Radiotherapy and Oncology, 25 (1992) 251-260 © 1992 Elsevier Science Publishers B.V. All rights reserved. 0167-8140/92/$05.00
251
RADION 01070
Clinical implications of heterogeneity of tumor response to radiation therapy Herman
Suit, S t e v e n S k a t e s , A l p h o n s e T a g h i a n , P a u l O k u n i e f f a n d J i m m y T. E f i r d
Department of Radiation Oncology, Massachusetts General Hospital, Harvard Medical School, Boston, MA, USA
(Received 13 January 1992, revision received 15 June 1992, accepted 2 July 1992)
Key words: Heterogeneity; Radiation sensitivity; Dose response curve; Gamma factor; SF2
Summary Heterogeneity of response of tumor tissue to radiation clearly exists. Major parameters include histopathologic type, size (number of tumor rescue units (TRUs)), hemoglobin concentration, cell proliferation kinetics and immune rejection reaction by host. Further, normal and presumably tumor tissue response is altered in certain genetic diseases, e.g. ataxia telanglectasia. Any assessment of response of tumor tissue to a new treatment method or the testing of a new clinical response predictor is optimally based upon a narrow strata, viz., uniform with respect to known parameters of response, e.g. size, histological type. Even among tumors of such a clinically defined narrow strata, there will be residual heterogeneity with respect to inherent cellular radiation sensitivity, distributions of pO2, (SH), cell proliferation etc. The value of a response predictor of an individual tumor will be determined by the heterogeneity of values for these and or other characteristics and by the coefficient of variation (CV) of the measured values of the individual parameters. Heterogeneity of one or more parameters of response is reflected in the slope of the dose response curve for local control, viz. the greater the heterogeneity the less steep the slope. To examine for this effect, the slope of dose response curves for control of model tumors of 10s tumor rescue units (TRU) and the SF 2 = 0.5 (survival fraction after a single dose of 2 Gy) has been used to assess the impact of inter- and intra-tumoral variation of SF 2 on slope, defined as 750 values. The 750 is the increase in local control expressed in percent points for a one percentage increment in dose, at the mid-point on the dose-response curve. The )'50 was 6.5 for CV = 0.0. For inter-tumoral CVs of 10%, 2 0 ~ and 40%, the 750 rapidly decreased to 2.4, 1.3 and 0.7. Intra-tumoral variation was less important, viz., for CVs of 10%, 20%, and 40% the V50 values were reduced to 5.3, 3.8 and 2.2. Combining inter- and intra-tumoral variation reduced the 750 only slightly below that for inter-tumoral variation alone. For example, were the CV 10% for inter- and intra-tumoral variation, the 750 would be 2.1 as compared to 2.4 for inter-tumoral variation alone. The number of TRUs also affects slope, viz. 750 increased from 1 to 9.7 as the TRU number increased from 101 to 1012. However, the number of TRUs within a specified T stage would be expected to vary over a rather limited range, e.g. ~< a factor of 101-2. Accordingly, the effect of heterogeneity with respect to TRU numbers would affect 750 to a lesser degree than the probable heterogeneity of cellular radiation sensitivity. The CVs for response of tumor and normal tissue in rodents (TCDs0 of independent tumor systems or LDs0 for different strains of mice) were in the range of 9-20%, i.e. less than found for SF 2 of human tumor cells as determined in vitro, 20-50%. Were the 750 for a narrow strata of human tumors to be ,,~2, as judged likely, then the CV of radiation sensitivity of cells in vivo would be ~< 10-15%, a value comparable with that found for independent tissue systems.
Introduction Heterogeneity of r e s p o n s e of h u m a n t u m o r s to radiation clearly exists. T h e radiation oncologist's concerns are: (1) the extent o f that heterogeneity; (2) the k n o w n
and potentially i m p o r t a n t p a r a m e t e r s which determine that heterogeneity; ( 3 ) t h e i m p a c t o f heterogeneity o f one or m o r e o f the p a r a m e t e r s o f t r e a t m e n t r e s p o n s e on o u t c o m e ; and ( 4 ) t h e capacity to determine the values for the radiation sensitivity p a r a m e t e r s in the individ-
Address for correspondence: Dr. H. Suit, Department of Radiation Oncology, Massachusetts General Hospital, Harvard Medical School, Boston, MA 02114, USA.
252 ual patient and, hence, know where the individual tumor fits in the distribution of radiation sensitivity values. This consideration of the impact of heterogeneity in cellular radiation sensitivity will be based upon the endpoint of local control, as the concerns of clinical radiation oncology are directed almost entirely to that endpoint. Further, it is the only one for which there is even a modicum of quantitative clinical data. Known parameters of heterogeneity of radiation response Tumor response
There is manifest heterogeneity of tumor response in terms of the dose required to achieve a specified probability of long term local control for human tumors of the different histological types. For example, the radiation doses which have a high likelihood of achieving local control of seminoma, Hodgkin's disease, squamous cell carcinoma, and giioblastoma multiforme are 30, 40, 65 and > 80 Gy for radiation given at 1.82.0 Gy/fraction for 5 treatment sessions/week. Additionally, for each histological type, the probability of local control is quite dependent on the size of tumor at irradiation, viz. the number of tumor rescue units 1 (TRU). This is reflected in the fact that for a given dose, TCP (tumor control probability) decreases with increasing tumor size and TCDp (dose which achieves tumor control probability p) increases with size [29]. Tumor cell proliferation kinetics vary widely among tumors which are similar histologically. Begg et al. [3] reported findings of a Phase III clinical trial of standard or accelerated dose fractionation of squamous cell carcinomas of the head/neck which included the study of Tpot as a predictor of local control. Those tumors with a potential doubling time (/'pot) > 4.6 appeared to experience a higher local control rate when treated at an accelerated dose schedule; Tpot (potential doubling time) was not a predictor for tumors with lower Tpot values. Hemoglobin concentration is another significant determinant of TCP for virtually all tumors investigated [ 7,11,16,19,24,26 ]. Gender is an important determinant of tumor control probability for squamous cell carcinomas of the head/neck [24]. Another clinical parameter of tumor response is the clinical presenta-
tion, as shown by the squamous cell carcinomas of the oral cavity/oropharynx viz. tumors which are necrotic/ ulcerative have a markedly lower probability of local control than do tumors which are non-necrotic [15]. An important clinical factor for non-uniformity between patients is dose heterogeneity across the tumor; this is responsible for some of the local and marginal failures. Additional factors which have been studied, particularly in laboratory systems, and are judged to be important determinants of the tumor lethal response include: distributions of inherent cellular radiation sensitivities2; in vivo radiation sensitivity of cells as affected by distributions of pO2 (SH), and other metabolites; cellular capacity to repair radiation damage (kinetics, completeness and fidelity); cell age density distributions; cell age response functions; cell proliferation kinetics; immune rejection reaction by host against tumor; extent of loss of tumor clonogens by exfoliation from the surface or into the vascular spaces; non-specific host effects against the tumor, e.g. poor blood flow through certain of the tumor capillaries with resultant micro-infarcts, etc. Normal tissue response
There is also heterogeneity of radiation response of normal tissues. Clinical experience has shown that patients with auto-immune disease, previously traumatized tissues, tissues at poorly vascularized sites (e.g. foot) and tissues of patients with certain genetic diseases respond to radiation excessively. There is now evidence from four hospitals which demonstrates that the normal tissues of patients with ataxia telangiectasia (AT) exhibit an enormously enhanced response to radiation [1,8,17,25]. This was the first genetic disease with a known associated abnormal sensitivity to x-radiation. Two reports describe patients who developed fatal reactions at dose levels ,,~ 30 Gy [8,25]. Hart et al. [ 17] reported in 1986 that an 11-year-old boy with medulloblastoma and AT was treated by fractionated radiation using their standard fraction number but only one-third of the normal dose per fraction, hence the total dose was one-third of the usual dose. They based the dose reduction upon the greatly increased radiation sensitivity of the normal bone marrow cells determined for that individual patient. The tumor regressed com-
1 T R U = a tumor cell which is not killed by radiation, survives in the micrometabolic milieu of the irradiated tissue and proceeds to produce a continuously expanding progeny, viz. a regrowth of tumor. 2 The parameters of cellular sensitivity most commonly used in studies related to clinical radiation therapy are SF 2 [9,14], MID or mean inactivation dose [ 13], and the 0t and fl of the linear quadratic model [ 10]. These are favored by most workers as they are judged to be the most relevant to clinical radiation therapy where radiation is commonly administered in small doses per fraction, viz. 1.2-3 Gy. Inherent radiation sensitivity usually refers to sensitivity as determined by in vitro assays, where metabolic conditions, which are known to affect sensitivity, are defined and controlled.
