Kinetics of recovery from sublethal radiation damage in four murine tumors

Radiotherapy and Oncology, 18 (1990) 79-88 Elsevier

79

RADION 00699

Kinetics of recovery from sublethal radiation damage in four murine tumors R. G u t t e n b e r g e r i, j. K u m m e r m e h r I and D. C h m e l e v s k y z GSF-Institute .~r 1 Strahlenbiologie und 2 Strahlenschutz, Neuherberg, F.R.G.

(Received 8 August 1989, revision received 5 December 1989, accepted 19 December 1989)

Key words: SLD repair kinetics; Murine tumors; Tumor growth delay; Direct analysis

Summary The kinetics of repair of sublethal radiation damage (SLD) was studied in four transplantable C3H mouse tumors, i.e. mammary carcinoma AT17, fibrosarcoma SSK2, and squamous cell carcinomas AT51 and AT478. Tumors were irradiated with 4 fractions of 300 kV X-rays given under local hypoxia at intervals ranging from 0 to 6 h. Radiation response was measured by growth delay, which was directly analyzed using a general curve description based on the extended linear-quadratic model (exponential repair kinetics). In contrast to existing methods all growth delay values were utilized to estimate the ~/fl ratios and the half-times as well as their confidence limits in a non-linear least squares analysis. The half-times were 42, 44, 54 and 31 min, respectively. It is concluded that repair of SLD is virtually complete after 5 h in these tumors. This is also due to the relatively small proportion of repairable damage in these tumors reflected in their 0qfl values, which were 38, 30, 54 and 42 Gy, respectively.

Introduction Among the biomathematical models proposed to describe the response to fractionated irradiation, the linear-quadratic dose relationship has become most popular as it fits reasonably well to a large number of in vivo endpoints [6,28,34]. Recently, the linear-quadratic model was extended [4,31 ] as altered fractionation protocols made the kinetics Address for correspondence: R. Guttenberger, GSF-lnstitut f'fir Strahlenbiologie, D-81M2 Neuherberg, F.R.G.

of recovery from sublethal radiation damage (SLD) a matter of great interest [ 1,9,20,22,36]. So far, there have been several reports on repair kinetics in normal tissues [2,3,5,7,14,16,23,25,33, 37,38 ], but very few on tumors in vivo [ 13,17,24]. The present paper reports on the kinetics of recovery from SLD in four transplantable tumors using growth delay as the endpoint. A direct method of analysis was employed since conventional methods are not suitable for estimation of a second parameter besides the ~/fl value. This is for the reason that existing methods of fitting

016%8140/90/$03.50 © 1990 Elsevier Science Publishers B.V. (Biomedical Division)

80 mathematical models to growth delay data involve a number of steps: After the growth delay to a chosen endpoint has been calculated and plotted against the dose, the decision has to be made at which growth delay level, i.e. iso-effect level, the corresponding iso-effective doses should be determined. As exactly iso-effective treatment is the exception rather than the rule, the iso-effective doses at any chosen effect level have to be obtained by interpolation between the actual doses given. However, the major drawback is that choosing an iso-effect level necessarily excludes a large proportion of the data from parameter estimation. This pronounced loss of information met with general acceptance as the resulting linear plots were readily analysed by linear regression. However, with the incomplete repair parameter (T,/2) included, the plots derived from these transformations are no longer linear. Therefore, a direct method of analysis was employed in the present study which makes use of all the data and lends itself to non-linear regression. A similar approach was used previously by Henkelman et al. [ 14] to analyse the acute skin response in mice to fractionated and low dose rate irradiation.

Materials and methods

All experiments were carried out with female C3H mice (inbred colony Neuherberg) from which the tumor systems have been derived. Four established transplantable tumors of different histology were used in the present study: (1) Mammary carcinoma A TI 7, a slow growing (volume doubling time Td = 5d), well differentiated adenocarcinoma [ 19], which arose at the margin of a curative radiation field in a tumor-bearing C3H mouse; (2)fibrosarcoma SSK2, an undifferentiated tumor with Ta - 1.5d, cloned in vitro from a methylcholanthren-induced fibrosarcoma in the dorsal skin ofa C3H mouse, but devoid of specific immunogenicity when tested as described by Embleton [8]; (3) squamous cell carcinoma AT478, a spontaneous, differentiated, non-keratinizing SCC with Ta -- 3.5d; (4) squamous cell

