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Tumor-to-tumor variability in the hypoxic fractions of experimental rodent tumors
Radiotherapy and Oncology, 2 (1984) 57-64 Elsevier
57
RTO 00051
Tumor-to-tumor variability in the hypoxic fractions of experimental rodent tumors Sara R o c k w e l l 1, J o h n E. M o u l d e r 2 a n d D o u g l a s F. M a r t i n 1 1Department of Therapeutic Radiology, Yale University School of Medicine, 333 Cedar St., New Haven, CT 06510 and 2Department of Radiation Oncology, Medical College of Wisconsin, 8700 IV. Wisconsin Ave., Milwaukee, WI 53226, U.S.A.
(Received 19 December 1983, revision received24 February 1984, accepted 5 March 1984)
Key words: Experimentaltumors; Hypoxiccells
Summary Paired determinations of the radiation responses of normally-aerated and artificially hypoxic rodent tumors, performed to measure the hypoxic fractions of the tumors, were obtained from our own laboratories and from the literature. The data were reanalyzed to assess whether the variabilities in the radiation responses of the normally-aerated and artificially hypoxic tumors were similar. If there were large differences in the hypoxic fractions of individual tumors within the experiments, the variability in the data from aerobic tumors would be expected to be greater than the variability in the data from artificially hypoxic tumors (which should all be brought to uniform hypoxia and therefore uniform radioresistance). The analyses revealed the variability to be as great or greater for hypoxic tumors as for normally-aerated tumors. This finding suggests that factors other than tumor-to-tumor differences in oxygenation produce most of the variability in the radiation responses of individual tumors from an experimental tumor line.
Introduction The hypoxic fractions of experimental rodent tumors have been measured using a variety of radiobiological techniques [9,11,18,24]. Studies in a large number of tumor systems have shown that the vast majority of solid tumors contain significant numbers of viable, radioresistant hypoxic cells, which are capable of forming new tumors in animals or colonies in cell culture, of leading to recurrences, and of contributing to tumor growth after irradiation. Within a given tumor line, the hypoxic fractions of the tumors may vary with the size of the 0167-8140/84/$03.00 9 1984 Elsevier SciencePublishers B.V.
tumors, the site of implantation, the host characteristics (e.g. age, sex, host hematocrit), and the experimental conditions (e.g. the use of anesthesia during irradiation). These data are summarized in a recent review [18]. One question which has not been addressed definitively is whether individual tumors from the same tumor line, implanted into the same site, in similar hosts, and studied at the same size, using similar experimental techniques, show extensive tumor-to-tumor variability in hypoxic fractions. It has been suggested that significant tumor-to-tumor differences in oxygenation may occur and may be
58 largely responsible for the variability in the response of individual tumors to treatment with radiation and/or drugs. In the studies reported here, data on the radiation responses of individual tumors irradiated in air and under acute hypoxia were analyzed to determine whether the variabilities in the radiation responses of the normally-aerated and hypoxic tumors were similar. If there are large differences in the hypoxic fractions of individual tumors, the variability in the radiation responses of aerobic tumors should be greater than that of the hypoxic tumors, as tumorto-tumor variability in oxygenation (and therefore radiosensitivity) would be eliminated by the induction of artificial, uniform hypoxia. If the variabilities for the normally-aerated and artificially hypoxic tumors are similar, factors other than differences in the fraction of hypoxic cells in individual tumors at the time of irradiation are probably responsible for the variation in tumor response.
available for individual tumors. Most survival determinations are performed using tumor cell suspensions prepared from pools of 3-6 tumors; in contrast, survival determinations for B A l l l 2 tumors are performed using individual tumors. Third, large numbers of data points are available for BA 1112 tumors, while many studies in the literature are based on only a few observations and therefore are not amenable to analyses of variability.
Hypoxic fraction assays. The experimental methodology and analytical techniques used to determine hypoxic fractions, and the biological, technical, and statistical limitations of the techniques are discussed in detail elsewhere [18]. In paired survival curve assays radiation survival curves are determined for cells from aerobic and hypoxic tumors (Fig. 1). The survival data are fitted with the parallel lines [1] using Eqns. (1) and (2): [log(e)][D]
log(Sa) = log(na)
(l)
Do
Materials and methods
Tumors and hosts. Our most extensive analyses were performed using data on the radiation responses of B A l l l 2 rhabdomyosarcomas. The BA1112 tumor line, derived from a rhabdomyosarcoma in a WAG/Rij rat in 1962 in the Netherlands, has been maintained in SPF WAG/Rij rats and used for experimental therapy studies at Yale and Medical College of Wisconsin for over 10 years. During these studies, the hypoxic fractions of BA1112 tumors have been measured using three different techniques: paired survival curve assay, clamped growth delay assay, and clamped tumor control dose assay. The data [13,16-18] and the hypoxic fractions calculated from the data [17,18] have been published previously. These studies of BA 1112 tumors were used as the primary data for the analyses reported here, for three reasons. First, nine independent comparisons of aerobic and hypoxic tumors exist for this tumor line, and these studies include data obtained under different experimental conditions and with all three assay techniques. Second, for all the experiments, data are
1.0
Z
O (o
~\~
~
,, 1 HYPOXICCURVE
0,1
rr 14.
".
Z
0.01 rr O~
ox,c
~
N
0.001 _
L
I
I
1000 DOSE (tad)
I
I
2000
Fig. 1. Paired survival assay for EMT6 mouse tumors. Cells irradiated in vitro under fully oxygenated conditions (A). Cells irradiated in tumors in unanesthetized air-breathing mice ( 9 Cells irradiated under hypoxic conditions in situ or in vitro ( 0 ) . Dashed lines are best fits to the individual data sets and assume multi-target single-hit kinetics. Solid lines are the best parallel lines which could be fitted to the air and hypoxic curves for doses of 1000 rad and above. Reprinted with permission from Moulder and Rockwell [18].
59 100
-
9 i 9149
o0o
8O
o
o o 60
time during the terminal portion of post-irradiation growth. The value of Th -- T, is determined by fitting parallel lines [1] to the dose-delay relationships for aerobic and clamped tumors using a dose range in which the dose-delay relationship is linear. Alternatively, the hypoxic fraction can be derived from the increase in dose required to produce equal delay in normal and clamped tumors using Eqn. (5):
o o~176
",
.
.// ff/ t
"//:/,,
-
uJ
AE.os,c TUMORS
40-
o / , ' V ,~=, / o ' / = , /
,,!