253 pletely and the acute and late reactions of the normal tissues were approximately those which would have been seen in regular pediatric cancer patients following full dose treatment. He died at 3 years following treatment, but with control of the medulloblastoma and no evidence of radiation damage to the CNS (R. Evans, personal communication, 1991). Deschavanne et al. [ 10] presented results of measurements of the MID (mean inactivation dose) for fibroblasts from normal individuals and patients with a variety of genetic diseases. They found that a number of genetic diseases are associated with an increased radiation sensitivity of the patient's fibroblasts when assayed in vitro: e.g. Huntington's chorea, Cockaynes syndrome, 5 oxo-prolinuria, Gardner's syndrome, Fanconi's anemia. Importantly, for certain of these diseases, individuals who appear to be normal clinically but are, in fact, heterozygous for the disease exhibit an increased radiation sensitivity, e.g. AT, 5-oxo-prolinuria. Their sensitivity is intermediate between that seen in patients with the full-blown disease (homozygous) and normal individuals. The distribution of sensitivities for the heterozygotes tends to lie within that of the sensitive end of the range for normals; that is, there is not a distinct or separate range of sensitivities which is between that for the homozygotes and the normals. Although not well established in quantitative terms, there is almost assuredly some variability of radiation response due to genetic heterogeneity among patients who have no known genetic disease. Estimates of the frequency of heterozygosity for AT in patients with breast carcinoma have been ~ 8 ~ [23,32]. The presumption that the tumor developing in a genetically determined radiation-sensitive person would exhibit an augmented sensitivity seems entirely reasonable, although unproven. This seems to have been true for the patient of Hart et al. [ 17], vide supra. Limited evidence for heterogeneity of the acute response of normal tissues has been published: inherent radiation sensitivity (SF2, MID of D O values) for fibroblasts from apparently normal patients exhibiting acute radiation reaction judged to be unusually severe have been high or on the high side of normal in many of the patients studied [22,28,36,38]. There is, however, one disquieting report that there is no discernable correlation between the in vitro determined SF 2 values for skin fibroblasts and lymphocytes in individual subjects [20], i.e. were the radiation sensitivity of cells of one tissue from an indi-
vidual to be relatively sensitive then the cells from the other tissues would also be expected to be relatively sensitive.
Stratification of patients and study of response predictors The interest of the clinician in current studies of heterogeneity of tumor response lies in the potential of employing physiological, biochemical and or genetic parameters as predictors of response. This would mean that the values determined for the parameter would contribute predictive information beyond that now available. Today's clinician would, of course, know the histological type and grade of tumor, tumor size, clinical presentation, patient age, gender and Karnofsky performance status etc. Hence, the accurate assessment of the power of a parameter as a predictor of tumor or normal tissue response would have to be based on progressively more narrow strata of patients viz. one histopathological type, a narrow range of size, hemoglobin concentration, pattern of clinical presentation etc. If narrow strata are not part of the study design, the heterogeneity among the tumors would necessarily confound the examination for predictive power of the parameter under consideration. The result could be an erroneous conclusion that the tests were of no clinical value and should not be further studied. Multivariate analyses will be, almost certainly, employed in the evaluation of data from any clinical testing of a potential predictor. Even so, there will be important advantages to perform the testing on relatively homogeneous categories of patients, since assumptions upon which multivariate analyses are based can be difficult to verify. Slope of the dose response curve for local control of tumor
Slope of dose-response curve as a measure of response heterogeneity A powerful measure of heterogeneity of response amongst a population of tumors is the slope of the dose-response curve. At any dose level there will be a proportion of local controls and local failures. The observed tumor control probability following treatment to a specified radiation dose will be a function of the true TCP for that dose and the workings of binomial statistics 3. In the absence of heterogeneity among tumors,
3 The underlying TCP and it's steepness is computationally determined by Poisson statistics because of the very large number of TRUs, e.g. > 1000. Both Poisson and Binomial statistics require that the inactivation of the individual T R U s be independent. This latter condition is judged to obtain for mammalian cells in tissues, even though the actual degree of cellular radiation sensitivity may be modified due to cell-cell contact.
254 10'
8'
o t~
E E (.9
6'
4
2
10g TRU
Fig. 1. The relationship of 75o and Log number of TRUs for model tumors characterized by SF2 = 0.5 for all cells in all tumors.
the slope of the dose-response curve will be maximally steep; this will be simply a function of the operation of Poisson statistics on the killing of cells. Any heterogeneity amongst tumors in an assay causes a flattening of the dose-response curve. The greater the heterogeneity the less steep will be the slope. Discussions of the slope of the dose-response curve has been considered by other workers [4,34]. To describe slope in this paper, we employ the parameter ~ factor which is the increase in TCP in percentage points for a 1~o increase in dose [5]. At the mid-range of the dose response curve, the slope may be described by the ~30. For example, were the 73o to be 2 and TCP = 0.5 at a dose of 70 Gy, then an increase in dose by 10~o or to 77 Gy, would push the TCP to ~0.7 4. The concept of the ~3o has the advantage of being a simple descriptor, i.e. it is independent of the choice of mathematical model for tumor cell inactivation. The slope of the dose-response curve for a population of tumors each of which has 108 tumor rescue units and all TRUs are of the same radiation sensitivity would correspond to a ~3o of 6.5. Although not intuitively obvious, the slope of the dose-response curve is dependent upon the number of TRUs. As shown in Fig. 1 s, there is a steep and linear increase in ~3o with log (TRU), viz. the 73o increases from 0.92 to 9.7 at 101 and 1012 TRUs, respectively. In an earlier report, we analyzed the slope estimates published in three reviews of dose-response results for local control of human tumors [31]. There were 41 separate estimates of slopes, almost entirely derived
from retrospective analyses. The median values for the ~3o was judged to be ,~ 2; the range was < 1 to ~ 7. There can not be attached great importance to the value of 2 derived from that analysis because the data bases for the various 73o estimates were of necessity generated from clinical practice which naturally utilized quite narrow ranges of doses and TCPs. Further, there was virtually certain to have been substantial heterogeneity in the tumor/patient populations. The difference in the ~3o of ~ 6.5 (a reasonable value for human tumors of a specified size, say, 108 TRUs, all of the same radiation sensitivity) and g 2 is judged to be a reflection of the heterogeneity of the tumors in clinical studies.
