repair capacity and kinetics of human skin during ... · the repair capacity for late...

Radiotherapy and Oncology, 15 (1989) 169-188 Elsevier 169

RTO 00576

Repair capacity and kinetics of human skin during fractionated radiotherapy: erythema, desquamation, and telangiectasia after

3 and 5 year’s follow-up

Ingela Turesson ’ and Howard D. Thames2 ’ Department of Oncology, The University of Gothenburg, Sahlgrenska Hospital, Gothenburg. Sweden, and 2 Department of

Biomathematics, The University of Texas M. D. Anderson Cancer Center, Houston, TX 77030, U.S.A.

(Received 23 February 1988, revision received 28 October 1988, accepted 29 November 1988)

Key words: Skin; Radiotherapy; Dose fractionation; Repair capacity; Repair kinetic; Overall time effect; Acute radiation effect; Late radiation effect

Summary

Prospective clinical fractionation studies on acute and late reactions in skin have been going on since 1972 at the Radiotherapy Department in Gothenburg. The clinical assay consisted of breast cancer patients irradiated postoperatively to the internal mammary nodes from unilateral or bilateral fields exposed to various dose schedules. 750 fields in 450 patients have been analysed. Schedules with 1,2 or 5 fractions per week and 2 or 3 fractions per day were evaluated with erythema, desquamation and telangiectasia as endpoints. For some schedules a dose-response relationship was established in a limited dose range, but often there was only one dose group per schedule. These data are suited to analysis by the method of direct analysis of quantal response. This was used in the present analysis, along with the linear quadratic (LQ) model and its generalization, the incomplete repair (IR) model. The repair capacity was similar for erythema and desquamation, with a/j? ratios between 7.5 and 11.2 Gy. Unexpectedly, there was no significant time factor during radiotherapy courses up to 6 weeks for erythema and desquamation, but the repair capacity was changed after 4 weeks for both endpoints, and alpincreased to between 18.3 and 34.5 Gy. The repair capacity for late telangiectasia differed significantly from that for erythema and desquamation, with a/j3 values between 2.8 and 4.3 Gy. There was a significant time factor for telangiectasia with characteristic doubling time of about 16 days, when an exponential function for time was used. Concerning the repair kinetics in skin, there were insufficient data to obtain precise estimates, but there was a suggestion of two components of repair. This was inferred from higher-than-predicted recovery with 15-min intervals, when the data were fitted with the monoexponential model. The monoexponential fit gave t; between 1.1 and 1.3 h for acute effects and 3.5 h for late effects. Recovery after 15-min fractionation intervals, if it resulted from a fast repair component, would be consistent with a

Address&r correspondence: Ingela Turesson, Department of Oncology, The University of Gothenburg, Sahlgrenska Hospital, S 4 13 45 Gothenburg, Sweden.

0167-8140/89/$03.50 0 1989 Elsevier Science Publishers B.V. (Biomedical Division)

170

half-time of 0.3-0.4 h. The time factor and the relative long half-time for repair for late effects have important implications for multiple-fraction-per-day treatment, and imply that interfraction intervals of 4 h or less, as commonly used, will be insufficient. Instead, intervals of 6 h or longer are recommended. Using accelerated fractionation with a significant reduction in overall treatment time a dose reduction is still necessary to take into account the time factor for late effects. Further data are necessary for more reliable estimates of the time factor and the repair kinetics for both acute and late effects.

Introduction

Determination of the influence of various fractionation parameters, such as dose per fraction, interfraction interval and duration of rest periods on the response of acutely and late-reacting normal tissues is of basic importance in clinical radiotherapy. Such studies require dose-response data, and with humans these’can only be established for a very narrow dose range. Most often the only ethical design of a clinical study is to test a null hypothesis. Under these constraints, prospective dose-response data for various fractionation schedules have been obtained at the Department of Radiotherapy in Gothenburg. The studies were designed to determine:

(1)

(2)

(3)

(4)

All

The validity of the NSD and CRE formula to predict isoeffective total doses when changing the number of fractions [ 12,19,46]. The degree of sparing due to rest periods [44,48]. The degree of repair of sublethal damage with a 4-h interfraction interval [27,54]. The degree of repair of sublethal damage with very short interfraction intervals, 15 min. The intention was to measure the influence of the overall time of each treatment session, which is of clinical relevance when using a complicated multifield technique [ 5 11.

studies concerned adjuvant radiotherapy given postoperatively. The dose levels were chosen, as far as one knew at that time, to be equivalent to 60 Gy or less with 5 x 2.0 Gy/week during the period 1972 to 1980, and since then close to 50 Gy. In most of the studies two fractionation schedules predicted to result in identical normal-

tissue effects were compared on the same patient. The number of patients per dose group varied between 8 and 35, mostly about 25. With this design and the dose range used, a dose difference of about 5 y0 could be resolved for acute reactions and, after 5 years, for irreversible late effects [44,50].

The results of these previous studies have been reanalyzed using a different technique, and the aim of this paper is to present values of the capacity and rate of repair of sublethal and poten- tially lethal damage in human skin. The values were derived by direct analysis from dose- response data [38] for acute skin erythema and desquamation as well as from telangiectasia, 3 and 5 years after radiotherapy with various fractionation schedules.

Materials and methods

Dose schedules

The clinical assay consisted of breast cancer patients irradiated postoperatively to the internal mammary nodes from unilateral or bilateral fields, with various dose schedules:

(4

(b)

Conventional fractionation with 5 fractions/ week, dose per fraction between 1.8 and 2.5 Gy and overall time between 22 and 40 days. Hypofractionation with 1 fraction/week, dose per fraction between 5.7 and 7.3 Gy and overall time between 22 and 40 days, and 2 fractions/week dose per fraction between 3.5 and 4.4 Gy and overall time between 29 and 40 days.

171

(c) Two and 3 fractions per day with 4-h intervals, dose per fraction 1.1 Gy, 1.6-1.8 Gy and 3.3 Gy, overall time between 11 and 23 days, and finally 3 fractions per day of 2.4 Gy with 15-min intervals, repeated once-a-week, 4 times, in an overall time of 22 days.

Previous accounts of these studies have appeared elsewhere (see references in Tables I and III). The dose schedules, referring to the absorbed dose to skin, are presented in detail in these tables. All studies were done prospectively with stand- ardized skin area, field size and radiation quality.

Dosimetry

Electrons, 12 and 13 MeV and X-rays, 200 kV HVL 1.2 mm Cu, were used. The absorbed doses in water at the depths of 0.1 mm and 1 .O mm were 84 and 88 %, respectively for electrons and 100%) respectively for X-rays. An f-factor of 0.0092 Gy/R was applied for X-rays. Correction factors of 0.99 and 1.02 for electrons and X-rays were used to convert absorbed dose in water to muscle. The RBE was determined at 0.83 in this clinical assay (unpublished data) and was used in the present analysis, i.e. all doses quoted are electron equivalent.

Careful dosimetric control was maintained in all the studies. At each treatment session the absorbed dose was checked with 5 TL dosimeters [22,46]. Contributions to the absorbed dose from any adjacent field were included. If necessary, the dose in the last fraction was corrected according to the TLD determination in order to achieve the prescribed dose. The TL dosimeter reading corresponds very closely to the absorbed dose at the depth of 1 mm, and was considered adequate to use for both the acute and late response measured in this study.