'/I, 9/ //
/
. "
o -~.X/op A X .o
o
p t
. o~ I~" J ~ ' ~ ' "
II,'~ " ' ~ I
-
"
I
CLAMPED
I
2000
I
4000 DOSE
f=
TUMORS I
(tad)
[log(e)][D] Do
(5)
I
6000
Fig. 2. Clamped growth delay assay for BA1112 sarcomas. The time required for the tumors to grow from 8 to 15 m m in diameter is shown for tumors irradiated under normal aeration (O) and under hypoxic conditions ( 0 ) . Solid lines are the best parallel linear fit; dashed lines are the best parallel fit to a log (delay) vs dose relationship. Reprinted with permission from Moulder and Rockwell [18].
log(Sh) = log(nh)
e(Dnt'-Dclamp)/Do'h
(2)
is the dose difference between the parallel dose-response curves [1] and Do,h is the Do for naturally-occurring hypoxic cells. The dose range used for the parallel fit and the choice of a delay or a log(delay) relationship is based on minimizing the confidence interval o n Dair - - Delamv. In the clamped tumor control dose assays, tumor control dose-response curves are determine.d for aerobic and clamped tumors (Fig. 3). Using probit analysis [2], the best parallel lines are fitted to the tumor control data, and the hypoxic fraction, f is calculated from Eqn. (6): w h e r e Dair - - Delamo
f = eW.t'-Do'="p)/D~ where S~ and Sh are the survival of cells from aerobic and hypoxic tumors; Do is the slope of the parallel lines; and n~ and nh are the extrapolation numbers of the parallel lines. The hypoxic fraction, f, was derived from Eqn. (3): log(f) = log(n~) - log(rib)
(3)
In clamped tumor growth delay assays tumors are irradiated under aerobic conditions and with the blood supply to the tumor clamped off; and the size of each tumor is measured until it reaches a predetermined size (Fig. 2). The hypoxic fraction, f, can be calculated from the increase in growth delay due to hypoxia using Eqn. (4): f = 0.5(rh- Ta)/Td
(4)
where Th -- T, is the time displacement of the growth delay curves, and Ta is the volume doubling
.99
-
-J
.95
-
<~ m
.90
>I.-
(6) !
AEROBIC TUMORS
.80
o
n ~
-8 0--
.50
-
.20
-
.10
~-
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0
o
o /~LAMPEO
TUMORS
.05
.01 !~ I
I
4OOO
I
I
60OO DOSE (rad)
I
I
8OOO
Fig. 3. Clampedtumor control assay for BA1112 sarcomas.Tumors irradiated under normal aeration (O), and under hypoxic conditions (0). Solid lines are the best parallel fit. Reprinted with permission from Moulder and Rockwell [18].
60 is the dose difference between the parallel dose-response curves and Do,h is the Do for naturally-occurring hypoxic cells. w h e r e D a i r - - Delamp
Analytical and stat&tical techniques. The techniques used in this study were based on the hypoxic fraction techniques described above; but were used to analyze the variances of the hypoxic and aerobic data, rather than to calculate a hypoxic fraction. For survival curve data, the basic question posed was whether the total variability of the points around an aerobic cell survival curve was different from the variability of the points around the corresponding hypoxic curve. The best parallel least squares regression lines were fitted to the hypoxic and aerobic cell survival data as shown in Fig. 1. The mean squared deviation ('!the variance") of each set of data points from the respective line was calculated. The ratio of the aerobic and hypoxic variances was then calculated and a "variance ratio test" was used to determine whether the ratio was significantly different from 1.0 [1]. The data relating tumor growth delay to radiation dose for each hypoxic and aerobic data set were fitted with the best parallel linear and the best parallel logarithmic lines as shown in Fig. 2. The variance of each aerobic and hypoxic data set around the respective line was calculated. A variance ratio test [I] was used to determine whether the ratio of the variances of the corresponding aerobic and hypoxic data sets was significantly different from 1.0. The variance ratio test has some limitations, which were considered in performing the analyses. First, the test is most sensitive when large numbers of data points, determined for individual tumors, are analyzed. In practice, reasonable sensitivity requires a total of 30 data points, with at least 8 points on both the aerobic and hypoxic (clamped) curves; most data sets in the literature do not include this amount of data. The test is adversely affected by any deviations from linearity and parallelism: each aerobic or hypoxic data set was therefore tested to ensure that the data did not deviate significantly from linearity. The appropriate best fit lines to each individual set of aerobic data and to
the corresponding set of hypoxic data were compared and tested to ensure that the lines did not differ significantly from parallelism. All data passed linearity and parallelism tests (17 > 0.1) except as noted in results. For tumor control data, the best probit curve was fitted to the data points defining the proportion of the tumors controlled at each radiation dose under aerobic conditions or under hypoxic conditions, as shown in Fig. 3. The points on a tumor control dose-response curve represent the response of groups of 8 to 20 tumors. This grouping decreases the effect of tumor-to-tumor variability, and thus the variance of the data is not a sensitive indicator of heterogeneity. The slope of a tumor control doseresponse curve, on the other hand, is a sensitive indicator of heterogeneity, with a very uniform population yielding a very steep dose-response curve and any non-uniformity in the population acting to reduce the slope of the curve [3]. The slopes of the best-fitting dose-response curves for hypoxic and aerobic tumors were therefore compared, using standard statistical techniques for comparing probit curves [2], to determine whether their slopes were different (i.e. whether the heterogeneities in the data were the same or different). Variance ratio testing was also performed on all clamped tumor control dose assays; no significant differences were seen between the variances of aerobic and hypoxic tumors, and the results of these tests are not reported here.
Results
The survival data determined for normally-aerated and hypoxic BA 1112 tumors were analyzed (Table I). Variance ratio analyses were obtained for three individual data sets under slightly different experimental conditions (tumors on the head, treated with rats anesthetized with sodium pentobarbital; head tumors on unanesthetized animals; back tumors on unanesthetized animals) and for the pooled, total data. None of the variance ratios were significantly different from 1.0. Moreover, for two of three individual data sets and also for the pooled data, the variance ratio was less than 1.0, indicating that the
61 TABLE I Variance ratio tests for individual and pooled BA1112 cell survival curves. Data set
No. o f points
Variance ratio (aerobic/hypoxic)
Significance
Aerobic curve
Hypoxic curve
Head, sc, anesthetized
12
11
1.51
p > 0.I0
Head, s c : unanesthetized
35
20
0.71
p > 0.10
Back, sc, unanesthetized
15
10
0.60
p > 0.10
Pooled b
66
46
0.70
0.10 > p > 0.05
" For parallelism test 0.I0 > p > 0.05. b Pooled data include all three subgroups plus d a t a from Reinhold [19] determined using TDs0 assays for cell survival.