Measurement of slope of the dose-response curve Most reports of experimental studies of dose-response relationships describe results in terms of a single point on the dose-response curve, viz. the TCDso or the TCD37 (the radiation dose which achieves local control in 50~o or 37~o of the irradiated tumors). Slopes of those curves are infrequently defined because of the associated wide uncertainty bands [30]. D o s e response assays are planned to obtain reliable estimates of the mid-point or of the slope, but rarely both. Good estimates of the former are far easier to generate and have generally been judged to be of the greater interest. The slope of the dose-response curve is difficult to measure with high precision as the assay needs to be based upon substantial numbers of tumors assigned to several dose levels which yield TCPs at the extremes of the dose-response curve, viz. ~10.8 [30]. In addition, there has to be provided a good means for censoring the data for losses due to distant metastasis, intercurrent disease or lost to follow-up. To illustrate the difficulty in defining the slope where conditions for data generation and collection are near optimal, Table I is presented [30]. This shows results of four independent dose response assays for local control of the MCa IV mammary carcinoma. These were 3rd generation isotransplants of the spontaneous mouse mammary carcinoma MCa IV, growing in the right leg of C3H/Sed mice and irradiated by a single dose under conditions of clamp hypoxia on the day that the mean diameter reached 8 mm ( ~ 250 #1). Importantly there is essentially no immune rejection reaction by the C3H / Sed mice against the MCa IV tumor. Thus, this curve is based upon a tumor system with a near minimum of heterogeneity. These rather standard assays were designed prima-
4 The true TCP would be slightly less than 0.7 as the 7 factor does decrease over the range considered, viz. 0.5-0.7. s The y factor of the dose-response curve is not a function of cellular radiation sensitivity, see Eqn. 19 of the Appendix.
255 TABLE I TCDlo, TCD9o, Derived D O and )'so values from 4 successive doseresonse assays for local control of 8 mm MCa IV isotransplants [28]. Assay no.
No. Tumors
1 50 2 46 3 37 4 46 Pooled (1-4) 179
TCD90-TCDlo (Gy)
Do~ (Gy)
750b
7.9 17.4 3.9 28.8
2.5 5.6 1.3 9.3
7.7 3.3 15.4 2.1
12.1
3.9
4.5
Table I is presented in Fig. 2. Under these virtually optimal conditions the slope of the curve corresponds to a 750 of 4.5 (CI95: 3.62, 5.38). This slope for a population of perfectly uniform tumors would serve as an indicator of the number of TRUs in the individual tumors. In the example here, the 750 of 4.5 is consistent with a T R U number of ~ 1055. As the group of tumors was not perfectly uniform, the true value of number of TRUs is larger than the 105.5 value.
Heterogeneity of SF2 and slope of dose-response curve
[CI9s: 3.62, 5.38]
Single dose irradiation, clamp hypoxia. 750 is estimated by the relationship: 0.20 + [((TCDro + TCD4o ) - 1)]. a Do estimated from slope of dose response curve is approximately: [TCDgo - TCD10]/3.1. b 75o derived from differnces between TCDro and TCD40.
rily to determine TCDso and n o t slope values. One measure of the slope is the difference between the TCD9o and the T C D l o , which is the equivalent of 3.1 × Do. As shown, the four values for the derived Dos differ sharply, viz. 1.3, 2.5, 5.6 and 9.3 Gy. These were the experimental results despite the fact that there were 37-50 tumors per assay and the experiment was designed to minimize inter-tumor heterogeneity. When the data from the four separate assays were pooled (179 tumors), the calculated Do was 3.9 Gy, a value consistent with the conventional expectations. Further, 750 values for the four individual curves and that for the pooled data for the four curves are given. These results illustrate the difficulty in determining the slope even in a laboratory study where the investigator has access to all the tumors desired unless the assay is designed for the specific purpose of deriving a slope estimate. The dose-response curve generated from the pooled data of the four independent assays (179 tumors) from o
.95
3750=4-5
2
o
.75
o
1
.5
0 .J -1
.25 o
-2 .05
-3
45
60
50
65
Dose (Gy)
Fig. 2. Dose-response curve for 179 third generation isotransplants (250 mm 3) of MCa IV (a C3H/Sed mouse mammary carcinoma) growing in the right leg and irradiated in a single dose and under conditions of local tissue hypoxia (clamp technique).
In this section, the influence of heterogeneity of cell radiation sensitivity on the slope of dose-response curves is considered. The parameter for radiation sensitivity employed is the SF 2 (the survival fraction after a dose of 2 Gy) and heterogeneity of SF2 is described in terms of the coefficients of variation (CV). Studies of SF2 of cell lines developed from human tumors or for primary cultures of human tumors consistently exhibit CVs in the range of 20-50~o. This is documented in Table II by data from many laboratories and for a representative range of tumor pathologic types. Brock et al. [6] reported that the CVs for SF2 for primary cultures from squamous cell carcinomas of the head/neck region to be: 9 ~ , 23~o and 43~o for multiple measurements on one cell suspension, multiple specimen from a single tumor and samples from independent tumors, respectively. The effect of heterogeneity of SF 2 between tumors and heterogeneity within tumors is illustrated by Figs. 3 and 4. For the former, we consider that each tumor TABLE II Coefficients of variation of SF 2 values. Tumor
No. studies
SF 2
CV
Ref.
SCC cervix SCC H/N SCC H/N ADK ovary STS A D K colon Melanoma SCC cervix ADK Endometrium High grade glioma High grade glioma
52 140 34 15 15 20 21 17 19
0.47 0.32 0.45 0.46 0.29 0.44 0.43 0.27 0.25
38~o 47~o 26~o 33~o 43~o 21~o 41 ~o 51~o 37~o
a b 35, 37
16 21
0.52 0.51
42~o 28~o
2 33
35 21 27 2 2
SCC, squamous ceU carcinoma; ADK, adenocarcinoma; STS, soff tissue sarcoma. a West, C., unpubHshed dma, 1991. b Brock, W., unpubhshed data, 1991.
256
M=IO 8
8"
SF2=o~O
7.
c~=o~
w ~ , , ~ SF2
6" ~
Inlrattmxx 5-
Inn~un~'~
~ 4
i
0
0
i
i
i
i
10
20
30
40
Coe~ent of Vat.on (%) Fig. 3. Curves demonstrating the relationship between )'50 and coefficient of variation of SF 2 value for inter- and intra-tumoral variation in SF 2 in model tumors of 10s TRUs and SF 2 = 0.5.
within a population of tumors is homogeneous with respect to SF2, but that there is heterogeneity between the tumors for SF2. Intra-tumoral heterogeneity means that within an individual tumor there is variation in SF 2 values, but that all tumors have exactly the same intratumoral distribution of SF 2 values. In all of the calculations made for Figs. 3 and 4, the distribution of values for a particular parameter are defined as logitnormal. As shown by Fig. 3, inter-tumor variation in SF2 (no intra-tumoral heterogeneity) has a much more dramatic impact on the slope than does intra-tumoral variation (no inter-tumoral heterogeneity). For a model tumor of 108 TRUs (SF2 = 0.5 and the CV = 0.0) the Yso is 6.5. As the CV for inter-tumoral variation alone in SF2 is increased from 0~o to 10~'o, 2 0 ~ and then to 40~o, the 750 decreases rapidly from 6.5 to 2.4 to 1.3 and to 0.7, respectively. In contrast were the variation only intratumoral, the 7so would decrease from 6.5 to only 5.3 to 3.8 and to 2.2 respectively6. The super-imposition of the intra-tumoral variation onto the inter-tumoral heterogeneity has little effect on the slope of the doseresponse curve. For example, the 2'50would be reduced from 6.5 to 2.4 were the CV for SF2 inter-tumoral variation to be increased from zero to 10~o; if additionally, there were a CV of 10~o for intra-tumoral variation, the ~5o would only be decreased further from 2.4 to 2.1. The drastic flattening of the dose response curve with progressively higher CVs for inter-tumoral heterogeneity is illustrated in Fig. 4, which displays the 7 factor vs. the tumor control probability (TCP). Although the dose-response curve is steep at the mid6 The formulae used in these calculations are given in the Appendix.