carcinoma A T51, a moderately well differentiated, radiation-induced SCC with Td = 4.5d. Tumor fragments of I mm 3 were transplanted by trocar into the subcutaneous tissue of the right flank of 8 to 10-week-old mice under hexobarbital anesthesia. Each experiment contained tumors from one passage only. They were allocated to treatment groups, when tumors had reached 80-150 mg. Six to 12 mice were included in each dose group and 3-4 dose levels were used for each treatment arm. The tumors were locally irradiated with a Seifert & Co Isovolt 320 X-ray set operated at 300 kV and 10-13 mA, to give a dose rate of 4.6-5.7 Gy. min - ' at a focus-to-skin distance of 21 cm. The beam was filtered with 0.5 mm Cu and 1 mm AI. Mice were anesthetized with hexobarbital-Na (120 mg/kg) given i.p. Tumors were clamped 5 min prior to and throughout irradiation. To minimize dose inhomogeneities, mice were placed on a revolving plate that performed alternate rotations at a frequency of 1 rev/min. By means of an ionization chamber located in tumor position and connected to a SN4 dosimeter (Phywe, Freiburg) doses were monitored during irradiation. The mice were kept at 3 2 ° - 3 7 ° C during fractionation intervals while anesthetized in order to prevent hypothermia which might influence repair kinetics. In the standard regime to determine repair kinetics, 4 equal fractions were delivered at equal intervals varying from 0 to 70 min; in all tumors except AT17 an extended 4F protocol was given with two 6-h intervals and one overnight split (15 h). In SCC AT51 eight additional experimental groups were introduced to test three further aspects of interest (see Table I): (1) 2 dose groups (20-min interval and 4 x 10 or 4 x 12 Gy) were kept at ambient temperature between fractions; (2) 2 further dose groups (as above) were recruited from the latest tumors of the passage reaching treatment size; and (3) 4 groups were irradiated with an identical dose of 4 x 15.9 Gy separated by intervals of 2, 3, 4 and 5 h (time line protocol), in an intent to visualize the possible influence of redistribution during longer intervals. Following radiation treatment tumor mass was

81 TABLE I Treatment groups in SCC AT51 in addition to the standard regime. Treatment n x d(Gy), At(h)

Aspect of interest

T G D Id] (SEM)

Local control

4 × 10, 0.33 4 × 10, 0.33 4 × 10, 0.33

Standard regime Ambient temperature Late tumors

29.4 (27.4, 31.7) 28.4 (27.0, 29.8) 27.4 (25.9, 28.9)

0,,'8 0/7 0/7

4 × 12, 0.33 4 × 12, 0.33 4 x 12, 0.33

Standard regime Ambient temperature Late tumors

43.7 (37.5, 51.0) 38.0 (33.1, 43.5) 47.3 (40.5, 55.3)

0/8 0/7 0/8

4 4 4 4

Cell Cell Cell Cell

57.0 45.2 44.6 43.1

2/8 2/7 1/8 1/8

x x x x

15.9, 2 15.9, 3 15.9, 4 15.9, 5

cycle cycle cycle cycle

effects effects effects effects

measured regularly 1-3 times a week according to the growth rate until 5 times the pretreatment size was reached. The method employed a perspex ruler containing a series of bore holes of increasing diameter which previously were calibrated to tumor mass. The tumor treatment size was normalized to 100 mg and an individual growth curve plotted for each tumor. From this, the time necessary after treatment to grow to a chosen weight (see Fig. 1) was derived, the mean time of untreated controls was subtracted and the resuiting net growth delay was entered into a computer routine. The occasional local controls in higher dose groups were arbitrarily allocated the longest growth delay value observed in that group. These dose points are indicated by an upward arrow in the graphs (Fig. 1A,D). The experiment with SCC AT51 turned out to be overdosed, and rendered both growth delay data and a complete set of local control data. All the dose groups containing more than 5 0 ~ of local controls were omitted from the growth delay data. Tumors were considered locally cured when the residual mass (usually < 2 0 m g ) failed to increase within 180 days after irradiation. This cut-off time appears reasonably safe; the longest growth delay observed was 120 days. The local control data were analyzed using the logistic model of the direct method, which has been proposed by

(50.1, (41.5, (40.0, (39.7,

64.9) 49.2) 49.6) 46.6)

