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Repopulation capacity during fractionated irradiation of squamous cell carcinomas and glioblastomas in vitro
Int. J. Radiation
ELSEVIER
l
Oncology
Biol.
Phys., Vol. 39, No. 3. pp. 743-750, 1997 Copyright 0 1997 Elsevier Science Inc. Printed in the USA. All rights reserved 0360.3016/97 $17.00 + .OO
PI1 SO360-3016(97)00362-3
Biology
Contribution
REPOPULATION SQUAMOUS
CAPACITY DURING FRACTIONATED IRRADIATION OF CELL CARCINOMAS AND GLIOBLASTOMAS ZiV VITRO
WILFRIED BUDACH, M.D.,’ DANIELLE GIOIOSO, B.S., ALPHONSE TAGHIAN, M.D., MARTIN STUSCHKE, M.D.2 and HERMAN D. SUIT, M.D., D.PHIL
PH.D.,
Departmentof RadiationOncology, MGH, Boston,MA, USA Purpose: Determination of clonogenic cell proliferation of three highly malignant squamous cell carcinomas (SCC) and two gliohlastoma cell lines during a 20-day course of fractionated irradiation under in vitro conditions. Methods and Materials: Tumor cells in exponential growth phase were plated in 24-well plastic flasks and irradiated 24 h after plating with 250 kV x-rays at room temperature. Six fractions with single doses between 0.6 and 9 Gy were administered in 1.67, 5, 10, 15, and 20 days. Colony growth was monitored for at least 60 days after completion of irradiation. Wells with confluent colonies were considered as “recurrences” and wells without colonies as “controlled.” The dose required to control 50% of irradiated wells (WCD,,) was estimated by a logistic regression for the different overall treatment times. The effective doubling time of clonogenic cells (T,,) was determined by a direct fit using the maximum likelihood method. Results: The increase of WCD,, within 18.3 days was highly significant for all tumor cell lines accounting for 7.9 and 12.0 Gy in the two glioblastoma cell lines and for 12.7, 14.0, and 21.7 Gy in the three SCC cell lines. The corresponding Tens were 4.4 and 2.0 days for glioblastoma cell lines and 2.4,4.2, and 1.8 days for SCC cell lines. Population doubling times (PDT) of untreated tumor cells ranged from 1.0 to 1.9 days, showing no correlation with T,p. T,, was significantly longer than PDT in three of five tumor cell lines. No significant differences were observed comparing glioblastomas and SCC. Increase of WCD,, with time did not correlate with T,, but with T,n* InSF2 (surviving fraction at 2 Gy). Conclusion: The intrinsic ability of SCC and glioblastoma cells to repopulate during fractionated irradiation could be demonstrated. Repopulation induced dose loss per day depends on T,, and intrinsic radiation sensitivity. Proliferation during treatment was decelerated compared to pretreatment PDT in the majority of cell lines. Pretreatment cell kinetics did not predict for tumor cell proliferation during treatment. 0 1997 Elsevier Science Inc. Repopulation,
Radiation,
Squamous
cell carcinoma,
Glioblastoma.
INTRODUCTION
significant repopulation of surviving clonogensduring fractionated radiation, particularly in squamouscell carcinomas (SCC). However, in caseof tumor irradiation under ambient conditions, tumor cell reoxygenation remains an uncontrolled factor, and in caseof irradiation of clamped tumors, possible differences between the repopulation capacity of acutely hypoxic and chronically hypoxic tumor cells cannot be controlled. Therefore, an in vitro assaysystem has been establishedthat allows for control of all listed factors. In this system the intrinsic ability of tumor cells to proliferate during fractionated irradiation was determined in a panel of five human tumor cell lines, three SCC, and two glioblastomas, during a 20-day course of fractionated radiation therapy.
Repopulation during fractionated radiation therapy hasbeen proposedto be the mechanismbehind clinical observations that local tumor control decreaseswith increasing overall treatment times (11, 15, 17, 19, 28). However, most evidence came from retrospective studiesand were associated with different methodological problems(1). Becauseimportant radiobiological parameters including o//3, Do, and a constant or absent hypoxic tumor cell fraction had to be assumedto estimate the extent of tumor cell repopulation from these studies, some authors have challenged the conclusions (3, 7, 8, 10). Better control of theseparameterscan be achieved by using experimental tumors in animals. Results from such studies (1, 13, 18, 24) also suggest a ’ Present address of W. Budach: Department of Radiation Oncology, University of Ttibingen, Germany. ‘Present address of M. Stuschke: Department of Radiation Oncology, Essen University, Germany. Reprint requests to: Wilfried Budach, M.D., Department of Radiation Oncology, University of Tiibingen, Hoppe-Seyler-Str. 3, 72076 Tubingen, Germany.
Acknowledgments-This work was supported by Public Health Service Grant CA-1331 1 from the National Cancer Institute, National Institutes of Health, Department of Health and Human Services; and by a research fellowship from the Deutsche Forschungsgemeinschaft, Germany. Accepted for publication 19 May 1997. 743
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METHODS
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Oncology
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MATERIALS
Tumor cell lines Five tumor cell lines, three SCC of head and neck origin, and two glioblastomas were used for the studies. The SCC cell lines SQ20B and JSQ3 were derived from the Harvard School of Public Health (Dr. Little) and the two glioblastoma cell lines, D54MG and HGL21, were provided by Duke University (Dr. Bigner). The SCC cell line FADU was obtained from the American Type Culture Collection. All cell lines were karyotyped and found to be human in origin. The cell lines were maintained in Dulbecco’s modified Eagles medium supplemented with 10% heat-inactivated fetal bovine serum and 0.05 mg penicillin/ml, 0.05 mg streptomycin/ml, and 0.1 mg neomycin sulfate/ml at 37°C in an atmosphere of 5% CO, in air. All tumor cell lines showed rapid growth and high clonogenicity when cultured in vitro on plain plastic. Population doubling time Tumor cell lines in exponential growth phase were trypsinized to generate a single cell suspension. Approximately 100,000 single cells per tumor cell line were plated in 75 cm2 flasks and incubated for 48, 96, 144, 168, and 192 h. Afterward, flasks were trypsinized again and the total number of tumor cells per flask at the respective time was determined by using a count chamber. Population doubling times (PDT) were estimated by plotting time vs. logarithm of total cell number. Standard errors of slopes were used to calculate 95% confidence limits of PDT. Colony-forming assays The cell survival in vitro after single-dose irradiation was measured for all tumor cell lines. For the experiments, cells incubated in 75 cm2 flasks were trypsinized in exponential growth phase to get a single cell suspension. An appropriate number of single cells depending on plating efficiency and dose level was plated in 25 cm2 plastic flasks. Six flasks per dose level were used. Heavily irradiated feeder cells, which had originated from the same cell line, were added to achieve a total cell density of 1600 cells per well. The flasks were incubated for 18 to 24 h after plating before singledose irradiation with graded dose levels between 1 and 12 Gy at a temperature of 20°C. A 250 kVp x-ray machine with HVL of 0.4 mm Cu at a dose rate of 1.71 Gy/min was used for all assays. After irradiation the flasks were incubated for 1 to 2 weeks as described before. Experiments were terminated when visible colonies were observed in the test flasks. The colonies were fixed with methanol and stained with crystal violet. The number of colonies per flask was determined by counting cell aggregates of more than 50 cells. To take into consideration the proliferation between plating and irradiation, the surviving fractions (SF) were corrected for multiplicity: SF = [(I - (1 - CFU/PL)l/M)]/PE with CFU = colony-forming units (sum of cell aggregates >50 cells in a flask), PL = number of plated cells, M = multiplicity [number of cell aggregates (l-4 cells) at the time of
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irradiation divided by the number of plated cells in the multiplicity flask], PE = plating efficiency. The logarithm of the mean SFs of two experiments per cell line weighted by the number of flasks was used to estimate alpha and beta according to the linear quadratic model using least-squares analysis. Surviving fractions at 2 Gy (SF2) were calculated by using alpha and beta of the linear quadratic model. The 95% confidence limits were calculated for all data points, taking into account the uncertainties of the plating efficiency. Well control assays For well control experiments, tumor cell lines incubated in 75 cm* flasks were trypsinized in exponential growth phase and single-cell suspension generated. Depending on the known plating efficiency and radiation sensitivity of the respective tumor cell line, between 100 and 4000 tumor cells of the single cell suspension were plated in 24-well plastic flasks. Two different dilutions with one log difference in cell number were used for the plating of each 24-well flask, resulting in 12 wells with a high and 12 wells with a low tumor cell number per flask. Heavily irradiated feeder cells, which had originated from the same cell line, were added to wells with the lower tumor cell number to achieve the same total cell density in all wells for each tumor cell line. A total of 30 flasks were employed for each tumor cell line. Medium and culture conditions were the same as describe under “tumor cell lines.” To determine the plating efficiency, tumor cells from the same dilutions were plated into three 75 cm* plastic flasks per cell line and lethally irradiated feeder cells added to reach the same cell density per cm2 as in the 24-well flasks. Radiation of the 24-well flasks started 24 h after plating with 250 kVp x-rays at room temperature. Graded single doses between 3.0 Gy and 15.0 Gy and six fractions with single doses between 0.6 Gy and 9.0 Gy were administered in 1.67 days, 5 days, 10 days, 15 days, and 20 days, with a minimal interfraction interval of 8 h in the 1.67 day schedule. Colony growth was monitored twice a week for at least 60 days after completion of irradiation. Wells with confluent colonies were considered as “recurrences” and wells without colonies as “controlled.” Data analysis The dose required to control 50% of irradiated wells (WCD,,) was estimated by a previously described method (26) using a logistic regression for single-dose and fractionated irradiation and different overall treatment times. Furthermore, the linear quadratic model extended by the time or repopulation factor y as shown in the equation (eq. 1) was employed to describe the data.