0
0.0
i
i
i
i
i
0.2
0.4
0.6
0.8
1.0
TumorConlrolProbability Fig. 4. Curves showing the relationships between the y factor and tumor control probability for model tumors of 108 TRUs and SF 2 = 0.5. The coefficients of variation for the SF2s are set at 0%, 10% and 20% for inter- and intra-tumoral variation in SF 2. For CV = 0% the inter- and intra-tumoral curves coincide.
portion for CV = 0.0, the 7 factor decreases very rapidly at low and high TCPs. Further, at CVs of ~>20~ the curve has a very shallow slope throughout the range of TCP from 0.1-0.9. There will be some degree of inter- and intra-tumoral variation in SF 2 values in a population of spontaneous tumors. Although intra-tumoral variation in SF2 affects the slope modestly relative to inter-tumoral variation, the TCDso is quite sensitive to the former. Sample calculations of TCDso are presented in Table III. The TCDso was 54.2 Gy for CV = 0.0 and SF2 -- 0.5. The TCDso increases only to 54.6 Gy for CV of 10~o for inter-tumoral variation. However, the TCDso is 63.2 Gy for an intra-tumoral CV of 10~o. This is due to the presence of some quite radiation resistant tumor cells in every tumor due to the intra-tumoral heterogeneity. Allowing the CV of SF 2 for inter- and intra-tumoral variation to be 10~, each increases the TCD5o to only 63.9 Gy. The proportion of relatively resistant cells increases rapidly with the CV for intra-tumoral SF 2. This is illustrated further by the powerful effect of setting the CV for intra-tumoral variation to 20 ~o: the TCDso increases to 113 Gy, while a similar increment in CV for inter-tumoral variation produces minimal change, viz. only to 55.3 Gy. The implication of these computations is that there is unlikely to be a large CV for intratumoral variation in SF2 values in vivo. To iterate, the CV of SF2 for inter-tumoral variation affects slope and the CV of SF2 for intra-tumoral variation primarily affects the TCDs0.
257 TABLE III
OCI/UTSCC
TCDs0 values for model tumors of 108 TRU and SF2 = 0.5 as affected by CV of SF2.
TeD 5 0 DATA
1 0.8
TCDs0 [Gy] 54.2 54.6 63.2 63.9 55.3 113 117
Inter-tumoral CV
Intra-tumoral CV
yo
%
0 10 0 10 20 0 20
0 0 10 10 0 20 20
kI.
d
,,
%~ o/Y
0.2
:" ~
Tumor
o OCI M Ca - - ~ - - UT M Ca .... ~---- UT sarcoma
CV (%~ 12.8 10.7 21.9 i
50
60
70
80
9O
TCD5o (Gy)
7 m
6
E E ¢~
o
o ~ ,. ,,
40
The few studies in the literature of the response o f ind e p e n d e n t tissue systems reveal CVs o f the order o f ,,~ 10~o. In Fig. 6, the cumulative TCDso values deter-
8 TRU = 10 (_+CV) ~ , SF 2 = 0.5 CV of SF 2 = (P/o ....... CV of S F2 = 10%
.
0
CV of response of independent tissue systems
5
/
0.4
Heterogeneity o f n u m b e r of T R U s will also result in a flattening o f the d o s e - r e s p o n s e curve. The change in Yso with CV o f T R U for tumors of 108 is presented in Fig. 5 for tumors with CVs o f 0~o and 10~o for S F 2 values. This assumes a logit-normal distribution of T R U s as might be expected in tumors growing exponentially. CVs for inter-tumoral variation in T R U number must be substantially greater than variation in SF2 values to modify the 75o to an important degree. Consider that the 75o would vary only from 6.5 to 5.0 for tumors varying in T R U s from 108 d o w n to 106, a factor o f 100.
,
~ 0.6-
~
Fig. 6. Cumulative TCD5o values for three tumor categories which were irradiated at the Ontario Cancer Institute or at the University of Texas Cancer Center [18]. mined at the Ontario Cancer Institute are shown for a series o f 8 spontaneous m a m m a r y carcinomas [18]. T h e tumors were first generation transplants in syngenic mice. They were 8 m m in diameter at irradiation, which was given as single doses and under conditions o f clamp hypoxia. This plot indicates the shape and position of the d o s e - r e s p o n s e curve for first generation iso-transplants which would be expected for spontaneous m a m m a r y carcinomas as they might appear in a population of C3H mice. The Yso for the resultant curve is 2.2 and the CV is 12.8~o. T h e ysoS for the similarly derived curves at the University of Texas M . D . Anderson Hospital [18] for 4 m a m m a r y carcinomas and 5 sarcomas (non-immunogenic) are 2.5 and 2.0 respectively; the CVs are 10.7 and 2 1 . 9 ~ . These measurements are also o f interest in providing data on the relative radiation sensitivity o f spontaneous murine m a m m a r y adenocarcinomas and fibrosarcomas. The TCDsos were 56, 54 and 67 G y for the m a m m a r y carcinomas and the fibrosarcomas series, respectively.
LDs0/30Values
3 o
2
~
lor 9 Strains
of Mice
Yuhas and Storer, 1969 o
1
0.8 -
0.6-
o
50
1so CV of TRU (%)
Fig. 5. Graphic display of the relationship between Yso and coefficient of variation of number of TRUs, using a logit-normal probability distribution and a median number for TRUs of 108 for tumor populations with CVs of 0~ or 10~o for inter-tumoral variation in SF 2 values. A CV of 100~ would correspond to 63~o of the TRU numbers lying in the range from 5 x 10 7 tO 2 X 108, viz. less than a range of a factor of 10.
0.4 ._ >~
/ /
/
median=7.08 Gy = . Oo CV=8.8%
o
"B 0.2. E 0
i 6.5
i 7
~ 7.5
i 8
i 8,5
LDso(Gy)
Fig. 7. Cumulativedistribution of LDso/3o values for 9 strains of mice irradiated at Bar Harbor Laboratories [39].