Thames et al. [32] for the analysis of quantal radiation effects. In the present paper a method of direct analysis of growth delay data is employed. Only the principles of this method will be explained here, and the mathematical validation will be given elsewhere (Chmelevsky et al., submitted to Int. J. Radiat. Biol.). It is generally accepted that isoeffective doses should fit the linear-quadratic (LQ) model, if the data reflect the dose response to fractionated irradiation. With our data an incomplete repair model is required, because the intervals between the fractions often are too short for completion of SLD repair. Our choice was the simplest model available [4,31], which is based on first order kinetics for SLD repair. Therefore, the first assumption: At any effect level this generalized LQ-model predicts iso-effective doses as a function of the number of fractions and the time between fractions [29]. Such a mathematical transformation can be called "dose metameter", an expression taken from Finney [ 11 ]. Although every effect level by itself should be exactly described by the dose metameter, it is, yet, impossible to make any predictions about the dose increment necessary to reach another effect level, i.e. the effect levels are not linked to each other. However, it is known from growth delay that it increases with dose and that this increase is more

82 doys to grow 'o 3 • VO

doys to grow ,o Vo t mommory

co

AT 17

fibrosclrcoma

I

200

SSK 2

t,O

I

160

120

20 r

0

,

0 20 55

20 SO min

360 rn,n

B)

A) A

i

6O Gy

20

0

totol dose

t.O fOtOl dose

80

60

Gy

doys 'o grow tO 2 •Vo

days ,o grow 'o 2 .Vo

scc AT t.78

scc AT 51 I00

t

8C

60 ~.0

0 ZO 50

0 3C 70 3~0 "n,n

C) 0 20

t.0 totct dose

360 rain

13) 60

80 13/

20

i t.0 ,ol'al dose

i 60

0y

Fig. 1. (A-D) Growth delay response (mean _+SEM) of four murine tumors to 4 fractions of X-rays delivered at intervals indicated on the curves (clamp hypoxia). Net growth delay curves shown in (A-D) are simultaneous computer fits of all data points except those in brackets. (A) The fit of the model to the data is acceptable. (B) The residual of the data point in brackets suggested it to be an outlier. The fit of the model to the rest of the data is acceptable. (C) The residual of the data point in brackets suggested it to be an outlier. However, the fit of the model to the rest of the data still is not satisfactory. (D) The fit of the model to the data is excellent.

p r o n o u n c e d with higher doses, i.e. growth delay curves are continuously rising and get steeper and steeper in the dose range of interest. Therefore, our second assumption: The effect level can be " t r a n s l a t e d " into a t u m o r growth delay value by a "link function". This function does not have to have any biological relevance. It is introduced simply to be able to include all the data irrespec-

tive o f effect level into estimating the p a r a m e t e r s o f the dose metameter. The actual link function chosen is a power function, but as shown elsewhere this is not critical (Chmelevsky et al., submitted to Int. J. Radiat. Biol.). Put together, the dose m e t a m e t e r and the link function describe how the net growth delay r e s p o n d s to changes in dose, n u m b e r o f fractions, or time between

83 fractions. To compute estimates and confidence limits of a/fl values and half-times of repair, the net growth delay value of every treated tumor was entered into a routine non-linear regression program (SAS) using the following formalism: TGD = bl[ct/fl. D + (D2/n), (I + h)] b2 T G D = net tumor growth delay; bl, b2 = parameters of the link function; D = t o t a l dose; n = number of fractions (in our experiments = 4); (1 + h) = the "incomplete repair" term [31], where h = (2/n)[0/(1

-

0)][n

- (1 -

- 0)]

and

0 = exp( - At ln2/T,/2 )

Results

The data sets from all four tumors could be fitted using the direct analysis method. The graphs in Fig. 1A-D, show the data points with their error bars (+ 1 SEM) and the curves calculated from the parameter estimates of the dose metameter (shown in Table II) and of the link function (not shown). The data of ATI7 in Fig. 1A, are relatively restricted in that they lack longer intervals. The reason for this is that they were obtained in an experiment where two assays were done in parallel, i.e. tumor growth delay and an in situ colony-formation assay that is possible in this particular tumor system [ 19]. The estimates ofthe T,/2 and 0t/flvalue from the two assays are in good TABLE 11 Parameter estimates fitting the data from Figs. 1 and 2. Tumor

ct/fl(Gy) (95% C.L.)

T,,,~(min) (95,% C.L.)

