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??Biology Original Contribution

THE ACCELERATED REPOPULATION OF A MURINE FIBROSARCOMA, FSA-II, DURING THE FRACTIONATED IRRADIATION AND THE LINEAR-QUADRATIC MODEL YOSHINAOABE, M.D.,

PH.D.,

MUNJZYASU URANO, M.D.,

JULIA KAHN, B.S. Edwin L. Steele Laboratory,

Department

AND CHRISTOPHER G.

of Radiation Medicine, Massachusetts Boston, MA 02114

PH.D., WILLET,

LYDIA A. KENTON, B.A., M.D.

General Hospital,

Harvard Medical School,

Radiation response of a spontaneous mouse ilbrosarcoma, FSa-II, to various fractionated doses was studied in viva together with single dose cell survival curves. Early generation isotransplants were used. Animals were C3Hf/Sed mice derived from our defined flora mouse colony. Lung colony and TD, assays were used to determine cell survival. Surviving fractions were determined following fractionated irradiations of 1.0 to 5.0 Gy each per fraction with interfractional time intervals of 4 hr. The a/l3 ratio based on fractionated irradiations was 8.8 Gy for aerobic FSa-II tumor cells and flexure dose was less than 1.3 Gy. Multiple fractions of 5.0 Gy each given with 4, 12, and 24 hr intervals showed an increase in survival with increasing interfractional time interval, suggesting a rapid repopulation of tumor cells between fractions; namely, cell doubling time was shortened between fractions after the first 5.0 Gy doses. These results indicated that tumor cell repopulation is a critical factor in the fractionated radiotherapy. Linear-quadratic model was fitted to single dose survival data. Single dose survival curve of aerobic FSa-II tumor cells following lung colony assays which allowed determination of minimal survival of approximately 3.0 X 10m3 showed that OL,g, and o/p ratios were 0.25 Gy-‘, 0.048 Gy-*, and 8.47 Gy, respectively. Single dose survival curve of the same aerobic cells determined by both lung colony and TD,, assays to a survival level of approximately 3.0 X 10m6 demonstrated that CL,p, and a/g ratios were 0.375,0.0127, and 29.5, respectively. Similar determination for hypoxic FSa-II tumor cells showed that a, p values were smaller whereas the a/S ratio was much larger than for aerobic cells. The oxy gen enhancement ratio calculated by the a/p ratios was greater than 3.0. Repopulation, Accelerated repopulation, Fractionation, L-Q model, cl/S ratio, FSa-II tumor. INTRODUCTION

daily doses require a short interfractional interval and a small fraction size of 2.0 Gy or less. For the effective use of accelerated fractionation and hyperfractionation, an understanding of flexure doses (5, 22, 24), repair (14, 20), and repopulation during fractionated treatments (1, 21) is required. In this study, we examined these factors using lung colony assay of a murine fibrosarcoma, FSa-II. Furthermore, single dose survival curves for aerobic and hypoxic tumor cells were investigated to compare the a/p ratio based on multiple fractions and that on the cell survival curve.

The successful introduction of Linear-Quadratic (LQ) model for the analysis of radiation response to multiple fractions provided theoretical basis for the radiotherapy consisting of multiple daily doses, including hyperfractionation and accelerated fractionation schedules (3, 16, 19). Hyperfractionation is defined as an increase in the number of fractions and a reduction in the fraction size in the same overall time as the 2.0 Gy/day radiotherapy schedule (15). The rationale of this therapy is to reduce the damage in the late-responding tissues without impairing the tumor control probability. Accelerated fractionation is defined as a reduction in the overall treatment time with an appropriate adjustment in dose per fraction and the number of fractions (15). The aim of this therapy is to minimize proliferation of tumor cells that may occur during the fractionated treatments and may cause a failure of radiotherapy. Multiple

Eight- to 12-week-old female C3Hf/Sed mice were used throughout this experiment. They were bred and maintained in our defined flora and pathogen-free mouse colony.