258 Figure 7 is a plot of the cumulative LD50 values for 9 strains of mice as determined at Bar Harbor Laboratories by Yuhas and Storer [39]; the ~5o is 3.4 and the CV is 8.8~o. The CVs for these few tissue systems in vivo are smaller than the CVs obtained for determination of S F 2 values for tumor cells in vitro. The observed 750 values for the experimental tumor systems are only marginally larger than the estimated 75o for a narrow strata of human tumors of ~ 2 [31 ]. Were the true value for the 7so for a narrow strata of human tumors to be ~ 2, as judged likely, then the CV of radiation sensitivity of cells in vivo would be expected to be ~
251
RADION 01070
Clinical implications of heterogeneity of tumor response to radiation therapy Herman
Suit, S t e v e n S k a t e s , A l p h o n s e T a g h i a n , P a u l O k u n i e f f a n d J i m m y T. E f i r d
Department of Radiation Oncology, Massachusetts General Hospital, Harvard Medical School, Boston, MA, USA
(Received 13 January 1992, revision received 15 June 1992, accepted 2 July 1992)
Key words: Heterogeneity; Radiation sensitivity; Dose response curve; Gamma factor; SF2
Summary Heterogeneity of response of tumor tissue to radiation clearly exists. Major parameters include histopathologic type, size (number of tumor rescue units (TRUs)), hemoglobin concentration, cell proliferation kinetics and immune rejection reaction by host. Further, normal and presumably tumor tissue response is altered in certain genetic diseases, e.g. ataxia telanglectasia. Any assessment of response of tumor tissue to a new treatment method or the testing of a new clinical response predictor is optimally based upon a narrow strata, viz., uniform with respect to known parameters of response, e.g. size, histological type. Even among tumors of such a clinically defined narrow strata, there will be residual heterogeneity with respect to inherent cellular radiation sensitivity, distributions of pO2, (SH), cell proliferation etc. The value of a response predictor of an individual tumor will be determined by the heterogeneity of values for these and or other characteristics and by the coefficient of variation (CV) of the measured values of the individual parameters. Heterogeneity of one or more parameters of response is reflected in the slope of the dose response curve for local control, viz. the greater the heterogeneity the less steep the slope. To examine for this effect, the slope of dose response curves for control of model tumors of 10s tumor rescue units (TRU) and the SF 2 = 0.5 (survival fraction after a single dose of 2 Gy) has been used to assess the impact of inter- and intra-tumoral variation of SF 2 on slope, defined as 750 values. The 750 is the increase in local control expressed in percent points for a one percentage increment in dose, at the mid-point on the dose-response curve. The )'50 was 6.5 for CV = 0.0. For inter-tumoral CVs of 10%, 2 0 ~ and 40%, the 750 rapidly decreased to 2.4, 1.3 and 0.7. Intra-tumoral variation was less important, viz., for CVs of 10%, 20%, and 40% the V50 values were reduced to 5.3, 3.8 and 2.2. Combining inter- and intra-tumoral variation reduced the 750 only slightly below that for inter-tumoral variation alone. For example, were the CV 10% for inter- and intra-tumoral variation, the 750 would be 2.1 as compared to 2.4 for inter-tumoral variation alone. The number of TRUs also affects slope, viz. 750 increased from 1 to 9.7 as the TRU number increased from 101 to 1012. However, the number of TRUs within a specified T stage would be expected to vary over a rather limited range, e.g. ~< a factor of 101-2. Accordingly, the effect of heterogeneity with respect to TRU numbers would affect 750 to a lesser degree than the probable heterogeneity of cellular radiation sensitivity. The CVs for response of tumor and normal tissue in rodents (TCDs0 of independent tumor systems or LDs0 for different strains of mice) were in the range of 9-20%, i.e. less than found for SF 2 of human tumor cells as determined in vitro, 20-50%. Were the 750 for a narrow strata of human tumors to be ,,~2, as judged likely, then the CV of radiation sensitivity of cells in vivo would be ~< 10-15%, a value comparable with that found for independent tissue systems.
Introduction Heterogeneity of r e s p o n s e of h u m a n t u m o r s to radiation clearly exists. T h e radiation oncologist's concerns are: (1) the extent o f that heterogeneity; (2) the k n o w n
and potentially i m p o r t a n t p a r a m e t e r s which determine that heterogeneity; ( 3 ) t h e i m p a c t o f heterogeneity o f one or m o r e o f the p a r a m e t e r s o f t r e a t m e n t r e s p o n s e on o u t c o m e ; and ( 4 ) t h e capacity to determine the values for the radiation sensitivity p a r a m e t e r s in the individ-
Address for correspondence: Dr. H. Suit, Department of Radiation Oncology, Massachusetts General Hospital, Harvard Medical School, Boston, MA 02114, USA.
252 ual patient and, hence, know where the individual tumor fits in the distribution of radiation sensitivity values. This consideration of the impact of heterogeneity in cellular radiation sensitivity will be based upon the endpoint of local control, as the concerns of clinical radiation oncology are directed almost entirely to that endpoint. Further, it is the only one for which there is even a modicum of quantitative clinical data. Known parameters of heterogeneity of radiation response Tumor response
There is manifest heterogeneity of tumor response in terms of the dose required to achieve a specified probability of long term local control for human tumors of the different histological types. For example, the radiation doses which have a high likelihood of achieving local control of seminoma, Hodgkin's disease, squamous cell carcinoma, and giioblastoma multiforme are 30, 40, 65 and > 80 Gy for radiation given at 1.82.0 Gy/fraction for 5 treatment sessions/week. Additionally, for each histological type, the probability of local control is quite dependent on the size of tumor at irradiation, viz. the number of tumor rescue units 1 (TRU). This is reflected in the fact that for a given dose, TCP (tumor control probability) decreases with increasing tumor size and TCDp (dose which achieves tumor control probability p) increases with size [29]. Tumor cell proliferation kinetics vary widely among tumors which are similar histologically. Begg et al. [3] reported findings of a Phase III clinical trial of standard or accelerated dose fractionation of squamous cell carcinomas of the head/neck which included the study of Tpot as a predictor of local control. Those tumors with a potential doubling time (/'pot) > 4.6 appeared to experience a higher local control rate when treated at an accelerated dose schedule; Tpot (potential doubling time) was not a predictor for tumors with lower Tpot values. Hemoglobin concentration is another significant determinant of TCP for virtually all tumors investigated [ 7,11,16,19,24,26 ]. Gender is an important determinant of tumor control probability for squamous cell carcinomas of the head/neck [24]. Another clinical parameter of tumor response is the clinical presenta-
tion, as shown by the squamous cell carcinomas of the oral cavity/oropharynx viz. tumors which are necrotic/ ulcerative have a markedly lower probability of local control than do tumors which are non-necrotic [15]. An important clinical factor for non-uniformity between patients is dose heterogeneity across the tumor; this is responsible for some of the local and marginal failures. Additional factors which have been studied, particularly in laboratory systems, and are judged to be important determinants of the tumor lethal response include: distributions of inherent cellular radiation sensitivities2; in vivo radiation sensitivity of cells as affected by distributions of pO2 (SH), and other metabolites; cellular capacity to repair radiation damage (kinetics, completeness and fidelity); cell age density distributions; cell age response functions; cell proliferation kinetics; immune rejection reaction by host against tumor; extent of loss of tumor clonogens by exfoliation from the surface or into the vascular spaces; non-specific host effects against the tumor, e.g. poor blood flow through certain of the tumor capillaries with resultant micro-infarcts, etc. Normal tissue response
There is also heterogeneity of radiation response of normal tissues. Clinical experience has shown that patients with auto-immune disease, previously traumatized tissues, tissues at poorly vascularized sites (e.g. foot) and tissues of patients with certain genetic diseases respond to radiation excessively. There is now evidence from four hospitals which demonstrates that the normal tissues of patients with ataxia telangiectasia (AT) exhibit an enormously enhanced response to radiation [1,8,17,25]. This was the first genetic disease with a known associated abnormal sensitivity to x-radiation. Two reports describe patients who developed fatal reactions at dose levels ,,~ 30 Gy [8,25]. Hart et al. [ 17] reported in 1986 that an 11-year-old boy with medulloblastoma and AT was treated by fractionated radiation using their standard fraction number but only one-third of the normal dose per fraction, hence the total dose was one-third of the usual dose. They based the dose reduction upon the greatly increased radiation sensitivity of the normal bone marrow cells determined for that individual patient. The tumor regressed com-
1 T R U = a tumor cell which is not killed by radiation, survives in the micrometabolic milieu of the irradiated tissue and proceeds to produce a continuously expanding progeny, viz. a regrowth of tumor. 2 The parameters of cellular sensitivity most commonly used in studies related to clinical radiation therapy are SF 2 [9,14], MID or mean inactivation dose [ 13], and the 0t and fl of the linear quadratic model [ 10]. These are favored by most workers as they are judged to be the most relevant to clinical radiation therapy where radiation is commonly administered in small doses per fraction, viz. 1.2-3 Gy. Inherent radiation sensitivity usually refers to sensitivity as determined by in vitro assays, where metabolic conditions, which are known to affect sensitivity, are defined and controlled.