with p = probability of well control, d = single dose, t = overall treatment time, n = number of fractions, cx and p =
Repopulation in vitro l
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et
al
parameters of radiation sensitivity, k = number of clonogenie cells per well, y = repopulation factor. The double logarithmic form of eq. 1 results in: ln( -In(p))
= In(k) +
yt -
n ((Ed + pd2)
(2)
The parametersk, cy, and y with 95% confidence limits were estimated by fitting the quanta1data to eq. 2 by using the maximum likelihood method of the SAS NonLin procedure. Because LYIPratios derived from single-dosevs. six fractions in 1,67 days were not significantly different from the value 10 in any investigated tumor cell line, ar/p was set to be 10 for the fitting procedure. The effective doubling time of clonogenic cells (T,,,) during fractionated irradiation was calculated as: ln(2) Tee = ~ Y
01 A
’
c
O
5
s
10 Time [days]
1s
Time 10[days]
IS
2o
B
20
D
0
5
10
15
20
1s
20
Time [days1
O
5
10 Tine [days]
To describe the WCD,, increment as a function of time according to the LQ-model, eq. 2 was resolved for d: a d=-zpt
CY 2
ln( -In(p))
- In(k) -
(3)
Pn
d(-1w
yt
For p = 0.5 the total dose D (calculated as D = nd) is identical with the WCD,, resulting in: WCD,, =
The estimated parametersk, CX,and y as well as a fixed value al/3 (see above) were used to plot the WCD,, vs. overall treatment time (Fig. 1). To calculate the dose per day needed to counteract repopulation during a radiation course at 2 Gy per fraction, d in eq. 2 was set to be 2 Gy and eq. 2 resolved for n:
n=
ln(-ln(0.5) - In(k) -(2a + 4p)
yt
(5)
The difference of n derived from eq. 5 for t = 20 days and t = 1,67 days multiplied by 2 Gy results in the dose needed to counteract repopulation within 18.3 days at 2 Gy. per fraction. The significance of correlations was tested using Fisher’s z-transformation. RESULTS The results of colony-forming and well-control dose experiments are summarized in Tables 1 and 2. The primary radiation sensitivities expressed as SF2 ranged from 0.39
-. E
’
_ 5 Tii
_
_
_
10 [days,
IS
20
Fig. 1. The dose to prevent colony growth in 50% of irradiated wells (WCD,,) has been plotted against overall treatment time for three squamous cell carcinoma (SCC) cell lines (A-C) and two glioblastoma (GBM) cell lines (D + E). Error bars represent 95% confidence limits of WCD,,. The parallel lines have been fitted simultaneously according to the LQ-Model1to datapointsof two different numbers of clonogens per well (one log difference) at the start of treatment (see also Tables 1 and 2).
(FADU) to 0.65 (JSQ3) in the colony-forming assays. WCD,, values after single dose irradiation (Table 1) do not allow for a direct comparison of cellular radiation sensitivities, becausevery different numbersof clonogens per well were used (Table 2). After correction for number of clonogenie cells (WCD&logk[plated]), SQ20B was the most radiation resistant(5.1 Gy/log cell kill) and HGL21 the most radiation sensitive (2.2 Gy/log cell kill) tumor cell line, resulting in a different ranking of primary radiation sensitivities dependent on the employed assay.However, calculated SF2-values obtained from WCD,, assays(maximum likelihood fit to eq. 2) did not significantly differ from colony-forming assay-derivedSF2-values in four out of five tumor cell lines (Table 2). Independentof the assay,primary radiation sensitivity of squamouscell carcinomasand glioblastoma cell lines overlapped. Well control doses increased significantly with prolonged overall treatment time in all investigated tumor cell lines (Fig. l), accounting for 7.9 Gy and 12.0 Gy for the two glioblastoma cell lines and ranging from 12.7 Gy
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Volume 39, Number 3, 1997
Table 1. Summary of well control doses Tumor cell line cells per well
JSQ3 (SCC) 203 Tumor cells
SQ20B (SCC) 257 Tumor cells
FADU (SCC) 420 Tumor cells
HGL2 1 (GBM) 236 Tumor cells
D54MG (GBM) 213 Tumor cells
Treatment time n
[days]
1 6 6 6 6 6
0 1.67 5 10 15 20
WC&o GY) 6.2 10.5 12.7 13.5 19.4 20.3
(5.5-7.1) (8.9-12.5) (11.1-14.6) (11.5-15.8) (17.3-21.8) (16.8-24.5)
2025 Tumor cells 1 6 6 6 6 6
0 1.67 5 10 15 20
10.6 16.4 18.7 28.6 31.8 34.6
(9.7-l 1.6) (14.4-18.7) (12.8-25.7) (20.8-39.4) (26.7-37.5) (29.4-40.0)
WC&o
GY)
14.1 (11.6-17.0) 18.2 (17.3-19.1) 24.2 (21.1-27.7) 27.6 (25.1-30.3) 3 1.7 (29.c34.6) 36.8 (31.1-43.6) 2567 Tumor cells >15.5 24.0 28.2 33.9 38.5 48.7
(14.5-NA) (18.2-31.7) (23.3-34.0) (28.141.0) (32.246.0) (43.7-54.3)
WC&o
9.4 10.1 14.7 19.1 20.8 22.2
(GY)
(8.8-10.0) (9.5-10.8) (11.8-18.3) (15.5-23.7) (19.5-22.2) (19.4-25.4)
4200 Tumor cells 12.0(11.5-12.5) 13.9 (11.6-16.8) 21.7 (18.8-25.0) 23.8 (20.9-27.3) 25.9 (20.8-32.4) 27.2 (24.8-29.8)
WC%, 5.1 10.4 12.4 12.0 16.8 15.2
GY)
(4.1-6.3) (8.8-12.2) (10.7-14.4) (10.7-13.5) (14.3-19.9) (12.8-18.1)
2358 Tumor cells > 12.0 14.5 20.5 19.0 21.6 25.4
NA (10.5-20.1) (18.8-22.4) (15.9-22.7) (18.0-25.9) (23.1-28.0)
WC&o
7.9 13.9 15.4 18.1 21.4 23.5
(GY)
(6.5-9.6) (11.7-16.5) (13.6-17.4) (15.0-21.9) (18.0-25.5) (20.5-26.9)
2125 Tumor cells 11.5 16.4 22.4 26.5 30.3 30.7
(9.5-13.8) (13.4-20.0) (18.5-27.0) (21.9-32.0) (25.6-36.0) (26.9-35.2)
SCC = squamous cell carcinoma; GBM = glioblastoma; n = number fractions; treatment time = overall treatment time from first to last fraction; WCD,, = required dose to prevent colony growth in 50% of irradiated wells (95% confidence limits).
(FADU) to 21.7 Gy (SQ20B) for the three SCC cell lines within 18.3 days (Table 2). The average increment of WCD,, per day varied between 0.43 Gy (HGL21) and 1.2 Gy (SQ20B). As predicted by the linear-quadratic model, the required dose increment for well control decreasedwith increasing overall treatment time asa result of higher doseper fraction at longer treatment times as shownby moderateflattening of time vs. dose isoeffect curves in Fig. 1. The results of the
direct three-parameterfits to estimatek, (Y,and y are shown in Table 2. Observed and predicted repopulation induced doseincrement within 18.3 days were almost identical (Table 2), indicating that no significant deviations from the model were observed. However, model predictions for the number of clonogenic tumor cells per well [k(calc), Table 21 were, on average, 44% lower than the number of plated clonogenie cells [k(plated), Table 21 estimated from the number
Table 2. Summary of radiation sensitivities and repopulation Cell line Histology Cells/well PE k (plated) k (talc) a (talc) [Gy-‘1 Y (talc) SF2 (WCD) SF2 (Col) PDT [days]
T,, [days1 Gy08.3 Gy08.3 Gy/day Gy/day Gylday
days (m) days (talc) (measured) (talc) (2 Gy/fx)
SQ20B
JSQ3
see 0.13 266 30 0.16 0.17 0.69 0.65 1.4 4.2 14.0 12.7 0.77 0.70 0.89
2025 (0.07-0.20) (142-405) (20-46) (0.13-0.18) (0.13-0.20) (0.6550.72) (0.60-0.70) (1.2-1.6) (3.4-5.2) (9.2-19.3) (12.2-13.2) (0.5-1.1) (0.67-0.72) (0.82-0.95)
see 0.24 609 269 0.19 0.38 0.64 0.52 1.9 1.8 21.7 19.4 1.18 1.06 1.70
2567 (0.19-0.28) (488-719) (93-754) (0.14-0.23) (0.27-0.48) (0.58-0.71) (0.45-0.59) (1.7-2.2) (1.4-2.5) (14.9-29.9) (18.8-19.8) (0.8-l .6) (1.03-I .08) (1.60-1.75)
capacities in vitro
FADU
HGL21
see 4200 0.30 (0.274.33) 1264 (1134-1386) 456 (136-1527) 0.31 (0.23-0.38) 0.29 (0.20.39) 0.48 (0.4w.57) 0.39 (0.324.46) 1.0 (0.9-1.1) 2.4 (1.8-3.4) 12.7 (9.6-16.3) 11.0(10.2-11.5) 0.69 (0.5-0.9) 0.60 (0.56-0.63) 0.80 (0.73-0.85)
0.10 230 84 0.25 0.16 0.55 0.56 1.0 4.4 7.9 7.9 0.43 0.43 0.52
GBM 2358 (0.05-0.15) (118-354) (5 1-136) (0.22-0.29) (0.12-0.19) (0.50-0.59) (0.51-0.61) (0.9-1.1) (3.6-5.7) (4.0-12.8) (7.2-8.4) (0.2-0.7) (0.39-0.46) (0.46-0.56)
D54MG
0.30 646 845 0.32 0.34 0.47 0.49 1.8 2.0 12.0 11.9 0.65 0.65 0.90
GBM 2125 (0.25-0.36) (531-765) (418-1710) (0.28-0.36) (0.29-0.39) (0.43-0.5 1) (0.44-0.53) (1.6-2.0) (1.8-2.4) (7.7-17.0) (11.5-12.2) (0.4-0.9) (0.63-0.66) (0.86-0.93)
SCC = squamous cell carcinoma; GBM = glioblastoma; values in parenthesis represent 95% confidence limits; PE = plating efficiency; k = # of clonogenic cells; k (plated) = cells per well * PE; k (talc), (Y (talc) and y (talc) = values derived from maximum likelihood fit (see Methods); SF2 = surviving fraction at 2 Gy estimated from well control (WCD) or colony-forming (Col) assays; PDT = population doubling; T,, = effective doubling time of surviving clonogens during fractionated radiation; Gy/18.3 days = measured (m) and calculated (talc) increase of WCD,, within 18.3 days; Gy/day = measured and calculated (talc) increase of WCD,, per day; Gy/day (2 Gy/fx) = repopulation induced dose loss per day calculated for 2 Gy per fraction.