By using TLD measurements any relative dose variation between the two schedules compared on the same patient, between patients in one series, and between various series was minimized. How- ever, the result of the analysis is influenced by absolute errors in absorbed dose. These are due

to type B uncertainties, which depend on the physical parameters employed [ 11,241. Uncer- tainties in RBE and the choice of relevant depth for the target cells responsible for the acute and late endpoints also contribute to absolute errors in absorbed dose. In the dose-response analysis presented here, we used the skin dose averaged over the 5 dosimeters per field corrected to absorbed dose to muscle.

Acute endpoint

Skin erythema was measured by reflectance spectrophotometry, twice a week until the reactions had faded away [46]. The degree of erythema E(t), %, at a time t from start of irradiation was calculated according to the formula:

E(t) = R -R, 0. 100

R0

where R, is the reflectance before irradiation and R, the reflectance at time t.

The quantal response was obtained by classify- ing the patients as responders or non-responders according to their maximum erythema reaction, E(t,,,). The present analysis was done for E(t,,,) 2 45, 50 and 55 %, which were the most suitable.

The patients were also photographed once or twice a week. The acute reaction was scored blindly by two observers from the photographs according to an arbitrary scale: no, mild, moder- ate and brisk erythema, spotted and confluent moist reaction (score 0,1,2,3,4 and 5). Quantal response was obtained in analogy with the erythema measurements. Moist reaction as endpoint was analyzed, i.e. patients with spotted or confluent moist reaction, score 24, at maximum were classified as responders. The aim of the latter analysis was to compare erythema as the endpoint with moist reaction, since the latter is more closely related to basal-cell death.

Patients who showed a confluent moist acute reaction were excluded from the analysis of late effects [54]. These comprised 10 out of 452.

172

Late endpoint

The patients were investigated and the fields photographed every 3 months up to 5 years, and then every 6 months during the rest of the patients’ lives. The response at 3 and 5 years was used in the present analysis. The degree of telangiectasia was used as late endpoint, and was scored on an arbitrary scale blindly by 2 observers; no, minimal, distinct and very marked telangiectasia (score 0,1,2 and 3).

The percentage (+ S.E.) of patients with score >/ 1, score >2 and score = 3 after various follow-up times was calculated for each dose group with the life-table method [7,53]. For the quantal analysis, the actual numbers, not just the percentage, were required. These were calculated in the following way: from the initial number of patients, the number lost to follow-up divided by 2 was subtracted. After rounding off to an integer, the number of responders was calculated from this corrected number of subjects and the actuarial percentage. The present analysis was done for telangiectasia score > 1 and score 22 at 3,4 and 5 years. The response rate for score = 3 was still too low at 3 and 5 years for a reliable analysis, but will be relevant for an analysis at 10 years.

The dose-response parameters derived for the acute and late endpoints are presented with 95 y0 confidence limits.

Data analysis

The analysis of the repair capacity and repair kinetics of acutely and late-responding tissues is based on the following assumptions:

(4

(b)

cc>

When proliferation is negligible the linear- quadratic (LQ) model describes the survival curve for the underlying target cells of the tissue response, in the range between 1 and 8 Gy per fraction. A monoexponential model describes the kinetics of Elkind repair. Elkind repair is completed after 24 h independently of the size of the dose per fraction.

(d) An exponential increase in cell survival of the target cells with protraction of the overall treatment time within a limited range [ 5,36,42].

The acutely responding cell population might be spared by cell proliferation, which seems to start after a time lag of 4 weeks [48]. There- after, we assumed a fractionation-dependent increase in a cell survival due to repopulation. Further, we assumed that the late-responding cell population is spared without time lag and independently of fractionation with protraction of overall time up to 6 weeks (the longest overall time in the study). The biological phenomenon behind the sparing of late- responding cell populations with protraction of overall time is not understood, but possi- bilities included slow (intracellular) repair and regeneration of survivors.

Direct analysis [38] and the incomplete-repair (IR) model [ 371 (see Appendix) were used to estimate a, /I and p and y from pooling all dose- response data without any restriction on the interfraction interval At. A comparison of the parameters estimated from complete-repair data (24-h intervals) only with those obtained by pooling all data and use of the IR model gave an idea of the internal consistency of the two methods.

Patients were lost to follow-up due to death from malignancy of intercurrent disease. The response rate was modified by an actuarial method [7,53,55] to account for censorship.

Results

Acute endpoints

The detailed results for erythema > 50% and desquamation score > 4 are presented in Table I. For the analysis of the fractionation parameters the dose schedules used were divided into two groups depending on the overall treatment time:

(1) Dose schedules with an overall time T between 11 and 29 days, during which any

173

TABLE I

Series

CRE I CRE I CRE II CRE II CRE II CRE III CRE III CRE IVa CRE IVa CRE IVb CRE IVb CRE V CRE V CRE VI CRE VI CRE VIIa CRE VIIb CRE VIIc CRE VIIa CRE VIIa CRE VIIb CRE VIIc CRE VIIa CRE VIIa CRE VIIa CRE VIIa CRE XIIb CRE XIIb CRE XIIc CRE XIIc CRE XIIIa CRE XIIIa D III D III

(2)

Fractions per week

5 2 5 5 5 5 5 5 1 5 1 5

15 4 2 5 5 5 5 5 2 2 2 2 2 1 5

10 5

10 5

15 1 3

Dose schedule

Fractions Nd(Gy) N d per day

At(h) T

1 1 1 1 1 1 1 1 1 1 1 1 3 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 3 1 3

48.0 39.2 41.7 41.4 23.9 40.5 38.4 40.7 29.2 39.6 25.8 41.6 55.1 34.2 40.5 34.8 36.5 36.5 44.6 52.4 29.3 29.1 35.4 38.7 42.3 34.3 44.4 44.2 49.9 44.8 47.3 40.8 28.3 28.3

21 2.28 24 29 9 4.36 >24 29

18 2.32 24 24 17 2.44 24 23 10 2.39 24 12 16 2.53 24 22 16 2.40 24 22 16 2.54 24 22 4 7.30 >24 22

16 2.48 24 22 4 6.44 >24 22

17 2.45 24 23 50 1.10 4 23 10 3.42 4 15 10 4.05 >24 33 20 1.74 24 26 20 1.83 24 26 20 1.83 24 26 25 1.78 24 33 30 1.75 24 40

8 3.66 >24 26 8 3.63 >24 26

10 3.54 >24 33 11 3.52 >24 36 12 3.52 >24 40 6 5.72 >24 40

25 1.78 24 33 25 1.77 4 17 25 2.0 24 33 25 1.79 4 17 25 1.89 24 33 25 1.63 4 11

4 7.08 >24 22 12 2.36 0.25 22

influence of cell progression and proliferation was considered negligible ([48] unpublished data). Dose schedules with an overall time T between 33 and 40 days, for the reason that after 4 weeks irradiation cell progression and proliferation would have influenced the response in a way which was dependent on interfraction interval and fraction size.

Erythema Desquamation Ref. score B 4

9113 217 43 11/13 217 43

617 417 44

417 417 44 o/14 o/14 44 4110 z/10 44 3/10 o/10 44

12127 5121 45 14127 3121 45 19135 6136 unpublished 1 l/35 O/36 unpublished 4/11 l/l1 45 9/11 5/11 45

13/31 l/32 unpublished 21/31 10133 unpublished

2112 o/13 48 6129 l/34 48 3125 O/25 unpublished

16126 7121 48 24126 11/21 48

6129 l/34 48 2125 O/25 48 9127 2121 48 8125 2126 48

17125 3123 48 518 O/8 48

21/31 8/31 54 20/3 1 813 1 54 21123 17125 54 18/23 9125 54 21127 1 l/28 54 1 l/27 4128 54 14127 4129 51 7127 2129 51

Responders/subjects

Cell progression and prol$eration negligible (T < 29 days) Table IIa summarizes the dose-response parameters and the repair capacity for erythema and desquamation derived from various fractionation schedules with an interfraction interval of 24 h or more using the complete-repair model. T varied between 22 and 29 days. The number of dose groups was 18 and there were on average 20 fields per dose group.

