Tumor heterogeneity, tumor size, and radioresistance

Inl. J. Radiotim Oncdogy Bid Phys.. Vol. 17, pp. 993-1005 Printed in the U.S.A. All rights reserved.

Copyright

0360-3016/89 $3.00 + .I0 0 1989 Pergamon Press plc

??Original Contribution

TUMOR

HETEROGENEITY,

TUMOR

ROBERT J. YAES, Department

SIZE, AND RADIORESISTANCE

Sc.D., M.D.

of Radiation Medicine, University of Kentucky Medical Center, Lexington, KY 40536-0084

Mutant clonogenic cells, resistant to individual chemotherapeutic agents, are known to play a central role in clinical chemotherapy failure. The possibility that mutant cells, resistant to conventionally fractionated megavoltage photon radiotherapy, exist in human tumors is considered. Applying the mutation theory of Luria and Delbruck to describe the appearance of resistant cells, several conclusions follow: (a) the mean number of resistant cells in a tumor will be determined by the tumor size and the mutation rate; (b) a wide variation in radiosensitivity in tumors of the same histology is expected, because of a large variation in the number of resistant cells that they contain; (c) the presence of a resistant clone will not reduce the tumor-control probability until the tumor becomes sufficiently large; (d) initial response will not be a reliable predictor of long-term control; (e) clonogenic assays may not accurately predict treatment outcomes; (f) the mutation rate may be the most accurate predictor of tumor aggressiveness and resistance to various treatment modalities; (g) tumors with a low mutation rate, which may include seminoma, Hodgkin’s disease and many pediatric tumors would be curable by either chemotherapy or radiation; (h) pleomorphic tumors with a high mutation rate, which may include glioblastoma multiforme, would be difficult to cure by any means. Clinical and experimental evidence is reviewed for the existence of radioresistant cell lines in human and animal tumors, and further experiments are proposed to test this hypothesis. Treatment strategies for targeting radioresistant clones are discussed. Tumor control, Mutation theory, Resistant clones, Luria-Delbruck

INTRODUCTION

model, Neutron therapy.

There is considerable evidence that individual human tumors may each develop from a single transformed cell (47). Often the same biochemical marker or chromosomal abnormality will be present in every cell of a tumor, confirming a unicellular origin (47). There is, however, equally compelling evidence that the stem cell population in many of these same tumors is heterogeneous (3, 10, l&24, 3 1, 33, 35, 36,44,49, 52,69) as, distinct subpopulations differing in such properties as karyotype (29, 60, 6 I), metastatic potential (4, 12, 13, 23, 37, 69), resistance to cytotoxic drugs (64,65), culture morphology (76), doubling time (76), colony forming ability (76), antigenic expression (76), or receptor status (87) can often be cloned from the same tumor. This clonal heterogeneity can be easily explained by the occurrence of mutations in an initially homogeneous stem cell population ( 17, 38). Once we admit that mutations can occur, we must consider the possibility

that they could alter the response to both chemotherapy and radiation. The existence of mutations that confer resistance to individual chemotherapy agents is well established (17, 64, 65) and the nature of the mutations responsible for resistance to some specific agents is known. In the case of methotrexate, a dihydrofolate reductase antagonist, for example, resistance is often conferred by gene amplification (the presence of multiple gene copies) of the dihydrofolate reductase gene (56, 57). In 1943, Luria and Delbruck (38) proposed a simple mathematical model for the appearance of mutations in an asexually reproducing population, to describe the development of phage resistance in bacterial cultures. This model has been applied to the problem of chemotherapy resistance (64) in neoplastic cells by Goldie and Coldman (5, 17, 18, 19, 20) with results that are in qualitative and quantitative agreement with the clinical and experimental data. The appearance of mutant clones, resistant to single and multiple chemotherapeutic agents, provides the best

Preliminary versions of this work were presented at the Meetings of the Radiological Society of North America, Chicago, IL, November 29-December 4, 1987, the Radiation Research Society, Philadelphia, PA, April 16-21, 1988 and the American Society of Therapeutic Radiology and Oncology, New Orleans, LA, October 9-14, 1988. Acknowledgments-The author is grateful to many colleagues for valuable conversations and correspondences and in particular to Yosh Maruyama, M.D. and Justine Yoneda, M.D. for many

discussions concerning the Kentucky Califomium Brachytherapy Program for locally advanced Cervix Cancer. The author is also grateful to Dr. Maruyama for critically reviewing the manuscript and to Barry Bemer, Ph.D. and Steven Gorman, Ph.D. for computational assistance. The author is grateful to Ms. Terry Stuart for preparing the manuscript. This work is supported in part by a small research projects grant from the University of Kentucky Medical Center Research Fund. Accepted for publication 17 May 1989. 993

994

I. J. Radiation Oncology 0 Biology 0 Physics

explanation of the clinical course often observed in chemotherapy treatment, an initial complete or partial response followed by eventual failure and tumor progression (64, 65). It is well known that the long-term control rates with both chemotherapy (64,65) and radiotherapy (14,63) are inversely related to tumor size. This effect is often attributed to the magnitude of the “tumor burden” (the number of neoplastic cells that must be killed) and to host and tumor bed effects such as hypoxia (14). However, in discussing “tumor burden” per se, we are implicitly assuming that the tumor stem cell population is homogeneous, and this may be an oversimplification. If resistant cells are present, they will also contribute to this effect since, as Goldie and Coldman have shown (5, 17), the larger the tumor, the more likely it will be that it contains resistant mutant cells. If mutant cells resistant to both chemotherapy and radiotherapy occur the question arises as to why the clinical effects of their presence have been noted by medical oncologists but not by radiation oncologists. There are essentially two reasons. First, with a few exceptions such as that of Adriamycin cardiotoxicity, cumulative late organ damage which depends on the total dose delivered to an organ, does not usually occur in chemotherapy treatment (53) as in radiotherapy. Thus, the total amount of most chemotherapy agents that can be given is not limited by normal tissue tolerance. As long as one allows sufficient time for normal tissue to recover between treatments, one can, at least in principle, repeat most chemotherapy regimens indefinitely, or at least until disease progression becomes apparent (64,65). If the tumor contains resistant cells, it will eventually become refractory to treatment. Cells that are resistant to specific chemotherapeutic agents, particularly in the case of antimetabolites, can be very resistant. Thus, for some resistant cells, concentrations of the agent may have to be increased hundreds of times to achieve the same proportionate cell kill as for sensitive cells (56, 65). Thus, the presence of even a very small number of tumor cells resistant to an agent can preclude tumor cure with physiologically achievable concentrations of that agent. Indeed, in the Goldie-Coldman model, the presence of a single resistant cell is considered tantamount to treatment failure ( 17, 18). Not surprisingly, then, there are very few malignancies that can be cured by single agent chemotherapy. Multiagent chemotherapy is effective, in many cases, because of the smaller probability that a tumor will contain cells that are simultaneously resistant to multiple non-cross-resistant agents ( 18). On the other hand, radioresistant cells are likely to be only moderately resistant. In most cases, the dose necessary to achieve a given level of cell kill among resistant cells will be greater by only a factor of 2 or 3 over what is necessary for sensitive cells (11, 40, 45). This can be reflected by a corresponding increase in DO or a decrease in (Yor /3 in the resistant cell survival curve. A small ra-