Repopulationin vitro
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et al.
n.s.
25
0
1
2
3
4
5
6
Teff [days]
A
=
A
094
0
1
2
3
4
5
Teff [days]
RZ = 0.84 R* = 0.88 p = 0.02
093
032
091
0
1
2
3
4
5
6
Teff [days] Fig. 2. (A, B) T,, of surviving clonogensduring fractionated irradiationhasbeenplotted vs. pretreatmentpopulationdoubling time in vitro (A) or platingefficiency (B). Error bar indicated95% confidencelimits. n.s. = correlationnot significant;p-value from Fisher’sz-transformation. of plated tumor cells multiplied by plating efficiency. This difference reached significance in only one (JSQ3) out of five tumor cell lines. Population doubling times ranged from 1.O days (FADU, HGL21) to 1.9 days (SQ20B), and T,, varied between 1.8 days (SQ20B) and 4.4 days (HGL21). No significant correlation was found between these two parameters, indicating that pretreatment PDT is a poor predictor of T,, (Fig. 2a). Proliferation during fractionated radiation as expressed by Tee was significantly decelerated in three out of five tumor cell lines comparedwith pretreatment PDT (Table 2). Plating efficiency was a better predictor of T,, asillustrated in Fig. 2b. Whereas no significant correlation was found between T,, and increaseof WCD,, within 18.3 days (Fig. 3a), a highly significant correlation was observed between T,, multiplied by -ln(SF2) [SF2 (WCD), Table 21 and
1
2 -InSFZ*Teff
3
4
[days]
Fig. 3. (A, B) The effective doublingtime (T,,) of surviving clonogensduringfractionatedirradiation(A) and-InSF2*T,, (B) havebeenplottedvs. repopulationinduceddoseincrementwithin 18.3 days. -InSF2*T,, = negativelogarithm of the surviving fraction at 2 Gy multipliedby T,,. n.s. = correlationnot significant; p-value from Fisher’sz-transformation.Error bar indicated 95% confidencelimits.
increaseof WCD,, (Fig. 3b), demonstrating that repopulation-induced dose increment per day dependson both T,, and radiation sensitivity. Comparing SCC cell lines with glioblastoma cell lines, no detectable differences in PDT, T,,, or radiation sensitivity were observed (Table 2). The absolute and relative increaseof WCD,, over time was lower in glioblastoma cell lines compared to squamouscarcinoma cell lines (Fig. 4). However, this difference did not reach statistical significance ($9= 0.2). The hypothetical dose per day needed to counteract re-
1. J. Radiation Oncology l Biology l Physics
SQ20B
JSQ3 FADU D54MG HGL21
5
10
15
20
25
Time [days] FADU JSQ3 SQ20B 1.8
D54MG
1.8
HGL21
1.4 1.2 1.0 0
5
lo
15
20
25
Time [days] Fig. 4. (A, B) The absolute (A) and relative (B) increase of WCD,, has been plotted against overall treatment. Regression lines represent the average increase derived from two different numbers of clonogens per well (one log difference) at the start of treatment (see also Tables 1 and 2). Closed symbols and solid lines: squamous cell carcinomas. Open symbols and dotted lines: gliobastomas.
population calculated according
during a radiation course of 2 Gy per fraction, by using the estimated parameters k, (Y, p, and y to the linear-quadratic model, ranged from 0.5 Gy
per day (HGL21) to 1.7 Gy per day (SQ20B). DISCUSSION The repopulation capacity during fractionated radiation therapy was studied in a panel of five highly malignant human tumor cell lines under in vitro conditions. Although
Volume 39, Number 3, 1997
assayconditions allowed avoiding disturbancesof cell proliferation as a consequenceof reoxygenation, hypoxic cell fraction, and tumor clamping, no attempts were made to account for the influence of other environmental factor upon cell kinetics. Under these plain in vitro conditions, the intrinsic ability of tumor cells to repopulateduring fractionated irradiation could be demonstrated.The doserequired to prevent colony growth in irradiated wells increasedsignificantly over time for all tumor cell lines accounting for 7.9 Gy (HGL21) to 21.7 Gy (SQ20B) within 18.3 days (Fig. 1). Surviving clonogens showed rapid proliferation during treatment as reflected by short effective tumor doubling times ranging from 1.8 days (SQ20B) to 4.4 days (HGL21). Repopulation started without lag phasewithin the first days of radiation showing no evidence for a hockey stick-like shapeof time vs. dose plots (Fig. la-e). On the contrary, increment of WCD,, over time was less pronounced with increasing overall treatment time as predicted by the linearquadratic model as a result of larger dosesper fraction at longer overall treatment times. Retrospective clinical studies on head and neck tumors (28) and SCC of the skin (15) suggestan average 0.5-0.7 Gy doselossper day by acceleratedrepopulation after a 3-4 week lag phasewith a low repopulation rate. However, the existence of a lag phase has been challenged (7, 8), and according to Dubben et al. (10) the observeddoseincrement in the retrospective studiesmight simply reflect prescription practice of radiation oncologists. The first interim analysis of the CHART protocol on head and neck tumors (19) suggests(al@corrected> a loss of 0.5 Gy per day. In animal studies on experimental tumors an increase of tumor control doseswith increasingoverall treatment times hasbeen well documented(1,4,6, 16,22,24,25). Although Speke and Hill (21) found no evidence for different repopulation kinetics comparing experimental tumors irradiated under clamped (hypoxic) or unclamped (aerobic) conditions, controversy exists whether oxygenation status may influence repopulation rate (2, 14). Proliferation of the surviving clonogensis the most likely explanation for clinical and experimental observations. Nevertheless,none of the studiesrules out that other mechanisms
like
an increase
of hypoxic
cell fraction
during
fractionated irradiation contributed to the results. In the present study, problems associatedwith different proliferation rates for oxygenated and hypoxic tumor cells and differences in hypoxic cell fractions during radiation series were obviated using the describedassayconditions. Therefore, increase of WCD,, at longer overall treatment times clearly reflects proliferation of surviving clonogens during fractionated radiation therapy. The observed repopulation-induced dose loss per day in the three investigated SCC lines (on average 0.89 Gy calculated for 2 Gy per fraction) was higher compared to most clinical series. On the one hand, this appears to be a consequence of a selection of highly malignant, relatively ra-
diation resistant SCC lines. The median SF2 of 0.52 was remarkably above the reported median values of 0.32-0.42
Repopulation in vitro
in large patient-basedseries(9, 12, 27). On the other hand, the tumor environment in situ may profoundly influence cell kinetics. However, well control assaysin vitro and tumor control assaysin vivo (1) gave essentially the sameresults for T,, and repopulation-induced doselossper day in one of the tested tumor cell lines (FADU). The high repopulation capacity of one SCC cell line (SQ20B), amounting to 1.7 Gy per day (calculated for 2 Gy per fraction) or 11.9 Gy per week (Fig. 1, Table 2), indicates that somerelatively radiation resistant and additionally fast repopulating tumor cell lines have the potential, at least on the cellular level, to produce more clonogensper week than will be on average killed by conventionally fractionated radiation therapy. The repopulation rate of glioblastoma has, at least to the knowledge of the authors, not been studied before. The radiation sensitivity of the two tested glioblastomacell lines expressedas SF2 (0.49 and 0.56) ranged close to the median SF2 of 0.50 in a large panel of studied cell lines from different institutions (23). Therefore, dose increments of 0.5-0.9 Gy per day (calculated for 2 Gy per fraction) may give an estimate for the average repopulation capacity of glioblastoma cells. Repopulation-induced dose increment was lower in glioblastoma cell lines than in SCC lines (Fig. 4). However, due to the low number of cell lines, the overlap of T,, values comparing glioblastomas and SCC, and the selection of relatively radiation resistant SCC lines, one cannot conclude that the cellular repopulation capacity is lower in glioblastomas. Pretherapeutic population doubling times (PDT) in vitro and potential tumor doubling time (Tpot) are thought to be measuresof tumor cell proliferation without cell loss (5). PDT times were extremely short (1.0-1.9 days) in the investigated panel of tumor cell lines and did not predict tumor cell proliferation during fractionated irradiation (T,,,) (Fig. 2a). T,, was significantly longer than PDT in three out of five tumor cell lines. Similar findings were reported by
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Speke and Hill (20) in four out of five studied murine tumor cell lines. Neither PDT in the present study nor Trot in the investigation of Speke and Hill (20) were predictive for T,, during fractionated irradiation, indicating that both parameters are poor predictors for T,, in the experimental setting. Whereas T,, was not predictive (Fig. 3a), the product of T,, X negative logarithm of SF2 was a significant predictor of the increaseof WCD,, within 18.3 days (Fig. 3b). This observation emphasizesthat repopulation-induced dose loss per day depends on both T,, and radiation sensitivity. Hence, rapid proliferation of surviving clonogens during radiation therapy doesnot necessarilylead to clinical failure in a radiation-sensitive tumor and a low proliferation rate does not guarantee local control in relatively radiationresistanttumors. BecauseT,, and radiation sensitivity were independentproperties of tumor cells in the tested panel of cell lines and can be expected to be generally independent, a preclinical evaluation of both Trot and SF2 might have a much higher potential to predict clinical outcome compared to only one parameter. The ability of tumor cells to form colonies within 2 1 days after trypsinization and plating predicted T,, during radiation therapy in the panel of tested cell lines (Fig. 2b). The mechanismbehind this relationship is unclear; however, it appearsthat the capability to proliferate after different kinds of cellular stress(trypsinization, radiation) might be associated properties of tumor cells. In summary, the intrinsic ability of squamouscell carcinoma and glioblastoma cells to repopulate during fractionated radiation therapy could be demonstratedunder in vitro conditions. Repopulation-induced dose loss per day was dependenton T,, and intrinsic radiation sensitivity. Proliferation during treatment was decelerated compared to pretreatment population doubling time in the majority of cell lines. Pretreatment cell kinetics did not predict for tumor cell proliferation during treatment.