174

TABLE IIa

Direct analysis with the complete repair model, T within 22-29 days.

Erythema Desquamation 350% score 34

hlK 4.81 (3.61, 6.01) 5.57 (3.93, 7.21) ax lO,Gy-’ 0.95 (0.68, 1.23) 1.02 (0.67, 1.37) gx 102, Gy-* 1.27 (0.92, 1.61) 0.91 (0.51, 1.31) u/E x 10, Gy-’ 0.20 (0.10, 0.38) 0.18 (0.08, 0.39) b/E x lo’, Gy-’ 0.26 (0.14, 0.48) 0.16 (0.06, 0.37) u/B, GY 7.5 (5.4, 10.4) 11.2 (7.8, 18.6)

Table IIb summarizes the dose-response parameters, the repair capacity and repair kinetics derived from all fractionation schedules without any restriction on the inter-fraction interval using the IR model. T varied between 11 and 29 days. The number of dose groups with shortened interfraction interval, At < 24 h, was 6 with an average of 25 fields per group. However, in this analysis the maximum likelihood process resulted in two maxima with nearly the same estimates of all parameters except for the half-time 5 (h). One maximum corresponded to a short repair half- time of about 0.3-0.4 h and the other a slower half-time of about 1.1-1.3 h. The confidence limits are relatively large and impossible to determine for some endpoints. However, these findings might indicate a biphasic repair process instead of a monoexponential one, as was assumed in the model.

TABLE II\,

A comparison of Tables IIa and IIb shows that the values of the dose-response parameters a, j3, a/E, /3/E and the ratio or//? derived from “complete-repair data” only and from pooled data were approximately the same. Moreover, the dose- response parameters for erythema agree with those for desquamation. There was no significant difference between the parameters derived for erythema, 45, 50 and 55%.

For 4 fractions and for a dose per fraction of 2.44 Gy, there were 3 or more dose groups, and so the fit of these data has been presented as dose-response curves. Figure 1 shows the observed response and the estimated dose- response curves for 4 fractions in 22 days and for 5 x 2.44 Gy/week, using erythema 2 50% and desquamation score 24. The estimated dose- response curves were calculated from the parameters in Table IIb. The consistency between observed and estimated response for isolated dose groups was in the same range.

Cell progression and proliferation of sig@cance (T > 29 days) Table IIc summarizes the dose-yesponse parameters from various fractionation schedules with overall time longer than 29 days (between 33 and 40 days) and At 3 24 h. The number of dose groups was 10, with an average of 23 fields per group. Although confidence intervals were wide, there was a tendency for a to increase and fi to decrease, a/E to remain constant and /I/E to

Direct analysis with the incomplete repair model, T within 1 l-29 days.

Erythema 2 50% Desquamation score 2 4

1nK 5.26 (4.12, 6.40) 5.33 (4.21, 6.44) 5.51 ( 4.15, 6.87) 5.31 (4.01, 6.61) ax lO,Gy-’ 1.10 (0.84, 1.35) 1.11 (0.88, 1.35) 1.01 ( 0.74, 1.27) 0.97 (0.71, 1.22) B x 102, GY-~ 1.24 (0.91, 1.58) 1.30 (0.96, 1.64) 0.90 ( 0.53, 1.27) 0.96 (0.53, 1.39) a/E x 10, Gy-’ 0.21 (0.12, 0.36) 0.21 (0.13, 0.35) 0.18 ( 0.10, 0.34) 0.18 (0.10, 0.34) B/E x lo’, Gy-’ 0.24 (0.13, 0.42) 0.24 (0.14, 0.42) 0.16 ( 0.07, 0.34) 0.18 (0.07, 0.38) a/B, GY 8.8 (6.9, 11.6) 8.8 (6.8, 11.3) 11.2 ( 8.5, 17.6) 10.1 (7.2, 17.8) p, h-’ 0.52 (0.18, 1.21) 1.64 (0.09, 3.19) 0.61 (-0.08, 1.31) 2.53 (1.59, 3.46) $9 h 1.34 (0.57, ?) 0.42 (0.22, 7.8) 1.13 ( 0.53, ?) 0.27 (0.20, 0.43) - lo&k 295.99 295.72 161.30 161.97

175

Erythema 50% Desquamation score24 100

j b / /

?? d=2.44Gy

. N+T=22d

10 20 30 40 50 60 70 80 10 20 30 40 50 60 70 80 Dose,Gy Dose,Gy

Fig. l(a) Dose response for erythema 2 50% : A, observed response for 4 fractions, 1 fraction/week; ??, observed response for 5 x 2.44 Gy/week (range 2.32-2.54 Gy/fraction). Solid lines are expected dose response calculated from the parameters derived by direct analysis using the Poisson and the LQ models assuming no influence of overall time. The parameters are given iu Table IIb. ED,+ are 28.4 Gy for 4 fractions and 40.1 Gy for 5 x 2.44 Gy/week. Note that the curve for 5 x 2.44 Gy/week is only valid for overall times up to 29 days, i.e. 21 fractions and a total dose of 51.2 Gy. (b) Dose response for desquamation score 24: A, observed response for 4 fractions, 1 fraction/week; ??, observed response for 5 x 2.44 Gy/week (range 2.32-2.54 Gy/fraction). Solid lines are expected dose response calculated from the parameters derived by direct analysis using the Poisson and the LQ models assuming no influence of overall time. The parameters are given in Table IIb. ED,,+ are 33.4 Gy for 4 fractions and 47.8 Gy for 5 x 2.44 Gy/week. Note that the curve for 5 x 2.44 Gy/week is only valid for overall times up to 29 days, i.e. 21 fractions and

a total dose of 51.2 Gy.

TABLE IIc

Direct analysis with the complete-repair model, T within 33-40 days.

Erythema 2 50 %

1tlK c(x 10,Gyy’ /Ix lo’, Gy-’ a/E x 10, Gy- ’ j/E x lo’, Gy - * aI/% GY

7.31 ( 4.30, 10.3) 1.67 ( 1.10, 2.23) 0.91 ( 0.13, 1.69) 0.23 ( 0.009, 0.64) 0.13 ( 0.00, 0.48)

18.3 (10.6, 30.2)

decrease compared to those derived for T 6 29 days. The ratio a//? was higher, a factor of about 2 to 3. Dose-response curves are shown (Fig. 2) for 1.77 and-,3..53 Gy per fraction, and for 10 and 25 fractions in 5 weeks.

The time factor A time-factor analysis was done according to Eqn. (2) (Appendix) to make clear the reason for the change in dose-response parameters with protraction of the overall time [ 481. A check of the variation of the number of fractions and the overall time for all dose groups showed that there

Desquamation score > 4

5.72 ( 3.25, 8.20) 1.17 ( 0.71, 1.62) 0.34 ( - 0.28, 0.95) 0.20 ( 0.08, 0.49) 0.06 ( - 0.05, 0.34)

34.5 (?)

was no significant correlation between the two parameters (thus reducing the possibility for compounding the effects of repair and repopulation with treatment protraction). For the pooled data, analyzed for all T (i.e. T, = 0 days) and separately for T < 29 days (i.e. T, = 0 days) and for T > 29 days (i.e. T, = 29 days) there was no significant influence of time. When analyzing the 5 fractions per week schedules and the 1 to 2 fractions per week schedules separately, the procedure did not converge due to too few dose groups and limited variations in d for each subgroup.