Reprint requests to: Yoshinao Abe, Department of Radiology & Nuclear Medicine, Research Institute for Tuberculosis and Cancer, Tohoku University, 4-1, Seiryo-cho, Sendai 980, Japan. Acknowledgements - We would like to acknowledge Howard D. Thames, Ph.D., Dept. of Biomathematics, University of Texas

System Cancer Center for his valuable discussions and assistance in the preparation of this manuscript, and Yosh Maruyama, M.D., for his advice in the preparation of this paper. Supported in part by grant CA 26350 awarded by NCI, DHHS. Accepted for publication 29 March 199 1,

METHODS

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Single cell suspensions of the third generation isotransplants of a fibrosarcoma, FSa-II, which arose spontaneously in a female C3Hf/Sed mouse, were prepared by the enzymatic method described elsewhere (6, 23). Briefly, intact FSa-II tumor tissues were minced finely and trypsinized (0.1% trypsin). This suspension was centrifuged and the sediment was resuspended in Hanks solution to an appropriate concentration. Lethally irradiated (LR) cells were prepared by irradiating single cell suspensions with 100 Gy. The LR cells were mixed with an appropriate number of viable cells as a ratio of one viable cell to 500 to 1000 LR cells. Cell viability was tested by the dyeexclusion method. Cell survival was determined by two types of lung colony assay methods (23). Single dose survival curves were determined by lung colony type A and TD,, assays. Single cell suspensions were irradiated in vitro with graded radiation doses at room temperature after flushing 5% CO? gas balanced by air for 5 min. Cell concentrations were less than lo6 cells/ml to maintain aerobic conditions. The cell suspensions were diluted immediately after irradiation to contain the appropriate number of tumor cells that was expected to produce a total of 30 to 50 colonies in both lungs. This solution was injected intravenously into animals that had been treated with an intraperitoneal injection of 200 mg/kg of cyclophosphamide 48 hr before transplantation and survival was determined. LR cells were also admixed as described above. TD,, assays were also used to determine low survivals. This method will be described below. For fractionation experiment, the type B assay was used. Namely, single cell suspensions were diluted to contain an appropriate number of viable tumor cells which produced 30 to 50 colonies in a mouse. This solution was injected intravenously into mice pretreated with cyclophosphamide as described above. Fifteen to 20 hr after injection of the single cell suspension, irradiations of the mouse thorax were initiated by a 13’Cs irradiator at a dose rate of approximately 7.2 Gy/min. Before irradiation, animals were anesthetized by sodium pentobarbital (60 mg/kg) and taped on a brass plate. The fraction size was 1 to 5 Gy , and the number of fractions was 1 to 10. The interfractional time interval was 4 hr for every fraction size. In experiments to investigate cell repopulation, interfractional intervals of 1, 4, 12, and 24 hr were used. Five animals were used to determine a survival point. In both type A and B assays, mice were sacrificed by cervical dislocation 13 days following the termination of irradiation. Lungs were removed and fixed in Bouin’s solution. The number of colonies on the surface of each lobe was counted and survival was calculated. The plating efficiency was the ratio of the number of colonies formed to the number of cells injected into the control group.

*Gibco, Grand Island, NY

November

1991, Volume 21, Number 6

To determine survival of hypoxic tumor cells, tumors were irradiated 2 min after applying a brass clamp at the proximal portion of the tumor-bearing leg and animals were sacrificed immediately after termination of irradiation. Single cell suspensions were prepared and lung colony type A or TD,, assays were performed to determine survival. TD,, assay was the determination of the number of tumor cells to transplant a progressive tumor in one-half of transplanted animals. Recipient animals received a whole body irradiation of 6.0 Gy 1 day before transplantation and were randomized into groups. Single cell suspensions were serially diluted and injected intramuscularly into the leg. Five to eight animals were used for each cell dilution and a total of 35 to 40 mice were used for one TD,, assay. TD,, assays were used to determine survival to - 10p6. To analyze o/B values from fractionation experiments, linear-quadratic model was rewritten as follows; -In(SF)=nd(o

+ pd).