November 1989, Volume 17, Number 5

dioresistant clone will thus have little effect on tumor radiocurability as the dose, necessary to kill all of the cells in a large radiosensitive clone of 10’ or lo* cells, might be more than adequate to simultaneously kill all of the cells in a small resistant clone of several hundred cells. Only when the resistant clone becomes sufficiently large will it significantly affect the cure probability. The total radiation dose that can be safely delivered to a tumor is limited by the tolerance of surrounding late reacting normal tissue (14). Except in the case of very radiosensitive tumors [e.g. seminoma (8 l)], this maximum tolerable dose is usually significantly less than one would like to deliver to the tumor to achieve a high probability of tumor control. Thus, the prescribed dose is usually determined more by normal tissue tolerance than by tumor response. A tumor may indeed contain a resistant clone, but if the dose it receives is inadequate to kill off all of the sensitive cells, the effect of the presence of these resistant cells will not be seen. When a tumor recurs after a complete response to a given chemotherapy regimen, the recurrent tumor will almost invariably be found to be refractory to that same chemotherapy regimen (65). Similarly, a tumor that recurs locally after a radiation therapy failure may consist of radioresistant cells that have survived the previous course of treatment, but we would not know this unless we were to re-treat with radiation to a full therapeutic dose. However, as the normal tissue tolerance has already been “used up” in the first course of treatment, this is not often done. Because of the limits of normal tissue tolerance, it is virtually impossible to salvage a radiotherapy failure with an additional course of radiation. Even for those tumors, such as nasopharyngeal carcinomas, where local recurrences are reradiated simply because there are no other treatment modalities available, such retreatment is usually ineffective except for palliation. There is, however, evidence that nasopharyngealcarcinomas that recur within 2 years, which are likely to be true recurrences, are more radioresistant than later recurrences which may be second primaries (75). Thus, it is clear that if both chemotherapy resistant and radiotherapy resistant cells exist, the clinical effects of such cells would be more readily apparent to the chemotherapist than to the radiotherapist. The presence of mutant chemotherapy resistant cells is well recognized as one of the most important causes of clinical chemotherapy failure (65). There is increasing in vitro evidence that radioresistant cells do exist (7, 30,41, 58, 59, 78, 79, 80, 86), and, in some situations, these cells, rather than hypoxia or cell number, may be the cause of treatment failure. In this paper the clinical consequences of the existence of mutant radioresistant cells is investigated. The evidence for variation in intrinsic cellular radioresistance and the salient features of the Luria-Delbruck (38),-Goldie-Coldman (17, 18) Mutation Theory model are reviewed. This formalism will be applied to a simple model tumor with a single possible radioresistant mutation and it will be

Tumor heterogeneity 0 R. J. YAES shown that the importance of the radioresistant clone will depend on the tumor size.

METHODS

AND MATERIALS

Intrinsic cellular radiosensitivity and tumor radiocurability Intrinsic cellular radiosensitivity, as measured in vitro, is only one of several factors influencing the ability to obtain local control of a tumor in vivo. Inadequate tumor vasculature may lead to areas of hypoxia and to cells that are non-cycling because they receive inadequate nutritional support. Host immune response may play an important, but still largely unelucidated role in obtaining tumor cures. However, in order to understand how these factors interact to determine the eventual treatment outcome, each of them must first be considered separately. We will therefore be concerned only with intrinsic cellular radiosensitivity and thus, “a tumor containing lo9 cells” will mean a simple tumor model, where all cells are assumed to be well oxygenated, well nourished, and continuously in cycle. This is probably the case in most microscopic tumors and, because of reoxygenation and recruitment, this may not be an unreasonable assumption, for a fractionated course of radiation, even when the tumor has become large. Published data on the intrinsic radiosensitivity of a large number of human tumor cell lines has been studied by Malaise and collaborators (11, 40) and they have made several interesting observations. Greater differences between cell lines were found in the initial part of the cell survival curves, which could be best fit with the linearquadratic (LQ) model, than in the distal part of the survival curve which is best fit with the multitarget model. It thus seems reasonable that if clinical radiosensitivity were to be described by a single parameter, this parameter should be chosen to reflect the behavior of the initial part of the survival curve. Such a parameter would be I), the mean inactivation dose, or S2, the surviving fraction at 2 Gy. Fertil and Malaise ( 11) noted that cell lines derived from histological types of tumors that are known to be clinically radioresistant, had on the average larger values of D and Sz than lines derived from more sensitive tumor types (1 I). Since conventional clinical radiotherapy is usually given in 1.8 to 2 Gy fractions, a correlation between S2 and clinical response should not be surprising. Assuming complete repair between fractions and ignoring proliferation during the treatment course, the surviving fraction after a course of n 2 Gy fractions would be S = (&)n. If a tumor contains N identical clonogenic cells with survival probability S, the probability of killing all N cells, and thus of curing the tumor, is determined by Poisson statistics to be (45) P = emNSand thus the probability, P, of tumor cure after n 2 Gy fractions would be p = e--N6~)“,

995

Not surprisingly, if N is large, a small change in S2 will cause a large change in P. This can be seen in Figure 1 where we plot P versus S2 for tumors of various sizes treated with 30 2 Gy fractions (6,000 cGy in 6 weeks). For example, for a tumor containing lo9 cells, P would fall from .995 to .005 when SZ is increased from .42 to .53. In view of this sensitivity of the tumor control probability to small changes in SZ, note that there is a wide variation in SZ for cell lines derived from tumors of the same histological type. Thus, for the melanoma cell lines studied by Fertil and Malaise (11) S2 varied from 0.22 to 0.77, and for the glioblastoma cell lines that they studied, S2 varied from 0.31 to 0.72. Similarly, Peters et al. (51) using a clonogenic radiosensitivity assay based on the cell adhesion matrix technique (2) found values of S2 for squamous cell carcinomas of the head and neck ranging from 0.2 1 to 0.9 1. Some authors appear to implicitly assume that each individual patient’s tumor will contain a single tumor cell type with a given S2 but there is no explicit evidence to support this assumption. The other possibility that should be considered is that individual tumors contain more than one cell type with significant differences in SZ. An average tumor control dose can be defined to be TCD3,, the dose at which the probability of tumor control, P, is equal to l/e = 37%. Thus, if a tumor containing 10” cells is treated with n 2 Gy fractions, TCD3, is the dose for which

I

P

0 0

Fig. 1. Probability P, of tumor control, as a function of S1, survival probability at 2 Gy, for various tumor sizes, for treatment with 30 2 Gy fractions (6000 cGy in 6 weeks). A relatively small change in SZ will produce a large change in tumor control probability. For example, for a tumor containing lo9 clonogenic cells, the probability of tumor control will fall from .995 to .005 when S2 for these clonogenic cells increase from .42 to S3.

996

I. J. Radiation Oncology 0 Biology0 Physics

P = e-NS = l/e,

NS = 1O”S,”= 1

or

n = -m/(logl&). Thus, for a melanoma containing lo9 identical clonogenie cells with an S2 of 0.22, a 37% probability of local control would be predicted with a course of 14 2 Gy fractions for a total dose of 28 Gy in 3 weeks, and a glioblastoma with lo9 cells with an Sz of 0.3 1 would have a 37% control probability with 18 2 Gy fractions, a total dose of 36 Gy in 4 weeks. At the other extreme, a squamous cell carcinoma containing lo9 cells with an S2 of 0.9 1, would require 220 2 Gy fractions or a total dose of 440 Gy (44,000 cGy in 44 weeks) to obtain 37% probability of local control. Examples in the clinical literature of melanomas and glioblastomas for which local control has been obtained with radiation alone, even with doses as high as 80 Gy in 8 weeks (55), are anecdotal. Thus, as it is unlikely that hypoxia or other extrinsic microenvironmental factors alone could be responsible for the radioresistance of melanomas and glioblastomas, if glioblastomas encountered clinically do contain cell lines with S2 as small as 0.3 1, and melanomas contain cell lines with an S2 of .22, they must also contain cell lines that are more radioresistant as well. The conclusion is inescapable that some human tumors contain multiple clonogenic cell types of differing radiosensitivities. Since tumors have been explicitly shown to be heterogeneous in regard to other properties including karyotype (60), metastatic potential (13) and resistance to specific chemotherapeutic agents (65), this conclusion is not inplausible. Thus, a given patient’s tumor may contain a predominant cell type with a given value of S2, to which most of the clonogenic tumor cells belong, but also may contain other cell types with greater and lesser radiosensitivity. Cell types that are more radiosensitive than the predominant cell type will not affect the control probability and can be ignored. On the other hand, even a relatively small clone of cells that is significantly less radiosensitive than the predominant cell type, can significantly increase the dose necessary for tumor control. A clone of only lo5 cells with an Sz of 0.77 would require 44 2 Gy fractions (8,800 cGy in 9 weeks) for a 37% probability of control, and its presence in a melanoma with lo9 cells with an S2 of .22 would preclude tumor cure with a lower dose. The presence of a small radioresistant clone in an otherwise radiosensitive tumor would be difficult to detect by the use of a clonogenic assay. It would not be adequate simply to treat the cells obtained from the tumor biopsy, in vitro, to a large single dose and look for a “break” in the cell survival curve. To understand why this may be the case, consider two of the melanoma cells lines discussed by Fertil and Malaise ( 11). The two melanoma cell lines that show the greatest differences in radiosensitivity in both the high dose and the low dose regions have been deliberately chosen to best illustrate the point. One line