176

Erythema 50% Erythema 50% 100

10 20 30 40 50 60 70 80 Dose, Gy

Desquamation score24 IOO-

80-

. N=lO, T=33 d

??N.25, T133 d

10 20 30 40 50 60 70 80 Dose, Gy

10 20 30 40 50 60 70 80 Dose, Gy

Desquamation score24

100

80-

z !i 60-

5 '- ii 40 P

20- o dzl.77 Gy

o dz3.53 Gy

10 20 30 40 50 60 70 80 Dose, Gy

Fig. 2(a) Dose response for erythema > 50%. Observed response for 10 fractions (+) and 25 fractions (m) in 33 days, and for 5 x 1.77 Gy/week (0) (range 1.75-1.78 Gy/fraction) and 2 x 3.53 Gy/week (0) (range 3.52-3.54 Gy/fraction). Solid lines are expected dose response calculated from the parameters derived by direct analysis using the Poisson and the LQ models for schedules with an overall time between 33 and 40 days. The parameters are given in Table IIc (ED,,s are 38.1 Gy for 10 fractions, 42.1 Gy for 25 fractions, 41.9 Gy for 5 x 1.77 Gy/week and 38.6 Gy for 2 x 3.53 Gy/week). Note that the curves for 5 x 1.77 Gy/week and 2 x 3.53 Gy/week are only valid for overall times between 33 and 40 days. (b) Dose response for desquamation score 24. Observed response for 10 fractions (+) and 25 fractions (m) in 33 days, and for 5 x 1.77 Gy/week (0) (range 1.75-1.78 Gy/fraction) and 2 x 3.53 Gy/week (0) (range 3.52-3.54 Gy/fraction). Solid lines are expected dose response calculated from the parameters derived by direct analysis using the Poisson and the LQ models for schedules with an overall time between 33 and 40 days. The parameters are given in Table II (ED,,s are 45.9 Gy for 10 fractions, 49.2 Gy for 25 fractions, 49.5 Gy for 5 x 1.77 Gy/week and 47.2 Gy for 2 x 3.53 Gy/week). Note that the curve for 5 x 1.77 Gy/week and 2 x 3.53 Gyjweek

are only valid for overall times between 33 and 40 days.

Late endpoints number of dose groups was 19 with an average of 23 fields per group. Table IVa summarizes the

Detailed results for telangiectasia score > 1 at 3 parameters for score 2 1 and score >2 at 3 and years and a >2 at 5 years are presented in 5 years, respectively. Table III. The analysis of the fractionation Secondly, we repeated the analysis of the same parameters was done under three conditions. dose groups including the time factor without time First, we considered any influence of the overall lag, i.e. T, = 0 days in Eqn. (2) (Appendix), see time negligible as is usually done for late effects, Table IVb. The time factor y was small but signif% i.e. y = 0 in Eqn. (2) (Appendix) and derived the cant by a maximum likelihood ratio test. A com- dose-response parameters and repair capacity parison of Tables IVa and IVb shows that the from dose schedules with the interfraction interval values of CI, j3 and the ratio a/p derived without and long enough for complete Elkind repair, i.e. with a time factor differ slightly, but not signif% At > 24 h. T varied between 22 and 40 days. The cantly.

177

TABLE III

Series Fractions Fractions per week per day

Dose schedule Responders/subjects Ref.

Nd(Gy) N d At(h) T Initial

(days) no. of subjects

Telangiectasia

score > 1 3 yrs

CRE I 5 1 48.0 21 2.28 24 29 12 5/l 1 CRE I 2 1 39.2 9 4.36 >24 29 12 7/11 CRE IVa 5 1 40.7 16 2.54 24 22 27 9127 CRE IVa 1 1 29.2 4 7.30 >24 22 27 17127 CRE IVb 5 1 39.6 16 2.48 24 22 35 13135 CRE IVb 1 1 25.8 4. 6.44 >24 22 35 13135 CRE V 5 1 41.6 17 2.45 24 23 11 4/11 CRE V 15 3 55.1 50 1.10 4 23 11 6/11 CRE VI 4 2 34.2 10 3.42 4 15 33 28128 CRE VI 2 1 40.5 10 4.05 >24 33 32 27127 CRE VIIa 5 1 34.8 20 1.74 24 26 12 I/l1 CRE VIIa 5 1 44.6 25 1.78 24 33 27 5123 CRE VIIa 5 1 52.4 30 1.75 24 40 26 6124 CRE VIIa 2 1 35.4 10 3.54 >24 33 26 5125 CRE VIIa 2 1 38.7 11 3.52 >24 36 24 6122 CRE VIIa 2 1 42.3 12 3.53 >24 40 24 lo/24 CRE VIIa 1 1 34.3 6 5.12 >24 40 8 718 CRE VIIb 5 1 44.4 25 1.78 24 33 28 2126 CRE VIIb 0 2 44.2 25 1.77 4 17 28 13126 CRE XIIc 5 1 49.9 25 2.0 24 33 22 1 l/20 CRE XIIc 10 2 44.8 25 1.79 4 17 22 13120 CRE XIIIa 5 1 47.3 25 1.89 24 33 28 9125 CRE XIIIa 15 3 40.8 25 1.63 4 11 28 13126 D III 1 1 28.3 4 7.08 >24 22 25 1 S/25 D III 3 3 28.3 12 2.36 0.25 22 25 1 l/24

TABLE IVb

TABLE IVa Direct analysis with the complete repair model and time correction.

Direct analysis with the complete repair model and no time correction.

Telangiectasia ~__~

Score > 1, 3 yrs Score > 2, 5 yrs

1nK 3.98 (2.63, 5.32) 5.36 (3.78, 6.94) u x 10, Gy-’ 0.48 (0.25, 0.72) 0.64 (0.38, 0.91) p x lo’, GY-~ 1.73 (1.31, 2.16) 2.29 (1.77, 2.80) u/E x 10, Gy- ’ 0.12 (0.04, 0.32) 0.12 (0.05, 0.27) b/E x lo*, Gy - ’ 0.44 (0.22, 0.93) 0.43 (0.23, 0.82) aiS> GY 2.8 (1.4, 3.9) 2.8 (1.7, 3.8)

score 2 2 5 yrs

s/11 9/11 8125

20126 10134 14134 3/11 7111

22126 21125

O/IO 3122 7123 3123 7122

12123 718 2122

14124 1 o/20 13/20

15123 7121

SO 50 49 49 unpublished unpublished 27 21 unpublished unpublished 50 50 50 50 50 50 unpublished 54 54 54 54 54 54 51 51

Telangiectasia

Score > 1, 3 yrs Score > 2, 5 yrs

1tlK 4.46 (3.07, 5.84) 6.27 (4.53, 8.00) ax lO,Gy-’ 0.82 (0.50, 1.13) 1.06 (0.69, 1.44) B x 102, Gyy2 2.04 (1.56, 2.51) 2.76 (2.14, 3.38) a/E x 10, Gyy’ 0.18 (0.07, 0.41) 0.17 (0.08, 0.35) /3/E x 102, Gym2 0.46 (0.25, 0.91) 0.44 (0.25, 0.82) a/B, GY 4.0 (2.6, 5.2) 3.9 (2.7, 4.8) yx 10, dayy’ 0.42 (0.16, 0.67) 0.46 (0.19, 0.73) Ts, day 17 (11,43) 15 (10, 37)

178

TABLE IVc

Direct analysis with the incomplete repair model and time correction.