variability in the hypoxic data set was greater than in the aerobic data set; for the pooled data, this difference was marginally significant (Table I). The data from one experiment (Fig. 3) measuring the hypoxic fraction of BA1112 tumors using a growth delay assay were analyzed. The analysis was performed using both logarithmic and linear fits to
the delay versus dose data because neither formulation provided an obviously better fit to the data. The numbers of data points analyzed were different for the linear formulation (37 aerobic points and 49 hypoxic points) and for the logarithmic formulation (44 aerobic points and 60 hypoxic points), because data at lower radiation doses were adequately
T A B L E I1 Slope ratio tests for individual and pooled T C D s 0 determinations on BAI 112 tumors. Data set
No. of tumors (No. of points)
Slope ratio
Significance
(hypoxic/aerobic) Aerobic curve
Clamped curve
78 (6) 80 (6)
91 (7) 60 (6)
60 (8) Back, sc, anesthetized Back, sc, unanesthetized
60 (6)
0.75 0.62 0.77
p > 0.10 p > 0.I0 p > 0.10
60 (6)
80 (8)
0.63
p > 0.10
80 (8)
70 (7)
0.84
p > 0.10
358 (34)
361 (34)
0.68
0.05 > p > 0.02
Head, sc, a anesthetized
Pooled b
" Three separate assays. b For linearity test p < 0.001.
62 fit only by the l o g a r i t h m i c f o r m u l a t i o n a n d therefore were included o n l y in that analysis. The variance ratios for the linear a n d l o g a r i t h m i c fits were 1.3 a n d 1.2, respectively, suggesting t h a t the aerobic d a t a m a y be m o r e variable t h a n the h y p o x i c data, b u t neither ratio was significantly different f r o m 1.0
best fitting h y p o x i c curve. This difference was statistically significant o n l y for the p o o l e d data. This suggests t h a t the variability in the h y p o x i c d a t a w i t h i n e x p e r i m e n t s a n d b e t w e e n e x p e r i m e n t s was at least as great as the variability in the a e r o b i c data.
(p > 0.10).
I n s u m m a r y , d a t a for B A l l l 2
Five sets o f d a t a relating t u m o r c o n t r o l to radiation dose were a n a l y z e d ( T a b l e II). F o r each o f the five i n d i v i d u a l d a t a sets, as well as the p o o l e d data, the best fitting aerobic curve was steeper t h a n the
t u m o r s suggest
t h a t the variabilities o f the r a d i a t i o n responses o f hypoxic t u m o r s were similar to or greater t h a n the variabilities for a e r o b i c t u m o r s , w h e t h e r in situ endp o i n t s ( t u m o r growth, t u m o r c o n t r o l ) or a n exci-
TABLE III Results of variability analyses in other tumor systems. Tumor
Ref.
Assay
No. of points Aerobic
Hypoxic
curve
curve
Variance ratio (aerobic/hypoxic)a
Significance
EMT6
11,18
Surv. curve
29
28
1.2
p > 0.I0
Lewis Lung 10 mm s.c. 2.3 mm lung 3.5 mm lung
21 23 23
Surv, curve Surv. curve Surv. curve
19 14 14
15 18 18
0.36 6.0 2.5
p < 0.05 p < 0.01 p < 0.05
Surv. curve
20
7
1.4
p > 0.10
Sq. cell ca.
4,5
KHJJ
10
Surv. curve
12
14
2.7
p > 0.10
Fib/T
15
Surv. curve
14
12
0.78
p > 0.10
MT
14
Surv. curve
9
8
0.98
p > 0.10
B16
6
Surv. curve
24
13
1.1
p > 0.10
6
9
0.65
p > 0.10
EMT6
22
Growth delay
Slope ratio (hypoxic/aerobic)a MT
14
TCDso
5
5
1.4
p > 0.10
MT1
20
TCD~o
9
5
1.0
p > 0.I0
TCDso
5
6
1.3
p > 0.I0
TCDs0
7
5
2.7
p < 0.01
Mam ca. SSK31
7,8 12
a A ratio greater than 1 implies greater variability in the aerobic data.
63 sion endpoint (cell survival) were used in the studies. This suggests that the variability in the data reflects not tumor-to-tumor differences in oxygenation, but rather other experimental and biological sources of variability (tumor size differences, host differences, differences in radiation dose delivered, etc.). The general nature of this observation was tested by performing similar analyses on data from other tumor systems. The data sets used in these analyses were those used for our survey of hypoxic fraction measurements [18]. Only a limited number of the 92 data sets used in that survey could be used for analysis of tumor variability because of the large number of data points necessary for the analyses and because individual determinations of surviving fractions and growth delays, rather than the mean values often published, are preferable for the analysis. Another problem arises because many cell survival determinations with mouse tumors are performed using cell suspensions prepared from 3 to 6 tumors. The effect of tumor-to-tumor variability in determinations performed on pooled samples will be partially masked by the pooling process. As a result, there should theoretically be less variability among aerobic determinations based on pooled tumors than among aerobic determinations based on individual tumors and the variance ratios should be close to 1i0 (assuming oxygenation differences are responsible for the variability). As Table III shows, the variance ratios for the survival curve data range from 0.36 to 6.0. The only ratios which are significantly different from 1.0 are those for Lewis Lung. For subcutaneous (s.c.) Lewis Lung tumors, the hypoxic data are significantly more variable than are the aerobic data; for small pulmonary tumors, the reverse is true. The one growth delay assay showed no differences in variability between aerobic and clamped tumors. The analyses of TCDso data by slope ratio tests revealed only one significant difference between the variabilities for normally-oxygenated and hypoxic tumors (i.e. that for SSK31 tumors). This survey shows that in several experimental tumor systems the variabilities in the radiation response of aerobic and hypoxic tumors are similar,
and implies that tumor-to-tumor differences in hypoxic fractions are not the dominant factor producing the variability in the tumor radiosensitivity.