November 1989, Volume 17, Number 5 ( 19-4) which we call “A” has parameters (Y’= 0 Gy-‘, p’

= .0639 Gy-*, S2 = 0.77. Another, (H X 34) which we call “B” has: a! = .277 Gy-‘, ,L3= .O152 Gy-*, S2 = 0.54. Thus, if both cell lines were treated to a dose of 2 Gy or with a number of 2 Gy fractions, cell line A with the larger value of S2 would be more radioresistant than cell line B. However, since the curves cross at 5.7 Gy, (Fig. 2) if these two cell lines were treated with a large single dose, line B would be more radioresistant than line A. Thus, if a melanoma contained mostly B cells, a small clone of A cells, with a relatively large S2, could effect the tumor control probability when the tumor is treated with a course of 2 Gy fractions. Nevertheless, this clone would not be discovered by treating with a large single fraction in a clonogenie assay, since for such a treatment the A cell line would be more radiosensitive than the B cell line. It would, of course, be impractical to use a fractionated course of radiation in a clonogenic assay, as it would then take as long to obtain a result as it would to actually treat the patient. From the cell lines studied by Fertil and Malaise (1 l), two extreme examples have been deliberately chosen so that the relationship between the survival curves for the A and B cell lines should not be considered typical for two cell lines derived from the same tumor. Nevertheless, the observation of Fertil and Malaise, that differences in radiosensitivity are greater in the initial than in the distal part of the survival curves, would itself make it unlikely that a radioresistant clone would be discovered in

I

S

I#_

IO

0

DOSE (Gyl Fig. 2. Cell survival curves for two of the melanoma cell lines studied by Fertil and Malaise (11). Cell line 19-4 which we call “A” has parameters (Y = 0 Gy-‘, p = .0639 Gy-‘, Sz = 0.77 (solid line) whereas cell line H X 34 which we call “B” has parameters LY= .277 Gy-‘fi = .0152 GyM2, S2 = 0.54 (dashed line). For a treatment course with multiple 2 Gy fractions, cell line A, with the larger value of Sz will be more radioresistant. On the other hand, since the curves cross at 5.7 Gy, for treatment with a large single fraction, cell line B will be more radioresistant than cell line A.

Tumor heterogeneity 0 R. J. YAES

a clonogenic assay by treating with large single dose. If the predominant cell type in a tumor is radioresistant, this would readily be demonstrated by a clonogenic assay which would accurately predict that the tumor is radioincurable. If however, the predominant cell type is radiosensitive but the tumor contains a radioresistant clone, a clonogenic assay could inaccurately predict that the tumor is curable with radiation. Such assays may provide little more information than is obtained by observing clinically the rate of tumor regression during treatment or the response at the end of a course of radiation (68, 70). Even for a homogeneous tumor treated with a fractionated course of radiation, it would be insufficient to determine only S2 to predict the treatment response. The proliferation rate must also be determined so that repopulation between fractions can be estimated (39, 50, 82, 84). The observed increase of the TDsO dose with increasing overall treatment time implies that during a course of treatment, after a delay of 3-4 weeks the proliferation rate will be determined by the tumor’s potential doubling time, rather than the observed preradiation tumor growth rate (39, 84). If a single cell line possesses two properties, a large S2 and a rapid proliferation rate, it will be very resistant to treatment with a conventionally fractionated course of radiation and tumors containing such cells could actually grow during treatment ( 14,34). The solution to this problem has been to treat such tumors with an accelerated fractionation regimen delivering two 1.5-2 Gy fractions per day [concomitant boost ( 14, 34)]. Another way to deal with these “doubly resistant” (DR) cells would be to use high LET radiation such as neutrons. If the large SZ results from an increased ability to repair sublethal and/or potentially lethal damage (59, 78), this increased repair capacity would be ineffective for the single-hit nonreparable damage caused by heavily ionizing particles (i.e., the recoil protons that actually transfer the neutron energy to tissue). Because of the lack of repair capacity for these lesions in normal tissue there would no great disadvantage to giving the high LET treatment in a single dose or several large fractions. The advantage of doing so would be that a rapidly proliferating clone would not get a chance to proliferate between fractions. If these doubly resistant cells exist in a tumor, they would be likely to result from two successive mutations in the same cell line. Thus, for any reasonable estimate of the mutation rate, there would be very few such cells initially in a tumor. However, once we treat the tumor with conventially fractionated radiation and begin killing the sensitive cells, the cells of the resistant clone, freed from metabolic constraints, would proliferate rapidly, and there might be many more of them at the end of a course of treatment than at the beginning. This argument suggests that the optimum way to combine neutron and photon therapy is to treat with neutrons first, giving a boost to the central tumor mass where the resistant cells are likely to be, in one or several large fractions. This would give a

997

significant probability of killing all of the cells in any small resistant clone that might be present. The tumor and draining lymph nodes would then be treated with conventionally fractionated photon therapy to kill the large number of remaining sensitive cells. As it may be possible to exclude radiosensitive structures, such as the spinal cord, from the boost field, the high complication rate, often encountered in neutron beam therapy could be avoided with this technique. Using neutrons for boost treatments only, and giving these boost treatments in a few large factions would also make the most efficient use of the few existing neutron therapy facilities and ensure that neutron therapy would be available to a large number of patients. This approach has been used emperically by Maruyama et al. (42), in the treatment of locally advanced cervix cancer with the combination of fractionated photon external beam therapy and Californium neutron brachytherapy. When the external beam treatment was given first, to shrink the tumor, as is usually done with conventional Cesium therapy, the results were no better than with Cesium. However, a significant improvement over the results obtained with Cesium was found when the Californium brachytherapy was performed first. An explicit mathematical model to describe this phenomenon will be presented in a subsequent publication. Evidence for the existence of radioresistant clones in human and animal tumors If small, repair efficient radioresistant clones exist in solid tumors, their existence could, in principle, be demonstrated in vivo by applying persistant selective pressure in the form of a protracted course of fractionated radiation. It has already been noted that if the radioresistant clone initially contains only a few cells, and the differences in radiosensitivity are not great, the doses needed to eliminate all of the sensitive cells so that the resistant cells could be observed would likely exceed the tolerance of the host tissues. Nevertheless, the experiment could still be performed in vivo in syngeneic mice if the irradiated tumor cells were transferred to a new host mouse whenever normal tissue tolerance was reached. Hoffman et al. (25) studied a transplantable mammary adenocarcinoma that had arisen spontaneously in a CH3/ wr mouse. The tumors were transplanted to the hind legs of four groups of mice and allowed to grow to 1.2 cm diameter. The mice were treated as follows: Control group A received no treatment; group B received a fractionated course of radiation, 2 Gy per day for 30 fractions, for a total dose of 60 Gy; group C received three high dose fractions of 15 Gy each; group D received a single dose of 45 Gy. The tumors were allowed to regrow to a diameter of 1.7 cm and then retransplanted. The same treatment was repeated for each group and the whole process was repeated for ten transplant generations. At each transplantation, an in vivo assay of growth rate and radiosensitivity was performed by transplanting the tumor from