Mammary ca ATI7 Fibrosarcoma SSK2 SCC AT478 SCC AT51 (growth delay) SCC AT51 (local control)

38 (0-81) 30 (20-40) 54 (23-84) 42 (25-59) 56 (33-91)

42 (23-62) 44 (29-59) 59 (27-92) 31 (17-45) 29 (18-66)

agreement, i.e. 42 vs. 57 rain and 38 vs. 33 Gy [ 13]. The vast confidence limits of the ~/fl value given in Table II can be explained by the restricted amount of data, in particular the lack of longer intervals. The data sets of fibrosarcoma SSK2 and SCC AT478 (Fig. 1B,C, respectively) showed considerable lack of fit indicating that the parameter estimates are not reliable. In both data sets the data point with the highest residual was considered an outlier (points in brackets). In SSK2 (Fig. 1B) omitting the outlier from the analysis resulted in an acceptable fit, whereas in SCC AT478 (Fig. IC) the fit remained unsatisfactory. There is no obvious systematic deviation of observed and predicted results in Fig. 1C. Therefore, the nature of the inconsistency encountered remains unclear. The parameter estimates in Table II have been obtained omitting the outliers. For SCC AT478 it should be stressed that the data do not support the model from which the estimates are derived. The growth delay and local control data from the experiment with SCC AT51 are shown in Fig. 1D and Fig. 2. Several data points had to be excluded from the growth delay analysis and others "corrected" for infinite growth delay. However, there was little difference whether nonrecurring tumors were assigned the largest T G D observed in this dose group or twice that value (decrease in T,~: from 31 to 26 min). Fortunately, the analysis was augmented by the 8 additional dose groups mentioned in Materials and methods and listed in Table I. The delay values from the time line experiment, i.e. 4 x 15.9 Gy separated by 2, 3, 4 and 5 h intervals were 57.0, 45.2, 44.6 and 43.1 days, respectively, after correcting for local controls. This indicates an apparent completion of SLD repair after approximately 3 h. The growth delays of the other groups compared well to those of the corresponding groups receiving standard treatment at the two dose levels tested, which were 29.4 and 43.7 days, respectively. The groups added to test for an influence of temperature yielded 28.4 and 38.0 days, respectively; the late tumors yielded 27.4 and 47.3 days, respectively (see Table I). As there was no signifi-

84 % l o c a l control

of the dose per fraction. This was done by analysing subsets of data omitting either the highest or the lowest dose per interfraction interval. Although a significant impact was not necessarily expected, the results failed to show even a systematic effect of the dose per fraction on the

scc AT 51 100

80

TV2.

60

Discussion

o

0 LO

60

80

0y

rotor dose Fig. 2. Dose-response curves of local control in SCC AT51 from the same experiment as in Fig. 1D directly analyzed with a logistic model [32]. Similar parameter values are estimated from the growth delay analysis of Fig. ID. Same symbols as in Fig. 1D: Z~, single dose; ~ , 20-min interval; Fq, 50-min interval; A, at least 6-h interval.

cant difference between these groups, all were included in the analysis. The fit of the model to these additional data points (for reasons of clarity not shown in the graph) and those shown in Fig. 1D was excellent. Moreover, direct analysis of the local control data (i.e. all the data points included) with the logistic model [32] gave similar parameter estimates (see Table II). However, as can be seen in Fig. 2, the local control data for the 20 and 50 min interval deviated considerably from the fitted curves. Finally, three out of four data sets gave a satisfactory fit, and there seems to be no systematic deviation of the growth delay values (mean + SEM) from the fitted curves in the present four tumor systems. The derived 7",/2 and ~t/fl values are 42, 44, 59 and 31 min and 38, 30, 54 and 42 Gy, respectively (for 95 ~o confidence limits see Table II). In addition, an attempt was made to check all data sets for a possible influence