Discussion
The analyses summarized in Tables I-III indicate that the variability in the radiation response of normally-aerated tumors generally is not significantly greater than the variability for artificially, uniformly hypoxic tumors. Of the 25 data sets tested, three showed significantly more variability in the aerobic data than in the hypoxic data (SSK31, and the two studies on small pulmonary Lewis Lung tumors). Three showed significantly more variability in the hypoxic data sets (pooled B A l l l 2 TCDso data, pooled B A l l l 2 survival curve data, and subcutaneous Lewis Lung). The other 19 data sets showed no significant differences. If there had been large tumor-to-tumor variations in the effective hypoxic fractions of individual tumors, the radiation responses of the normally-aerated tumors would be expected to be large, because the radiosensitivity of each tumor would depend strongly on the oxygenation of that particular tumor. In contrast, hypoxic tumors would be expected to show less variability, as irradiation would be performed on artificially, uniformly hypoxic cell populations. The similarity of the variabilities in the data sets for normally-aerated and hypoxic tumors suggests that tumor-totumor variations in the hypoxic fractions were relatively small and that factors other than differences in oxygenation produced most of the variability in the response of the tumors to irradiation. Other possible sources of variability include differences in tumor size or cellularity, differences in the radiation doses received by the tumors, differences in the inherent clonogenicity of cells in individual tumors, and differences in the host response to the tumors. For hypoxic determinations, variability in the effects of the techniques used to induce artificial hypoxia could introduce variability, if, for example, the techniques sometimes failed to produce complete, uniform hypoxia in all the tumors or sometimes damaged the tumor, bed, or vascu-
64 lature and therefore directly affected the growth or v i a b i l i t y o f t h e t u m o r cells. A s s o m e d a t a sets s u g gest g r e a t e r v a r i a b i l i t y in t h e h y p o x i c d a t a t h a n in the corresponding aerobic data, the possibility that s o m e t e c h n i q u e s u s e d to i n d u c e h y p o x i a in t u m o r s m a y be i n a d e q u a t e a n d / o r m a y h a v e d i r e c t effects o n the t u m o r m u s t be c o n s i d e r e d in p l a n n i n g a n d interpreting studies of tumor oxygenation.
Acknowledgements This study was supported by USPHS Grants CA06519 a n d C A - 2 7 0 8 4 . A p r e l i m i n a r y r e p o r t o f t h e f i n d i n g s in this m a n u s c r i p t
w a s p r e s e n t e d to t h e
American Society of Therapeutic Radiologists, Los A n g e l e s , Oct. 4, 1983.
References 1 Brownlee, K. A. Simple linear regression. In: Statistical Theory and Methodology in Science and Engineering, 2nd edn., pp. 334-396. John Wiley & Sons, New York, 1965. 2 Finney, D. J. Probit Analysis, 3rd edn. Cambridge University Press, Cambridge, 1971. 3 Fischer, J. J. and Moulder, J.E. The steepness of the doseresponse curve in radiation therapy. Radiology 117: 17% 184, 1975. 4 Hewitt, H. B., Chan, D. P.-S. and Blake, E . R . Survival curves for clonogenic cells of a murine keratinizing squamous carcinoma irradiated in vivo or under hypoxic conditions. Int. J. Radiat. Biol. 12: 535-549, 1967. 5 Hewitt, H. B. and Sakamoto, K. The comparative survival of clonogenic cells of a murine epithelioma after irradiation in mice breathing air, oxygen and carbon dioxide, or hyperbaric oxygen. Br. J. Radiol. 44: 457-463, 1971. 6 Hill, R. P. and Stanley, J.A. The response ofhypoxic B16 melanoma cells to in vivo treatment with chemotherapeutic agents. Cancer Res. 35:1147 1153, 1975. 7 Howes, A.E. An estimation of changes in the proportions and absolute numbers of hypoxic cells after irradiation of transplanted C3H mouse mammary tumours. Br. J. Radiol. 42: 441-447, 1969. 8 Howes, A. E., Page, A. and Fowler, J. F. The effect of single and fractionated doses of X-rays on the effective proportion of hypoxic cells in C3H mouse mammary tumours. Br. J. Radiol. 45: 25(~256, 1972. 9 Kallman, R.F. The phenomenon of reoxygenation and its implications for fractionated radiotherapy. Radiology 105: 135 142, 1972.
10 Kallman, R . F . The oxygen effect and reoxygenation. In: Excerpta Medica, International Congress Series No. 353, Vol. 5, pp. 13(~140. Surgery, Radiotherapy, and Chemotherapy of Cancer (XI International Cancer Congress), 1974. 11 Kallman, R. F. and Rockwell, S. Effects of radiation on animal tumor models. In: Cancer: A Comprehensive Treatise, Vol. 6, pp. 225-279. Editor: F. F. Becker. Plenum Press, New York, 1977. 12 Kummermehr, J., Fink, R., Preuss-Bayer, G. and Trott, K.-R. Reoxygenierung in einem transplantablen Fibrosarkom der Maus. Strahlentherapie 157: 272-276, 1981. 13 Martin, D. F., Rockwell, S. and Fischer, J.J. Development of an in vitro assay for the survival of cells suspended from BA1112 rat sarcomas. Eur. J. Cancer Clin. Oncol. 19: 791797, 1983. 14 McNally, N. J., Denekamp, J., Sheldon, P., Flockhart, I. R. and Stewart, F. A. Radiosensitization by misonidazole (Ro-07-0582). The importance of timing and tumor concentration of sensitizer. Radiat. Res. 73:568 580, 1978. 15 McNally, N. J. and Sheldon, P.W. The effect of radiation on tumour growth delay, cell survival, and cure of the animal using a single tumour system. Br. J. Radiol. 50: 321-328, 1977. 16 Moulder, J. E., Fischer, J. J. and Milardo, R. Time-dose relationships for the cure of an experimental rat tumor with fractionated radiation. Int. J. Radiat. Oncol. Biol. Phys. 1: 431-438, 1976. 17 Moulder, J. E. and Martin, D . F . Hypoxic fraction determinations in the BA1112 rat sarcoma: variations within and among assay techniques. Radiat. Res. 99, in press, 1984. 18 Moulder, J. E. and Rockwell, S. Hypoxic fractions of solid tumors: experimental techniques, methods of analysis, and a survey of existing data. Int. J. Radiat. Oncol. Biol. Phys. 10, in press, 1984. 19 Reinhold, H.S. Quantitative evaluation of the radiosensitivity of cells of a transplantable rhabdomyosarcoma in the rat. Eur. J. Cancer 2: 33-42, 1966. 20 Sheldon, P. W. and Hill, S.A. Further investigations of the effect of the hypoxic cell radiosensitizer Ro-07-0582 on local control of a mouse tumour. Br. J. Cancer 36: 198~05, 1977. 21 Shipley, W. U., Stanley, J. A., Courtenay, V. D. and Field, S.B. Repair of radiation damage in Lewis lung carcinoma cells following in situ treatment with fast neutrons and gamma-rays. Cancer Res. 35:932 938, 1975. 22 Siemann, D . W . Tumour size: a factor influencing the isoeffect analysis of tumour response to combined modalities. Br. J. Cancer 41 (Suppl. IV): 294~298, 1980. 23 Stanley, J. A., Shipley, W. U. and Steel, G.G. Influence of tumor size on hypoxic fraction and therapeutic sensitivity of Lewis lung tumour. Br. J. Cancer 36:105 113, 1977. 24 Van Putten, L. M. and Kallman, R.F. Oxygenation status of a transplantable tumor during fractionated radiation therapy. J. Natl. Cancer Inst. 40: 441-451, 1968.