998

I. J. Radiation Oncology 0 Biology 0 Physics

each treatment group into two other groups of mice. One group was followed until death, and the time interval from when the tumor reached 1 cm diameter to when it killed the mouse was noted. A second group received a single dose of 45 Gy and regrowth times were noted. After the completion of the experiment, an in vitro assay was used to obtain cell survival curves for the four groups of tumors. This assay showed no significant differences between groups A, C, and D. Only group B, which received the fractionated course of radiation, showed a significantly greater growth rate in vivo, when untreated, and after receiving a single dose of 45 Gy. The Da for group B cells was 3 Gy compared to 2.4 Gy for the control group A. While tumors in group A were well differentiated and noninvasive, group B tumors were poorly differentiated and showed evidence of invasion and necrosis. Cell line B was also noted to be more aneuploid than the others on measurement of DNA content by microspectrophotometry. The results of this experiment can be interpreted in terms of tumor heterogeneity and mutation theory. The mouse mammary carcinoma could have had a small preexisting radioresistant clone. Without selective pressure, this clone would have remained small. However, when selective pressure was imposed by protracted, fractionated irradiation in a succession of host animals the presence of the resistant clone was demonstrated. The resistant clone was seen only in that group treated with a fractionated course of radiation with 2 Gy fractions. Treatment with a large single dose or even three large fractions did not impose enough selective pressure to demonstrate the resistant clone. The B cells appear to be more radioresistant, in vivo, when treated with a fractionated course of radiation, not only because of greater radioresistance as determined by the in vitro cell survival curve, but also because they have a shorter potential doubling time (as indicated by a shorter regrowth time) and hence would repopulate more rapidly between fractions. The question of the effect of the radioresistant variant on tumor cure was not directly addressed in this animal model. The tumor itself was rather radioresistant and was not cured by any of the three treatment arms used. It would be instructive if this type of experiment were repeated with modern techniques and with this question specifically addressed. More recently, it has been shown that for a transplantable LS/BL murine lymphosarcoma ascites tumor (30) and for L5 178~ lymphoma cells (86), continuous low dose irradiation can lead to increased radioresistance in the tumor cell population. As this radioresistance can be manifested by the appearance of a shoulder on a survival curve that was originally linear (i.e. pure a! in the LQ model or n = 1 in the multitarget model), it can be inferred that the increased radioresistance resulted from increased capacity to repair sublethal damage (30). This increased repair capacity was confirmed by split dose experiments. A similar result was obtained earlier by Courtney (7)

November 1989, Volume 17, Number 5

who subjected L5 178~ mouse leukemia cells to continuous low dose-rate irradiation (4.8 cGy/hr) by incorporating tritiated water in the culture medium. The doserate was chosen so that the rate of cell killing by radiation would almost match the rate of cell increase due to proliferation. The cell number doubling time was 170 hr for cells during continuous irradiation compared to 10 hr for unirradiated L5 178~ cells in log phase culture. After about 40 days, overgrowth of these cultures by radioresistant mutant cell lines with much smaller doubling times during irradiation than 170 hr was noted. When compared to the cell survival curve for the unirradiated cells, which had no shoulder, curves for the mutant strains showed either the appearance of a shoulder or an increased Do. Mutant cell lines were stable when grown in unirradiated cultures, but, when grown in cultures receiving continuous low dose rate irradiation, radioresistance continued to increase, suggesting the occurrence of successive mutations conferring increased radioresistance, and successive overgrowth by the most radioresistant cell line. The similarity to the development of increasing methotrexate resistance in cells exposed to methotrexate in vitro was noted. By comparing the doubling times of the mutant strains to the time at which their appearance was noted, Courtney concluded that these mutants were not present in the original culture, but rather the mutations occurred during the course of continuous low dose rate irradiation. A common feature of all of these experiments is the fact that resistant cell lines were selectively spared by either a fractionated course of radiation or by continuous low dose rate irradiation and not by treatment with a single large dose at high dose rate. This feature is consistent with the observation of Fertil and Malaise (11) that differences in radiosensitivity are greater in the initial part than in the distal part of the cell survival curves, and implies that this radioresistance may result from an increased repair capacity. Weichselbaum and collaborators (59, 78, 79, 80) have found an increased capacity for potentially lethal damage repair in cell lines derived from human tumors that had failed radiotherapy treatment, suggesting that the presence of radioresistant, repair proficient cells may, in some cases, be responsible for clinical radiotherapy failure. Murray et al. found that cells from two mouse fibrosarcoma tumors actually repaired DNA strand breaks faster than cells from normal mouse tissue (46). The analogy between the increasing radioresistance that develops in cell cultures exposed to continuous low dose rate radiation, with methotrexate resistance that develops in cultures exposed to increasing concentrations of that chemotherapy agent, may be instructive. The genetic basis of methotrexate resistance is well understood. Although it can result from a mutation to the dehydrofolate reductase gene that makes the enzyme less sensitive to methotrexate inhibition, or from increased transport of methotrexate out of the cell, a common cause is gene amplification (56). Increasing methotrexate resistance can develop as cell lines appear with more and more copies

999

Tumor heterogeneity 0 R. J. YAES

of the dihydrofolate reductase gene and, consequently with more and more molecules of the enzyme. Gene amplification is common in neoplastic cells (26, 56, 57,73), and repair of DNA damage is known to play a critical role in determining a cell’s response to a fractionated course of radiation (9). In particular, if gene amplification of one or more of the enzymes involved in the DNA repair process occurred, this could lead to increased repair capacity and the consequent increased radioresistance. Other mechanisms for increased radioresistance have been seen in bacteria (1, 16) as well as in mammalian cells. Marklund et al. have noted increased levels of superoxide radical scavengers in radioresistant cell lines (4 1). Sklar has shown that activation of the ras oncogene can increase radioresistance in N/H 3T3 cells (66). Ikebucki et al. have noted an increased resistance to cell killing by UV light in Chinese hamster cells exposed to a fractionated course of UV light (28). There is indirect clinical evidence for the existence of radioresistant cells in human tumors. Suit et al. (70) found no correlation between the initial response of advanced head and neck cancers to radiation and the probability of long-term local control. Sobel et al. also found little correlation between tumor persistance at the end of treatment and local control (68). If these tumors were homogeneous, one might expect such a correlation. In the Luria-Delbruck model, however, the initial response would be determined by the sensitivity of the predominant cell type whereas the probability of long-term local control might depend on the size and sensitivity of the small radioresistant clone, and no such correlation would be expected. If radioresistant cells are a significant cause of clinical radiotherapy failure, one would expect that tumors that recurred after radical radiotherapy treatment, consisting of the progeny of these radioresistant cells, would be more resistant to radiation than the original tumor. As we have previously noted, because of the limitations imposed by normal tissue tolerance, radical retreatment of radiotherapy failures is seldom attempted, which could explain why such “induced radioresistance” is seldom observed. Years ago, when only orthovoltage X ray beams were available and late effects in deep-seated tissues were not of great concern, radioresistance that was “induced” by previous radiotherapy was accepted as an established fact. In this context, a 1954 review of the subject by Windeyer (83) is worth quoting: “It is well established in clinical practice that tumors recurring after previous irradiation have increased radioresistance. Undoubtedly this is due in part to damage to the cells of the normal supporting stroma and particularly to the vascular supply, but in addition there is strong evidence that the actual cells of the tumor are more radioresistant. This is particularly apparent in the case of a rodent ulcer recurrent after previous irradiation, especially if it has been treated by multiple small doses. . . . If further recurrence occurs outside the area previously treated, in tissues which have a normal and

adequate blood supply, it is nevertheless found to be markedly radioresistant.”

Mutation theory The mutation theory of Luria and Delbruck (38), in its simplest form was originally applied to bacterial cultures in exponential growth phase. The number, N, of cells in the culture would therefore satisfy the equation: dN -=yN. dt If we assume that we start with a single cell at time t = 0, the solution is: N = e7’.

(2)

The number of cells would increase exponentially with the time, t. If t2 is the doubling time for the number of cells in the culture, y = In 2/t2. Luria and Delbruck considered the specific mutation that confers phage resistance. This mutation is assumed to leave all other properties of the bacteria unchanged. A similar assumption can be made concerning mutations in neoplastic cells that confer resistance to specific chemotherapeutic agents or to radiation, so that, in the absence of the agent, the predominant sensitive (P) cell type is indistinguishable from the mutant resistant (M) cell type. In particular, the cell cycle time and the doubling time of the M type cells will be the same as those of the P type cells. For simplicity we assume that mutations occur during DNA replication, although this is not essential for the model. Thus, at each cell division, there is a probability, t, that one of the daughter cells will be mutant. The number t, which is a measure of the mutation rate, satisfies t < 1. Instead of Eq 1 the mean number of mutant cells, p, will satisfy:

-

dt

= yp + tyN.