Hence, - ln(SF)lnd

= a + f3d

(1)

where n and d were the number of fractions and the fraction size, respectively. Based on surviving fractions (SF) following various nd, linear regression was fitted to calculate (Yand B. This method was used, since the poor statistical properties of the Fe-plot to estimate o/B ratio has been discussed (13). RESULTS The first experiment investigated the effect of the time interval between i.v. injection of tumor cells and irradiation of mouse thorax on cell survival. It is likely that tumor cells start to proliferate soon after injection and the cell multiplicity increases at the time of irradiation. The mouse thorax was irradiated with graded radiation doses between 4 and 24 hr after i.v. injection of tumor cells. Cell survival curves were very similar and independent of the time interval (Fig. 1). Accordingly, (Y and B values were calculated for combined date which resulted in (Y = 0.197?0.022, B = 0.0209+0.0019 and a/B ratio = 9.43 & 1.36. In subsequent experiments, thorax irradiations were started 15 to 20 hr after i.v. injection of tumor cells. Previous study indicated that the extension of the time interval to 48 hr increased both the shoulder size and the slope of the survival curve (23). In the next experiments, multiple fractions of 1, 1.5, 2, and 5 Gy each were given to the mouse thorax with an interfractional interval of 4 hr. Survival was determined by lung colony assay and plotted as a function of total dose (Fig. 2). In the same figure, multi-doses of 1 .O Gy each

Accelerated repopulation of a murk

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Table 1. Do values following fractionated doses of various fraction sizes given with 4 hr intervals. The Do for a fraction scheme given with one hour interval is also presented. .

8h Fraction size Do, Gy 1 GY 1 GY (lh) 1.5 Gy 2 GY 5 GY Single dose

.

10-4

F!Wl

.

0

bmmcd.

.

tZSii&d

’ .

4.67 k0.34 4.69 k0.22 4.12 ? 0.09 3.61kO.10 2.75 kO.07 -

.

.

5

’ . . . . ’ . .

10

R~dimtion

Dow

15

. 20

(Gy)

Fig. 1. Cell survival curves of FSa-II tumor cells irradiatied at 4 to 24 hr after i.v. injection of tumor cell suspensions. Mouse thorax was irradiated with graded doses since tumor cells were expected to be trapped in the lung tissues. Colonies formed in the lung were counted for determination of survival. Vertical bars are

standard errors.

with interfractional interval of 1 hr are also shown. This experiment was designed to test if irradiated cells proliferated within one to 4-hr time intervals of 1 .O Gy each. Survival curves following multi-doses were exponential. The Do value (the radiation dose to reduce surviving fraction from 1 to 0.37 on the exponential portion of the survival curve) appeared to increase with decreasing fraction size. The Do values following multiple 1 .O Gy doses with land 4-hr intervals were not significantly different (Table

I), indicating that no cells repopulated during the 4-hr interval and sublethal radiation damage, if it was induced by one Gy, was completely repaired within an hour. The D, following multiple 1.5 Gy doses was not significantly different from the D, following multiple 1.0 Gy doses. This result may suggest the presence of the flexure dose for the FSa-II tumor cells at a dose less than 1.5 Gy. The single dose survival curve shown in the same figure is character(S.D.) Gy-‘, l3 = ized by (Y = 0.25OkO.048 0.0295+0.0057 Gyp*, and all.3 = 8.47-+ 1.15 Gy. The o and l3 values were also calculated from fractionation experiments shown in Figure 2. Equation (1) in the previous section was fitted to these data. Calculated results were (Y = 0.232kO.021, l3 = 0.0263kO.0076, and a/p = 8.82 k 1.37. These values were within experimental error of those obtained from single dose cell survival curves. Interfractional time intervals of 4, 12, and 24 hr following multiple fractions of 5.0 Gy each were used to investigate possible repopulation during these intervals (Fig. 3). The survival curves following 5.0 Gy doses with an interval of 4 hr were exponential, whereas the survival curves following the same doses given with 12- or 24-hr intervals

s

‘\

10-l

0

Vhr

0

24hr

:

E F

p1os2;

IA.