57
RTO 00051
Tumor-to-tumor variability in the hypoxic fractions of experimental rodent tumors Sara R o c k w e l l 1, J o h n E. M o u l d e r 2 a n d D o u g l a s F. M a r t i n 1 1Department of Therapeutic Radiology, Yale University School of Medicine, 333 Cedar St., New Haven, CT 06510 and 2Department of Radiation Oncology, Medical College of Wisconsin, 8700 IV. Wisconsin Ave., Milwaukee, WI 53226, U.S.A.
(Received 19 December 1983, revision received24 February 1984, accepted 5 March 1984)
Key words: Experimentaltumors; Hypoxiccells
Summary Paired determinations of the radiation responses of normally-aerated and artificially hypoxic rodent tumors, performed to measure the hypoxic fractions of the tumors, were obtained from our own laboratories and from the literature. The data were reanalyzed to assess whether the variabilities in the radiation responses of the normally-aerated and artificially hypoxic tumors were similar. If there were large differences in the hypoxic fractions of individual tumors within the experiments, the variability in the data from aerobic tumors would be expected to be greater than the variability in the data from artificially hypoxic tumors (which should all be brought to uniform hypoxia and therefore uniform radioresistance). The analyses revealed the variability to be as great or greater for hypoxic tumors as for normally-aerated tumors. This finding suggests that factors other than tumor-to-tumor differences in oxygenation produce most of the variability in the radiation responses of individual tumors from an experimental tumor line.
Introduction The hypoxic fractions of experimental rodent tumors have been measured using a variety of radiobiological techniques [9,11,18,24]. Studies in a large number of tumor systems have shown that the vast majority of solid tumors contain significant numbers of viable, radioresistant hypoxic cells, which are capable of forming new tumors in animals or colonies in cell culture, of leading to recurrences, and of contributing to tumor growth after irradiation. Within a given tumor line, the hypoxic fractions of the tumors may vary with the size of the 0167-8140/84/$03.00 9 1984 Elsevier SciencePublishers B.V.
tumors, the site of implantation, the host characteristics (e.g. age, sex, host hematocrit), and the experimental conditions (e.g. the use of anesthesia during irradiation). These data are summarized in a recent review [18]. One question which has not been addressed definitively is whether individual tumors from the same tumor line, implanted into the same site, in similar hosts, and studied at the same size, using similar experimental techniques, show extensive tumor-to-tumor variability in hypoxic fractions. It has been suggested that significant tumor-to-tumor differences in oxygenation may occur and may be
58 largely responsible for the variability in the response of individual tumors to treatment with radiation and/or drugs. In the studies reported here, data on the radiation responses of individual tumors irradiated in air and under acute hypoxia were analyzed to determine whether the variabilities in the radiation responses of the normally-aerated and hypoxic tumors were similar. If there are large differences in the hypoxic fractions of individual tumors, the variability in the radiation responses of aerobic tumors should be greater than that of the hypoxic tumors, as tumorto-tumor variability in oxygenation (and therefore radiosensitivity) would be eliminated by the induction of artificial, uniform hypoxia. If the variabilities for the normally-aerated and artificially hypoxic tumors are similar, factors other than differences in the fraction of hypoxic cells in individual tumors at the time of irradiation are probably responsible for the variation in tumor response.
available for individual tumors. Most survival determinations are performed using tumor cell suspensions prepared from pools of 3-6 tumors; in contrast, survival determinations for B A l l l 2 tumors are performed using individual tumors. Third, large numbers of data points are available for BA 1112 tumors, while many studies in the literature are based on only a few observations and therefore are not amenable to analyses of variability.
Hypoxic fraction assays. The experimental methodology and analytical techniques used to determine hypoxic fractions, and the biological, technical, and statistical limitations of the techniques are discussed in detail elsewhere [18]. In paired survival curve assays radiation survival curves are determined for cells from aerobic and hypoxic tumors (Fig. 1). The survival data are fitted with the parallel lines [1] using Eqns. (1) and (2): [log(e)][D]
log(Sa) = log(na)
(l)
Do
Materials and methods
Tumors and hosts. Our most extensive analyses were performed using data on the radiation responses of B A l l l 2 rhabdomyosarcomas. The BA1112 tumor line, derived from a rhabdomyosarcoma in a WAG/Rij rat in 1962 in the Netherlands, has been maintained in SPF WAG/Rij rats and used for experimental therapy studies at Yale and Medical College of Wisconsin for over 10 years. During these studies, the hypoxic fractions of BA1112 tumors have been measured using three different techniques: paired survival curve assay, clamped growth delay assay, and clamped tumor control dose assay. The data [13,16-18] and the hypoxic fractions calculated from the data [17,18] have been published previously. These studies of BA 1112 tumors were used as the primary data for the analyses reported here, for three reasons. First, nine independent comparisons of aerobic and hypoxic tumors exist for this tumor line, and these studies include data obtained under different experimental conditions and with all three assay techniques. Second, for all the experiments, data are
1.0
Z
O (o
~\~
~
,, 1 HYPOXICCURVE
0,1
rr 14.
".
Z
0.01 rr O~
ox,c
~
N
0.001 _
L
I
I
1000 DOSE (tad)
I
I
2000
Fig. 1. Paired survival assay for EMT6 mouse tumors. Cells irradiated in vitro under fully oxygenated conditions (A). Cells irradiated in tumors in unanesthetized air-breathing mice ( 9 Cells irradiated under hypoxic conditions in situ or in vitro ( 0 ) . Dashed lines are best fits to the individual data sets and assume multi-target single-hit kinetics. Solid lines are the best parallel lines which could be fitted to the air and hypoxic curves for doses of 1000 rad and above. Reprinted with permission from Moulder and Rockwell [18].
59 100
-
9 i 9149
o0o
8O
o
o o 60
time during the terminal portion of post-irradiation growth. The value of Th -- T, is determined by fitting parallel lines [1] to the dose-delay relationships for aerobic and clamped tumors using a dose range in which the dose-delay relationship is linear. Alternatively, the hypoxic fraction can be derived from the increase in dose required to produce equal delay in normal and clamped tumors using Eqn. (5):
o o~176
",
.
.// ff/ t
"//:/,,
-
uJ
AE.os,c TUMORS
40-
o / , ' V ,~=, / o ' / = , /
,,!