REFERENCES 1. Baumarm, M.; Liertz. C.; Baisch, H.; Wiegel, T.; Lorenzen,
2.
3.
4.
5.
J.; Arps, H. Impact of overall treatment time of fractionated irradiation on local control of human fadu squamous cell carcinoma in nude mice. Radiother. Oncol. 32:137-143; 1994. Beck Bomholdt, H. P. Should tumors be clamped in radiobiological fractionation experiments? Int. J. Radiat. Oncol. Biol. Phys. 21:675-682; 1991. Beck-Bornholdt, H. P. Is there sufficient evidence for accelerated repopulation in tumours during fractionated radiotherapy? In: Hagen, U.; Jung, H., Streffer, C, eds. Radiation research 1895-1995, tenth international congress of radiation research, 27-Aug-1-Sep 1995. Wtirzburg, Germany. 1995: p. 84. Beck-Bomholdt, H. P.; Omniczynski, M.; Theis, E.; Vogler, H.; Wurschmidt, F. Influence of treatment time on the response of rat rhabdomyosarcoma RlH to fractionated irradiation. Acta Oncol. 3057-63; 1991. Begg, A. C. The clinical status of Tpot as a predictor? Or why
6.
7. 8. 9.
10. 11.
no tempest in the Tpot Int. J. Radiat. Oncol. Biol. Phys. 32:1539-1541; 1995. Begg, A. C.; Hofland, I.; Kummermehr, J. Tumour cell repopulation during fractionated radiotherapy: Correlation between flow cytometric and radiobiological data in three murine tumours. Eur. J. Cancer 27:537-543; 1991. Bentzen, S. M.; Thames, H. D. Clinical evidence for tumor clonogen regeneration: Interpretations of the data. Radiother. Oncol. 22:161-166; 1991. Bentzen, S. M.; Thames, H. D. Overall treatment time and tumor control dose for head and neck tumors: The dog leg revisited. Radiother. Oncol. 25:143-144; 1992. Brock, W. A.; Baker, F. L.; Wike, J. L.; Sivon, S. L.; Peters, L. J. Cellular radiosensitivity of primary head and neck squamous cell carcinomas and local tumor control. Int. J. Radiat. Oncol. Biol. Phys. 18:1283-1286; 1990. Dubben, H. H. Local control, TCDSO and dose-time prescription habits in radiotherapy of head and neck tumours. Radiother. Oncol. 32: 197-200; 1994. Fowler, J. F.: Lindstrom, M. J. Loss of local control with
750
12.
13.
14. 15. 16.
17.
18. 19.
I. J. Radiation Oncology l Biology l Physics prolongation in radiotherapy. Int. J. Radiat. Oncol. Biol. Phys. 23:457-467; 1992. Girinsky, T.; Lubin, R.; Chavaudra, N.; Pignon, J. P.; Gazeau, J.; Haie, C.; Wibaut, P.; Socie, G.; Cosset, J. M.; Geara, F.; Fertil, B.; Brock, W. A.; Malaise. E. P. In vitro radiosensitivity and calculated cell growth fraction in primary cultures from head and neck cancers and cervical carcinomas: Preliminary correlations with treatment outcome. In: Dewey, W. C.; Edington, M.; Fry, R. J. M.; Hall, E. J.; Whitmore, G. F., eds. Radiation research, a twentieth-century perspective. San Diego: Academic; 1992:700-705. Kummermehr, J.; Dorr, W.; Trott, K. R. Kinetics of accelerated repopulation in normal and malignant squamous epithelia during fractionated radiotherapy. Br. J. Radio. Suppl. 24: 193199; 1992. Kummermehr, J.; Trott, K. R. Should tumors be clamped in radiobiological fractionation experiments? Int. J. Radiat. Oncol. Biol. Phys. 25154-155; 1993. Maciejewski, B. A.; Skates, S.; Zajusz, A.; Lange, D. Importance of tumor size and repopulation for radiocurability of skin cancer. Neoplasma 40:51-54; 1993. Milas, L.; Yamada, S.; Hunter, N.; Guttenberger, R.; Thames, H. D. Changes in TCDSO as a measure of clonogen doubling time in irradiated and unirradiated tumors. Int. J. Radiat. Oncol. Biol. Phys. 21:1195-1202; 1991. Roberts, S. A.: Hendry, J. H. The delay before onset of accelerated tumour cell repopulation during radiotherapy: A direct maximum-likelihood analysis of a collection of worldwide tumour-control data. Radiother. Oncol. 2969-74; 1993. Rofstad, E. K. Repopulation between radiation fractions in human melanoma xenografts. Int. J. Radiat. Oncol. Biol. Phys. 23:63-68; 1992. Saunders, M. I.; Dische, S.; Barrett, A.; Parmar, M. K.; Harvey, A.; Gibson, D. Randomised multicentre trials of CHART vs conventional. Radiotherapy in head and neck and non-
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20.
21. 22.
23.
24.
25. 26. 27.
28.
small-cell lung cancer: An interim report. CHART Steering Committee. Br. J. Cancer 73:1455-1462; 1996. Speke, A. K.; Hill, R. P. Repopulation kinetics during fractionated irradiation and the relationship to the potential doubling time Tpot. Int. J. Radiat. Oncol. Biol. Phys. 3 1:847-856; 1995. Speke, A. K.; Hill, R. P. The effects of clamping and reoxygenation on repopulation during fractionated irradiation. Int. J. Radiat. Oncol. Biol. Phys. 31:857-863; 1995. Suit, H. D.; Howes, A. E.; Hunter. N. Dependence of response of a C3H mammary carcinoma to fractionated irradiation on fractionation number and intertreatment interval. Radiat. Res. 72:440-454; 1977. Taghian, A.; Ramsay, J.; Allalunis-Turner, J.; Budach, W.; Gioioso, D.; Pardo, F.; Okunieff, P.; Bleehen, N.; Urtasun, R.; Suit, H. D. Intrinsic radiation sensitivity may not be the major determinant of the poor clinical outcome of glioblastoma multifotme. Int. J. Radiat. Oncol. Biol. Phys. 25:243-249; 1993. Trott, K. R.; Kummermehr, J. Rapid repopulation in radiotherapy: A debate on mechanism. Accelerated repopulation in tumours and normal tissues. Radiother. Oncol. 22:159-160; 1991. Tsunemoto, H.; Ando, K.; Koike, S.; Urano, M. Repopulation of tumour cells following irradiation with x-rays or low energy neutrons. Int. J. Radiat. Biol. 65:61; 1994. Walker, A. M.; Suit, H. D. Assessment of local tumor control using censored tumor response data. Int. J. Radiat. Oncol. Biol. Phys. 9:383-386; 1983. Weichselbaum, R. R.; Beckett, M. A.; Vijayakumar. S. Radiobiological characterization of head and neck and sarcoma cells derived from patients prior to radiotherapy. Int. J. Radiat. Oncol. Biol. Phys. 19:313-319; 1990. Withers, H. R.; Taylor, J. M. G.; Maciejewski, B. The hazard of accelerated tumor clonogen repopulation during radiotherapy. Acta Oncol. 27:131-146; 1988.
