0 < D 5 62.0 0 62.0 < D < 67.0 P 62.0 < D < 68.0

* Treatment regimen.

2.8 < x < 4.5 2.6 < x 5 2.8 2.2 5 x < 2.6 2.3 5 x 5 2.5 2.5 < x 5 2.7 2.3 < x I 3.0 1.9 5 x I 2.3 2.3 < x 5 2.6 2.3 < x 5 2.5 2.5 < x 5 2.7 1.7 I x 5 2.25

2.25 < x 5 2.5 2.3 < x 5 2.5 2.7 5 x 5 3.5 2.2 < x s 2.5 2.5 < x < 2.7

TzNo.,,>

T3No. 1.2

T,TzNo. I

T3No

T3N1.2.3

is 9 h 23 i 11 j 14 h 7 j 3

? = 0.73 p = 0.0001~

Tonsil k 6 k 13 4

1 13 m 13

? = 0.69 p = O.OOOlt

Buccal mucosa

0 P : n 3 P 7 0 5 P 5

? = 0.88 p = 0.001t

* Treatment regimen (see Table 4). t Represents mean value of Spearmans correlation coefficient.

U-C) vs (0 Spearmans corr. coeff.

0.62 1.00 0.81 1.00 0.87 1 .oo 0.89

-1.00 0.87 0.95 0.84 0.77 0.82 0.67 0.86 0.81 0.61

1 .oo 0.87 0.81 0.77 0.60 0.91 0.89 1 .oo 0.79 0.90 0.85

-1.00 0.73 0.57 0.91 0.72 0.4 0.87

0.67 0.89 0.41 0.80 0.87

0.95 0.87 0.87 0.82 0.87 0.92

Dose fractionation and regeneration 0 B. MACIUEWSKI et al. 837

and prognosis based on T and N stage. They were inho- mogeneous with respect to normalized total dose and overall treatment duration. Responses were classified as local control ( 1) , recurrence after initial clearance ( 2)) or persistence of tumor (3). These outcomes of treatment in the 12 groups are plotted against the normalized total dose (NTD) and overall treatment time (Figs. 2-5 ) .

Figures 2-5 illustrate dramatically how strongly overall treatment time influences the chance of local control, at least over the range of times employed. In all 12 groups,

increasing the overall treatment time decreased the probability of local control.

To quantify the effect on the dose response relationship of changes in the overall treatment time, the logistic regression model was used

lOg(p/(l - p)) = & + AI(NTD) + Az(t - 14)+ + Ei,

where NTD = nd((cr//3 + d)/(cu/fl+ 2.5)) and was normalized for (Y/B = 25 Gy and for dose per fraction of 2.5

2 TONGUE

3 Tz N, .N, ,N,

and T, N,

Fig. 2-5. Results of radiotherapy for various stages of squamous cell carcinoma of various sites, plotted against normalized total dose (NTD) and overall treatment time. Normalized total doses were calculated as equivalent to total doses given as 2.5 Gy fractions using an a/B value of 25.0 Gy. Responses to treatment represent local control ( 1) , recurrence after initial clearance ( 2 ), persistence of tumor ( 3 ) . The curves plot the relationship between total dose and overall time for a fixed probability of local control: 50% ( TCDso), solid line: 90% (TCD,, ) , dashed line.

838 1. J. Radiation Oncology 0 Biology 0 Physics March 1989, Volume 16, Number 3

ORAL CAVITY

70 !

10 20 30 40 50 60 70 60 10 10 30 40 so

DAYS DAYS

Fig. 3.

Gy. Part of the formula (t - 14)+ is positive and excludes the possibility that accelerated tumor repopulation began within 2 weeks after the start of radiation therapy. Based on this model, doses to yield 50% and 90% probability of local control ( TCDso and TCDgO) were estimated (9, 18 ) and the curves for these values were added to Fig- ures 2-5.