'/I, 9/ //
/
. "
o -~.X/op A X .o
o
p t
. o~ I~" J ~ ' ~ ' "
II,'~ " ' ~ I
-
"
I
CLAMPED
I
2000
I
4000 DOSE
f=
TUMORS I
(tad)
[log(e)][D] Do
(5)
I
6000
Fig. 2. Clamped growth delay assay for BA1112 sarcomas. The time required for the tumors to grow from 8 to 15 m m in diameter is shown for tumors irradiated under normal aeration (O) and under hypoxic conditions ( 0 ) . Solid lines are the best parallel linear fit; dashed lines are the best parallel fit to a log (delay) vs dose relationship. Reprinted with permission from Moulder and Rockwell [18].
log(Sh) = log(nh)
e(Dnt'-Dclamp)/Do'h
(2)
is the dose difference between the parallel dose-response curves [1] and Do,h is the Do for naturally-occurring hypoxic cells. The dose range used for the parallel fit and the choice of a delay or a log(delay) relationship is based on minimizing the confidence interval o n Dair - - Delamv. In the clamped tumor control dose assays, tumor control dose-response curves are determine.d for aerobic and clamped tumors (Fig. 3). Using probit analysis [2], the best parallel lines are fitted to the tumor control data, and the hypoxic fraction, f is calculated from Eqn. (6): w h e r e Dair - - Delamo
f = eW.t'-Do'="p)/D~ where S~ and Sh are the survival of cells from aerobic and hypoxic tumors; Do is the slope of the parallel lines; and n~ and nh are the extrapolation numbers of the parallel lines. The hypoxic fraction, f, was derived from Eqn. (3): log(f) = log(n~) - log(rib)
(3)
In clamped tumor growth delay assays tumors are irradiated under aerobic conditions and with the blood supply to the tumor clamped off; and the size of each tumor is measured until it reaches a predetermined size (Fig. 2). The hypoxic fraction, f, can be calculated from the increase in growth delay due to hypoxia using Eqn. (4): f = 0.5(rh- Ta)/Td
(4)
where Th -- T, is the time displacement of the growth delay curves, and Ta is the volume doubling
.99
-
-J
.95
-
<~ m
.90
>I.-
(6) !
AEROBIC TUMORS
.80
o
n ~
-8 0--
.50
-
.20
-
.10
~-
I- o
0
o
o /~LAMPEO
TUMORS
.05
.01 !~ I
I
4OOO
I
I
60OO DOSE (rad)
I
I
8OOO
Fig. 3. Clampedtumor control assay for BA1112 sarcomas.Tumors irradiated under normal aeration (O), and under hypoxic conditions (0). Solid lines are the best parallel fit. Reprinted with permission from Moulder and Rockwell [18].
60 is the dose difference between the parallel dose-response curves and Do,h is the Do for naturally-occurring hypoxic cells. w h e r e D a i r - - Delamp
Analytical and stat&tical techniques. The techniques used in this study were based on the hypoxic fraction techniques described above; but were used to analyze the variances of the hypoxic and aerobic data, rather than to calculate a hypoxic fraction. For survival curve data, the basic question posed was whether the total variability of the points around an aerobic cell survival curve was different from the variability of the points around the corresponding hypoxic curve. The best parallel least squares regression lines were fitted to the hypoxic and aerobic cell survival data as shown in Fig. 1. The mean squared deviation ('!the variance") of each set of data points from the respective line was calculated. The ratio of the aerobic and hypoxic variances was then calculated and a "variance ratio test" was used to determine whether the ratio was significantly different from 1.0 [1]. The data relating tumor growth delay to radiation dose for each hypoxic and aerobic data set were fitted with the best parallel linear and the best parallel logarithmic lines as shown in Fig. 2. The variance of each aerobic and hypoxic data set around the respective line was calculated. A variance ratio test [I] was used to determine whether the ratio of the variances of the corresponding aerobic and hypoxic data sets was significantly different from 1.0. The variance ratio test has some limitations, which were considered in performing the analyses. First, the test is most sensitive when large numbers of data points, determined for individual tumors, are analyzed. In practice, reasonable sensitivity requires a total of 30 data points, with at least 8 points on both the aerobic and hypoxic (clamped) curves; most data sets in the literature do not include this amount of data. The test is adversely affected by any deviations from linearity and parallelism: each aerobic or hypoxic data set was therefore tested to ensure that the data did not deviate significantly from linearity. The appropriate best fit lines to each individual set of aerobic data and to
the corresponding set of hypoxic data were compared and tested to ensure that the lines did not differ significantly from parallelism. All data passed linearity and parallelism tests (17 > 0.1) except as noted in results. For tumor control data, the best probit curve was fitted to the data points defining the proportion of the tumors controlled at each radiation dose under aerobic conditions or under hypoxic conditions, as shown in Fig. 3. The points on a tumor control dose-response curve represent the response of groups of 8 to 20 tumors. This grouping decreases the effect of tumor-to-tumor variability, and thus the variance of the data is not a sensitive indicator of heterogeneity. The slope of a tumor control doseresponse curve, on the other hand, is a sensitive indicator of heterogeneity, with a very uniform population yielding a very steep dose-response curve and any non-uniformity in the population acting to reduce the slope of the curve [3]. The slopes of the best-fitting dose-response curves for hypoxic and aerobic tumors were therefore compared, using standard statistical techniques for comparing probit curves [2], to determine whether their slopes were different (i.e. whether the heterogeneities in the data were the same or different). Variance ratio testing was also performed on all clamped tumor control dose assays; no significant differences were seen between the variances of aerobic and hypoxic tumors, and the results of these tests are not reported here.
Results
The survival data determined for normally-aerated and hypoxic BA 1112 tumors were analyzed (Table I). Variance ratio analyses were obtained for three individual data sets under slightly different experimental conditions (tumors on the head, treated with rats anesthetized with sodium pentobarbital; head tumors on unanesthetized animals; back tumors on unanesthetized animals) and for the pooled, total data. None of the variance ratios were significantly different from 1.0. Moreover, for two of three individual data sets and also for the pooled data, the variance ratio was less than 1.0, indicating that the
61 TABLE I Variance ratio tests for individual and pooled BA1112 cell survival curves. Data set
No. o f points
Variance ratio (aerobic/hypoxic)
Significance
Aerobic curve
Hypoxic curve
Head, sc, anesthetized
12
11
1.51
p > 0.I0
Head, s c : unanesthetized
35
20
0.71
p > 0.10
Back, sc, unanesthetized
15
10
0.60
p > 0.10
Pooled b
66
46
0.70
0.10 > p > 0.05
" For parallelism test 0.I0 > p > 0.05. b Pooled data include all three subgroups plus d a t a from Reinhold [19] determined using TDs0 assays for cell survival.