The first term is the contribution from cell division of mutant cells already present. The second term is the contribution from additional mutations that occur during the cell division of sensitive cells. Since N is given by Eq 2, it is easy to verify that, if we assume that no mutant cells are present at t = 0, the solution of Eq 3 is p = cyte?‘.

(4)

We can use Eq 2 to eliminate the time t from Eq 4 and to express the mean number of mutant cells in the tumor, in terms of the total number of tumor cells, N. p = tN In N,

(5)

1000

I. J. Radiation Oncology 0 Biology 0 Physics

November 1989, Volume 17, Number 5

or, alternatively, the proportion, p, of resistant cells in the tumor is p = p/N = t In N.

(6)

Thus, for a given mutation rate, the number of mutant cells is determined by the total number of cells, N, and will increase faster than N. Nevertheless, if t 6 1, the number of resistant cells will always be much less than the number of sensitive cells. For example, if e = 10e6 then even when N = 1012,the proportion, p, of resistant cells will be 2.7 X 10m5.As a first approximation we are justified in equating the number of sensitive cells and the total number of cells and in ignoring back mutations from resistance to sensitivity. It is an oversimplification to think of a solid tumor as growing exponentially with time. It has been argued that tumor growth is best described by a Gompertzian function of time, rather than an exponential function, particularly when the tumor becomes large. However, as Goldie and Coldman have shown (18), even though Eqs 1 through 4 would no longer be valid, Eqs 5 and 6 would still hold. It is sometimes more useful to think of a tumor in terms of the number of “generations” rather than the number of cells. Thus, if an exponentially growing tumor contains 2k cells, it would have taken k generations of doublings to reach that size. If there is cell loss, then it would take a larger number of generations to produce a tumor of a given size than if cell death did not occur. Since there is a fixed probability of a mutation occurring at each cell division, in a tumor with significant cell loss (6), what determines the ratio of resistant to sensitive cells is not the number of cells present but the number of doublings that have occurred ( 18). Thus, in such a tumor, for a given mutation rate, the number of resistant cells would be larger than expected for a tumor of similar size with no cell loss, or conversely, the same number of resistant cells would imply a smaller mutation rate (18). Mutation theory also predicts a wide variation in the sensitivity of individual tumors resulting from a wide variation in the number of mutant cells that they contain. The number of mutant cells in a tumor would not depend only on the number of mutations that have occurred but also on when they occurred. For example, in a tumor containing N = 2k cells, a mutation occurring in the ith generation would give rise to 2k-i mutant cells. There is, for example, a probability E that the first cell division would produce a mutation, and in this case there would be 2k-’ mutant cells, that is, fully half of the cells in the tumor would be mutant. On the other hand, a single mutation in the last generation of cell division would give rise to a single mutant cell (Fig. 3). Therefore, while the distribution of mutations would be Poisson, the distribution of mutant cells would be wider than Poisson, with a long tail at high numbers. It has already been noted that the mean number of mutant cells in an exponentially growing tumor is tN In N. Delbruck and Luria have shown

A.

B.

Fig. 3. The number of mutant cells in a tumor will depend not only on the number of mutations that have occurred, but also on when they have occurred. Thus, if a mutation occurs at the first cell division, half of the cells in the tumor will be mutant (Fig. 3A). On the other hand, a single mutation occurring during the final cell division would lead to a single mutant cell (Fig. 3B).

(38) that the variance in the distribution of the number in mutant cells is EN’. The distribution for mutant cells must therefore be wider than a Poisson distribution for which the mean and the variance would be equal. Note that a wide variation in tumor radiosensitivity would not necessarily imply a wide variation in cellular radiosensitivity. In this simple model there are only two types of cells, sensitive “P” cells and resistant “M” cells. The variation in tumor radiosensitivity results from the variation in the number of resistant cells that the tumors contain. This variation in turn is a result of the randomness with which mutations occur. The generalized Munro-Gilbert model If a tumor containing N identical clonogenic cells receives a radiation dose D, it will be cured if all N clonogenie cells are killed. If the survival probability of each individual cell is S, then Poisson statistics imply that the probability, P, of tumor control, is (45) p = e-NS_

(7)

If the survival probability is given by the linearquadratic model then S = eCE, E=cwD+pD2.

(8)

If the dose D is given in n equal fractions of fixed size d and the total dose is varied by varying the number of fractions, then we would have (85) E = SD, 6. = oz + pd.

(9

Since the survival probability is now a negative exponential function of dose, the tumor control probability will be a double negative exponential function of dose.

Tumor heterogeneity 0 R. J. YAES

25

0

50

75

DOSE (Gy) I N=lO’ ~‘1.8

x lo3

P

:*

I

0

25

I

50

75

I

DOSE (Gy) I

f : I

N=lO” ~=2.3

x lo5

: I

P

C

0

I

I

25

50

fl/ 75

I

100

I 125

DOSE (Gy)

Fig. 4. Probability of tumor control as a function of dose for three different tumor sizes for a model tumor containing the two melanoma cell lines in Figure 2. The tumor is treated with a conventionally fractionated course of radiation with 2 Gy fractions. We assume that the tumor initially consists entirely of “B” cells but that there is a probability t = lO-‘j of a mutation from a B cell type to an A cell type. The mean number of mutant A cells in the tumor will then be determined by the Luria-Delbruck (38) relation, g = eNInN. For microscopic disease, N

1001

Generalization of the Munro-Gilbert model to a polyclonal tumor is straightforward. The probability of controlling each clone will have the form of Eq 7. The probability of controlling the tumor as a whole will be the product of such terms (85). In practice, the clone whose control curve lies furthest to the right will determine the tumor control probability. If a tumor does contain resistant cells these would result from mutations in an initially sensitive stem cell population. The mean number of resistant cells will then be determined by the mutation rate by Eq 5. A simple model can be constructed by specifying parameters (Yand @for the sensitive cells, (Y’and p’ for the resistant cells, and the mutation rate, C. It is then a simple matter to determine the control probabilities for a typical tumor containing the mean number of resistant cells as a function of the total number of clonogenic tumor cells, N. We will obtain the control probabilities for the large sensitive clone, for the small resistant clone, and for the tumor as a whole. To construct a heterogeneous tumor model we can use the two melanoma cell lines A and B that we have previously discussed, with parameters (Y’= 0 Gy-‘, /3’= .0639 Gye2, 6 (2Gy) = .128 Gy-‘, S2 = 0.77 and (Y= .277 Gy-‘, p = .0152 GY-~, Ly(2Gy) = .307 Gy-‘, S2 = .54, respectively. Since both these cell lines were derived from human melanomas, it is not implausible that cell lines with similar parameters might be present in the same tumor. When treating with 2 Gy fractions, the B clone will be the more radiosensitive. We will assume that the tumor is initially homogeneous and contains only B cells but there is a small probability t = lop6 of a mutation from the B cell type to the A cell type at each cell division. Thus, for a microscopic tumor with N = lo6 cells, the mean number of resistant A cells would be p = 14. In Figure 4A we present the sigmoid dose-response curves for control of this tumor when treated with a course of 2 Gy fractions. The curve for a control of the small resistant A clone (dotted line) lies entirely to the left of the curve for the large sensitive B clone (solid line). The control curve for the tumor as a whole is thus identical to the control curve for the large sensitive clone.

= 106, p = 14, (Fig. 4A) the control curve for the small resistant clone (dotted line) will lie entirely to the left of the curve for the large sensitive clone (solid line). The control curve for control of the tumor as a whole will be identical to that for the large sensitive clone and the presence of the resistant clone will have no effect on the tumor control probability. For gross disease, N = lo*, p = 1.8 X lo3 (Fig. 4B), the control curve for the small resistant clone (dotted line) will cross the curve for the large sensitive clone (dashed line) and both will contribute to the control curve for the tumor as a whole (solid line) which is the product of the two. For massive disease, N = lOlo, p = 2.3 X 105, (Fig. 4C) the control curve for the small resistant clone (solid line) will now lie entirely to the right of the curve for the large sensitive clone (dashed line) and the control curve for the whole tumor will be identical to that for the small resistant clone.