Telangiectasia

Score 3 1, 3 yrs Score 3 2, 5 yrs

1llK 4.59 (3.28, 5.90) 6.32 (4.90, 7.74) ax lO,Gy-’ 0.84 (0.63, 1.05) 1.11 (0.89, 1.34) B x lo’, GY-~ 2.06 (1.67, 2.45) 2.61 (2.18, 3.04) u/E x 10, Gy-’ 0.18 (0.009, 0.36) 0.18 (0.11, 0.30) p/E x 102, Gy - 2 0.45 (0.26, 0.84) 0.41 (0.26, 0.68) a/B, GY 4.1 (3.4, 4.7) 4.3 (3.7, 4.8) PL, h-’ 0.19 (0.16, 0.23) 0.21 (0.17, 0.25) t;, h 3.6 (3.0, 4.5) 3.4 (2.8, 4.2) y x 10, day-’ 0.42 (0.16, 0.67) 0.46 (0.19, 0.73) Ts, day 17 (11,43) 15 (10,37)

Thirdly, Table IVc summarizes the dose- response parameters, the repair capacity and repair kinetics derived from all fractionation schedules without any restriction on the interfraction interval, taking into account the overall time and using the IR model. T varied between 11 and 40 days. The number of dose groups with shortened interfraction interval, At < 24 h, was 6 with an average of 25 fields per group. The complete analysis was based on 25 dose groups with an average of 23 fields per group. The analysis for telangiectasia score 22 at 3 years showed 2 maxima of nearly identical height in the likelihood function as was found for acute reactions. One showed a repair half-time of about 0.38 (0.16) h and the other a slower half-time of 4.2 (3.5,5.3) h, but all other parameters were about the same.

A comparison of Tables IVb and IVc shows that the values of the dose-response parameters, 0; j3, a/E, /3/E and the ratio a/p derived from “complete-repair data” only and from the pooled data were almost identical. However, the confidence limits in the latter case were tighter as more data were included. Moreover, there were no signiticant differences in the parameters deduced from score > 1 and score > 2 at 3,4 and 5 years.

Figure 3 shows the observed late response, score 22 at 5 years and the estimated dose-

response curves for 4 and 16 fractions in 22 days, 10 and 25 fractions in 33 days, and also 5 x 1.76 Gy/week and 2 x 3.53 Gy/week. The dose response derived for 5 x 2.0 Gy/week was plotted as reference. The estimated dose-response curves were calculated from the parameters in Table IVc. The consistency between the observed and estimated response for isolated dose groups is illustrated for the multiple-fractions-per-day schedules studied (Fig. 3~).

Discussion

Repair capacity and repair kinetics have been determined for erythema, desquamation and telangiectasia in human skin by direct analysis of quantal dose-response data and the IR model [ 37,381. The influence of overall time was modelled by an exponential function of time.

The repair capacity is the sensitivity of a specific tissue reaction to changes in dose per fraction and it is proportional to the steepness of the graph of the isoeffective total dose versus number of fractions. The log-log graph can be approximated with a straight line over a limited range in fraction number. The exponent for the fraction number is a measure of the fractionation sensitivity and repair capacity in this range (ref. [ 391, Table 2.6).

However, the number of fractions exponent, exp N (= 0.24 in the NSD model), is also related to the a and j3 coefficients in the LQ model and fraction size d Gy [34,39]:

expIV=: d/(1+2 $ d)

The ration /?/a is an effect-independent measure of repair capacity [ 351. However, from Eqn. (1) it is evident that the exp N varies with fraction size and a single value cannot properly describe the repair capacity, if the LQ model is adequate. There is now evidence that the LQ model is valid for various tissue responses, at least for clinically relevant fraction sizes.

Information on tissue repair kinetics is of clinical relevance for certain dosage methods in radio-

179

Telangiectasia 5 Years

loo- Score 2 2,

a

80 - 0

S 5 60 5 ._ G 40 P

:/!/IT.,.

. N=4

0 N=lO

20 + N=16

0 Nn25 0 20 30 40 50 60 70 80 90

Dose, Gy

80

ui 60 E .9! iii 40 P

20 30 40 50 60 70 80 90 Dose, Gy

Telangiectasia Score 2 2, 5 Years

C

100

80

J g 60

5 ‘- z 40 n

20

0

Telangiectasia Score z-2, 5 Years

. dz1.76 Gy

x -d1=2.0 Gy

+ dz3.53 Gy

2 fract/day 3 fract/day 3 fractlday At = 4 hrs At ??4 hrs At = 0.25 hrs

T

i

;I

I

20 40 60 20 40 60 20 40 60

Dose, Gy Dose, Gy Dose, Gy

Fig. 3(a) Dose response for telangiectasia, score > 2 at 5 years. Observed response for 4 fractions (A) and 16 fractions ( + ) in 22 days, 10 fractions (0) and 25 fractions (0) in 33 days. Solid lines are expected dose response calculated from the parameters derived by direct analysis using the Poisson and the IR models with time factor. The parameters are given in Table IVc. ED,, are26.9Gy(A),42.6 Gy( +),38.7 Gy(O),and50.2 Gy(O).(b)D ose response for telangiectasia, score 3 2 at 5 years. Observed response for 5 x 1.76 Gy/week (m), 5 x 2.0 Gy/week ( x ) and 2 x 3.53 Gy/week (+). Solid lines are expected dose response calculated as in Fig. 3(a). ED,,+ are 54.6,50.8 and 42.0 Gy, respectively. (c) Dose response for telangiectasia, score 2 2 at 5 years. Symbols represent observed response for various fractionation schedules with only one dose group and the deviation from the

expected value is represented by the bar. The expected response was calculated as in Fig. 3(a).

therapy, i e. continuous low dose rate irradiation and multiple fractions per day. The dose response varies with the dose rate. The lower the dose rate the longer the irradiation time and the more sublethal damage is repaired. Concerning multiple- fractions-per-day schedules, the interfraction interval may be too short for complete Elkind repair. Under these circumstances, a dose correction must be applied to correct for the degree of incomplete repair to avoid an increase in com- plication rates [54]. Also, the short rest periods between portals in one treatment session when multifield techniques are used could be of biological significance due to rapid repair of DNA dam-

age [ 511. These effects were accounted for by a generalization of the LQ model, the IR model [37].

A two-step procedure was first used to estimate fractionation parameters from dose-response data. First, the isoeffective total doses for various fractionation schemes were established. Second- ly, the isoeffect data were used in a model, such as the Douglas and Fowler linear-linear plot of the reciprocal isoeffective total dose versus dose per fraction [ lo]. From this plot, the ratio a//3 (Gy) in the LQ model for dose response could be determined [ 341. The relatively large quantity of clinical dose-response data, based upon about 750

180

irradiation fields, which will be presented here, is reduced to 3 to 5 data points using this procedure.

However, this disadvantage can be cir- cumvented by using direct analysis of quantal response to fractionated irradiation [ 381. All raw dose-response data are pooled in a maximization of log likelihood, and the fractionation parameters are obtained as the maximum likelihood estimates. Therefore, even the information from a schedule with only one dose level is utilized to full extent. Other advantages are that the direct method results in more accurate confidence limits and on average parameter estimates closer to the “true” values.