The kinetics of SLD repair were tested in four murine tumors using a standardized treatment protocol and evaluation by growth delay. The data were analyzed with a direct method which does not require calculation of iso-delay doses. This is a similar approach as taken in a recent direct analysis method for quantal effects [32]. Although it is possible to quantalize growth delay data, this is not necessary for applying direct analysis, and there have been successful attempts to include all data points of quantitative radiation response data irrespective of iso-effect or effect level into a simultaneous analysis [14,27]. Henkelman et al. [ 14] analyzed the fractionation response of mouse skin this way after assigning increasing score numbers to acute skin damage of increasing severity. In a theoretical paper using computer simulation, Stuschke [27] showed that virtually the same approach is superior to an indirect analysis modified after Tucker's nonlinear estimation method [34]. It is clear that the more parameters there are to be estimated, the more data points are necessary and the more powerful the statistical analysis must be. The advantage of a direct analysis can also be illustrated, e.g. in Fig. 1D, where the TGD to 49.5 Gy single dose is not matched by data points from other treatment arms but still contributes to the parameter estimation. Although our experiments were not specifically designed to measure repair capacity, the derived ~/fl v',dues are useful estimates and compare reasonably well to previous results of the same tumors obtained from experiments allowing complete SLD repair between fractions [18]. When

85 divided by 2.7 as a tentative OER, the oc/flvalues found in the four tumors range from 11 to 20 Gy. In a review article on 0t/fl values of experimental tumors, Williams et al. [39] found a mean 0t/fl value of 11.6 Gy (SD 5.3) for murine tumors that were irradiated under clamped conditions. Our confidence limits are similar to those reported by Williams et al. [39], which also show considerable variation. However, it should be kept in mind that we used only two different numbers of fractions (i.e. 4 and SD) and that the confidence limits given by Williams et al. are underestimates as pointed out by the authors. Nevertheless, it can be safely stated that the ~/fl ratios in the four tumor lines under study are considerably higher than those reported for late responding normal tissues [ 12,28]. For analysis, repair kinetics were assumed to be mono-exponential. There is no evidence from our data that this assumption is not valid. On the other hand, the results do not disprove the possibility of more than one component to repair kinetics. This is to say that the influence of such a potential second component is not strong enough to be picked up with this experimental design. The half-times we obtained ranged from 29 to 59 min (for details see Table II), in reasonably good agreement with the few published data [17,24]. The T,/~ values measured in five tumors by Ito et al. [ 17] were 4, 11, 11, 36, and 102 min, displaying an extremely wide range. The endpoint was the number of lung nodules after 2 fractions given at different intervals. The T,/: was estimated from the recovery ratio, which was defined as the ratio of number of lung colonies resulting from split-dose irradiation to that of single-dose irradiation. As the total dose and the number of fractions was constant, 0c//~values cannot be calculated. However, it is unknown how stable the results from the employed endpoint and design are, or to what extent the vast range of half-times is due to differences in the underlying tumor systems, which in vitro yielded half-times ranging from 19 to 96 min. Similar half-times were found in vitro for 16 human tumor cell lines with a range from 14 to 140 min [26].

In a more directly comparable experiment, Rojas et al. [24] found for their CaNT tumor an ~/fl value of 43.3 Gy for local control (clamped) and 23.0 Gy for growth delay (clamped). In our SCC AT51 we also found a higher ~//~ value for local control (Table II), but the difference was less pronounced. The 0t/~ value for growth delay reported by Rojas et al. is lower than in our tumors, although in view of the confidence limits the difference is not substantial. The same is true for the 7",/2values; they are 19 min (local control) and 17 min (growth delay), which is lower than ours, but their upper 95 ~ confidence limits are 28 min and 31 min, respectively, which is within the confidence limits of the 7",/2of the four present tumors. However, it is not quite clear from the paper by Rojas et al. how the confidence limits were obtained. Their analysis involves logistic regression as a first step to obtain a growth delay curve and iso-delay doses for each interval. The incomplete repair model [4,31 ] has been reformulated by the authors to replace the usual parameters ~t/fl and T,/~ by new parameters, i.e. the isodelay doses at zero (Do) and complete (D~) repair. These doses and the observed iso-delay doses D t at short intervals served then to derive values of the h function. This was repeated for several effect levels. With the set of h values obtained in this way, the parameter T,/2 was calculated. In practice, it is difficult to carry over the uncertainties in the original dose points into a statistically correct calculation of confidence limits and goodness-of-fit statistics. In contrast, the present method is statistically straightforward and allows sound calculation of C.L. and goodness-of-fit, while it is less time consuming. There are two principal experimental designs for measuring SLD repair kinetics after fractionated high-dose-rate irradiation [21]. In our experiments we used four equally spaced fractions at varying intervals. The rationale for this is that repair kinetics can be measured accurately only if there is enough SLD to be repaired to outweigh biological variation, e.g. proliferation-related fluctuations in radiosensitivity. To get a maximum of repairable damage we used as many fractions as