The pattern of control, recurrence, and persistence of tumors is remarkably well ordered as a function of time with little overlap between the three categories of outcome. Table 6 shows estimated TCDso values for various stages and sites of disease for treatment regimens of 35, 42, and 49 days duration. Except for tonsil and the small series of early stage tongue lesions, the estimated TCD50 value

for a 7 week regimen exceeded 65 Gy. The scattergrams (Figs. 2-5 ) show few patients with local control if the delivery of 60 Gy took more than 7 weeks.

Because there were very few data at overall treatment durations of less than 28 days, and because rates of clonogen increase were determined from regression lines fitted to the data, the assumption that accelerated repopulation did not begin within 14 days had no detectable influence on the calculations and conclusions. (The purpose of in- eluding a positive value for the onset of regeneration is to provide comparability with normal tissues and flexi- bility in this modeling.)

The estimate AZ/AI is the dose necessary to balance the effect of tumor repopulation during each extra day of

Dose fractionation and regeneration 0 B. MACIEJEWSKI et al.

TONSIL

DAYS

Fig.

overall treatment time. The estimates of this dose for four tumor sites are shown in Table 7, together with standard errors. Within the limits well defined by data (e.g. about 30-55 days), one extra fraction of 2.5 Gy is needed to balance the tumor repopulation occurring during each 4 days extension of overall treatment time. Estimated values for doses balancing one day of tumor repopulation are minimally dependent on the choice of CL/~ value above 10 Gy: a//3 = 10 Gy and (Y/B = 50 Gy gave very similar results. Also, limiting the time of onset of accelerated tumor repopulation between 7 and 2 1 days did not strongly influence the values shown in Table 7.

5A

BUCCAL MUCOSA

T, and T2 No ,N,

10 20 DA;: 40 50

Fig

TONSIL

T,N,,N,.N,

I

10 20 Jo 40 50 M

DAYS

4.

4. Dose response relationships for tumor control Just as the influence of overall treatment duration on

tumor control probability can be appreciated easily from the horizontal rows of responses (1,2, or 3) at any given normalized total dose in Figures 2-5, so the influence of total dose can be appreciated from a vertical comparison of responses at any given overall treatment duration. The relatively steep improvement in local control with increase in total dose is also readily apparent from the proximity of the TCDSO and TCDgO curves on each of the figures.

Values for TCDSo and TCDgO were calculated for three different overall treatment durations and are shown in

56 70

65

60

55.

50

45 -

40 -

35-

5.

BUCCAL UUCOSA

T3 No. N,, N2. NJ

3 10 20 30 40 50 60

DAYS

3


Table 6. Total doses* for 50% and 90% probability of tumor control (TCDSo and TCDw) calculated for overall treatment times of 3542, and 49 days

Tumor site and stage TCDS~ in Gy TCDvO in Gy

Treatment time (days): 35 42 49 (S.E.) 49

Tongue T,-zNoMo 53.3 57.3 61.3 (1.4) 65.3 TA-JT~NoMo 59.0 63.0 67.0 (1.1) 71.0 T~NI-~Mo 58.6 62.6 66.6 (1 .O) 70.6 T&MO 59.8 63.8 67.8 (1.3) 71.8

Oral cavity and oropharynx TI-zNoMo 55.1 59.4 63.6 (0.8) 66.8 TzNI-~TxNoMo 58.9 63.2 67.5 (0.8) 70.6 T~NI-~Mo 59.8 64.1 68.4 (0.9) 71.6 T&MO 63.6 67.9 72.2 (1.9) 75.4

Tonsil TzNo-2Mo 53.7 57.6 61.6 (1.2) 65.3 TsNo-2Mo 55.5 59.5 63.4 (1.9) 67.1

Buccal mucosa T,-~No- I MO 55.9 61.0 66.1 (-) 66.7 T~No-~Mo 61.1 66.2 71.3 (-) 71.9

* Given as 2.5 Gy fractions: for 2.0 Gy fractions and a/B value of 25.0 Gy values would be about 2% higher. TCDso and TCDgo values and approximate standard errors are estimated from logistic regression analysis.