1002

I. J. Radiation Oncology 0 Biology 0 Physics

When the tumor size reaches N = lo* and becomes clinically detectable, the mean number of mutant cells would be P = 1.8 X 103. In this case, the curve for control of the small resistant clone (dotted line) crosses the curve for control of the large sensitive clone (dashed line), and both contribute to the control probability of the tumor as a whole (solid line), which is the product of the two (Fig. 4B). When the tumor grows still larger and N = 10” we would have CL= 2.3 X 105. The control curve for the small resistant clone (solid line) will now lie entirely to the right of the control curve for the large sensitive clone (dashed line). The control curve for the tumor as a whole will now be identical to that for the small resistant clone. The dose needed to control this large tumor would be larger than predicted from the dose needed to control a tumor of smaller size. The details of the dose-response curves will depend on the parameters that we have chosen, in particular the mutation rate t and the difference in radiosensitivity between the predominant and mutant cell types. Although cell lines A and B may not be typical of cell lines present in the same tumor, the general picture will be valid in any case. When the tumor is small, the cure probability will be determined by the large sensitive clone and the presence of resistant cells will have no effect. As the tumor grows, the control curves for both the resistant clone and for the sensitive clone will move to the right but the curve for the resistant clone will move to the right faster. Therefore, the curves must eventually cross so that when the tumor becomes sufficiently large, the tumor control probability will be determined only by the radioresistant clone. DISCUSSION The Luria-Delbruck mutation theory model (38), was originally developed to describe phage resistance in bacterial cultures, and it has proven to be remarkably successful in describing the development of chemotherapy resistance in human tumors (5, 17, 18, 19, 20, 64, 65). Given the in vitro and in vivo evidence for the existence of radioresistant mutant cells (7, 25, 28, 58, 59, 62, 78, 79, 80), this model could also prove useful in describing the response of human tumors to radiation. As cross resistance between radiation and chemotherapy agents has been observed (58, 62), it is plausible that in some cases similar mechanisms may be involved in causing resistance to both types of agents. There is evidence that, among these mechanisms is the increased capacity to repair DNA damage (59, 78). Although a genetic basis for radioresistance in bacteria has been noted ( 1, 16), at this point any discussion of the precise nature of the mutations that could confer radiation resistance in mammalian cells would be highly speculative. Clarification must await the isolation of radioresistant cells and the study of their genome by modem molecular biology techniques. In some cases, however, the nature of the mutation

November 1989, Volume 17, Number 5

that produces chemotherapy resistance is known. Methotrexate resistance can be produced by a mutation that makes dihydrofolate reductase less susceptible to inhibition by methotrexate, by increased transport of methotrexate out of the cell and by gene amplification of the dihydrofolate reductase gene (56). Gene amplification is quite common in neoplastic cells (26, 56, 57) and can be responsible for resistance to drugs other than methotrexate (73). If an increased repair capacity is responsible for radiation resistance, then amplification of the genes that code for one or more of the enzymes involved in the DNA repair process could conceivably be responsible for this increased repair capacity. An enhanced repair capacity would confer resistance to conventionally fractionated photon irradiation but not to large single doses of radiation or to high LET radiation, where cell killing is accomplished largely by single hit nonrepairable damage. High LET radiation would thus be particularly efficient at killing repair-efficient radioresistant cells. If high LET radiation is combined with conventional photon irradiation, the high LET radiation should be given first to prevent the overgrowth of resistant cells during photon treatment. Such an approach has been used empirically by Maruyama et al. (42) in the use of “early” Californium neutron brachytherapy for locally advanced cervical cancer, with promising results. It is a well-known fact that, regardless of the chemotherapy regimen used, tumor cells will almost always become resistant whereas bone marrow stem cells, and other cells of normal tissue will never become resistant. If, as the Luria-Delbruck-Goldie Coldman model (17, 38) implies, resistance results from mutations that occur in a previously sensitive stem cell population, the neoplastic cells would have to have a significantly higher mutation rate than normal tissue stem cells to explain this fact. One would expect a correlation between the mutation rate and the probability that resistance to a particular treatment modality would occur. Thus, tumors like seminoma or Hodgkin’s Disease which are curable by either radiation or chemotherapy, would have a relatively low mutation rate whereas incurable plemorphic tumors like glioblastoma multiforme would have a high mutation rate. Mutant strains of E Coli with a higher than normal mutation rate have been isolated (8). These strains have an altered form of DNA polymerase III resulting in a decreased ability for excision repair of mismatched base pairs during DNA replication. It is conceivable that similar mutations could occur in the DNA polymerase complex of eukaryotic cells with similar consequences. Such “mutator mutations” could be early events in the development of neoplasia. A high mutation rate in neoplastic cells (3 1, 72) could help explain tumor progression (3, 10, 33, 47, 48), the development in neoplastic cells of all of the properties necessary for invasion and metastases (4, 12, 13, 23, 37), the pleomorphic appearance of many poorly differentiated tumors, the combined sequential effects of initiators and promotors (54,77) in the development of ma-

Tumor heterogeneity 0 R. J. YAES

lignancy, and the activation of proto-oncogenes (66, 67, 74) and the breakdown of gene regulation (2 1,22,26,27) that are characteristic of neoplasia. The Luria-Delbruck model may not provide an accurate description of all tumors (32). It is a fundamental assumption of the model that a mutation that confers resistance to a particular cytotoxic agent confers no selective advantage in the absence of that agent (17, 38). This assumption may not always be valid. If, for example, the mutation resulted in a shorter cell cycle time, the proportion of mutant cells in the tumor would not always be small. One would then have to consider competition of both cell types for metabolic resources and other interactions between the different cell populations. A model with these properties has been proposed by Michaelson and Leith (43) to describe the heterogeneous colon carcinoma studied by Leith and Collaborators (35, 36, 44). The Luria-Delbruck model, however, has two advantages: a single free parameter, the spontaneous mutation

1003

rate, t, and a simple analytic solution. The MichaelsonLeith model has seven free parameters and must be solved numerically by iterative techniques. The Luria-Delbruck model is known to be applicable to many human tumors as it has been used successfully by Goldie and Coldman to describe the development of clinical chemotherapy resistance. More complicated models are largely untested. While modern radiotherapy techniques have proven to be remarkably successful in curing some types of tumors, the results have been disappointing for other tumors. A better understanding of tumor biology is necessary if the results for these latter tumors are to be improved. If radioresistant mutant cells are responsible for failure in a significant number of cases, strategies designed specifically to deal with these cells could significantly improve local control and survival (71). Such strategies would involve optimal use of multiple treatment modalities, much as multiple agents are used in modern chemotherapy regimens.

REFERENCES 1. Adler, H. The genetic control of radiation sensitivity in micro-organisms. Adv. Radiat. Biol. 2: 167-19 1; 1966. 2. Baker, F.; Spitzer, G.; Ajani, J.; Brock, W.; Lukeman, J.; Patchak, S.; Tomasovic, B.; Thielvoldt, D.; Williams, M.; Vines, C.; Tofilon, P. Drug and radiation sensitivity measurements of successful primary monolayer culture of human tumor cells using cell-adhesive matrix and supplemental medium. Cancer Res. 46: 1263- 1274; 1986. 3. Cairns, J. Mutation selection and the natural history of cancer. Nature 255:197-200; 1975. 4. Cifone, M.; Fidler, I. Increasing metastatic-potential is associated with increasing genetic instability of clones isolated from murine neoplasms. Proc. Natl. Acad. Sci. 79:69496952; 1981. 5. Coldman, A. J.; Goldie, J. H. A mathematical model of drug resistance. In: Neoplasms in drug and hormone resistance in neoplasia. Boca Raton, Fla: CRC Press: 1982:5578. 6. Cooper, E.; Bedford, A.; Kenny, T. Cell death in normal and malignant tissue. Adv. Cancer Res. 21:59-120; 1975. 7. Courtenay, V. D. Radioresistant mutants of L5 178Y cells. Radiat. Res. 38: 186-203; 1969. 8. Echols, H.; Lu, C.; Burgers, P. Mutator strains of escherichia coli mutD and dnaQ with defective exonuclease editing by DNA polymerase III holoenzyme. Proc. Natl. Acad. Sci. 80: 2189-2192; 1983. 9. Elkind, M. Repair processes in radiation biology. Radiat. Res. 100:425-449; 1984. 10. Farber, E. The multistep nature of cancer development. Cancer Res. 44:42 17-4223; 1984. 11. Fertil, B.; Malaise, E. P. Inherent cellular radiosensitivity as a basic concept for human tumor radiotherapy. Int. J. Radiat. Oncol. Biol. Phys. 7:62 l-629; 198 1. 12. Fidler, I.; Hart, I. Biological diversity in metastatic neoplasms: origins and implications. Science 2 17:998-1003; 1982. 13. Fidler, I.; Kripke, M. Metastasis results from pre-existing variant cells within a malignant tumor. Science 197:893895; 1977. 14. Fletcher, G. H. Textbook of radiotherapy, 3rd edition. Philadelphia, Pa: Lea and Febiger; 1980. 15. Fraire, A.: Roggli, V.; Vollmer, R.; Greenberg, S.; Mc-