2 F&-II

10.4 0

.

5

tu”‘W &I, C3”ftSSd mOU.

’ 5

.

In

’. I .

10

loml

Dorr

15

20

25

10-3r

(Gy) Fsa-II hmw cell. WHvsed

Fig. 2. Cell survival curves of FSa-II tumor cells irradiated with multiple doses. Mouse thorax was irradiated with doses of 1 to 5 Gy each with an interfractional interval of 4 hours. The fist dose was given 15 to 20 hr after i.v. injection of tumor cells and lung colonies were counted for determination of survival. Vertical bars indicate standard errors. Cell survivals following doses of 1 Gy each given with a 1 hr interval are also shown.

10-4 0



.

.

.

’ .

10

.



.

20 Total

1

‘\

-

Dose

.

.

’ 30

.

.

1 40

(Gy)

Fig. 3. Cell survivals of FSa-II tumor cells irradiated with 1 to 6 doses of 5 Gy each with an interfractional interval of 4, 12, or 24 hr. Standard errors are shown by vertical bars.

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Table 2. a, p, and a/p values for FSa-II tumor cells based on single dose survival curves shown in Figure 4 Irradiation condition

o.z-sD (Gv-‘)

BlrSD (Gv-‘1

a/B&SD

(Gv)

Combined lung colony assay and TD,, assay data Hypoxic (H) Aerobic (A)

0.121~0.0133 0.375kO.0351

0.00103-t0.00028 0.0127kO.0025

117.5+ 17.0 29.5k5.1

OER (WA)

0.323%0.003

0.0811+-0.0090 3.9820.60 [0.285 (0.269~.300)]*

Lung colony assay data only Hypoxic (H) 0.0936kO.0318 Aerobic (A) 0.250 k 0.048

0.00207~0.00108 0.029520.0057

OER (H/A)

0.0702+0.0195 5.3320.91 [0.265 (0.2994.225)]*

0.374kO.073

45.22 14.1 8.47k 1.15

*To test whether the ratio of H to A for a and that for p are equal, square root of p (H) to p (A) is shown in [I. (Y(H)/a (A) is significantly different from the square root of p (H)/P (A).

showed an increase in survival after the first 5.0 Gy dose. This increase was greater for an interval of 24 hr than for an interval of 12 hr. These changes indicated that tumor cells repopulated during interfractional time intervals which were longer than 4 hr. The last experiment was performed to determine single dose survival curves at the survival level from 1.0 to - 3 x 10-6. The lowest survival that was successfully obtained by lung colony type A or TD,, assays was 1 x 10e3 or - 3 X 10m6, respectively. Hypoxic and aerobic cell survival curves were fitted to the L-Q model. All data are summarized in Figure 4 and Table 2. Hypoxic cells were characterized by smaller (Y and p values compared to aerobic cells. Survival curves which were obtained to minimum survival level of - 3 X lop6 were featured by

10-e’ . 10’ 0



20



30

Radlatlon



40

DOW



50



60



70



(Gy)

Fig. 4. Single dose cell survival curves for aerobic and hypoxic FSa-II tumor cells. Survivals were determined by lung colony assays (circles) and TD,, assays (squares).

-I

0

20

40 Overall

60 Treatment

80 Time

100

120

140

(Hourr)

Fig. 5. Relative number of FSa-II tumor cells which proliferated during extended interfractional intervals of 12 and 24 hr. The relative number was calculated by dividing survival (12- or 24-hr interval) by survival (4-hr interval) for the same total dose (or the same number of fractions), and was plotted as a function of overall treatment time.

smaller p values compared to survival curves determined by survival level above 10P3, indicating that survival curves became more exponential at lower survival levels. It is demonstrated by a difference of p values obtained by lung colony assays alone (minimum survival of - 10V3) and p values obtained from all data (minimum survival of - 3 x 10m6) (Table 2). Because of small p values, the alp ratios obtained from all data were larger than the u/p values obtained by lung colony assay alone and by the fractionation experiments.