variability in the hypoxic data set was greater than in the aerobic data set; for the pooled data, this difference was marginally significant (Table I). The data from one experiment (Fig. 3) measuring the hypoxic fraction of BA1112 tumors using a growth delay assay were analyzed. The analysis was performed using both logarithmic and linear fits to
the delay versus dose data because neither formulation provided an obviously better fit to the data. The numbers of data points analyzed were different for the linear formulation (37 aerobic points and 49 hypoxic points) and for the logarithmic formulation (44 aerobic points and 60 hypoxic points), because data at lower radiation doses were adequately
T A B L E I1 Slope ratio tests for individual and pooled T C D s 0 determinations on BAI 112 tumors. Data set
No. of tumors (No. of points)
Slope ratio
Significance
(hypoxic/aerobic) Aerobic curve
Clamped curve
78 (6) 80 (6)
91 (7) 60 (6)
60 (8) Back, sc, anesthetized Back, sc, unanesthetized
60 (6)
0.75 0.62 0.77
p > 0.10 p > 0.I0 p > 0.10
60 (6)
80 (8)
0.63
p > 0.10
80 (8)
70 (7)
0.84
p > 0.10
358 (34)
361 (34)
0.68
0.05 > p > 0.02
Head, sc, a anesthetized
Pooled b
" Three separate assays. b For linearity test p < 0.001.
62 fit only by the l o g a r i t h m i c f o r m u l a t i o n a n d therefore were included o n l y in that analysis. The variance ratios for the linear a n d l o g a r i t h m i c fits were 1.3 a n d 1.2, respectively, suggesting t h a t the aerobic d a t a m a y be m o r e variable t h a n the h y p o x i c data, b u t neither ratio was significantly different f r o m 1.0
best fitting h y p o x i c curve. This difference was statistically significant o n l y for the p o o l e d data. This suggests t h a t the variability in the h y p o x i c d a t a w i t h i n e x p e r i m e n t s a n d b e t w e e n e x p e r i m e n t s was at least as great as the variability in the a e r o b i c data.
(p > 0.10).
I n s u m m a r y , d a t a for B A l l l 2
Five sets o f d a t a relating t u m o r c o n t r o l to radiation dose were a n a l y z e d ( T a b l e II). F o r each o f the five i n d i v i d u a l d a t a sets, as well as the p o o l e d data, the best fitting aerobic curve was steeper t h a n the
t u m o r s suggest
t h a t the variabilities o f the r a d i a t i o n responses o f hypoxic t u m o r s were similar to or greater t h a n the variabilities for a e r o b i c t u m o r s , w h e t h e r in situ endp o i n t s ( t u m o r growth, t u m o r c o n t r o l ) or a n exci-
TABLE III Results of variability analyses in other tumor systems. Tumor
Ref.
Assay
No. of points Aerobic
Hypoxic
curve
curve
Variance ratio (aerobic/hypoxic)a
Significance
EMT6
11,18
Surv. curve
29
28
1.2
p > 0.I0
Lewis Lung 10 mm s.c. 2.3 mm lung 3.5 mm lung
21 23 23
Surv, curve Surv. curve Surv. curve
19 14 14
15 18 18
0.36 6.0 2.5
p < 0.05 p < 0.01 p < 0.05
Surv. curve
20
7
1.4
p > 0.10
Sq. cell ca.
4,5
KHJJ
10
Surv. curve
12
14
2.7
p > 0.10
Fib/T
15
Surv. curve
14
12
0.78
p > 0.10
MT
14
Surv. curve
9
8
0.98
p > 0.10
B16
6
Surv. curve
24
13
1.1
p > 0.10
6
9
0.65
p > 0.10
EMT6
22
Growth delay
Slope ratio (hypoxic/aerobic)a MT
14
TCDso
5
5
1.4
p > 0.10
MT1
20
TCD~o
9
5
1.0
p > 0.I0
TCDso
5
6
1.3
p > 0.I0
TCDs0
7
5
2.7
p < 0.01
Mam ca. SSK31
7,8 12
a A ratio greater than 1 implies greater variability in the aerobic data.
63 sion endpoint (cell survival) were used in the studies. This suggests that the variability in the data reflects not tumor-to-tumor differences in oxygenation, but rather other experimental and biological sources of variability (tumor size differences, host differences, differences in radiation dose delivered, etc.). The general nature of this observation was tested by performing similar analyses on data from other tumor systems. The data sets used in these analyses were those used for our survey of hypoxic fraction measurements [18]. Only a limited number of the 92 data sets used in that survey could be used for analysis of tumor variability because of the large number of data points necessary for the analyses and because individual determinations of surviving fractions and growth delays, rather than the mean values often published, are preferable for the analysis. Another problem arises because many cell survival determinations with mouse tumors are performed using cell suspensions prepared from 3 to 6 tumors. The effect of tumor-to-tumor variability in determinations performed on pooled samples will be partially masked by the pooling process. As a result, there should theoretically be less variability among aerobic determinations based on pooled tumors than among aerobic determinations based on individual tumors and the variance ratios should be close to 1i0 (assuming oxygenation differences are responsible for the variability). As Table III shows, the variance ratios for the survival curve data range from 0.36 to 6.0. The only ratios which are significantly different from 1.0 are those for Lewis Lung. For subcutaneous (s.c.) Lewis Lung tumors, the hypoxic data are significantly more variable than are the aerobic data; for small pulmonary tumors, the reverse is true. The one growth delay assay showed no differences in variability between aerobic and clamped tumors. The analyses of TCDso data by slope ratio tests revealed only one significant difference between the variabilities for normally-oxygenated and hypoxic tumors (i.e. that for SSK31 tumors). This survey shows that in several experimental tumor systems the variabilities in the radiation response of aerobic and hypoxic tumors are similar,
and implies that tumor-to-tumor differences in hypoxic fractions are not the dominant factor producing the variability in the tumor radiosensitivity.