86 compatible with complete repair in an overall treatment time of 30 h at the most to avoid repopulation. This concept requires relatively large doses, and if repair kinetics markedly depends on dose per fraction, our results would not be very relevant for the clinic, where the dose per fraction is considerably smaller. Fortunately, there is no evidence from our data that this is the case. To ascertain this, further experiments would be necessary that utilize a larger number of fractions, with or without top-up dose. The principal alternative is to give 2fractions at short intervals and await completion of SLD repair before giving repeats of such dose pairs. The idea of this design is that each pair of fractions can be regarded as contributing independently to the overall effect without complication from interactions between subsequent pairs. However, although at first sight a larger number of dose pairs suggests a greater total amount of recoverable damage, one must be aware that such a "quasi-clinical" schedule is at the expense of little difference seen between zero and full SLD repair. Depending on the ~t/fl value and the effect level, there is an optimal number of fractions (2n) which renders the maximum difference between n and 2n fractions. It can readily be calculated for any given ct/fl value and effect level by iteration over n. For an ~/fl value of 40 Gy (clamp) the "best" 2n is attained already with 4 fractions, where a single dose of 50 Gy is iso-effective to 57.2 and 70.4 Gy in 2 and 4 fractions, respectively. Interestingly, for a late responding normal tissue with an o~/flvalue of 4 Gy and an EDso of 20 Gy single dose, the total gain in repairable dose in schedules employing 2 daily fractions continuously increases up to 17 x 2 fractions, but approximately 90~o of the maximum difference is achieved already with 6 x 2 fractions. If2n were 12 in the above tumor example, the corresponding doses would be 72.5 and 83.1 Gy, and thus yield a considerably smaller dose increment. It remains to be examined in further studies whether the experimental design influences the estimate of the T,/2 systematically. If this is the case, there would be a number of possible explan-

ations, e.g. the interactions of a third or fourth (etc.) fraction could be inadequately described by the model. Moreover, there are biological phenomena which may interfere with the apparent repair process when doing experiments on proliferating tissues: Accumulation of cells in less sensitive phases of the cell cycle may result in spuriously fast SLD repair within short intervals; synchronized progress in cell cycle after a few hours could lead to increased cellular radiosensitivity, which may appear like a second phase of slower SLD repair. So far, it has not been examined if the T,/2 is influenced by repeatedly clamping the tumors within short time. It is interesting that Rojas et al. [24] report increased radioresistance when tumors are clamped twice within an hour following irradiation, e.g. their TCDso for 5 fractions in 5 days increases from 83.6 Gy to 88.9 Gy when the tumors were additionally clamped twice per day. We also found considerable increase in radioresistance in the fibrosarcoma SSK2 when it was pre-clamped once for 15 min one hour before irradiation, e.g. the iso-delay dose to 41 Gy became 43.5 Gy (Guttenberger, unpublished data). So far, there is no apparent explanation as to the mechanism. It has been suggested [30] that the unknown mechanisms causing the differences in repair capacity between normal tissues and tumors might also result in differences in repair kinetics. So far, half-times of repair in normal tissues have been reported that are in the same range or even longer than those of tumors, e.g. about 0.5 h in jejunum [5], 0.7 to 0.9 h in lung [7,33,37,38], 0.9 to 1.7 h in kidney [23,37], skin [ 14,23], and spinal cord [3,25]. There have been a few reports that repair kinetics is not mono-exponential in normal tissues [ 10,15,35]. Whether or not this reflects a basic difference in the repair mechanisms or simply shows that in tumors our assays do not pick up different repair kinetics, because there is too small an amount of SLD repair, remains unknown. In conclusion, the presented data as well as the data reported by other groups suggest that recovery kinetics in tumors are at least as fast as

87 in normal tissues. Therefore, interfraction intervals allowing only incomplete repair of SLD will be disadvantageous for tissues with large repair capacity, i.e. late responding normal tissue. The clinical implication of this is that an attempt must be made to minimize incomplete repair of SLD, especially in critical late responding normal tissues.

Acknowledgements The authors wish to thank Professors K.-R. Trott and U. Hagen for positive criticism and helpful comments.