ELSEVIER
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Oncology
Biol.
Phys., Vol. 39, No. 3. pp. 743-750, 1997 Copyright 0 1997 Elsevier Science Inc. Printed in the USA. All rights reserved 0360.3016/97 $17.00 + .OO
PI1 SO360-3016(97)00362-3
Biology
Contribution
REPOPULATION SQUAMOUS
CAPACITY DURING FRACTIONATED IRRADIATION OF CELL CARCINOMAS AND GLIOBLASTOMAS ZiV VITRO
WILFRIED BUDACH, M.D.,’ DANIELLE GIOIOSO, B.S., ALPHONSE TAGHIAN, M.D., MARTIN STUSCHKE, M.D.2 and HERMAN D. SUIT, M.D., D.PHIL
PH.D.,
Departmentof RadiationOncology, MGH, Boston,MA, USA Purpose: Determination of clonogenic cell proliferation of three highly malignant squamous cell carcinomas (SCC) and two gliohlastoma cell lines during a 20-day course of fractionated irradiation under in vitro conditions. Methods and Materials: Tumor cells in exponential growth phase were plated in 24-well plastic flasks and irradiated 24 h after plating with 250 kV x-rays at room temperature. Six fractions with single doses between 0.6 and 9 Gy were administered in 1.67, 5, 10, 15, and 20 days. Colony growth was monitored for at least 60 days after completion of irradiation. Wells with confluent colonies were considered as “recurrences” and wells without colonies as “controlled.” The dose required to control 50% of irradiated wells (WCD,,) was estimated by a logistic regression for the different overall treatment times. The effective doubling time of clonogenic cells (T,,) was determined by a direct fit using the maximum likelihood method. Results: The increase of WCD,, within 18.3 days was highly significant for all tumor cell lines accounting for 7.9 and 12.0 Gy in the two glioblastoma cell lines and for 12.7, 14.0, and 21.7 Gy in the three SCC cell lines. The corresponding Tens were 4.4 and 2.0 days for glioblastoma cell lines and 2.4,4.2, and 1.8 days for SCC cell lines. Population doubling times (PDT) of untreated tumor cells ranged from 1.0 to 1.9 days, showing no correlation with T,p. T,, was significantly longer than PDT in three of five tumor cell lines. No significant differences were observed comparing glioblastomas and SCC. Increase of WCD,, with time did not correlate with T,, but with T,n* InSF2 (surviving fraction at 2 Gy). Conclusion: The intrinsic ability of SCC and glioblastoma cells to repopulate during fractionated irradiation could be demonstrated. Repopulation induced dose loss per day depends on T,, and intrinsic radiation sensitivity. Proliferation during treatment was decelerated compared to pretreatment PDT in the majority of cell lines. Pretreatment cell kinetics did not predict for tumor cell proliferation during treatment. 0 1997 Elsevier Science Inc. Repopulation,
Radiation,
Squamous
cell carcinoma,
Glioblastoma.
INTRODUCTION
significant repopulation of surviving clonogensduring fractionated radiation, particularly in squamouscell carcinomas (SCC). However, in caseof tumor irradiation under ambient conditions, tumor cell reoxygenation remains an uncontrolled factor, and in caseof irradiation of clamped tumors, possible differences between the repopulation capacity of acutely hypoxic and chronically hypoxic tumor cells cannot be controlled. Therefore, an in vitro assaysystem has been establishedthat allows for control of all listed factors. In this system the intrinsic ability of tumor cells to proliferate during fractionated irradiation was determined in a panel of five human tumor cell lines, three SCC, and two glioblastomas, during a 20-day course of fractionated radiation therapy.
Repopulation during fractionated radiation therapy hasbeen proposedto be the mechanismbehind clinical observations that local tumor control decreaseswith increasing overall treatment times (11, 15, 17, 19, 28). However, most evidence came from retrospective studiesand were associated with different methodological problems(1). Becauseimportant radiobiological parameters including o//3, Do, and a constant or absent hypoxic tumor cell fraction had to be assumedto estimate the extent of tumor cell repopulation from these studies, some authors have challenged the conclusions (3, 7, 8, 10). Better control of theseparameterscan be achieved by using experimental tumors in animals. Results from such studies (1, 13, 18, 24) also suggest a ’ Present address of W. Budach: Department of Radiation Oncology, University of Ttibingen, Germany. ‘Present address of M. Stuschke: Department of Radiation Oncology, Essen University, Germany. Reprint requests to: Wilfried Budach, M.D., Department of Radiation Oncology, University of Tiibingen, Hoppe-Seyler-Str. 3, 72076 Tubingen, Germany.
Acknowledgments-This work was supported by Public Health Service Grant CA-1331 1 from the National Cancer Institute, National Institutes of Health, Department of Health and Human Services; and by a research fellowship from the Deutsche Forschungsgemeinschaft, Germany. Accepted for publication 19 May 1997. 743
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METHODS
AND
Oncology
l Biology
l
Physics
MATERIALS
Tumor cell lines Five tumor cell lines, three SCC of head and neck origin, and two glioblastomas were used for the studies. The SCC cell lines SQ20B and JSQ3 were derived from the Harvard School of Public Health (Dr. Little) and the two glioblastoma cell lines, D54MG and HGL21, were provided by Duke University (Dr. Bigner). The SCC cell line FADU was obtained from the American Type Culture Collection. All cell lines were karyotyped and found to be human in origin. The cell lines were maintained in Dulbecco’s modified Eagles medium supplemented with 10% heat-inactivated fetal bovine serum and 0.05 mg penicillin/ml, 0.05 mg streptomycin/ml, and 0.1 mg neomycin sulfate/ml at 37°C in an atmosphere of 5% CO, in air. All tumor cell lines showed rapid growth and high clonogenicity when cultured in vitro on plain plastic. Population doubling time Tumor cell lines in exponential growth phase were trypsinized to generate a single cell suspension. Approximately 100,000 single cells per tumor cell line were plated in 75 cm2 flasks and incubated for 48, 96, 144, 168, and 192 h. Afterward, flasks were trypsinized again and the total number of tumor cells per flask at the respective time was determined by using a count chamber. Population doubling times (PDT) were estimated by plotting time vs. logarithm of total cell number. Standard errors of slopes were used to calculate 95% confidence limits of PDT. Colony-forming assays The cell survival in vitro after single-dose irradiation was measured for all tumor cell lines. For the experiments, cells incubated in 75 cm2 flasks were trypsinized in exponential growth phase to get a single cell suspension. An appropriate number of single cells depending on plating efficiency and dose level was plated in 25 cm2 plastic flasks. Six flasks per dose level were used. Heavily irradiated feeder cells, which had originated from the same cell line, were added to achieve a total cell density of 1600 cells per well. The flasks were incubated for 18 to 24 h after plating before singledose irradiation with graded dose levels between 1 and 12 Gy at a temperature of 20°C. A 250 kVp x-ray machine with HVL of 0.4 mm Cu at a dose rate of 1.71 Gy/min was used for all assays. After irradiation the flasks were incubated for 1 to 2 weeks as described before. Experiments were terminated when visible colonies were observed in the test flasks. The colonies were fixed with methanol and stained with crystal violet. The number of colonies per flask was determined by counting cell aggregates of more than 50 cells. To take into consideration the proliferation between plating and irradiation, the surviving fractions (SF) were corrected for multiplicity: SF = [(I - (1 - CFU/PL)l/M)]/PE with CFU = colony-forming units (sum of cell aggregates >50 cells in a flask), PL = number of plated cells, M = multiplicity [number of cell aggregates (l-4 cells) at the time of
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irradiation divided by the number of plated cells in the multiplicity flask], PE = plating efficiency. The logarithm of the mean SFs of two experiments per cell line weighted by the number of flasks was used to estimate alpha and beta according to the linear quadratic model using least-squares analysis. Surviving fractions at 2 Gy (SF2) were calculated by using alpha and beta of the linear quadratic model. The 95% confidence limits were calculated for all data points, taking into account the uncertainties of the plating efficiency. Well control assays For well control experiments, tumor cell lines incubated in 75 cm* flasks were trypsinized in exponential growth phase and single-cell suspension generated. Depending on the known plating efficiency and radiation sensitivity of the respective tumor cell line, between 100 and 4000 tumor cells of the single cell suspension were plated in 24-well plastic flasks. Two different dilutions with one log difference in cell number were used for the plating of each 24-well flask, resulting in 12 wells with a high and 12 wells with a low tumor cell number per flask. Heavily irradiated feeder cells, which had originated from the same cell line, were added to wells with the lower tumor cell number to achieve the same total cell density in all wells for each tumor cell line. A total of 30 flasks were employed for each tumor cell line. Medium and culture conditions were the same as describe under “tumor cell lines.” To determine the plating efficiency, tumor cells from the same dilutions were plated into three 75 cm* plastic flasks per cell line and lethally irradiated feeder cells added to reach the same cell density per cm2 as in the 24-well flasks. Radiation of the 24-well flasks started 24 h after plating with 250 kVp x-rays at room temperature. Graded single doses between 3.0 Gy and 15.0 Gy and six fractions with single doses between 0.6 Gy and 9.0 Gy were administered in 1.67 days, 5 days, 10 days, 15 days, and 20 days, with a minimal interfraction interval of 8 h in the 1.67 day schedule. Colony growth was monitored twice a week for at least 60 days after completion of irradiation. Wells with confluent colonies were considered as “recurrences” and wells without colonies as “controlled.” Data analysis The dose required to control 50% of irradiated wells (WCD,,) was estimated by a previously described method (26) using a logistic regression for single-dose and fractionated irradiation and different overall treatment times. Furthermore, the linear quadratic model extended by the time or repopulation factor y as shown in the equation (eq. 1) was employed to describe the data.
with p = probability of well control, d = single dose, t = overall treatment time, n = number of fractions, cx and p =
Repopulation in vitro l
W.