Table 6. The values shown in Table 6 were calculated for a 2.5 Gy fraction regimen, using an cu/p value of 25.0 Gy. The most widely-used range of dose per fraction in current radiotherapy practice is 1 S2.0 Gy, but the dose in 2 Gy fractions would be only about 2% higher than calculated for 2.5 Gy fractions.

Table 8 shows that, for the same probability of local control, the total dose must be increased by about 3 Gy, on average, for each unit increase in T stage. The increase in dose required for control of the primary tumor (not node control ) with each increase in node stage is not well established in that, for tonsil and buccal mucosa, a negative value was obtained, whereas when all the data were pooled, the average increase in isocontrol dose was about 0.5 Gy.

DISCUSSION

Methods: Homogeneity of prognosis among subgroups of site and stage

It was desirable to analyze the data after arrangement into subgroups of site and stage which were relatively homogeneous with respect to likely local outcome of a constant treatment regimen. It was impractical to test a large number of combinations of site and stage. Therefore, twelve subgroups were chosen (Table 6, Figs. 2-5). In general, the results presented justified the groupings in that they showed considerable distinctions such as increasing TCDSO values with increasing stage. To examine for the influence of inappropriate groupings of tumor sites, we reanalyzed separately the data for base of tongue and oral tongue. These two sites were chosen because there were reasonably large numbers in each group, and because

they are usually considered separately, but we had grouped them together in this series. Although the numbers in subgroups became rather small, the TCDso values determined independently for four Stage groups (after normalizing for treatment factors in the logistic regression), were similar for oral tongue and base of tongue (Table 9a). When the dose response curves for all eight subgroups were forced to a common slope, the TCDSo values for a 2.5 Gy per fraction regimen lasting 49 days (Table 9b) were 0.9 Gy higher, on average, for base of tongue than for oral tongue, which is not significant (p = 0.4). This does not establish that the groupings were the best possible but it does provide perspective on the possible influence (on the results reported in this paper) of this cause of heterogeneity.

Accelerated tumor repopulation History. For a long time, the slow growth of most hu-

man tumors (median volume doubling time about 2

Table 7. Dose increment required per day to compensate for accelerated tumor clonogen repopulation

Site

Dose equivalent* to each 1 day of extension of the overall

treatment time

Tongue Oral cavity oropharynx Tonsil Buccal mucosa

0.6 I Gy (kO.06) 0.58 Gy (kO.07) 0.49 Gy (f0.09) 0.76 Gy (kO.09)

Overall 0.60 Gy

* For doses per fraction of 2.5 Gy. Values for 2.0 Gy fractions would be about 2% higher.


Table 8. Increment in TCDsO* (+S.E.) required to compensate for each unit increase in T and N stage

Dose increment

Site For each T stage

Tongue 3.85 (kO.72) Gy Oral cavity

oropharynx 2.64 ( 1.2 1) Gy Tonsil 1.17 (k1.61) Gy Buccal mucosa 3.07 (+6.75) Gy

Overall 2.85 (kO.53) Gy

* In 2.5 Gy fractions.

For each N stage

0.22 (kO.44) Gy

1.10 (kO.46) Gy -0.59 (kO.66) Gy -0.76 (k2.12) Gy

0.48 (kO.26) Gy

months) (5,8,20), and the dogma that they grew auton- omously without a regenerative response after injury, influenced radiotherapists to ignore accelerated tumor repopulation as a cause of treatment failure. Recently, however, a few experimental and clinical studies have indicated that tumor repopulation is one of the most important factors influencing tumor control ( 12- 14, 16, 17, 20, 21, 24, 27, 28).

The present analysis shows a strong correlation between variations in overall treatment time and local control in subgroups of data otherwise fairly homogeneous with respect to tumor and treatment characteristics (Table 5A- D). This is also reflected in the increase in TCDso with time (Figs. 2-5).

Rate of accelerated repopulation. Using logistic regression it was estimated that, on average, an extra 0.6 Gy was required to balance the tumor repopulation occurring during each additional days protraction of treatment (Table 7)) at least within the limits employed for most of the patients in this series for example 30-55 days (Fig.