DISCUSSION The objectives of this project were (a) to investigate repopulation of tumor cells during interfractional interval, (b) to determine flexure dose and a/p ratio for FSa-II tumor cells, and (c) to examine any differences in CY/~ratios determined by various assay methods. Besides these objectives, we were interested in the capability of repairing sublethal radiation damage (SLD) after repeated irradiations. A treatment interval of 4 hr was used in this study, since our previous data indicated that the SLD was completely repaired within 2 to 4 hr in the FSa-II tumor cells (23). The present results demonstrated no impairment in the capability of repairing SLD up to 10 fractions of 1 .O to 2.0 Gy each, although an “in vitro” study indicated that repair capability was impaired after multiple fractions (9). To our knowledge, all in vivo studies reported no loss of the repair capability in normal tissues and tumors after multi-doses (2, 4, 8, 18, 20). Flexure dose is defined as the dose at which the singledose survival curve begins diverging from the initial exponential portion. In other words, if the fraction size is smaller than this dose, no sparing occurs and the isoeffect

Accelerated repopulation of a murine fibrosarcoma ??Y.

dose (a total radiation dose to induce an identical biological effect) becomes independent of fraction size (15). The flexure dose has been mathematically estimated to be 0.05 to 0.15 times greater than o/p ratio (5, 22). This suggests that the flexure dose of FSa-II tumor cells would be in the range from 0.42 to 1.27 Gy (from 0.44 to 1.32 Gy), if the a/p ratio of 8.47 Gy obtained from a single dose survival curve (that of 8.82 Gy based on fractionation experiment) was used. Our previous report demonstrated that the normal mutine foot tissue receiving fractionated irradiations rapidly repopulated during the treatment period (1). The present study also suggested a significant role of repopulation of tumor cells during fractionated treatment. This repopulation began soon after the initial 5.0 Gy dose with an interfractional time interval of 12 hr or greater. Figure 5 shows relative number of tumor cells which was calculated as a ratio of survival (12- or 24-hr intervals) to survival (4-hr interval) for a given total dose. The relative number of tumor cells was plotted as a function of overall treatment time where 0 hour was the time when the first radiation was given. Note that cells were rapidly repopulating within the first 12-hr interval. Assuming an exponential repopulation of tumor cells, the cell doubling times for 12- and 24-hr intervals were 12.9k3.2 and 17.lk3.6 hr, respectively. Flow cytometric analysis showed the cell cycle time of untreated FSa-II tumor cells was 17 2 1 hr in viva (J. Ramsay, oral communication, June 1988). These observations indicated that tumor cells were rapidly repopulating after irradiation with shortened cell cycle time, and that cells repopulated more rapidly in the first 12 hr than in the subsequent 12 hr after each irradiation. Trott and Kummermehr (21) suggested a substantial difference in the mode of repopulation during fractionated treatment among various tumors. Some tumors such as the FSa-II may rapidly repopulate during fractionated doses, while some may not. Ang et al. (2) reported using lung colony assay that accelerated growth of a murine spontaneous fibrosarcoma occurred during fractionated treatment. They concluded that this accelerated growth resulted from a decreased cell-loss factor and/or recruitment of quiescent cells. They used 4-day-old lung colonies instead of 20-hrold colonies used in the present study, and suggested a presence of a significant number of quiescent cells in the 4-day-old colonies. They estimated that the average number of clonogens in a 4-day-old colony was 2(4’o.71’= 49.5 (16.4 - 62.7). In our experimental system, tumor cells were mostly single cells at the time of the first irradiation. Accordingly, the shortening of cell cycle time was most likely attributable to accelerated tumor cell growth. Finally, our experiments showed that a/p ratio depended on the experimental methods. The (Y/P ratio ob-