253 pletely and the acute and late reactions of the normal tissues were approximately those which would have been seen in regular pediatric cancer patients following full dose treatment. He died at 3 years following treatment, but with control of the medulloblastoma and no evidence of radiation damage to the CNS (R. Evans, personal communication, 1991). Deschavanne et al. [ 10] presented results of measurements of the MID (mean inactivation dose) for fibroblasts from normal individuals and patients with a variety of genetic diseases. They found that a number of genetic diseases are associated with an increased radiation sensitivity of the patient's fibroblasts when assayed in vitro: e.g. Huntington's chorea, Cockaynes syndrome, 5 oxo-prolinuria, Gardner's syndrome, Fanconi's anemia. Importantly, for certain of these diseases, individuals who appear to be normal clinically but are, in fact, heterozygous for the disease exhibit an increased radiation sensitivity, e.g. AT, 5-oxo-prolinuria. Their sensitivity is intermediate between that seen in patients with the full-blown disease (homozygous) and normal individuals. The distribution of sensitivities for the heterozygotes tends to lie within that of the sensitive end of the range for normals; that is, there is not a distinct or separate range of sensitivities which is between that for the homozygotes and the normals. Although not well established in quantitative terms, there is almost assuredly some variability of radiation response due to genetic heterogeneity among patients who have no known genetic disease. Estimates of the frequency of heterozygosity for AT in patients with breast carcinoma have been ~ 8 ~ [23,32]. The presumption that the tumor developing in a genetically determined radiation-sensitive person would exhibit an augmented sensitivity seems entirely reasonable, although unproven. This seems to have been true for the patient of Hart et al. [ 17], vide supra. Limited evidence for heterogeneity of the acute response of normal tissues has been published: inherent radiation sensitivity (SF2, MID of D O values) for fibroblasts from apparently normal patients exhibiting acute radiation reaction judged to be unusually severe have been high or on the high side of normal in many of the patients studied [22,28,36,38]. There is, however, one disquieting report that there is no discernable correlation between the in vitro determined SF 2 values for skin fibroblasts and lymphocytes in individual subjects [20], i.e. were the radiation sensitivity of cells of one tissue from an indi-
vidual to be relatively sensitive then the cells from the other tissues would also be expected to be relatively sensitive.
Stratification of patients and study of response predictors The interest of the clinician in current studies of heterogeneity of tumor response lies in the potential of employing physiological, biochemical and or genetic parameters as predictors of response. This would mean that the values determined for the parameter would contribute predictive information beyond that now available. Today's clinician would, of course, know the histological type and grade of tumor, tumor size, clinical presentation, patient age, gender and Karnofsky performance status etc. Hence, the accurate assessment of the power of a parameter as a predictor of tumor or normal tissue response would have to be based on progressively more narrow strata of patients viz. one histopathological type, a narrow range of size, hemoglobin concentration, pattern of clinical presentation etc. If narrow strata are not part of the study design, the heterogeneity among the tumors would necessarily confound the examination for predictive power of the parameter under consideration. The result could be an erroneous conclusion that the tests were of no clinical value and should not be further studied. Multivariate analyses will be, almost certainly, employed in the evaluation of data from any clinical testing of a potential predictor. Even so, there will be important advantages to perform the testing on relatively homogeneous categories of patients, since assumptions upon which multivariate analyses are based can be difficult to verify. Slope of the dose response curve for local control of tumor
Slope of dose-response curve as a measure of response heterogeneity A powerful measure of heterogeneity of response amongst a population of tumors is the slope of the dose-response curve. At any dose level there will be a proportion of local controls and local failures. The observed tumor control probability following treatment to a specified radiation dose will be a function of the true TCP for that dose and the workings of binomial statistics 3. In the absence of heterogeneity among tumors,
3 The underlying TCP and it's steepness is computationally determined by Poisson statistics because of the very large number of TRUs, e.g. > 1000. Both Poisson and Binomial statistics require that the inactivation of the individual T R U s be independent. This latter condition is judged to obtain for mammalian cells in tissues, even though the actual degree of cellular radiation sensitivity may be modified due to cell-cell contact.
254 10'
8'
o t~
E E (.9
6'
4
2
10g TRU
Fig. 1. The relationship of 75o and Log number of TRUs for model tumors characterized by SF2 = 0.5 for all cells in all tumors.
the slope of the dose-response curve will be maximally steep; this will be simply a function of the operation of Poisson statistics on the killing of cells. Any heterogeneity amongst tumors in an assay causes a flattening of the dose-response curve. The greater the heterogeneity the less steep will be the slope. Discussions of the slope of the dose-response curve has been considered by other workers [4,34]. To describe slope in this paper, we employ the parameter ~ factor which is the increase in TCP in percentage points for a 1~o increase in dose [5]. At the mid-range of the dose response curve, the slope may be described by the ~30. For example, were the 73o to be 2 and TCP = 0.5 at a dose of 70 Gy, then an increase in dose by 10~o or to 77 Gy, would push the TCP to ~0.7 4. The concept of the ~3o has the advantage of being a simple descriptor, i.e. it is independent of the choice of mathematical model for tumor cell inactivation. The slope of the dose-response curve for a population of tumors each of which has 108 tumor rescue units and all TRUs are of the same radiation sensitivity would correspond to a ~3o of 6.5. Although not intuitively obvious, the slope of the dose-response curve is dependent upon the number of TRUs. As shown in Fig. 1 s, there is a steep and linear increase in ~3o with log (TRU), viz. the 73o increases from 0.92 to 9.7 at 101 and 1012 TRUs, respectively. In an earlier report, we analyzed the slope estimates published in three reviews of dose-response results for local control of human tumors [31]. There were 41 separate estimates of slopes, almost entirely derived
from retrospective analyses. The median values for the ~3o was judged to be ,~ 2; the range was < 1 to ~ 7. There can not be attached great importance to the value of 2 derived from that analysis because the data bases for the various 73o estimates were of necessity generated from clinical practice which naturally utilized quite narrow ranges of doses and TCPs. Further, there was virtually certain to have been substantial heterogeneity in the tumor/patient populations. The difference in the ~3o of ~ 6.5 (a reasonable value for human tumors of a specified size, say, 108 TRUs, all of the same radiation sensitivity) and g 2 is judged to be a reflection of the heterogeneity of the tumors in clinical studies.