Table 9a. TCD50 values (2.5 Gy/fx; 49 days) for base of tongue and oral tongue

Oral tongue (N = 133)

T,TzNo 62.6 T2N,,z,,TsNo 66.9 TsN1.2 66.4 T3N, 66.7

Base of tongue (N = 42)

58.2 67.6 66.7 70.4

Table 9b. TCDso values (2.5 Gy/fx; 49 days) assuming dose response curves of all stages to be parallel for both

base of tongue and oral tongue

Oral tongue Base of tongue

TITZNO 60.7 61.6 T~N,.~.~-I-~No 66.4 67.2 T3Nl.z 65.9 66.8 T3N3 67.2 68.1

Base of tongue is 0.9 Gy higher on average than oral tongue (not stat. sig. p = 0.4).

1). If the effective Do for tumor clonogen survival from exposure to multiple 2.5 Gy fractions ranged between 3.0 Gy and 4.5 Gy, a reasonable estimate from experimental animal studies ( 34)) the dose to reduce tumor cell survival to 50% (DSo) would lie between 2.1 Gy and 3.15 Gy. Since the D50 would counterbalance one doubling of clonogens, an increase in dose of 0.6 Gy per day for isocontrol is consistent with a doubling time of about 3.5 to 5 days for clonogens in oral and oropharyngeal tumors as a group. Such rapid tumor clonogen repopulation is consistent with estimates of the potential doubling time (3, 8, 20).

The constant slope of the TCDso curve (Figs. 2-5 ) for any given site or stage of disease reflects the model used in the analysis. A non-linear fit may be more biologically appropriate but the data are insufficient to resolve such a question.

Time of onset. Speculating about a time of onset of accelerated repopulation, between O-28 days, is largely irrelevant to the analysis because the lines were fitted to the data, few of which involved overall times less than 28 days. The assumed time of onset is only important in determining when a horizontal, or at least less steep curve would be appropriate for the back extrapolation of the curves in Figures 2-5 to shorter overall times than actually used in this series of patients.

Influence of stage on repopulation rate. The slopes of the TCDso curves (Figs. 2-5 ) are all similar, suggesting that neither T stage nor tumor site was very important in determining the rate of accelerated repopulation. That is not surprising since a small absolute number of surviving clonogens is involved in repopulation, and in all stages and sites would represent only an occasional cell in a large volume of dead and dying tumor cells.

Comparison with literature. Evidence similar to that presented here has been presented by Maciejewski et al. (16), showing that accelerated repopulation also occurs in squamous carcinoma of the supraglottic larynx. They estimated that, for a constant probability of control, extra dose of 0.5 Gy per day was required between 39 and 51 days. Hliniak et al. ( 13 ) and Allen ( 1) also found overall treatment time to be an important factor in local control of skin cancer by radiotherapy. The literature on human tumor repopulation will be analyzed in a later paper.

The clinical data presented here are qualitatively consistent with experimental results demonstrating a rapid repopulation in rodent tumors ( 12,2 1) , even in a slowly- growing adenocarcinoma of mouse prostate ( 14).

Dose per fraction and the (Y/P ratio Estimated values for cr//3 for squamous cell carcinoma.

The a! / /3 ratio is a measure of the curviness of the putative target cell survival curve and is useful in predicting the sensitivity of the response of tissues or tumors to change in dose per fraction (24,26,32,35). The high cu/@ value of 25 Gy or higher for squamous cell carcinoma of the oral cavity and oropharynx reflects only a slight, or no


fractionation response over the limited range of dose per fraction used in treating this series of patients. We chose an a/@ value of 25 Gy but any value larger than 15 Gy gave a similarly good fit to the data.

Estimates of cu//3 should be judged critically because any factor that leads to an unequal effect per dose fraction will lead to an error in the estimate. For example, variations in oxygenation and reoxygenation will usually lead to an overestimate of the cr/fl value (32). Also, if repopulation occurred in regimens using a large number of small dose fractions, but not in shorter regimens using larger dose fractions, the isoeffect curve for tumor control would be steeper than if influenced only by repair of sublethal injury: as a result, the estimate of ar/B would be too low. Our methods of analysis controlled for the influence of accelerated tumor repopulation: in the non-parametric method, analyses were only performed with groups homogeneous with respect to overall treatment time, while in the parametric method, the effects of variation in overall treatment time and dose per fraction were simultaneously estimated iteratively (see equation 9). There was little change in the estimates of a//3 values when the acceler- ation of repopulation was assumed to begin at 0 or 21 days, rather than 14 days, for reasons discussed earlier.