BUDACH
et
al
parameters of radiation sensitivity, k = number of clonogenie cells per well, y = repopulation factor. The double logarithmic form of eq. 1 results in: ln( -In(p))
= In(k) +
yt -
n ((Ed + pd2)
(2)
The parametersk, cy, and y with 95% confidence limits were estimated by fitting the quanta1data to eq. 2 by using the maximum likelihood method of the SAS NonLin procedure. Because LYIPratios derived from single-dosevs. six fractions in 1,67 days were not significantly different from the value 10 in any investigated tumor cell line, ar/p was set to be 10 for the fitting procedure. The effective doubling time of clonogenic cells (T,,,) during fractionated irradiation was calculated as: ln(2) Tee = ~ Y
01 A
’
c
O
5
s
10 Time [days]
1s
Time 10[days]
IS
2o
B
20
D
0
5
10
15
20
1s
20
Time [days1
O
5
10 Tine [days]
To describe the WCD,, increment as a function of time according to the LQ-model, eq. 2 was resolved for d: a d=-zpt
CY 2
ln( -In(p))
- In(k) -
(3)
Pn
d(-1w
yt
For p = 0.5 the total dose D (calculated as D = nd) is identical with the WCD,, resulting in: WCD,, =
The estimated parametersk, CX,and y as well as a fixed value al/3 (see above) were used to plot the WCD,, vs. overall treatment time (Fig. 1). To calculate the dose per day needed to counteract repopulation during a radiation course at 2 Gy per fraction, d in eq. 2 was set to be 2 Gy and eq. 2 resolved for n:
n=
ln(-ln(0.5) - In(k) -(2a + 4p)
yt
(5)
The difference of n derived from eq. 5 for t = 20 days and t = 1,67 days multiplied by 2 Gy results in the dose needed to counteract repopulation within 18.3 days at 2 Gy. per fraction. The significance of correlations was tested using Fisher’s z-transformation. RESULTS The results of colony-forming and well-control dose experiments are summarized in Tables 1 and 2. The primary radiation sensitivities expressed as SF2 ranged from 0.39
-. E
’
_ 5 Tii
_
_
_
10 [days,
IS
20
Fig. 1. The dose to prevent colony growth in 50% of irradiated wells (WCD,,) has been plotted against overall treatment time for three squamous cell carcinoma (SCC) cell lines (A-C) and two glioblastoma (GBM) cell lines (D + E). Error bars represent 95% confidence limits of WCD,,. The parallel lines have been fitted simultaneously according to the LQ-Model1to datapointsof two different numbers of clonogens per well (one log difference) at the start of treatment (see also Tables 1 and 2).
(FADU) to 0.65 (JSQ3) in the colony-forming assays. WCD,, values after single dose irradiation (Table 1) do not allow for a direct comparison of cellular radiation sensitivities, becausevery different numbersof clonogens per well were used (Table 2). After correction for number of clonogenie cells (WCD&logk[plated]), SQ20B was the most radiation resistant(5.1 Gy/log cell kill) and HGL21 the most radiation sensitive (2.2 Gy/log cell kill) tumor cell line, resulting in a different ranking of primary radiation sensitivities dependent on the employed assay.However, calculated SF2-values obtained from WCD,, assays(maximum likelihood fit to eq. 2) did not significantly differ from colony-forming assay-derivedSF2-values in four out of five tumor cell lines (Table 2). Independentof the assay,primary radiation sensitivity of squamouscell carcinomasand glioblastoma cell lines overlapped. Well control doses increased significantly with prolonged overall treatment time in all investigated tumor cell lines (Fig. l), accounting for 7.9 Gy and 12.0 Gy for the two glioblastoma cell lines and ranging from 12.7 Gy
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Volume 39, Number 3, 1997
Table 1. Summary of well control doses Tumor cell line cells per well
JSQ3 (SCC) 203 Tumor cells
SQ20B (SCC) 257 Tumor cells
FADU (SCC) 420 Tumor cells
HGL2 1 (GBM) 236 Tumor cells
D54MG (GBM) 213 Tumor cells
Treatment time n
[days]
1 6 6 6 6 6
0 1.67 5 10 15 20
WC&o GY) 6.2 10.5 12.7 13.5 19.4 20.3
(5.5-7.1) (8.9-12.5) (11.1-14.6) (11.5-15.8) (17.3-21.8) (16.8-24.5)
2025 Tumor cells 1 6 6 6 6 6
0 1.67 5 10 15 20
10.6 16.4 18.7 28.6 31.8 34.6
(9.7-l 1.6) (14.4-18.7) (12.8-25.7) (20.8-39.4) (26.7-37.5) (29.4-40.0)
WC&o
GY)
14.1 (11.6-17.0) 18.2 (17.3-19.1) 24.2 (21.1-27.7) 27.6 (25.1-30.3) 3 1.7 (29.c34.6) 36.8 (31.1-43.6) 2567 Tumor cells >15.5 24.0 28.2 33.9 38.5 48.7
(14.5-NA) (18.2-31.7) (23.3-34.0) (28.141.0) (32.246.0) (43.7-54.3)
WC&o
9.4 10.1 14.7 19.1 20.8 22.2
(GY)
(8.8-10.0) (9.5-10.8) (11.8-18.3) (15.5-23.7) (19.5-22.2) (19.4-25.4)
4200 Tumor cells 12.0(11.5-12.5) 13.9 (11.6-16.8) 21.7 (18.8-25.0) 23.8 (20.9-27.3) 25.9 (20.8-32.4) 27.2 (24.8-29.8)
WC%, 5.1 10.4 12.4 12.0 16.8 15.2
GY)
(4.1-6.3) (8.8-12.2) (10.7-14.4) (10.7-13.5) (14.3-19.9) (12.8-18.1)
2358 Tumor cells > 12.0 14.5 20.5 19.0 21.6 25.4
NA (10.5-20.1) (18.8-22.4) (15.9-22.7) (18.0-25.9) (23.1-28.0)
WC&o
7.9 13.9 15.4 18.1 21.4 23.5
(GY)
(6.5-9.6) (11.7-16.5) (13.6-17.4) (15.0-21.9) (18.0-25.5) (20.5-26.9)
2125 Tumor cells 11.5 16.4 22.4 26.5 30.3 30.7
(9.5-13.8) (13.4-20.0) (18.5-27.0) (21.9-32.0) (25.6-36.0) (26.9-35.2)
SCC = squamous cell carcinoma; GBM = glioblastoma; n = number fractions; treatment time = overall treatment time from first to last fraction; WCD,, = required dose to prevent colony growth in 50% of irradiated wells (95% confidence limits).
(FADU) to 21.7 Gy (SQ20B) for the three SCC cell lines within 18.3 days (Table 2). The average increment of WCD,, per day varied between 0.43 Gy (HGL21) and 1.2 Gy (SQ20B). As predicted by the linear-quadratic model, the required dose increment for well control decreasedwith increasing overall treatment time asa result of higher doseper fraction at longer treatment times as shownby moderateflattening of time vs. dose isoeffect curves in Fig. 1. The results of the
direct three-parameterfits to estimatek, (Y,and y are shown in Table 2. Observed and predicted repopulation induced doseincrement within 18.3 days were almost identical (Table 2), indicating that no significant deviations from the model were observed. However, model predictions for the number of clonogenic tumor cells per well [k(calc), Table 21 were, on average, 44% lower than the number of plated clonogenie cells [k(plated), Table 21 estimated from the number
Table 2. Summary of radiation sensitivities and repopulation Cell line Histology Cells/well PE k (plated) k (talc) a (talc) [Gy-‘1 Y (talc) SF2 (WCD) SF2 (Col) PDT [days]
T,, [days1 Gy08.3 Gy08.3 Gy/day Gy/day Gylday
days (m) days (talc) (measured) (talc) (2 Gy/fx)
SQ20B
JSQ3
see 0.13 266 30 0.16 0.17 0.69 0.65 1.4 4.2 14.0 12.7 0.77 0.70 0.89
2025 (0.07-0.20) (142-405) (20-46) (0.13-0.18) (0.13-0.20) (0.6550.72) (0.60-0.70) (1.2-1.6) (3.4-5.2) (9.2-19.3) (12.2-13.2) (0.5-1.1) (0.67-0.72) (0.82-0.95)
see 0.24 609 269 0.19 0.38 0.64 0.52 1.9 1.8 21.7 19.4 1.18 1.06 1.70
2567 (0.19-0.28) (488-719) (93-754) (0.14-0.23) (0.27-0.48) (0.58-0.71) (0.45-0.59) (1.7-2.2) (1.4-2.5) (14.9-29.9) (18.8-19.8) (0.8-l .6) (1.03-I .08) (1.60-1.75)
capacities in vitro
FADU
HGL21
see 4200 0.30 (0.274.33) 1264 (1134-1386) 456 (136-1527) 0.31 (0.23-0.38) 0.29 (0.20.39) 0.48 (0.4w.57) 0.39 (0.324.46) 1.0 (0.9-1.1) 2.4 (1.8-3.4) 12.7 (9.6-16.3) 11.0(10.2-11.5) 0.69 (0.5-0.9) 0.60 (0.56-0.63) 0.80 (0.73-0.85)
0.10 230 84 0.25 0.16 0.55 0.56 1.0 4.4 7.9 7.9 0.43 0.43 0.52
GBM 2358 (0.05-0.15) (118-354) (5 1-136) (0.22-0.29) (0.12-0.19) (0.50-0.59) (0.51-0.61) (0.9-1.1) (3.6-5.7) (4.0-12.8) (7.2-8.4) (0.2-0.7) (0.39-0.46) (0.46-0.56)
D54MG
0.30 646 845 0.32 0.34 0.47 0.49 1.8 2.0 12.0 11.9 0.65 0.65 0.90
GBM 2125 (0.25-0.36) (531-765) (418-1710) (0.28-0.36) (0.29-0.39) (0.43-0.5 1) (0.44-0.53) (1.6-2.0) (1.8-2.4) (7.7-17.0) (11.5-12.2) (0.4-0.9) (0.63-0.66) (0.86-0.93)
SCC = squamous cell carcinoma; GBM = glioblastoma; values in parenthesis represent 95% confidence limits; PE = plating efficiency; k = # of clonogenic cells; k (plated) = cells per well * PE; k (talc), (Y (talc) and y (talc) = values derived from maximum likelihood fit (see Methods); SF2 = surviving fraction at 2 Gy estimated from well control (WCD) or colony-forming (Col) assays; PDT = population doubling; T,, = effective doubling time of surviving clonogens during fractionated radiation; Gy/18.3 days = measured (m) and calculated (talc) increase of WCD,, within 18.3 days; Gy/day = measured and calculated (talc) increase of WCD,, per day; Gy/day (2 Gy/fx) = repopulation induced dose loss per day calculated for 2 Gy per fraction.