References i Ang, K. K., van der Schueren, E., Notter, G., Horiot, J. C., Chenal, Ch., Fauchon, F., Raps, J., van Peperzeel, H., Goffin, J.C., Vessiere, M. and van Glabbeke, M. Split course multiple daily fractionated radiotherapy schedule combined with misonidazole for the management of grade 3 and 4 Gliomas. Int. J. Radiat. Oncol. Biol. Phys. 8: 1657-1664, 1982. 2 Ang, K.K., Xu, F.-X., Landuyt, W. and van der Schueren, E, The kinetics and capacity of repair of sublethal damage in mouse lip mucosa during fractionated irradiations. Int. J. Radiat. Oncol. Biol. Phys. 11: 1977-1983, 1985. 3 Ang, K. K., Thames, H. D., van der Kogel, A. J. and van der Schueren, E. Is the rate of repair of radiationinduced sublethal damage in rat spinal cord dependent on the size of dose per fraction? Int. J. Radiat. Oncol. Biol. Phys. 13, 557-562, 1987. 4 Dale, R.G. The application of the linear-quadratic model to fractionated radiotherapy when there is incomplete normal tissue recovery between fractions, and possible implications for treatments involving multiple fractions per day. Br. J. Radiol. 59: 919-927, 1986. 5 Dale, R. G., Huczkowski, J. and Trott, K.-R. Possible dose rate dependence of recovery kinetics as deduced from a preliminary analysis of fractionated irradiation at varying dose rates. Br. J. Radiol. 61: 153-157, 1988. 6 Douglas, B. J. and Fowler, J.F. The effect of multiple small doses of X-rays on skin reactions in the mouse and a basic interpretation. Radiat. Res. 66: 401-426, 1976. 7 Down, J. D., Easton, D. F. and Steel, G.G. Repair in mouse lung during low dose-rate irradiation. Radiother. Oncol. 6: 29-42, 1986.

8 Embleton, M.J. How to determine tumor immunogenicity. In: Rodent Tumor Models in Experimental Cancer Therapy, pp. 19-22. Editor: R.F. Kallman. Pergamon Press, New York, 1987. 9 Edsmyr, F., Andersson, L., Esposti, P. L., Littbrand, B. and Nilsson, B. Irradiation therapy with multiple small fractions per day in urinary bladder cancer. Radiother. Oncol. 4: 197-203, 1985. 10 Field, S. B., Hornsey, S. and Kutsutani, Y. Effects of fractionated irradiation on mouse lung and a phenomenon of slow repair. Br. J. Radiol. 49: 700-707, 1976. 11 Finney, D.J. Statistical Method in Biological Assay, 3rd edn. Charles Griffin & Co Ltd., London, 1978. 12 Fowler, J.F. Total doses in fractionated radiotherapy implications of new radiobiological data. Int. J. Radiat. Biol. 46: 103-120, 1984. 13 Guttenberger, R., Kummermehr, J. and Sund, M. Kinetics of recovery from sublethal damage in adenocarcinoma ATI7 of the C3H mouse. In: Thirty-Sixth Annual Meeting of the Radiation Research Society, p. 69, Philadelphia, 1988. 14 Henkelman, R. M., Lam, G. K. Y., Kornelsen, R. O. and Eaves, C.J. Explanation of dose-rate and split-dose effects in mouse foot reaction using the same time factor. Radiat. Res. 84, 276-289, 1980. 15 Hopewell, J. W. and van den Aardweg, G. J. M.J. Current concepts of dose fractionation in radiotherapy. Normal tissue tolerance. Br. J. Radiol. Suppl. 22: 88-94, 1988. 16 Huczkowski, J. and Trott, K.-R. Jejunal crypt stem-cell survival after fractionated y-irradiation performed at different dose rates. Int. J. Radiat. Biol. 51: 131-137, 1987. 17 Ito, H., Ang, K. K., Nishiguchi, I., Thames, H. D., Peters, L. J. and Milas, L. The extent and kinetics of split-dose recovery in murine tumors. In: Thirty-Seventh Annual Meeting of the Radiation Research Society, p. 182, Seattle, 1989. 18 Kummermehr, J., Schropp, K. and Neuner, M. Splitdose recovery in transplantable mouse tumours - a linear-quadratic analysis of regrowth delay data. In: Experimentelle Tumortherapie, pp. 28-34, Annual Report 1983. Munich, GSF-Bericht B 1694, 1984. 19 Kummermehr, J. Measurement oftumour clonogens in situ. In: Cell Clones: Manual of Mammalian Cell Techniques, pp. 215-222, Editors: C.S. Potten and J.H. Hendry. Churchill-Livingstone, Edinburgh, 1985. 20 Marcial, V. A., Pajak, T. F., Chang, C., Tupchong, L. and Stetz, J. Hyperfractionated photon radiation therapy in the treatment of advanced squamous cell carcinoma of the oral cavity, pharynx, larynx and sinuses, using radiation therapy as the only planned modality: (Preliminary Report) by the Radiation Therapy Oncology Group (RTOG). Int. J. Radiat. Oncol. Biol. Phys. 13: 41-47, 1987. 21 Michael, B.D. Some considerations of repair in design -