Literature values for cx/& The fractionation response of squamous cell carcinoma of the oropharynx is similar to that for squamous cell carcinoma of skin (28), and acutely responding normal tissues ( 10,26, 35 ) . For squamous cell carcinoma of human skin, Trott et al. (28) and Douglas ( 10) calculated (Y/B values of 13.4 Gy and 10 Gy respectively. Reviewing the data for experimental tumors, Williams et al. ( 32) estimated a//3 values in the range of lo-20 Gy.

Clinical sign&ance. High a/P values indicate a greater predominance of the linear ( LY) term in tumor dose-response relationships, and little fractionation effect. Since late responding normal tissues are characterized by low a/@ values (26, 35, 36) changes in fraction size have a lesser effect on the response of tumors than on the de- velopment of late sequelae in normal tissues. Thus, hyperfractionation may yield a therapeutic gain (24,26,36) in the treatment of squamous cell carcinomas of the oral cavity and oropharynx.

Steepness of dose-tumor control probability curves The incremental doses estimated by logistic regression

to change the local control rate from 50% to 90% (Table 6) are about 4 Gy for tongue and tonsil, 3 Gy for oral cavity and oropharynx, and 1 Gy for buccal mucosa. A steep dose-response would be expected from radiobiological principles if the characteristics of the tumors and of treatment parameters were fairly homogeneous. Because of the large number of patients in the analysis, it was possible to reduce the heterogeneity of tumor characteristics by subdividing the 498 lesions into 12 subgroups of site and stage. The influence of variations in treatment parameters was also minimized by normalizing for vari-

ations in dose per fraction and for tumor clonogen repopulation with increase in overall treatment duration. Thus, to a considerable extent, the major causes for the shallow slopes of TCP curves drawn previously from retrospective analyses of clinical data appear to have been avoided. Of these variables, overall treatment time was clearly dominant in our analysis.

Stage vs. tumor control probability T-stage. Table 8 shows that each increase in T stage

required about 3 Gy more dose for a constant probability of control. Although T staging involves subjective judg- ment, and the multiple by which tumor volume is increased with each T stage varies with the shape and lo- cation of the tumor, it is surprising that the increase was so little, being consistent with only a 2-3 fold increase in clonogen number if experimental estimates of cellular radiosensitivity in man and rodents can be applied to human squamous carcinoma cells. If the tumors were spherical, a doubling in diameter would represent a potential 8 fold increase in clonogen number. Even if the tumor clonogens were distributed as a 2-dimensional disk, a doubling in diameter would represent a 4 fold increase in clonogen number. Whilst we cant explain completely the smallness of the increase in TCDso values with increase in T stage, the results are not consistent with a decrease in cellular radiosensitivity with increase in tumor size. Therefore, it is unlikely that hypoxia limited the radiocurability of larger tumors any more than it did earlier stages of disease.

N-stage. The influence of N stage on primary tumor response differed with different tumor sites. For tumors classified here as tongue, oral cavity and oropharynx, increasing N stage decreased slightly the probability of primary tumor control, as has been reported previously ( 3 1) . However, for tonsil and buccal mucosa, this effect was not observed, there being a decrease, not significant, in dose for primary tumor control with increased N stage.