Repopulationin vitro
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et al.
n.s.
25
0
1
2
3
4
5
6
Teff [days]
A
=
A
094
0
1
2
3
4
5
Teff [days]
RZ = 0.84 R* = 0.88 p = 0.02
093
032
091
0
1
2
3
4
5
6
Teff [days] Fig. 2. (A, B) T,, of surviving clonogensduring fractionated irradiationhasbeenplotted vs. pretreatmentpopulationdoubling time in vitro (A) or platingefficiency (B). Error bar indicated95% confidencelimits. n.s. = correlationnot significant;p-value from Fisher’sz-transformation. of plated tumor cells multiplied by plating efficiency. This difference reached significance in only one (JSQ3) out of five tumor cell lines. Population doubling times ranged from 1.O days (FADU, HGL21) to 1.9 days (SQ20B), and T,, varied between 1.8 days (SQ20B) and 4.4 days (HGL21). No significant correlation was found between these two parameters, indicating that pretreatment PDT is a poor predictor of T,, (Fig. 2a). Proliferation during fractionated radiation as expressed by Tee was significantly decelerated in three out of five tumor cell lines comparedwith pretreatment PDT (Table 2). Plating efficiency was a better predictor of T,, asillustrated in Fig. 2b. Whereas no significant correlation was found between T,, and increaseof WCD,, within 18.3 days (Fig. 3a), a highly significant correlation was observed between T,, multiplied by -ln(SF2) [SF2 (WCD), Table 21 and
1
2 -InSFZ*Teff
3
4
[days]
Fig. 3. (A, B) The effective doublingtime (T,,) of surviving clonogensduringfractionatedirradiation(A) and-InSF2*T,, (B) havebeenplottedvs. repopulationinduceddoseincrementwithin 18.3 days. -InSF2*T,, = negativelogarithm of the surviving fraction at 2 Gy multipliedby T,,. n.s. = correlationnot significant; p-value from Fisher’sz-transformation.Error bar indicated 95% confidencelimits.
increaseof WCD,, (Fig. 3b), demonstrating that repopulation-induced dose increment per day dependson both T,, and radiation sensitivity. Comparing SCC cell lines with glioblastoma cell lines, no detectable differences in PDT, T,,, or radiation sensitivity were observed (Table 2). The absolute and relative increaseof WCD,, over time was lower in glioblastoma cell lines compared to squamouscarcinoma cell lines (Fig. 4). However, this difference did not reach statistical significance ($9= 0.2). The hypothetical dose per day needed to counteract re-
1. J. Radiation Oncology l Biology l Physics
SQ20B
JSQ3 FADU D54MG HGL21
5
10
15
20
25
Time [days] FADU JSQ3 SQ20B 1.8
D54MG
1.8
HGL21
1.4 1.2 1.0 0
5
lo
15
20
25
Time [days] Fig. 4. (A, B) The absolute (A) and relative (B) increase of WCD,, has been plotted against overall treatment. Regression lines represent the average increase derived from two different numbers of clonogens per well (one log difference) at the start of treatment (see also Tables 1 and 2). Closed symbols and solid lines: squamous cell carcinomas. Open symbols and dotted lines: gliobastomas.
population calculated according
during a radiation course of 2 Gy per fraction, by using the estimated parameters k, (Y, p, and y to the linear-quadratic model, ranged from 0.5 Gy
per day (HGL21) to 1.7 Gy per day (SQ20B). DISCUSSION The repopulation capacity during fractionated radiation therapy was studied in a panel of five highly malignant human tumor cell lines under in vitro conditions. Although
Volume 39, Number 3, 1997
assayconditions allowed avoiding disturbancesof cell proliferation as a consequenceof reoxygenation, hypoxic cell fraction, and tumor clamping, no attempts were made to account for the influence of other environmental factor upon cell kinetics. Under these plain in vitro conditions, the intrinsic ability of tumor cells to repopulateduring fractionated irradiation could be demonstrated.The doserequired to prevent colony growth in irradiated wells increasedsignificantly over time for all tumor cell lines accounting for 7.9 Gy (HGL21) to 21.7 Gy (SQ20B) within 18.3 days (Fig. 1). Surviving clonogens showed rapid proliferation during treatment as reflected by short effective tumor doubling times ranging from 1.8 days (SQ20B) to 4.4 days (HGL21). Repopulation started without lag phasewithin the first days of radiation showing no evidence for a hockey stick-like shapeof time vs. dose plots (Fig. la-e). On the contrary, increment of WCD,, over time was less pronounced with increasing overall treatment time as predicted by the linearquadratic model as a result of larger dosesper fraction at longer overall treatment times. Retrospective clinical studies on head and neck tumors (28) and SCC of the skin (15) suggestan average 0.5-0.7 Gy doselossper day by acceleratedrepopulation after a 3-4 week lag phasewith a low repopulation rate. However, the existence of a lag phase has been challenged (7, 8), and according to Dubben et al. (10) the observeddoseincrement in the retrospective studiesmight simply reflect prescription practice of radiation oncologists. The first interim analysis of the CHART protocol on head and neck tumors (19) suggests(al@corrected> a loss of 0.5 Gy per day. In animal studies on experimental tumors an increase of tumor control doseswith increasingoverall treatment times hasbeen well documented(1,4,6, 16,22,24,25). Although Speke and Hill (21) found no evidence for different repopulation kinetics comparing experimental tumors irradiated under clamped (hypoxic) or unclamped (aerobic) conditions, controversy exists whether oxygenation status may influence repopulation rate (2, 14). Proliferation of the surviving clonogensis the most likely explanation for clinical and experimental observations. Nevertheless,none of the studiesrules out that other mechanisms
like
an increase
of hypoxic
cell fraction
during
fractionated irradiation contributed to the results. In the present study, problems associatedwith different proliferation rates for oxygenated and hypoxic tumor cells and differences in hypoxic cell fractions during radiation series were obviated using the describedassayconditions. Therefore, increase of WCD,, at longer overall treatment times clearly reflects proliferation of surviving clonogens during fractionated radiation therapy. The observed repopulation-induced dose loss per day in the three investigated SCC lines (on average 0.89 Gy calculated for 2 Gy per fraction) was higher compared to most clinical series. On the one hand, this appears to be a consequence of a selection of highly malignant, relatively ra-
diation resistant SCC lines. The median SF2 of 0.52 was remarkably above the reported median values of 0.32-0.42
Repopulation in vitro
in large patient-basedseries(9, 12, 27). On the other hand, the tumor environment in situ may profoundly influence cell kinetics. However, well control assaysin vitro and tumor control assaysin vivo (1) gave essentially the sameresults for T,, and repopulation-induced doselossper day in one of the tested tumor cell lines (FADU). The high repopulation capacity of one SCC cell line (SQ20B), amounting to 1.7 Gy per day (calculated for 2 Gy per fraction) or 11.9 Gy per week (Fig. 1, Table 2), indicates that somerelatively radiation resistant and additionally fast repopulating tumor cell lines have the potential, at least on the cellular level, to produce more clonogensper week than will be on average killed by conventionally fractionated radiation therapy. The repopulation rate of glioblastoma has, at least to the knowledge of the authors, not been studied before. The radiation sensitivity of the two tested glioblastomacell lines expressedas SF2 (0.49 and 0.56) ranged close to the median SF2 of 0.50 in a large panel of studied cell lines from different institutions (23). Therefore, dose increments of 0.5-0.9 Gy per day (calculated for 2 Gy per fraction) may give an estimate for the average repopulation capacity of glioblastoma cells. Repopulation-induced dose increment was lower in glioblastoma cell lines than in SCC lines (Fig. 4). However, due to the low number of cell lines, the overlap of T,, values comparing glioblastomas and SCC, and the selection of relatively radiation resistant SCC lines, one cannot conclude that the cellular repopulation capacity is lower in glioblastomas. Pretherapeutic population doubling times (PDT) in vitro and potential tumor doubling time (Tpot) are thought to be measuresof tumor cell proliferation without cell loss (5). PDT times were extremely short (1.0-1.9 days) in the investigated panel of tumor cell lines and did not predict tumor cell proliferation during fractionated irradiation (T,,,) (Fig. 2a). T,, was significantly longer than PDT in three out of five tumor cell lines. Similar findings were reported by
0
W.