16.

17.

18.

19.

20.

2 1. 22. 23.

24. 25.

26.

27. 28.

Gavron, M.; Spjut, H.; Yesner, R. Lung cancer heterogeneity, prognostic implications. Cancer 60:370-375; 1987. Francis, I.; Hernadi, S.; Szabolcs, M.; Hemadi, F. R46 and PKM 10 1 plasmid-mediated resistance to ionizing radiation in escherichia coli. Radiat. Res. 103:410-418; 1985. Goldie, J. H.; Coldman, A. J. A mathematical model for relating the drug sensitivity of tumors to their spontaneous mutation rate. Cancer Treat. Rep. 63: 1727- 1733; 1979. Goldie, J. H.; Coldman, A. J. Quantitative model for multiple levels of drug resistance in clinical tumors. Cancer Treat. Rep. 67:923-931; 1983. Goldie, J.; Coldman, A. The genetic origin of drug resistant neoplasms: implication for systematic therapy. Cancer Res. 44:3643-3653; 1984. Goldie, J. H.; Coldman, A. J. Applications of theoretical models to chemotherapy protocal design. Cancer Treat. Rep. 70:127-131; 1986. Goustin, A.; Leaf, E.; Shipley, G.; Moses, H. Growth factors and cancer. Cancer Res. 46:1015-1029; 1986. Hansen, M.; Cavenee, W. Tumor supressors: recessive mutations that lead to cancer. Cell 53:172-173; 1988. Harris, J.; Chambers, A.; Hill, R.; Ling, V. Metastatic variants are generated spontaneously at a high rate in mouse KHT tumor. Proc. Natl. Acad. Sci. 79:5547-5551; 1982. Heppner, G. Tumor heterogeneity. Cancer Res. 44:22592265; 1984. Hoffman, N.; Gollin, F.; Clifton, K. Acquired radioresistance of transplantable mammary adenocarcinoma in inbred mice after, serial irradiation. Radiology 88:568-575; 1967. Humphrey, A.; Wong, S.; Vogelstein, H.; Friedman, D.; Bigner, D.; Bigner, S. Loss of epidermal growth factor receptor gene amplifications as malignant human gliomas are established in culture (Abstract). Proceedings of the 79th American Associates for Cancer Research Meeting. New Orleans, LA; May 1988. Hunter, T. Cancer: cell growth and control mechanisms. Nature 322: 14- 16; 1986. Ikebuchi, M.; Osmak, M.; Han, A.; Hill, C. Multiple small exposures of far and mid-ultraviolet light change the sensitivity to acute ultraviolet exposures measured by cell lethality and mutagenesis in V79 Chinese hamster cells. Radiat. Res. 114:248-267; 1988.

1004

I. J. Radiation Oncology 0 Biology0 Physics

29. Jamasbi, R.; Ye, M.; Norvell, T. Cytogenetic heterogeneity

30.

31. 32.

33. 34.

35.

36.

37. 38. 39.

40.

41

42.

43.

44.

45.

46.

47. 48.

of pulmonary metastases developed from forestomach carcinoma of balb C/C mice (Abstract). Proceedings of the 79th American Association for Cancer Research Meeting. New Orleans, LA, May 1988. Juraskova, V.; Drasil, V. Response of lymphosarcoma LS/ BL cells to continuous radiation. Radiat. Res. 100:553-563; 1984. Kendall, W.; Frost, P. Constancy of genomic instability in tumor progression. J. Theo. Bill. 126:369-371; 1987. Kendall, W.; Frost, P. Pitfalls and practice of Luria-Delbruck fluctuation analysis: a review. Cancer Res. 48:1060-1065; 1988. Klein, G.; Klein, E. Evolution of tumors and the impact of molecular oncology. Nature 3 15: 190-195; 1985. Knee, R.; Fields, R.; Peters, L. Concomitant boost radiotherapy for advanced squamous cell carcinoma of the head and neck. Radiother. Oncol. 4: 1-7; 1985. Leith, J.; Dexter, D.; DeWyngaert, S.; Zeman, E.; Chu, M.; Calabresi, P.; Glicksman, A. Differential response to X-irradiation of subpopulations of two heterogeneous human carcinomas in vivo. Cancer Res. 42:2556-2561; 1982. Leith, J.; Faulkner, L.; Bliven, S.; Michaelsen, S. Compositional stability of artificial heterogeneous tumors in vivo: use of mytomycin as a cytotoxic probe. Cancer Res. 48: 2669-2673; 1988. Liotta, L. Tumor invasion and metastases-role of the extra cellular matrix. Cancer Res. 46: 1-7; 1986. Luria, S.; Delbruck, M. Mutations of bacteria from virus sensitivity to virus resistance. Genetics 28:49 l-5 11; 1943. Maciejewski, B.; Preuss-Bayer, G.; Trott, K. The influence of the number of fractions and overall treatment time on local control and late complication rate in squamous cell carcinoma of the larynx. lnt. J. Radiat. Oncol. Biol. Phys. 9:321-328; 1983. Malaise, E.; Fertil, B.; Chavaudra, N.; Guichard, M. Distribution of radiation sensitivities for human tumor cells of specific histological types: comparison of in vitro and in vivo data. lnt. J. Radiat. Oncol. Biol. Phys. 12:617-624; 1981. Marklund, S.; Westman, N.; Roos, G.; Carlsson, J. Radiation resistance and the CuZn superoxide dismutase Mn superoxide dismutase, catalase and glutathione peroxidaze activities of seven human cell lines. Radiat. Res. 100: 115-123; 1980. Maruyama, Y.; Kriscio, R.; Van Nagell, J.; Yoneda, J.; Donaldson, E.; Hanson, M.; Beach, J.; Feola, J.; Martin, A.; Parke, C. Clinical trial of 252 Cf neutron brachytherapy vs. conventional radiotherapy for advanced cervical cancer. lnt. J. Radiat. Oncol. Biol. Phys. 11:1475-1482; 1985. Michaelson, S.; Leith, J. Unexpected equilibria resulting from differing growth rates of subpopulations within heterogeneous tumors. Math. Biosci. 9 1: 119- 129; 1988. Michelson, S.; Leith, J.; Glicksman, A. A technique to analyse the emerging zonality of heterogeneous tumors. Cell Tissue Kin. 20:499-506; 1988. Munro, T.; Gilbert, C. Relation between tumor lethal dose and the radiosensitivity of tumor cells. Br. J. Radiol. 34: 246-251; 1961. Murray, D.; Jenkins, T.; Meyn, R. The efficiency of DNA strand-break repairs in two fibrosarcoma tumors and in normal tissues of mice irradiated in vivo with X rays. Radiat. Res. 100:171-181; 1984. Nowell, P. The clonal evolution of tumor cell populations. Science 194:23-28; 1976. Nowell, P. Genetic instability in cancer cells: relationship to tumor cell heterogeneity. In: Owens, A., Coffey, D., Baylin, S., eds. Tumor cell heterogeneity: origins and implications. New York: Academic Press; 1982.