Acute eflects - repair capacity and influence of overall time

Erythema and pigmentation were measured by reflectance spectrophotometry in all fractionation studies. Pigmentation was found to be a rather insensitive endpoint [44], and was therefore not reanalyzed in the present study. Erythema has been questioned as a relevant endpoint for several reasons. In fact, we really do not know the mechanism of erythema; is it a direct effect on blood vessels, or is it an indirect effect related to cell death in the epidermis or both? Also, the relia- bility in scoring erythema is rather poor [4]. However, contrary to what was concluded by Nias et al. [26], we have found that quantifying erythema by reflectance spectrophotometry is a reliable and sensitive method [44,46].

An analysis of the Gothenburg data with desquamation as endpoint is presented for the tirst time in this paper. In the design of the studies we chose dose levels which were predicted to be below the tolerance dose for moist reaction. The reason for this was to avoid an interaction between early and late effects, as moist reaction might cause infection and mechanical damage to dermis and thereby a “false” or consequential late effect. However, some patients showed a spotted moist reaction, score 4, and very few a confluent moist reaction, score 5. The number of responders was enough to perform an analysis for score 24.

There was a small but insignilicant difference in repair capacity for erythema and desquamation. The a/pratios were in the range of 7.5-8.8 Gy and 10.1-11.2 Gy respectively when T <29 days (Tables IIa and IIb). The other parameter estimates and the confidence limits were about the same for the two endpoints. Most important is that the repair capacity was in the same range as for well defined acute endpoints in animal studies [ 391.

For acutely responding tissues we expect some sparing due to repopulation with protraction of overall treatment time. The amount of sparing is related to the normal-cell turnover rate in the tissue, the fraction-size-dependent mitotic delay, and the rate of dose delivery. The higher the rate the sooner the critical cell-depletion level for the target cells is reached, resulting in compensatory rapid proliferation of surviving cells. However, in this analysis we found no sigmfiant time factor up to 40 days for erythema and desquamation.

In this analysis we employed a time lag TO of 29 days [see Eqn. (2) in Appendix]. This was based on previous observations of a change in repair capacity at about this time (Turesson and Notter [48]). It will be noted that this has no influence on the actual estimate or the significance of the time factor, y. Instead, it will alter the value of the constant of the fit, lti. A more serious objection would be that the mathematical form chosen is inappropriate, but there is unfortunately little data on this point.

The earlier analysis [47,48] showed a different repair capacity for T between 22 and 29 days and T between 33 and 40 days. This was the reason for splitting the data into the two subgroups here, though no time factor could be proven. The analysis of the dose groups with T between 33 and 40 days showed higher a/b ratios by a factor of 2-3 (Table 11~).

If the difference in a/j3 ratios is real several interpretations are possible.

(1) Redistribution in the cell cycle results in a net sensitization of the target cells in such a way that a//l increases [ 48,59,62].

(2) Increased movement of cells in the division cycle (although not sufficient to detect in terms of a time factor) results in relatively shorter times for repair, because of variable repair capacity through the cycle of fixation points. As a result, u is larger, and jI perhaps smaller, than before the proliferative response is triggered ([39], page 124).

Contrary to what we expected, no significant time factor could be detected up to 40 days. The response to 2 x 3.6 Gy/week and 5 x 1.8 Gy/ week for 4 to 6 weeks irradiation is presented in Table V. From the steepness in the dose response one can conclude that there is no obvious sparing by repopulation. As pointed out before, the fractionation sensitivity decreases with prolonged overall time [47,48,52], i.e. the isoeffect doses for the two schedules get closer. There might be some sparing by proliferation with the 2 fraction/week schedule but no sparing with the 5 fraction/week schedule, related to the length of the interfraction interval and division delay. However, there are not enough data to make the point clear. On the other hand, a rest period of 3 weeks after 4 weeks substantially reduced the acute reaction (Table V). In fact, the reaction due to the second

181

course could be interpreted as though the first course was forgotten ([48] unpublished data).

In a comprehensive study on mouse skin, Denekamp [8] determined the amount of proliferation in Gy per day after various degrees of radiation damage. The design of that experiment reflects chiefly the degree of sparing during a rest period. Experiments to demonstrate the degree of sparing due to repopulation duting a radiotherapy course have not yet been done for skin. However, in the paper of Moulder and Fischer [25], who studied the acute reactions in the rat foot, a decreased fractionation sensitivity with overall time beyond 17 days was found ([39], p. 121). Their results confirm our clinical findings, which indicate that after a lag period the response characteristics of the target-cell population will change.

The clearest evidence of tissue-sparing due to proliferation during a fractionated irradiation course was presented by Withers and Mason [ 601 using the colon colony assay. For interfraction intervals of 12 h or more, sparing by proliferation was sig&cant already after 2 days. The difference between skin and colon is due to the much faster cell turnover rate of the colonic mucosa.

TABLE V

Dose 2 and response 5 fractions/week (endpoint: erythema 3 50%). _ _ Dose/overall time 2 x 3.6 Gy/week Dose/overall time 5 x 1.8 Gy/week

____ Responders/subjects % Responders/subjects %

_

29.3 Gy/26 days 6129 21 36.5 Gy/26 days 6129 21 29.1 Gy/26 days 2125 8 36.5 Gy/26 days 3125 12

34.8 Gy/26 days 2112 17 35.4 Gy/33 days 9127 33 44.6 Gy/33 days 16126 61

44.4 Gy/33 days 21131 68 38.7 Gy/36 days 8125 32 42.3 Gy/40 days 17125 68 52.4 Gy/40 days 24126 92

3 weeks rest Response to 2nd course 3 weeks rest Response to 2nd course after 4 weeks after 4 weeks

43.6 Gy/60 days O/26 0 54.6 Gy/61 days O/26 0 50.5 Gy/67 days 4127 14 62.9 Gy/68 days 3127 10

182

Late eflects - repair capacity and influence of overall time We have scored the degree of telangiectasia regu- larly since completion of radiotherapy and the aim was to follow the patients during the rest of their lives. Telangiectasia progresses continuously for at least 15 years, the longest follow-up so far. In the dose range used, the progression rate is relatively slow but strongly dose-dependent [ 531. Therefore, both the number of responders per dose group and the degree of reaction of the responders increase with follow-up time. With a “progressive” late endpoint, the analysis by the present methods involves a fixed follow-up time, here 3, 4 and 5 years, which is long enough to obtain a sufficient number of responders using (a) score > 1, patients with minimal, distinct or very marked telangiectasia, and (b) score 22, patients with distinct or very marked telangiectasia. There was no significant difference between the parameters derived for the various endpoints. Latent-time models now under devel- opment will allow use of the actual times of observed injury to derive both dose-response and latency parameters [ 31.

A significant number of patients was lost from follow-up due to death from their malignancy or from intercurrent disease. The response rate was therefore estimated by an actuarial method [7,53,55]; a more natural way will be to use censorship in the latent-time models.

The mechanisms behind the telangiectasia are still not understood. They might include a defi- ciency in regenerated capillaries, or as proposed by Hopewell (personal communication), damage to the smooth muscle cells of the precapillary sphincters, which then fail in function.

The repair capacity (fx/firatio) for telangiectasia was 2.8 Gy, when the time factor was omitted (Table IVa), and between 3.9 and 4.3 Gy when the time factor was taken into account (Tables IVb and IVc). Most important for the relevance of telangiectasia as endpoint in the clinical model is that the repair capacity was in the same range as other experimental late endpoints related to damage to spinal cord [ 1,561, lung [29,41,57],

kidney [32], and rectum [33]. A summary of IX//~ ratios for various late effects derived from clinical data was presented by Thames and Hendry [ 393. The uncertainties are rather large but a//? was mostly below 8 Gy. An a//l ratio of 3.8 Gy has been derived for late complications in the supraglottic larynx [23]. Characteristics of progression rate and dose latency for the various experimental as well as clinical endpoints have not yet been presented on a comparable basis.