Discussion
The analyses summarized in Tables I-III indicate that the variability in the radiation response of normally-aerated tumors generally is not significantly greater than the variability for artificially, uniformly hypoxic tumors. Of the 25 data sets tested, three showed significantly more variability in the aerobic data than in the hypoxic data (SSK31, and the two studies on small pulmonary Lewis Lung tumors). Three showed significantly more variability in the hypoxic data sets (pooled B A l l l 2 TCDso data, pooled B A l l l 2 survival curve data, and subcutaneous Lewis Lung). The other 19 data sets showed no significant differences. If there had been large tumor-to-tumor variations in the effective hypoxic fractions of individual tumors, the radiation responses of the normally-aerated tumors would be expected to be large, because the radiosensitivity of each tumor would depend strongly on the oxygenation of that particular tumor. In contrast, hypoxic tumors would be expected to show less variability, as irradiation would be performed on artificially, uniformly hypoxic cell populations. The similarity of the variabilities in the data sets for normally-aerated and hypoxic tumors suggests that tumor-totumor variations in the hypoxic fractions were relatively small and that factors other than differences in oxygenation produced most of the variability in the response of the tumors to irradiation. Other possible sources of variability include differences in tumor size or cellularity, differences in the radiation doses received by the tumors, differences in the inherent clonogenicity of cells in individual tumors, and differences in the host response to the tumors. For hypoxic determinations, variability in the effects of the techniques used to induce artificial hypoxia could introduce variability, if, for example, the techniques sometimes failed to produce complete, uniform hypoxia in all the tumors or sometimes damaged the tumor, bed, or vascu-
64 lature and therefore directly affected the growth or v i a b i l i t y o f t h e t u m o r cells. A s s o m e d a t a sets s u g gest g r e a t e r v a r i a b i l i t y in t h e h y p o x i c d a t a t h a n in the corresponding aerobic data, the possibility that s o m e t e c h n i q u e s u s e d to i n d u c e h y p o x i a in t u m o r s m a y be i n a d e q u a t e a n d / o r m a y h a v e d i r e c t effects o n the t u m o r m u s t be c o n s i d e r e d in p l a n n i n g a n d interpreting studies of tumor oxygenation.
Acknowledgements This study was supported by USPHS Grants CA06519 a n d C A - 2 7 0 8 4 . A p r e l i m i n a r y r e p o r t o f t h e f i n d i n g s in this m a n u s c r i p t
w a s p r e s e n t e d to t h e
American Society of Therapeutic Radiologists, Los A n g e l e s , Oct. 4, 1983.
References 1 Brownlee, K. A. Simple linear regression. In: Statistical Theory and Methodology in Science and Engineering, 2nd edn., pp. 334-396. John Wiley & Sons, New York, 1965. 2 Finney, D. J. Probit Analysis, 3rd edn. Cambridge University Press, Cambridge, 1971. 3 Fischer, J. J. and Moulder, J.E. The steepness of the doseresponse curve in radiation therapy. Radiology 117: 17% 184, 1975. 4 Hewitt, H. B., Chan, D. P.-S. and Blake, E . R . Survival curves for clonogenic cells of a murine keratinizing squamous carcinoma irradiated in vivo or under hypoxic conditions. Int. J. Radiat. Biol. 12: 535-549, 1967. 5 Hewitt, H. B. and Sakamoto, K. The comparative survival of clonogenic cells of a murine epithelioma after irradiation in mice breathing air, oxygen and carbon dioxide, or hyperbaric oxygen. Br. J. Radiol. 44: 457-463, 1971. 6 Hill, R. P. and Stanley, J.A. The response ofhypoxic B16 melanoma cells to in vivo treatment with chemotherapeutic agents. Cancer Res. 35:1147 1153, 1975. 7 Howes, A.E. An estimation of changes in the proportions and absolute numbers of hypoxic cells after irradiation of transplanted C3H mouse mammary tumours. Br. J. Radiol. 42: 441-447, 1969. 8 Howes, A. E., Page, A. and Fowler, J. F. The effect of single and fractionated doses of X-rays on the effective proportion of hypoxic cells in C3H mouse mammary tumours. Br. J. Radiol. 45: 25(~256, 1972. 9 Kallman, R.F. The phenomenon of reoxygenation and its implications for fractionated radiotherapy. Radiology 105: 135 142, 1972.
10 Kallman, R . F . The oxygen effect and reoxygenation. In: Excerpta Medica, International Congress Series No. 353, Vol. 5, pp. 13(~140. Surgery, Radiotherapy, and Chemotherapy of Cancer (XI International Cancer Congress), 1974. 11 Kallman, R. F. and Rockwell, S. Effects of radiation on animal tumor models. In: Cancer: A Comprehensive Treatise, Vol. 6, pp. 225-279. Editor: F. F. Becker. Plenum Press, New York, 1977. 12 Kummermehr, J., Fink, R., Preuss-Bayer, G. and Trott, K.-R. Reoxygenierung in einem transplantablen Fibrosarkom der Maus. Strahlentherapie 157: 272-276, 1981. 13 Martin, D. F., Rockwell, S. and Fischer, J.J. Development of an in vitro assay for the survival of cells suspended from BA1112 rat sarcomas. Eur. J. Cancer Clin. Oncol. 19: 791797, 1983. 14 McNally, N. J., Denekamp, J., Sheldon, P., Flockhart, I. R. and Stewart, F. A. Radiosensitization by misonidazole (Ro-07-0582). The importance of timing and tumor concentration of sensitizer. Radiat. Res. 73:568 580, 1978. 15 McNally, N. J. and Sheldon, P.W. The effect of radiation on tumour growth delay, cell survival, and cure of the animal using a single tumour system. Br. J. Radiol. 50: 321-328, 1977. 16 Moulder, J. E., Fischer, J. J. and Milardo, R. Time-dose relationships for the cure of an experimental rat tumor with fractionated radiation. Int. J. Radiat. Oncol. Biol. Phys. 1: 431-438, 1976. 17 Moulder, J. E. and Martin, D . F . Hypoxic fraction determinations in the BA1112 rat sarcoma: variations within and among assay techniques. Radiat. Res. 99, in press, 1984. 18 Moulder, J. E. and Rockwell, S. Hypoxic fractions of solid tumors: experimental techniques, methods of analysis, and a survey of existing data. Int. J. Radiat. Oncol. Biol. Phys. 10, in press, 1984. 19 Reinhold, H.S. Quantitative evaluation of the radiosensitivity of cells of a transplantable rhabdomyosarcoma in the rat. Eur. J. Cancer 2: 33-42, 1966. 20 Sheldon, P. W. and Hill, S.A. Further investigations of the effect of the hypoxic cell radiosensitizer Ro-07-0582 on local control of a mouse tumour. Br. J. Cancer 36: 198~05, 1977. 21 Shipley, W. U., Stanley, J. A., Courtenay, V. D. and Field, S.B. Repair of radiation damage in Lewis lung carcinoma cells following in situ treatment with fast neutrons and gamma-rays. Cancer Res. 35:932 938, 1975. 22 Siemann, D . W . Tumour size: a factor influencing the isoeffect analysis of tumour response to combined modalities. Br. J. Cancer 41 (Suppl. IV): 294~298, 1980. 23 Stanley, J. A., Shipley, W. U. and Steel, G.G. Influence of tumor size on hypoxic fraction and therapeutic sensitivity of Lewis lung tumour. Br. J. Cancer 36:105 113, 1977. 24 Van Putten, L. M. and Kallman, R.F. Oxygenation status of a transplantable tumor during fractionated radiation therapy. J. Natl. Cancer Inst. 40: 441-451, 1968.