Measurement of slope of the dose-response curve Most reports of experimental studies of dose-response relationships describe results in terms of a single point on the dose-response curve, viz. the TCDso or the TCD37 (the radiation dose which achieves local control in 50~o or 37~o of the irradiated tumors). Slopes of those curves are infrequently defined because of the associated wide uncertainty bands [30]. D o s e response assays are planned to obtain reliable estimates of the mid-point or of the slope, but rarely both. Good estimates of the former are far easier to generate and have generally been judged to be of the greater interest. The slope of the dose-response curve is difficult to measure with high precision as the assay needs to be based upon substantial numbers of tumors assigned to several dose levels which yield TCPs at the extremes of the dose-response curve, viz. ~10.8 [30]. In addition, there has to be provided a good means for censoring the data for losses due to distant metastasis, intercurrent disease or lost to follow-up. To illustrate the difficulty in defining the slope where conditions for data generation and collection are near optimal, Table I is presented [30]. This shows results of four independent dose response assays for local control of the MCa IV mammary carcinoma. These were 3rd generation isotransplants of the spontaneous mouse mammary carcinoma MCa IV, growing in the right leg of C3H/Sed mice and irradiated by a single dose under conditions of clamp hypoxia on the day that the mean diameter reached 8 mm ( ~ 250 #1). Importantly there is essentially no immune rejection reaction by the C3H / Sed mice against the MCa IV tumor. Thus, this curve is based upon a tumor system with a near minimum of heterogeneity. These rather standard assays were designed prima-
4 The true TCP would be slightly less than 0.7 as the 7 factor does decrease over the range considered, viz. 0.5-0.7. s The y factor of the dose-response curve is not a function of cellular radiation sensitivity, see Eqn. 19 of the Appendix.
255 TABLE I TCDlo, TCD9o, Derived D O and )'so values from 4 successive doseresonse assays for local control of 8 mm MCa IV isotransplants [28]. Assay no.
No. Tumors
1 50 2 46 3 37 4 46 Pooled (1-4) 179
TCD90-TCDlo (Gy)
Do~ (Gy)
750b
7.9 17.4 3.9 28.8
2.5 5.6 1.3 9.3
7.7 3.3 15.4 2.1
12.1
3.9
4.5
Table I is presented in Fig. 2. Under these virtually optimal conditions the slope of the curve corresponds to a 750 of 4.5 (CI95: 3.62, 5.38). This slope for a population of perfectly uniform tumors would serve as an indicator of the number of TRUs in the individual tumors. In the example here, the 750 of 4.5 is consistent with a T R U number of ~ 1055. As the group of tumors was not perfectly uniform, the true value of number of TRUs is larger than the 105.5 value.
Heterogeneity of SF2 and slope of dose-response curve
[CI9s: 3.62, 5.38]
Single dose irradiation, clamp hypoxia. 750 is estimated by the relationship: 0.20 + [((TCDro + TCD4o ) - 1)]. a Do estimated from slope of dose response curve is approximately: [TCDgo - TCD10]/3.1. b 75o derived from differnces between TCDro and TCD40.
rily to determine TCDso and n o t slope values. One measure of the slope is the difference between the TCD9o and the T C D l o , which is the equivalent of 3.1 × Do. As shown, the four values for the derived Dos differ sharply, viz. 1.3, 2.5, 5.6 and 9.3 Gy. These were the experimental results despite the fact that there were 37-50 tumors per assay and the experiment was designed to minimize inter-tumor heterogeneity. When the data from the four separate assays were pooled (179 tumors), the calculated Do was 3.9 Gy, a value consistent with the conventional expectations. Further, 750 values for the four individual curves and that for the pooled data for the four curves are given. These results illustrate the difficulty in determining the slope even in a laboratory study where the investigator has access to all the tumors desired unless the assay is designed for the specific purpose of deriving a slope estimate. The dose-response curve generated from the pooled data of the four independent assays (179 tumors) from o
.95
3750=4-5
2
o
.75
o
1
.5
0 .J -1
.25 o
-2 .05
-3
45
60
50
65
Dose (Gy)
Fig. 2. Dose-response curve for 179 third generation isotransplants (250 mm 3) of MCa IV (a C3H/Sed mouse mammary carcinoma) growing in the right leg and irradiated in a single dose and under conditions of local tissue hypoxia (clamp technique).
In this section, the influence of heterogeneity of cell radiation sensitivity on the slope of dose-response curves is considered. The parameter for radiation sensitivity employed is the SF 2 (the survival fraction after a dose of 2 Gy) and heterogeneity of SF2 is described in terms of the coefficients of variation (CV). Studies of SF2 of cell lines developed from human tumors or for primary cultures of human tumors consistently exhibit CVs in the range of 20-50~o. This is documented in Table II by data from many laboratories and for a representative range of tumor pathologic types. Brock et al. [6] reported that the CVs for SF2 for primary cultures from squamous cell carcinomas of the head/neck region to be: 9 ~ , 23~o and 43~o for multiple measurements on one cell suspension, multiple specimen from a single tumor and samples from independent tumors, respectively. The effect of heterogeneity of SF 2 between tumors and heterogeneity within tumors is illustrated by Figs. 3 and 4. For the former, we consider that each tumor TABLE II Coefficients of variation of SF 2 values. Tumor
No. studies
SF 2
CV
Ref.
SCC cervix SCC H/N SCC H/N ADK ovary STS A D K colon Melanoma SCC cervix ADK Endometrium High grade glioma High grade glioma
52 140 34 15 15 20 21 17 19
0.47 0.32 0.45 0.46 0.29 0.44 0.43 0.27 0.25
38~o 47~o 26~o 33~o 43~o 21~o 41 ~o 51~o 37~o
a b 35, 37
16 21
0.52 0.51
42~o 28~o
2 33
35 21 27 2 2
SCC, squamous ceU carcinoma; ADK, adenocarcinoma; STS, soff tissue sarcoma. a West, C., unpubHshed dma, 1991. b Brock, W., unpubhshed data, 1991.
256
M=IO 8
8"
SF2=o~O
7.
c~=o~
w ~ , , ~ SF2
6" ~
Inlrattmxx 5-
Inn~un~'~
~ 4
i
0
0
i
i
i
i
10
20
30
40
Coe~ent of Vat.on (%) Fig. 3. Curves demonstrating the relationship between )'50 and coefficient of variation of SF 2 value for inter- and intra-tumoral variation in SF 2 in model tumors of 10s TRUs and SF 2 = 0.5.
within a population of tumors is homogeneous with respect to SF2, but that there is heterogeneity between the tumors for SF2. Intra-tumoral heterogeneity means that within an individual tumor there is variation in SF 2 values, but that all tumors have exactly the same intratumoral distribution of SF 2 values. In all of the calculations made for Figs. 3 and 4, the distribution of values for a particular parameter are defined as logitnormal. As shown by Fig. 3, inter-tumor variation in SF2 (no intra-tumoral heterogeneity) has a much more dramatic impact on the slope than does intra-tumoral variation (no inter-tumoral heterogeneity). For a model tumor of 108 TRUs (SF2 = 0.5 and the CV = 0.0) the Yso is 6.5. As the CV for inter-tumoral variation alone in SF2 is increased from 0~o to 10~'o, 2 0 ~ and then to 40~o, the 750 decreases rapidly from 6.5 to 2.4 to 1.3 and to 0.7, respectively. In contrast were the variation only intratumoral, the 7so would decrease from 6.5 to only 5.3 to 3.8 and to 2.2 respectively6. The super-imposition of the intra-tumoral variation onto the inter-tumoral heterogeneity has little effect on the slope of the doseresponse curve. For example, the 2'50would be reduced from 6.5 to 2.4 were the CV for SF2 inter-tumoral variation to be increased from zero to 10~o; if additionally, there were a CV of 10~o for intra-tumoral variation, the ~5o would only be decreased further from 2.4 to 2.1. The drastic flattening of the dose response curve with progressively higher CVs for inter-tumoral heterogeneity is illustrated in Fig. 4, which displays the 7 factor vs. the tumor control probability (TCP). Although the dose-response curve is steep at the mid6 The formulae used in these calculations are given in the Appendix.