Contrary to what we expected, there was a significant time factor for telangiectasia. The “doubling time” T, for this recovery was estimated at about 16 days, when the overall time varied between 22 and 40 days. The criticism might be raised that N and T were highly corre- lated and thus that we have simply removed some of the “fractionation effect” from the a//I term and put it in the time term. However, this correlation was tested and found insignificant (r = 0.14, p = 0.24).

We can exclude the possibility that the time factor was due to proliferation from a study with a rest period of 3 weeks which occurred after 4 weeks and onwards. There was no evidence for a reduced response compared to the same dose given without a rest, at least up to 5 years follow-up (Turesson, Notter, unpublished data). Thus, the time factor probably results from slow repair. Slow repair was demonstrated in an endo- thelial assay by Reinhold and Buisman [30], in lung by Field et al. [ 131 and probably also, but to a lesser extent in kidney by Williams and Denekamp [58]. Slow chromosome repair (to 6 months) has been demonstrated for hepatocytes and thyroid [6,14,31]. However, Maciejewski et al. [23] could not identify any significant influence of overall time for late effects in the larynx.

The time factor, whatever the mechanism involved, does have consequences for accelerated fractionation. Assuming that the interfraction interval is long enough to allow for complete Elkind repair, the total dose still has to be reduced a small but significant amount due to the shorter overall treatment time.

183

The simple arithmetics of using the LQ model for isoeffect calculations [2,39,61] can also be used when the time factor is added, for example, by using the time constant y//I [42]. For telangiectasia, the time constant r//I was between 1.8 and 2.0 Gy2/day, which is comparable with 2.2 Gy2/day derived for lung tissue [42].

Repair kinetics - acute and late efects

The rate of repair for erythema, desquamation and telangiectasia was estimated using the IR model [37], which is based on monoexponential repair kinetics [ 20,21,28]. In the present analysis there were two maxima of nearly equal height in the log likelihood function. The parameters differed significantly only in the values of the half- time for erythema 3 50% and desquamation (Table IIb) and also for telangiectasia score 2 2 at 3 years. The result is consistent with a fast repair component with a half-time of 0.3-0.4 h (about 20 min), similar for all endpoints, and a slower repair component of 1.1-1.3 h for acute effects and 3.4-3.6 h for late effects. Although the confidence intervals were wide, this outcome is consistent with biphasic exponential repair. How- ever, the data may not be considered conclusive on this point since the fast repair component was based on only one dose group, in which every fraction was divided into 3 subfractions separated by 0.25 h. The response was compared with that of the same dose fraction given in a single shot. This study, series DIII, was presented in detail elsewhere [ 511, and showed a significantly reduced response in the “subfractionated” field, corresponding to a dose reduction of about 10% both for acute and late effects. In comparing the observed and expected response rate for the multiple-fractions-per-day data, the parameter estimates for acute effects in Table IIb with the longer t; showed a rather poor agreement for the dose group with 0.25 h interfraction interval but good agreement for all dose groups with 4-h intervals. Also, the parameter estimates for late effects in Table IVc with the longer 5 resulted in incon- sistency between observed and expected response

for the dose group with 0.25 h interfraction interval (Fig. 3~). Thus for both acute and late effects the analysis indicate the possibility of a biphasic repair process. At present, the clinical significance of the fast repair component is virtually un- explored.

An extension of the IR model [40] to two- component repair kinetics was used to analyze lung data from Travis et al. [41] and spinal cord data from Ang et al. [l] and half-times of about 20 min and 2 h were demonstrated graphically (Thames, unpublished results). However, the experiments were not designed for the purpose of elucidating two components of repair and the results must be considered with caution. In a recent paper, Hopewell and van den Aard- weg [ 181 reviewed current experimental data on repair kinetics for skin, spinal cord and lung. They concluded that a biexponential function seemed to fit more adequately than a monoexponential model. Both the fast and the slow half-time were in the same range as we found for human skin, but the uncertainties were large due to the limited data base.

An elegant experiment was performed by Dikomey and Franzke [ 91 to determine the repair kinetics of DNA strand breaks in Chinese ham- ster ovary cells in vitro. They found that the rate of repair was best described by three exponential components with half-times about 2, 20 and 170 min. The two fast components were ascribed to two different classes of single-strand breaks and the slower component to repair of double- strand breaks.

Thames et al. [36] and Fowler [ 151 have addressed the question of different repair kinetics for acute and late-responding tissues. In the present analysis, the half-time for the slower component was longer for late than for acute effects. However, there were data only for 4 h interfraction interval and the confidence limits were too large to allow a definite conclusion. However, the relatively long half-time of about 3.5 h for late effects is of significance for the application of multiple fractions per day. Also of importance was that the dose reduction necessary for isoeffect

184

after accelerated fractionation was a consequence of both incomplete Elkind repair within 4 h and the shortened overall treatment time from 5 weeks to 1.5 and 2.5 weeks (the time factor).

Consistency in the analysis of fractionation parameters and dose response

The parameters derived from quantal response using the IR model agree well both for acute (Tables IIa and IIb) and late effects (Tables IVb and IVc). There were no significant differences between the two analyses. Moreover, the expected and observed response rates were in good agreement (Figs. l-3) for all endpoints.

The repair capacity was significantly lower for skin erythema and desquamation than for telangiectasia, cf. Tables IIa,b and Tables IVa-c. Comparing Tables IIa,b with IVa (no time factor) it is evident that there are no significant differences in either a or /3 for acute and late effects. There is a trend towards a smaller IX and a larger /I for late effects. The consequence is that the single dose-response curve for the late effect will cross that of the acute effect. However, in the analysis including the time factor for late effects, a was about the same as for the acute endpoints but /3 was significantly higher for telangiectasia than for erythema and desquamation (cf. Tables IIa,b and I&c). The consequence is that the single dose-response curve for the late effect is bending downwards faster than that for the acute effect, and they do not cross each other.

In order to illustrate the importance of various fractionation parameters for acute and late effects, we have plotted dose-response curves for 16 fractions in 22 days, 30 fractions in 40 days and 30 fractions in 18 days (2 fractions/day, 8-h intervals) for erythema, desquamation and telangiectasia (Fig. 4). These first two schedules are in common use and were recently discussed in detail by Fowler [ 161 concerning the sparing of late effects relative to acute effects by using smaller fraction sizes and larger fraction numbers. He also discussed the potential benefit of accelerated fractionation and the use of 30 fractions in 3

80

$ 60 E $ 40 p”

20 30 40 50 60 70 80

80

0

Erythema 50%

- N=16, T=22 d

-- N&O,T=l6d

Dose, Gy

Desquamation scorer4

- N=l6, T=22 d - - N=30,1=16 d ----- N=30,Ts40 d

20 30 40 50 60 70 80 Dose, Gy

Telangiectasia

100 Score 2 2, 5 Years

80 -

ae 5 60 -

E g 40 P

20 - - Nz16, T=22 d - - Nc30, T=18 d ----- Nz30, T=4Od

0 *1.(.1.1’1. 20 30 40 50 60 70 80

Dose, Gy

Fig. 4. Dose response curves for erythema, desquamation and telangiectasia. The ED,, for 16 fractions in 22 days is 39.8 Gy for erythema and 45.6 Gy for desquamation, calculated from Table IIb, and 42.6 Gy for telangiectasia (Table IVc). The ED,, for 30 fractions in 40 days is 42.7 Gy for erythema and 49.7 Gy for desquamation, calculated from Table IIc, and 54.3 Gy for telangiectasia (Table IVc). The ED,, for 30 fractions in 18 days, 2 fractions per day at 8 h intervals, is 43.9 Gy for erythema and 50.6 Gy for desquamation, calculated from Table IIb, and 47.1 Gy for

telangiectasia (Table IVc).