Tumor cell radiosensitivity The slope of the sigmoid curve for tumor control prob-

ability as a function of dose reflects the slope of the tumor clonogenic cell survival curve ( 18 ). In a completely homogeneous series of tumors, about 1.9 times the value of the effective DO(,DO) for tumor cells exposed to a mul- tifraction regimen would be required to increase the probability of tumor control from 50% to 90%. Thus, from the estimates presented in Table 6, mean values for eDo for the clonogens of squamous carcinomas of tongue and tonsil would be about 2.15 Gy, about 1.65 Gy for oral cavity, and about .55 Gy for buccal mucosa. These mean values for the eDo (2.5 Gy per fraction) are lower than expected from experimental animal data, and are not consistent with the total doses required for local tumor control (Table 6). (A dose of 65 Gy would reduce cell survival to about lo-l3 ifthe =DO for a 2.5 Gy per fraction regimen was 2.15 Gy.) It is obvious from the standard errors for estimates of TCDSO and TCDgO (Table 6 ) that

Dose fractionation and regeneration 0 B. MACIUEWSKI ef al. 843

estimating eD~ from the slopes of tumor control proba- termined values from experimental animals illustrates bility curve cannot be precise. Nevertheless, the fact that both the feasibility and the difficulty of quantifying human they are generally consistent with the more accurately de- radiobiology.

REFERENCES

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

Allen, E. P. A trial of radiation dose prescription based on and tumor volume relationships in irradiation of squamous dose-cell survival formula. AustraIas. Radiol. 28: 156- 160; cell carcinomas of the base of the tongue. Cancer 37:259 l- 1984. 2599; 1976. Battermann, J. J.; Breur, K.; Hart, G. A. M.; van Peperzeel, H. A. Observations on pulmonary metastases in patients after single doses and multiple fractions of fast neutrons and cobalt-60 gamma rays. Europ. J. Cancer 17:539-548; 1981.

20.

21.

Begg, A. C.; McNally, N. J.; Shrieve, D. C.; Karcher, H. A method to measure the duration of DNA synthesis and the potential doubling time for a single sample. Cytometry 6: 620-626; 1985. Chadwick, K. M.; Leenhouts, H. P. A molecular theory of cell survival. Phys. Med. Biol. l&78-87; 1973. Charbit, A.; Malaise, E. P.; Tubiana, M. Relation between the pathological nature and the growth rate of human tu- mours. Eur. J. Cancer 7:307-315; 1971. Choi, K. N.; Withers, H. R.; Rotman, M. Intracranial metastases from melanoma: Clinical features and treatment by accelerated fractionation. Cancer 56: 1-9; 1985. Cohen, L.; Redpath, J. L. Derivation of survival kinetic parameters for experimental cell populations by computer simulation of radiobiological data. Radiat. Res. 69:387-40 I; 1977.

22.

23.

24.

Steel, G. G. Growth kinetics of turnours. Great Britain: Ox- ford University Press; 1977. Suit, H. D.; Howes, A. E.; Hunter, N. Dependence of response of C3H mamlnary carcinoma to fractionated irradiation on fraction number and intertreatment interval. Radiat. Res. 72:440-454; 1977. Suit, H. D.; Wette, R.; Lindberg, R. Analysis of tumor- recurrence times. Radiology 88:3 1 l-32 1; 1967. Taylor, J. M. G. Kendalls and Spearmans correlation coefficients in the presence of a blocking variable. Biometrics 43:409-416; 1987. Thames, H. D.; Peters, L. J.; Withers, H. R.; Fletcher, G. H. Accelerated fractionation vs hyperfi-actionation: ra- tionales for several treatments per day. Int. J. Radiat. Oncol. Biol. Phys. 9:127-138; 1983.

25. Thames, H. D.; Rozell, M. E.; Tucker, S. L.; Ang, K. K.; Fisher, D. R.; Travis, E. L. Direct quantal analysis of radiation response data. Int. J. Radiat. Biol. 49:999-1009; 1986.

26.