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mined from fractionated treatments of single cells was small. Survival curves where surviving fraction was determined to very low level (approximately 3 X 10m6) showed the largest o/p ratio because of a small l3 value. This uncertain approximation of o/p ratio may be partly due to the low l3 value as suggested by Peacock et al. (11) and partly due to the use of different ranges of surviving fraction, that is, from 1.0 to low3 or 1.0 to 10m6. The range of survival fraction is likely a critical factor for obtaining the a/p ratio (7). Since the survival curve fitted to the L-Q model is continuously bending, thus limit the range of surviving fractions used for approximation. Our interest of how oxygen effect influenced the o/p ratio arose from a large o/p value for the same FSa-II tumor of 62.2 that was obtained from TCD,, (50% tumor control dose) experiments. TCD,, values were obtained following fractionated irradiations given to tumors which were acutely hypoxic at the time of irradiation (Zeitman, A., written communication, June 1988). Note that tumor control of our FSa-II tumors could be obtained by reducing surviving fraction to 10e6 or below, that is, the a/p ratio based on TCD,, values is likely influenced by very low survivals. A series of TCD,, experiments using C3H mouse mammary carcinoma (12) irradiated under hypoxic conditions indicated no cell repopulation up to 10 equal fractions given with a time interval of 24 hr but an apparent repopulation between 10 and 20 fractions, but 20 doses given with 12 hr time intervals inhibited the repopulation. Our calculation using these data (no cell repopulation data) showed an a/p value of 50.8 for hypoxic mouse mammary carcinoma. The oxygen enhancement ratio (OER) is usually obtained as a ratio of doses to induce an isoeffect. The OER is also obtained as a ratio of Do (hypoxic) to Do (aerobic). It could be obtained for IX,l3 and o/p ratios from aerobic and hypoxic survival curves (Table 2) (17). Our aerobic and hypoxic cell survival curves shown in Figure 4 indicated that the OER was approximately 3.2 at survival levels (isoeffects) from 0.3 to 10m5. If the OER is independent of radiation dose, the ratio of (Y (hypoxic) to (Y (aerobic) and the ratio of p (hypoxic) to l3 (aerobic) for our FSa-II cells would be l/3.2 and 1/3.22, respectively (17). However, the OER at low doses is likely less than 3.0 (7, lo), suggesting that the ratio of (Y(hypoxic) to (Y(aerobic) is greater than l/3.2. Our data showed that the ratio of l3 values was less than 1/3.22. In these situations, the OER for the o/l3 ratio is likely greater than 3 .O, and may vary depending on dose levels. This was tested by comparing the ratio of o. (hypoxic) to cx (aerobic) with the ratio of square root of l3 (hypoxic) to l3 (aerobic) (17). As shown in Table 2, these ratios are significantly different, indicating that the OER is not constant.

REFERENCES 1. Abe, Y.; Urano, M. Fraction size-dependentacute skin reaction of mice after multiple twice-a-day doses. Int. J. Radiat.

Oncol. Biol. Phys. l&359-364; 1990. 2. Ang, K. K.; Thames,

H. D.; Jones, S. D.; Jiang, G-l.; Mi-

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4.

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13.