185

weeks with 2 fractions per day instead of 30 fractions in 6 weeks and 16 fractions in 3 weeks.

For erythema and desquamation the isoeffect doses (ED,,: 42.7 Gy/40 days and 39.8 Gy/22 days for erythema, 49.7 Gy/40 days and 45.6 Gy/22 days for desquamation), differed 7-9x between 30 fractions in 40 days and 16 fractions in 22 days. For telangiectasia (ED,,: 54.3 Gy/40 days and 42.6 Gy/22 days) the difference was 27% between the two schedules for telangiectasia (54.3 Gy/42.6 Gy). Thus, there is a benefit of about 20% in dose for late effects relative to acute effects in using the larger fraction number and correspondingly smaller fraction size. This is a large difference considering the relative narrow range of fraction size, about 1.4-2.9 Gy (at ED,,).

Concerning accelerated fractionation, for erythema and desquamation the iso-effect doses, ED,,, were similar for 30 fractions in 6 weeks and 30 fractions in 3 weeks with 2 fractions per day at 8-h intervals but differed as much as 15 % for telangiectasia. The implication is that there is a reduced but still significant benefit of about 10% (47.1 Gy/42.6) Gy in dose for late effects relative acute effects in using 30 fractions in 3 weeks compared to 16 fractions in 3 weeks, despite the lack of complete repair and the time factor for late effects.

The analysis demonstrates how complicated the relationship between acute and late effects for various fractionation schedules may be. The figures derived from Fig. 4 cannot be extrapolated to other cell populations as the relationship between acute and late effects will vary con- siderably with the cell proliferation rate of the acutely responding target cells. The relatively large gain in sparing late effects found for skin in using smaller fraction size and a larger number of fractions, even in a short overall time, depends to a great extent on the fact that there was no significant sparing of acute effects by proliferation between 3 and 6 weeks after commencement of radiotherapy. Therefore, for skin the acute reactions will not be dose-limiting as often is the case for oral and gastrointestinal mucosa when using accelerated fractionation.

Finally, of most importance is the fact that the iso-effect dose for telangiectasia was found to be significantly lower for 3 weeks treatment with 2 fractions per day, even with 8-h intervals compared to 6 weeks treatment. Telangiectasia shows a repair capacity in the range of other late endpoints, and repair capacity may be related to repair kinetics. Therefore, until more data are available, it is reasonable to assume that this find- ing may be valid for various late normal tissues.

Conclusions

The analysis of the effect of various fractionation schedules on human skin showed the following.

Acute efects - erythema and desquamation

Repair capacity: (1)

(2)

T < 29 days (no significant influence of cell progression and proliferation) a/p between 7.5 and 11.2 Gy a between 0.095 and 0.111 Gy- ’ p between 0.0090 and 0.0130 Gy- 2 T > 29 days (signiticantly changed cell progression and proliferation) a/B between 18.3 and 34.5 Gy IX between 0.117 and 0.167 Gy- ’ /? between 0.0091 and 0.0034 Gyy2

Repair kinetics: A possibly biphasic repair rate with t; (I) between 0.3 and 0.4 h, and t; (II) between 1.1 and 1.3 h

Time factor: No significant time factor up to 6 weeks, but the repair capacity was reduced after 4 weeks.

Late efects - telangiectasia

Repair capacity : (1) Excluding the time factor:

a//? about 2.8 a between 0.048 and 0.064 Gy- ’ /I between 0.0173 and 0.0229 GY-~

186

(2) Including the time factor: or/#I between 3.9 and 4.3 Gy LX between 0.082 and 0.111 Gy - ’ p between 0.0204 and 0.0276 Gyp2

Repair kinetics :

fractions and T the overall treatment time in days, T, the time lag in days, y as above and K the number of tissue-rescuing units [ 151 initially at risk. We take T - To = 0 if T < To.

The model used assuming incomplete Elkind repair, i.e. when At < 24 h between M fractions per day is:

A possibly biphasic repair rate with t; (T) about 0.4 h, and 5 (II) about 3.5 h

Time factor:

Effect = -In s.J = aNd + fiNd2 + bNd2hhl(0) -

Y(T- To)

where

A significant time factor with “doubling time” Ts about 16 days.

where

Acknowledgements 0 = e-@ accounts for incomplete repair, and

We thank Miss Ingegerd Hermansson for helping us with the spectrophotometric measurements and careful registration and follow-up of the patients and Mr. Ole Roos for photographing the patients. We also thank Mrs. Ase Blennius for typing the manuscript.

P elsct = exp( - exp(lnK - uNd - j?Nd*{ 1 + &l(0)} +

Y(T- To))) (6)

all parameters defined as above.

Values of a/,?? and b/E are estimates of the intercept and slope of the reciprocal dose plot [lo]; E = In K - ln( - In Pew,,,).

This investigation was supported by grants from the Swedish Cancer Society, the Ring Gustav V Jubilee Clinic Cancer Research Foundation in Gothenburg and grant CA-29026 from the National Cancer Institute, DHHS- USA.

References

Appendix

The rate of Elkind repair is described by the first-order rate constant p (h- i) or half-time 5 (h), where p = ln2/1+ The effect of total overall treatment time is expressed by the rate constant y(day-‘) or Ts (days), where y = ln2/Ts.

The model used assuming complete Elkind repair, i.e. when the interfraction interval dt is equal to or greater than 24 h, is:

Effect = -1ns.x = uNd + /?Nd* - y(T- To) and (2)

P effect = exp( - exp(lnK - aNd - /lNd’ +

Y(T - To))) (3)

where s.J: is the surviving fraction of the target cells, and P-effect is the probability of the effect which corresponds to In s.$ d is the dose per fraction in Gy, N the number of

Ang, K. K., Thames, H. D., Van der Kogel, A. J. and van der Schueren, E. Is the rate of repair of radiation- induced sublethal damage in rat spinal cord dependent on the size of dose per fraction? Int. J. Radiat. Oncol. Biol. Phys. 13: 557-562, 1987. Barendsen, G. W. Dose fractionation, dose rate and iso-effect relationships for normal tissue responses. Int. J. Radiat. Oncol. Biol. Phys. 8: 1981-1997, 1982. Bentzen, S. M., Thames, H. D., Travis, E. L., Ang, K. K., van der Scheuren, E., Dewit, L. and Dixon, D. 0. Direct estimation of latent-time for radiation injury in late responding normal tissues: gut, lung, and spinal cord. Int. J. Radiat. Biol., in press, 1988. Chu, F. C. H., Conrad, J. T., Bane, H. N., Glicksman, A. S. and Nickson, J. J. Quantitative and qualitative evaluation of skin erythema. Radiology 75: 406-410, 1960. Cohen, L. Theoretical isosurvival formulae for fractionated radiotherapy. Br. J. Radiol. 41: 522-528, 1968. Curtis, H. J. Biological mechanisms of delayed radiation damage in mammals. In: Current Topics in Radiation Research, Vol. 3, pp. 139-174. Editors: M. Ebert and A. Howard. Amsterdam, Elsevier, 1967. Cutter, S. J. and Ederer, F. Maximum utilization of the

(4)

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