Denekamp, J. Cell kinetics and cancer therapy. Springfield, IL: C. C. Thomas; 1982. Dixon, W. BMDP program, statistical software. Berkeley: California Press; 1983. Douglas, B. G. Implications of the quadratic cell survival curve and human skin reaction tolerance doses in fractionation and superfractionation dose selection. Int. J. Ra- diat. Oncol. Biol. Phys. 8: 1135-l 142; 1982. Fletcher, G. H. Functional surgery and radiotherapy in head and neck cancer. In: Withers, H. R., Peters, L. J., eds. In- novations in radiation oncology. Heidelberg: Springer-Ver- lag; 1987:35-40. Hermens, A. F.; Barendsen, G. W. Changes of cell proliferation characteristics in a rat rhabdomyosarcoma before and after X-irradiation. Eur. J. Cancer 5: 176-18 1; 1969. Hliniak, A.; Maciejewski, B.; Trot& K. R. The influence of the number of fractions, overall treatment time and field size on the local control of cancer of the skin. Br. J. Radiol. 56:596-598; 1983. Kummermehr, J.; Trott, K. R. Rate of repopulation in a slow and a fast growing tumour. In: Karcher, K. H., Ko- gelnik, H. D., Reinartz, G., eds. Progress in radio-oncology II. New York: Raven Press; 1982:299-307. Lehmann, E. L. Nonparametrics: statistical methods based on ranks. San Francisco: Holden-Day; 1975:300. Maciejewski, B.; Preuss-Bayer, G.; Trott, K. R. The influence of the number of fractions and overall treatment time on the local tumour control of cancer of the larynx. Int. J. Radiat. Oncol. Biol. Phys. 9:321-328; 1983. Parsons, J. T.; Bova, F. J.; Million, R. R. A reevaluation of split-course technique for squamous cell carcinoma of the head and neck. Int. J. Radiat. Oncol. Biol. Phys. 6:1645- 1652; 1980. Porter, E. H. The statistics of dose/cure relationships for irradiated turnours. Part 1. Br. J. Radiol. 53:2 10-227; 1980. Spanos, W. J.; Shukovsky, L. J.; Fletcher G. H. Time, dose

Thames, H. D.; Withers, H. R.; Peters, L. J.; Fletcher, G. H. Changes in early and late radiation responses with altered dose fractionation: implications for dose-survival relationships. Int. J. Radiat. Oncol. Biol. Phys. 8:219-226; 1982.

27.

28.

29.

Trott, K. R.; Kummermehr, J. What is known about tumor proliferation rates to choose between accelerated fractionation or hyperfractionation? Radiother. Oncol. 3:1-9; 1985. Trott, K. R.; Maciejewski, B.; Preuss-Bayer, G.; Skoly- szewski, J. Dose-response curve and split-dose recovery in human skin cancer. Radiother. Oncol. 2:123-130; 1984. Tucker, S. L.; Thames, H.D. Optimal design of multifi-action assays of colony survival in vivo. Radiat. Res. 94280-294; 1983.

30. Van Peperzeel, H. A. Effects of single doses of radiation on lung metastases in man and experimental animals. Eur. J. Cancer 8:665-674; 1972.

31.

32.

33.

34.

Wall, T. J.; Peters, L. J.; Brown, B. W.; Oswald, M. J.; M&s, L. Relationship between lymph node status and primary tumor control probability in tumors of the supraglottic larynx. Int. J. Radiat. Oncol. Biol. Phys. 11: 1895- 1902; 1985. Williams, M. V.; Denekamp, J.; Fowler J. F. A review of alpha/beta ratios for experimental tumors: Implications for clinical studies of altered fractionation. Int. J. Radiat. Oncol. Biol. Phys. 11:87-96; 1985. Withers, H. R. The 4 Rs of radiotherapy. In: Let& J. T., Adler, H., eds. Advances in radiation biology, Vol 5. New York: Academic Press; 1975:241-269. Withers, H. R. Response of some normal tissues to low doses of gamma radiation. In: Alper, T., ed. Cell survival after low doses of radiation. New York: J. Wiley & Sons; 1975:369-375.

35.

36.

Withers, H. R.; Thames, H. D.; Peters, L. J. A new isoeffect curve for change in dose per fraction. Radiother. Oncol. 1: 187-191; 1983. Withers, H. R. Biologic basis for altered fractionation schemes. Cancer 55:2086-2095; 1985.

dose fractionation and regenration in readiotherapy for cancer of the oral cavity and oro pharynx...

Documents