November 1989, Volume 17, Number 5 49. Owens, A.; Coffey, D.; Balm, D., eds. Tumor cell heterogeneity: origins and implications. New York, MT: Academic Press; 1982. 50. Peacock, J.; Steel, G. The dose dependence of split-dose recovery in human tumor cell lines: implications for cell survival models (Abstract). In: Abstracts of papers for the 36th Annual Meeting of the Radiation Research Society, Philadelphia, Pennsylvania, 1988. 51. Peters, L. T.; Brock, W. A.; Johnson, T.; Meyn, R.; Tofilon, P.; Milas, L. Potential method for predicting tumor radiocurability. lnt. J. Radiat. Oncol. Biol. Phys. 12:459-463; 1986. 52. Poste, G.; Greig, R. The experimental and clinical implications of cellular heterogeneity in malignant tumors. J. Cancer Res. Clin. Oncol. 106:159-170; 1983. 53. Rubin, P. Late effects of chemotherapy and radiation therapy: a new hypothesis. Int. J. Radiat. Oncol. Biol. Phys. 10: 5-34; 1984. 54. Ruddon, R. Cancer biology, 2nd edition. New York, NY: Oxford University Press; 1987. 55. Salazar, 0.; Rubin, P.; McDonald, J.; Feldstein, M. High dose radiation therapy in the treatment of glioblastoma multiforme: a preliminary report. lnt. J. Radiat. Oncol. Biol. Phys. 1:7 17-727; 1976. 56. Schimke, R. Gene amplification, drug resistance and cancer. Cancer Res. 44: 1735-1741; 1984. 57. Schimke, R. Gene amplification in cultured animal cells. Cell 37:705-7 13; 1984. 58. Schwartz, J.; Rotmensch, J.; Beckett, M.; Jaffee, D.; Toohill, M.; Giovanazzi, S.; McIntosh, T.; Weichselbaum, R. X ray and cis-diamminedichloro platinum (II) cross resistance in human tumor cell lines. Cancer Res. 48:5 133-5 135; 1988. 59. Schwartz, J.; Rotmensch, J.; Giovanazzi, S.; Cohen, M.; Weichselbaum, R. Faster repair of DNA double-strand breaks in radioresistant human tumor cells. lnt. J. Radiat. Oncol. Biol. Phys. 15:907-912; 1988. 60. Shapiro, J.; Yung, W.; Shapiro, W. Isolation, karyotype and clonal growth of heterogeneous subpopulations of human malignant gliomas. Cancer Res. 4 1:2349-2357; 198 1. 61. Shapiro, J. R. Biology of gliomas: heterogeneity, oncogenes, growth factors. Sem. Oncol. 13:4-15; 1986. 62. Shimm, D.; Olson, S.; Hill, A. Radiation resistance in a multidrug resistant human T-cell leukemia cell line. lnt. J. Radiat. Oncol. Biol. Phys. 15:93 l-936; 1988. 63. Shipley, W.; Stanley, J.; Steel, G. Tumor size dependancy in radiation response of Lewis lung carcinoma. Cancer Res. 35:2488-2493; 1975. 64. Skipper, H. E. The forty year old mutation theory of Luria and Delbruck and its pertinence to cancer chemotherapy. Adv. Cancer Res. 40:33 l-362; 1983. 65. Skipper, H. E.; Simpson-Herrer, L. The relationship between tumor stem cell heterogeneity and responsiveness to chemotherapy. In: DeVita, V., Hellman, S., Rosenberg, S., eds. Important advances in oncology. Philadelphia, Pa: J. B. Lippincott; 1985. 66. Sklar, M. D. The ras oncogene increases the intrinsic resistance of N/H 3T3 cells to ionizing radiation. Science 239: 645-647; 1988. 67. Slamon, D. Proto-oncogens and human cancers. N. Eng. J. Med. 317:955-957; 1987. 68. Sobel, S.; Rubin, P.; Keller, B.; Poulter, C. Tumor persistance as a predictor of outcome after radiation therapy of head and neck cancer. lnt. J. Radiat. Oncol. Biol. Phys. 1: 873-880; 1976. 69. Spremulli, E.; Dexter, D. Human tumor cell heterogeneity and metastases. J. Clin. Oncol. 1:497-509; 1983. 70. Suit, H.; Lindberg, R.; Fletcher, G. H. Prognostic significance

Tumor heterogeneity 0 R. J. YAES

71 72. 73.

74. 75.

76.

77.

78.

79.

of extent of tumor regression at completion of radiation. Radiology 84:1100-l 107; 1965. Suit, H.; Westgate, S. Impact of improved local control on survival. Int. J. Radiat. Oncol. Biol. Phys. 12:453-458; 1986. Temin, J. Evolution of cancer genes as a mutation driven process. Cancer Res. 48:1697-1701; 1988. van der Bliek, A.; Baas, F.; van der Velde-Koerts, T.; Biedler, J.; Meyers, M.; Ozols, R.; Hamilton, T.; Joerje, H.; Borst, P. Genes amplified and overexpressed in human multidrugresistant cell lines. Cancer Res. 48:5927-5932; 1988. Verma, I.; Sassone-Corsi, P. Proto-oncogene fos: complex but versitile regulation. Cell 5 1:5 13-5 14; 1987. Wang, C. C. Re-irradiation of recurrent nasopharyngeal carcinomas-treatment techniques and results. Int. J. Radiat. Oncol. Biol. Phys. 13:953-956; 1987. Watanabe, H.; Takahashi, T.; Vedo, R.; Utsuni, K.; Sato, T.; Ariyoshi, Y.; Ota, K.; Obata, Y.; Takahi, T. Antigenic phenotype and biological characteristics of two distinct sublines, derived from an oat cell lung carcinoma cell line. Cancer Res. 48:2544-2549; 1988. Watson, J. D.; Hopkins, N.; Roberts, J.; Seitz, J.; Weiner, A. Molecular biology of the gene, Vol. II, 4th edition. Menlo Park, Cali: Benjamin/Cummings Publishing Co.; 1987: 1058-1094. Weichselbaum, R. Radioresistant and repair proficient cells may determine radiocurability of human tumors. Int. J. Radiat. Oncol. Biol. Phys. 12:637-639; 1986. Weichselbaum, R.; Beckett, M.; Dahlberg, W.; Dritschilo, A. Heterogeneity of radiation response of a parent human

80.

81

82.

83. 84.

85.

86.

87.

1005

epidermoid carcinoma and four clones. Int. J. Radiat. Oncol. Biol. Phys. 14:907-912; 1988. Weichselbaum, R.; Beckett, M.; Schwartz, J. Radioresistant tumor cells may account for clinical radiation failure (Abstract). In: Abstracts of papers for the 36th Annual Meeting of the Radiation Research Society, Philadelphia, Pennsylvania, 1988. White, R. L.; Maier, J. C. Testes tumors. In: Perez, C. A., Brady, L. W., eds. Principles and practice of radiation oncology. Philadelphia, Pa.: Lippincott Co.; 1987. Wilson, G.; McNally; Dische, S.: Bennett. M. Cell proliferation in human tumors measured by in vitro labeling with bromodeoxyoridine. Br. J. Radiol. 6 1:4 19-422; 1988. Windeyer, B. Clinical aspects of radioresistance. Acta Radiol. 116(Suppl.):108-119; 1954. Withers, J.; Taylor, J.; Maciejewski, W. The hazard of accelerated tumor clonogen repopulation during radiotherapy. Acta Oncol. 27(Fac. 2):98- 113; 1988. Yaes, R. J. Some implications of the linear-quadratic model for tumor control probability. Int. J. Radiat. Oncol. Biol. Phys. 14:147-157; 1988. Yau, T.; Gregg, E.; Kim, S. Production of radioresistant mutants in L5 178Y lymphoma cells. Radiat. Res. 80:50251 1; 1979. Zaino, R.; Clarke, C.; Moertel, R.; Satyaswaroop, P. Heterogeneity of progesterone receptor distribution in human endometrial adenocarcinoma. Cancer Res. 48: 1889-l 895; 1988.