BUDACH
et al.
749
Speke and Hill (20) in four out of five studied murine tumor cell lines. Neither PDT in the present study nor Trot in the investigation of Speke and Hill (20) were predictive for T,, during fractionated irradiation, indicating that both parameters are poor predictors for T,, in the experimental setting. Whereas T,, was not predictive (Fig. 3a), the product of T,, X negative logarithm of SF2 was a significant predictor of the increaseof WCD,, within 18.3 days (Fig. 3b). This observation emphasizesthat repopulation-induced dose loss per day depends on both T,, and radiation sensitivity. Hence, rapid proliferation of surviving clonogens during radiation therapy doesnot necessarilylead to clinical failure in a radiation-sensitive tumor and a low proliferation rate does not guarantee local control in relatively radiationresistanttumors. BecauseT,, and radiation sensitivity were independentproperties of tumor cells in the tested panel of cell lines and can be expected to be generally independent, a preclinical evaluation of both Trot and SF2 might have a much higher potential to predict clinical outcome compared to only one parameter. The ability of tumor cells to form colonies within 2 1 days after trypsinization and plating predicted T,, during radiation therapy in the panel of tested cell lines (Fig. 2b). The mechanismbehind this relationship is unclear; however, it appearsthat the capability to proliferate after different kinds of cellular stress(trypsinization, radiation) might be associated properties of tumor cells. In summary, the intrinsic ability of squamouscell carcinoma and glioblastoma cells to repopulate during fractionated radiation therapy could be demonstratedunder in vitro conditions. Repopulation-induced dose loss per day was dependenton T,, and intrinsic radiation sensitivity. Proliferation during treatment was decelerated compared to pretreatment population doubling time in the majority of cell lines. Pretreatment cell kinetics did not predict for tumor cell proliferation during treatment.
REFERENCES 1. Baumarm, M.; Liertz. C.; Baisch, H.; Wiegel, T.; Lorenzen,
2.
3.
4.
5.
J.; Arps, H. Impact of overall treatment time of fractionated irradiation on local control of human fadu squamous cell carcinoma in nude mice. Radiother. Oncol. 32:137-143; 1994. Beck Bomholdt, H. P. Should tumors be clamped in radiobiological fractionation experiments? Int. J. Radiat. Oncol. Biol. Phys. 21:675-682; 1991. Beck-Bornholdt, H. P. Is there sufficient evidence for accelerated repopulation in tumours during fractionated radiotherapy? In: Hagen, U.; Jung, H., Streffer, C, eds. Radiation research 1895-1995, tenth international congress of radiation research, 27-Aug-1-Sep 1995. Wtirzburg, Germany. 1995: p. 84. Beck-Bomholdt, H. P.; Omniczynski, M.; Theis, E.; Vogler, H.; Wurschmidt, F. Influence of treatment time on the response of rat rhabdomyosarcoma RlH to fractionated irradiation. Acta Oncol. 3057-63; 1991. Begg, A. C. The clinical status of Tpot as a predictor? Or why
6.
7. 8. 9.
10. 11.
no tempest in the Tpot Int. J. Radiat. Oncol. Biol. Phys. 32:1539-1541; 1995. Begg, A. C.; Hofland, I.; Kummermehr, J. Tumour cell repopulation during fractionated radiotherapy: Correlation between flow cytometric and radiobiological data in three murine tumours. Eur. J. Cancer 27:537-543; 1991. Bentzen, S. M.; Thames, H. D. Clinical evidence for tumor clonogen regeneration: Interpretations of the data. Radiother. Oncol. 22:161-166; 1991. Bentzen, S. M.; Thames, H. D. Overall treatment time and tumor control dose for head and neck tumors: The dog leg revisited. Radiother. Oncol. 25:143-144; 1992. Brock, W. A.; Baker, F. L.; Wike, J. L.; Sivon, S. L.; Peters, L. J. Cellular radiosensitivity of primary head and neck squamous cell carcinomas and local tumor control. Int. J. Radiat. Oncol. Biol. Phys. 18:1283-1286; 1990. Dubben, H. H. Local control, TCDSO and dose-time prescription habits in radiotherapy of head and neck tumours. Radiother. Oncol. 32: 197-200; 1994. Fowler, J. F.: Lindstrom, M. J. Loss of local control with
750
12.
13.
14. 15. 16.
17.
18. 19.
I. J. Radiation Oncology l Biology l Physics prolongation in radiotherapy. Int. J. Radiat. Oncol. Biol. Phys. 23:457-467; 1992. Girinsky, T.; Lubin, R.; Chavaudra, N.; Pignon, J. P.; Gazeau, J.; Haie, C.; Wibaut, P.; Socie, G.; Cosset, J. M.; Geara, F.; Fertil, B.; Brock, W. A.; Malaise. E. P. In vitro radiosensitivity and calculated cell growth fraction in primary cultures from head and neck cancers and cervical carcinomas: Preliminary correlations with treatment outcome. In: Dewey, W. C.; Edington, M.; Fry, R. J. M.; Hall, E. J.; Whitmore, G. F., eds. Radiation research, a twentieth-century perspective. San Diego: Academic; 1992:700-705. Kummermehr, J.; Dorr, W.; Trott, K. R. Kinetics of accelerated repopulation in normal and malignant squamous epithelia during fractionated radiotherapy. Br. J. Radio. Suppl. 24: 193199; 1992. Kummermehr, J.; Trott, K. R. Should tumors be clamped in radiobiological fractionation experiments? Int. J. Radiat. Oncol. Biol. Phys. 25154-155; 1993. Maciejewski, B. A.; Skates, S.; Zajusz, A.; Lange, D. Importance of tumor size and repopulation for radiocurability of skin cancer. Neoplasma 40:51-54; 1993. Milas, L.; Yamada, S.; Hunter, N.; Guttenberger, R.; Thames, H. D. Changes in TCDSO as a measure of clonogen doubling time in irradiated and unirradiated tumors. Int. J. Radiat. Oncol. Biol. Phys. 21:1195-1202; 1991. Roberts, S. A.: Hendry, J. H. The delay before onset of accelerated tumour cell repopulation during radiotherapy: A direct maximum-likelihood analysis of a collection of worldwide tumour-control data. Radiother. Oncol. 2969-74; 1993. Rofstad, E. K. Repopulation between radiation fractions in human melanoma xenografts. Int. J. Radiat. Oncol. Biol. Phys. 23:63-68; 1992. Saunders, M. I.; Dische, S.; Barrett, A.; Parmar, M. K.; Harvey, A.; Gibson, D. Randomised multicentre trials of CHART vs conventional. Radiotherapy in head and neck and non-
Volume 39. Number 3, 1997
20.
21. 22.
23.
24.
25. 26. 27.
28.
small-cell lung cancer: An interim report. CHART Steering Committee. Br. J. Cancer 73:1455-1462; 1996. Speke, A. K.; Hill, R. P. Repopulation kinetics during fractionated irradiation and the relationship to the potential doubling time Tpot. Int. J. Radiat. Oncol. Biol. Phys. 3 1:847-856; 1995. Speke, A. K.; Hill, R. P. The effects of clamping and reoxygenation on repopulation during fractionated irradiation. Int. J. Radiat. Oncol. Biol. Phys. 31:857-863; 1995. Suit, H. D.; Howes, A. E.; Hunter. N. Dependence of response of a C3H mammary carcinoma to fractionated irradiation on fractionation number and intertreatment interval. Radiat. Res. 72:440-454; 1977. Taghian, A.; Ramsay, J.; Allalunis-Turner, J.; Budach, W.; Gioioso, D.; Pardo, F.; Okunieff, P.; Bleehen, N.; Urtasun, R.; Suit, H. D. Intrinsic radiation sensitivity may not be the major determinant of the poor clinical outcome of glioblastoma multifotme. Int. J. Radiat. Oncol. Biol. Phys. 25:243-249; 1993. Trott, K. R.; Kummermehr, J. Rapid repopulation in radiotherapy: A debate on mechanism. Accelerated repopulation in tumours and normal tissues. Radiother. Oncol. 22:159-160; 1991. Tsunemoto, H.; Ando, K.; Koike, S.; Urano, M. Repopulation of tumour cells following irradiation with x-rays or low energy neutrons. Int. J. Radiat. Biol. 65:61; 1994. Walker, A. M.; Suit, H. D. Assessment of local tumor control using censored tumor response data. Int. J. Radiat. Oncol. Biol. Phys. 9:383-386; 1983. Weichselbaum, R. R.; Beckett, M. A.; Vijayakumar. S. Radiobiological characterization of head and neck and sarcoma cells derived from patients prior to radiotherapy. Int. J. Radiat. Oncol. Biol. Phys. 19:313-319; 1990. Withers, H. R.; Taylor, J. M. G.; Maciejewski, B. The hazard of accelerated tumor clonogen repopulation during radiotherapy. Acta Oncol. 27:131-146; 1988.