88

22

23

24

25

26

27

28

29

30

of multiple-fractions-per-day treatment schedules. In: The Scientific Basis of Modern Radiotherapy, BIR Report 19, pp. 5-9. Editor: N. J. McNally. British Institute of Radiology, London, 1989. Peters, L.J., Withers, H.R. and Thames, H.D. Radiobiological bases for multiple daily fractionation. In: Progress in Radio-Oncology, II, pp. 317-323. Editors: K. H. K~lrcher, H. D. Kogelnik and G. Reinartz. Raven Press, New York, 1982. Rojas, A. and Joiner, M.C. The influence of dose per fraction on repair kinetics. Radiother. Oncol. 14: 329-336, 1989. Rojas, A., Joiner, M.C. and Johns, H. Recovery kinetics in mouse skin and CaNT tumours. Radiother. Oncol. 16: 211-220, 1989. Scalliet, P., Landuyt, W. and van der Schueren, E. Repair kinetics as a determining factor for late tolerance of central nervous system to low dose rate irradiation. Radiother. Oncol. 14: 345-354, 1989. Steel, G.G. Recovery kinetics deduced from continuous low dose-rate experiments. Radiother. Oncol. 14: 337-344, 1989. Stusehke, M. A direct method for estimating the a//~ ratio from quantitative dose-response data. Strahlenther. Onkol. 165: 401-406, 1989. Thames, H. D., Withers, H. R., Peters, L. J. and 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. Thames, H.D. Effect-independent measures of tissue responses to fractionated irradiation. Int. J. Radiat. Biol. 45: 1-10, 1984. Thames, H. D., Withers, H. R. and Peters, L.J. Tissue repair capacity and repair kinetics deduced from multifractionated or continuous irradiation regimes with in-

complete repair. Br. J. Cancer 49 (Suppl. Vl): 263-269, 1984. 31 Thames, H.D. An "incomplete repair" model for survival affair fractionated and continuous irradiations. Int. J. Radiat. Biol. 47: 319-339, 1985. 32 Thames, H. D., Rozell, M. E., Tucker, S. L., Ang, K. K., Fisher, D. R. and Travis, E.L. Direct analysis ofquantal radiation response data. Int. J. Radiat. Biol. 49: 999-1009, 1986. 33 Travis, E. L., Thames, H. D., Watkins, T. L. and Kiss, I. The kinetics of repair in mouse lung after fractionated irradiation. Int. J. Radiat. Biol. 52: 903-919, 1987. 34 Tucker, S.L. Tests for the fit of the linear-quadratic model to radiation iso-effect data. Int. J. Radiat. Oncol. Biol. Phys. 10: 1933-1939, 1984. 35 Turesson, I. and Thames, H.D. Repair capacity and kinetics of human skin during fractionated radiotherapy: erythema, desquamation, and telangiectasia after 3 and 5 year's follow-up. Radiother. Oncol. 15: 169-188, 1989. 36 Van der Schueren, E., Ang, K.K., Horiot, J.C., Gonzalez, D. G., van Glabbeke, M., De Pauw, M. Concentrated radiotherapy schedules: role of repair and repopulation. In: Plenary Sessions, pp. 99-103. Proceedings, XVI International Congress of Radiology, Hawaii, 1985. 37 Van Rongen, E. The influence of fractionation and repair kinetics on radiation tolerance: studies on rat lung and kidney. Publication of the Radiobiological Institute TNO, Rijswijk, The Netherlands, 1989. 38 Vegesna, V., Withers, H. R. and Taylor, J. M.G. Repair kinetics of mouse lung. Radiother. Oncol. 15:115-124, 1989. 39 Williams, M.V., Denekamp, J. and Fowler, J.F. A review of g/Bratios for experimental tumors: implications for clinical studies of altered fractionation. Int. J. Radiat. Oncol. Biol. Phys. 11: 87-96, 1985.