0
0.0
i
i
i
i
i
0.2
0.4
0.6
0.8
1.0
TumorConlrolProbability Fig. 4. Curves showing the relationships between the y factor and tumor control probability for model tumors of 108 TRUs and SF 2 = 0.5. The coefficients of variation for the SF2s are set at 0%, 10% and 20% for inter- and intra-tumoral variation in SF 2. For CV = 0% the inter- and intra-tumoral curves coincide.
portion for CV = 0.0, the 7 factor decreases very rapidly at low and high TCPs. Further, at CVs of ~>20~ the curve has a very shallow slope throughout the range of TCP from 0.1-0.9. There will be some degree of inter- and intra-tumoral variation in SF 2 values in a population of spontaneous tumors. Although intra-tumoral variation in SF2 affects the slope modestly relative to inter-tumoral variation, the TCDso is quite sensitive to the former. Sample calculations of TCDso are presented in Table III. The TCDso was 54.2 Gy for CV = 0.0 and SF2 -- 0.5. The TCDso increases only to 54.6 Gy for CV of 10~o for inter-tumoral variation. However, the TCDso is 63.2 Gy for an intra-tumoral CV of 10~o. This is due to the presence of some quite radiation resistant tumor cells in every tumor due to the intra-tumoral heterogeneity. Allowing the CV of SF 2 for inter- and intra-tumoral variation to be 10~, each increases the TCD5o to only 63.9 Gy. The proportion of relatively resistant cells increases rapidly with the CV for intra-tumoral SF 2. This is illustrated further by the powerful effect of setting the CV for intra-tumoral variation to 20 ~o: the TCDso increases to 113 Gy, while a similar increment in CV for inter-tumoral variation produces minimal change, viz. only to 55.3 Gy. The implication of these computations is that there is unlikely to be a large CV for intratumoral variation in SF2 values in vivo. To iterate, the CV of SF2 for inter-tumoral variation affects slope and the CV of SF2 for intra-tumoral variation primarily affects the TCDs0.
257 TABLE III
OCI/UTSCC
TCDs0 values for model tumors of 108 TRU and SF2 = 0.5 as affected by CV of SF2.
TeD 5 0 DATA
1 0.8
TCDs0 [Gy] 54.2 54.6 63.2 63.9 55.3 113 117
Inter-tumoral CV
Intra-tumoral CV
yo
%
0 10 0 10 20 0 20
0 0 10 10 0 20 20
kI.
d
,,
%~ o/Y
0.2
:" ~
Tumor
o OCI M Ca - - ~ - - UT M Ca .... ~---- UT sarcoma
CV (%~ 12.8 10.7 21.9 i
50
60
70
80
9O
TCD5o (Gy)
7 m
6
E E ¢~
o
o ~ ,. ,,
40
The few studies in the literature of the response o f ind e p e n d e n t tissue systems reveal CVs o f the order o f ,,~ 10~o. In Fig. 6, the cumulative TCDso values deter-
8 TRU = 10 (_+CV) ~ , SF 2 = 0.5 CV of SF 2 = (P/o ....... CV of S F2 = 10%
.
0
CV of response of independent tissue systems
5
/
0.4
Heterogeneity o f n u m b e r of T R U s will also result in a flattening o f the d o s e - r e s p o n s e curve. The change in Yso with CV o f T R U for tumors of 108 is presented in Fig. 5 for tumors with CVs o f 0~o and 10~o for S F 2 values. This assumes a logit-normal distribution of T R U s as might be expected in tumors growing exponentially. CVs for inter-tumoral variation in T R U number must be substantially greater than variation in SF2 values to modify the 75o to an important degree. Consider that the 75o would vary only from 6.5 to 5.0 for tumors varying in T R U s from 108 d o w n to 106, a factor o f 100.
,
~ 0.6-
~
Fig. 6. Cumulative TCD5o values for three tumor categories which were irradiated at the Ontario Cancer Institute or at the University of Texas Cancer Center [18]. mined at the Ontario Cancer Institute are shown for a series o f 8 spontaneous m a m m a r y carcinomas [18]. T h e tumors were first generation transplants in syngenic mice. They were 8 m m in diameter at irradiation, which was given as single doses and under conditions o f clamp hypoxia. This plot indicates the shape and position of the d o s e - r e s p o n s e curve for first generation iso-transplants which would be expected for spontaneous m a m m a r y carcinomas as they might appear in a population of C3H mice. The Yso for the resultant curve is 2.2 and the CV is 12.8~o. T h e ysoS for the similarly derived curves at the University of Texas M . D . Anderson Hospital [18] for 4 m a m m a r y carcinomas and 5 sarcomas (non-immunogenic) are 2.5 and 2.0 respectively; the CVs are 10.7 and 2 1 . 9 ~ . These measurements are also o f interest in providing data on the relative radiation sensitivity o f spontaneous murine m a m m a r y adenocarcinomas and fibrosarcomas. The TCDsos were 56, 54 and 67 G y for the m a m m a r y carcinomas and the fibrosarcomas series, respectively.
LDs0/30Values
3 o
2
~
lor 9 Strains
of Mice
Yuhas and Storer, 1969 o
1
0.8 -
0.6-
o
50
1so CV of TRU (%)
Fig. 5. Graphic display of the relationship between Yso and coefficient of variation of number of TRUs, using a logit-normal probability distribution and a median number for TRUs of 108 for tumor populations with CVs of 0~ or 10~o for inter-tumoral variation in SF 2 values. A CV of 100~ would correspond to 63~o of the TRU numbers lying in the range from 5 x 10 7 tO 2 X 108, viz. less than a range of a factor of 10.
0.4 ._ >~
/ /
/
median=7.08 Gy = . Oo CV=8.8%
o
"B 0.2. E 0
i 6.5
i 7
~ 7.5
i 8
i 8,5
LDso(Gy)
Fig. 7. Cumulativedistribution of LDso/3o values for 9 strains of mice irradiated at Bar Harbor Laboratories [39].
258 Figure 7 is a plot of the cumulative LD50 values for 9 strains of mice as determined at Bar Harbor Laboratories by Yuhas and Storer [39]; the ~5o is 3.4 and the CV is 8.8~o. The CVs for these few tissue systems in vivo are smaller than the CVs obtained for determination of S F 2 values for tumor cells in vitro. The observed 750 values for the experimental tumor systems are only marginally larger than the estimated 75o for a narrow strata of human tumors of ~ 2 [31 ]. Were the true value for the 7so for a narrow strata of human tumors to be ~ 2, as judged likely, then the CV of radiation sensitivity of cells in vivo would be expected to be ~