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las, L.; Peters, L. J. Proliferation kinetics of a murine fibrosarcoma during fractionated irradiation. Radiat. Res. 116:327336; 1988. Douglas, B. G.; Fowler, J. F. The effect of multiple small doses of X rays on skin reactions in the mouse and a basic interpretation. Radiat. Res. 66401-426; 1976. Fisher, D. R.; Hendry, J. H. Response of clonogenic hepatocytes to fractionated irradiation. Br. J. Cancer 53 (Suppl. VII):298-299; 1986. Fowler, J. F.; Joiner, M. C.; Williams, M. V. Low doses per fraction in radiotherapy: a definition for flexure dose. Br. J. Radio]. 56:599-2; 1983. Gerweck, L. E.; Urano, M.; Koutcher. J.; Fellenz, M-P.; Kahn, J. Relationship between energy status, hypoxic cell fraction, and hyperthermic sensitivity in a murine fibrosarcoma. Radiat. Res. 117~l48-458; 1989. Gilbert, C. W.; Hendry, J. H.; Major, D. The approximation in the formulation for survival S = exp - (aD + BD’). Int. J. Radiat. Biol. 37:469-471; 1980. Joiner, M. C.; Denekamp, J. Evidence for a constant repair capacity over 20 fractions of X-rays. Int. J. Radiat. Biol. 49: 143-150; 1986. McNally, N. J.; DeRonde, J. The effect of repeated small doses of radiation on recovery from sub-lethal damage by Chinese hamster cells in the plateau phase of growth. Int. J. Radiat. Biol. 29:221-234; 1976. Palcic, B.; Skarsgard, L. D. Reduced oxygen enhancement ratio at low doses of ionising radiation. Radiat. Res. 100: 328-329; 1984. Peacock, J. H.; Cassoni, A. M.; McMillan, T. J.; Steel, G. G. Radiosensitive human tumour cell lines may not be recovery deficient. Int. J. Radiat. Biol. 54:945-953; 1988. Suit, H. D.; Howes, A. E.; Hunter, N. Dependence of response of a C3H mammary carcinoma to fractionated irradiation in fraction number and intertreatment interval. Radiat. Res. 72440454; 1977. Taylor, J. M. G.; Kim, D. K. The poor statistical properties

November 1991, Volume 21, Number 6 of the Fe-plot. Int. J. Radiat. Biol. 56:161-167; 1989. 14. Thames, H. D. An “incomplete-repair” model for survival after fractionated and continuous irradiation. Int. J. Radiat. Biol. 47:319-339, 1985. 15. Thames, H. D.; Hendry, J. H. Fractionation in radiotherapy. London: Taylor & Francis; 1987. 16. Thames, H. D.; Peters, L. J.; Withers, H. R.; Fletcher, G. H. Accelerated fractionation vs. hyperfractionation: rationales for several treatment per day. Int. J. Radiat. Oncol. Biol. Phys. 9:127-138; 1983. 17. Thames, H. D.; Rasmussen, S. L. A test for dose-modifying factors. Radiat. Res. 76:308-324; 1978. 18. Thames, H. D.; Withers, H. R. Test of equal effect per fraction and estimation of initial clonogen number in microcolony assays of survival after fractionated irradiations. Br. J. Radio]. 53:1071-1077; 1980. 19. Thames, H. D.; Withers, H. R.; Peters, L. J.; Fletcher, G. H. Changes in early and late radiation responses with altered dose fractionation: implications for dose-survival relationships. Int. J. Radiat. Oncol. Biol. Phys. 8:219-226; 1982. 20. Travis, E. L.; Parkins, C. S.; Down, J. D.; Fowler, J. F.; Maughan, R. L. Is there a loss of repair capacity in mouse lungs with increasing numbers of dose fractions? Int. J. Radiat. Oncol. Biol. Phys. 9:691699; 1983. 21. Trott, K. R.; Kummermehr, J. What is known about tumour proliferation rates to choose between accelerated fractionation or hyperfractionation? Radiother. Oncol. 3: l-9; 1985. 22. Tucker, S. L.; Thames, H. D. Flexure dose: the low-dose limit of effective fractionation. Int. J. Radiat. Oncol. Biol. Phys. 9:1373-1383; 1983. 23. Urano. M.; Goitein, M.; Verhey, L.; Mendiondo, 0.; Suit, H. D.; Koehler, A. Relative biological effectiveness of a high energy modulated proton beam using a spontaneous mutine tumor in vivo. Int. J. Radiat. Oncol. Biol. Phys. 6: 1187-1193; 1980. 24. Withers, H. R. Response of tissues to multiple small dose fractions. Radiat. Res. 71:24-33; 1977.

The accelerated repopulation of a murine fibrosarcoma, FSA-II, during the fractionated irradiation and the linear-quadratic model.

Radiation response of a spontaneous mouse fibrosarcoma, FSa-II, to various fractionated doses was studied in vivo together with single dose cell survi...
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