l Radiation
Sensitivity:
INTRINSIC
Facts and Models
AND EXTRINSIC VARIABLES AFFECTING RADIATION CARCINOGENESIS JOHN
Cancer Research and Treatment
M.
YUHAS,
SENSITIVITY
TO
Ph.D.
Center and Department of Radiology, Albuquerque, NM 87131, U.S.A.
University
of New Mexico,
Mathematical models relating observed yield of cancers vs administered radiation dose have become popular in recent years, especially as means of predicting hazards associated with exposure conditions which are beyond the realm of practical experimentation. While the validity of these predictions remains a controversy, these models, especially the cxD + PD’ model, have more recently been used to infer the mechanism(s) underlying the carcinogenic process. Through the analysis of simple experimental systems, we demonstrate in this report that aD + hD2 kinetics can result from injury to the cells which eventually develop into the cancer (target cells) or from injury to those cells which affect target cell survival. Further, these kinetics can fail to predict the consequences of dose protraction, largely due to the fact that transformation increases with dose, while survival decreases. The role of these models in helping to develop an understanding of mechanisms should be restricted, therefore, to the formulation of basic hypotheses which are subject to direct testing in the laboratory. Radiation carcinogenesis,
Linear plus quadratic model, Target cells
INTRODUCTION
forest because of all of the trees which are in the way, and it might be possible, that many of the potential variables are, in fact, of minor consequence, and sensitivity may be determined by one or a few key factors. If this is true, then development of a clear understanding of radiation carcinogenesis would proceed more rapidly, and this possibility forms the subject matter of this discussion. A particularly useful model in radiation carcinogenesis is the linear plus quadratic model, which can be fitted to most if not all, experimental data on the subject. As an example of mathematical models in general, we will examine this model in terms of the types of injury which can contribute to it, and in terms of its reliability in predicting the effects of dose protraction. The conclusions reached below, which are equally applicable to other purely mathematical models, are that linear plus quadratic kinetics can result from a variety of types of injury in different types of tissues, and that since this model does not take this complexity and variety into account it is often unable to predict the consequences of dose protraction.
A simple listing of all of the variables which can, at least theoretically, affect the sensitivity of mammalian cells and organisms to radiation carcinogenesis would occupy all of the space available for this discussion. Alternatively, we can examine the generalities which have been put forth to accpunt for the overall process. Given what is clearly a complex and varied problem, investigators have taken one of two approaches: development of mathematical models which ignore the underlying biological complexity in favor of precise quantification of the end result, or identification of single variables involved transformation, immunosuppression, etc.) (e.g. without regard to their relative importance or their interaction with other variables. We have suggested” that neither approach is entirely adequate, especially when one tries to predict qualitative aspects from strictly quantitative data and vice versa. We proposed, instead, that the logical study of radiation carcinogenesis requires both quantitative and qualitative information, and that both aspects must be investigated simultaneously or at least sequentially. Mathematical models, or more precisely dose response curves would serve as tools for the development of working hypotheses, which would then be tested in the hope of identifying the nature of the variables involved and their quantitative importance. Biologists are, however, often unable to see the
The linear PLUS quadratic The linear plus quadratic is of the form:
model model of radiation
Effect = crD + pD* 111
injury
1118
Radiation
Oncology
0 Biology 0 Physics
In the specific case being discussed here, effect is in terms of radiation-induced increases in the yield of cancers. While this model has been used by a number of authors, its formal inclusion in a model of radiation carcinogenesis can be traced to Kellerer and Rossi.* The microdosimetric considerations which led to the use of this model have been described elsewhere in this symposium by Kellerer.’ In brief, the “dual action theory” of radiation carcinogenesis argues that radiation exposure can produce cancer in one of two ways: through the production of single hit events, each of which is able in itself to produce the cancer; or, through the summation of multiple hits, each of which is unable to produce the cancer. These correspond to the olD and pD* terms, respectively. For sparsely ionizing radiation, such as X-or gamma-rays, which are the primary concern of the present report, the slope of the D2 term /3 is large, resulting in a curvilinear relationship between dose and yield of cancers. Beyond proposing that the linear and quadratic terms in the model had a microdosimetric basis, the original authors” made no further comments regarding the nature of the injury involved, its location, or the consequences of dose protraction. This model can, however, be fitted to many experimental data, and this, coupled with its reasonable microdosimetric basis, has increased its popularity dramatically. Quite often, however, the application of this model is made without regard to our limited understanding of it; assumptions are made regarding the cells and type of injury involved,‘* and predictions are made from it regarding the effects of dose protraction.3 We show below that oD+ pD2 kinetics can result from a variety of types and sites of injury, and that failure to take this into account makes the predictive value of the model poor in many instances.
Target cell us non-target cell injury We define target cells as those which can develop into the induced cancer, and non-target cells as any others. The question posed here is whether non-target cell injury can produce aD + BD2 kinetics even if the number of carcinogenic events bears a linear relationship to dose. If the only cells capable of producing these kinetics are target cells, then the value of in vitro transformation systems is markedly increased, but if both types of cells can, it is unlikely that the shape of the single dose curve will be predictive of the consequences of dose protraction. A number of systemic control mechanisms are logical candidates for non-target cell contributions, and certain published studies5,” are consistent with a role for them in determining dose-response curve shape. The clearest demonstration that non-target cell injury can affect curve shape, however, comes from experiments specifically designed to test this pos-
July 1979, Volume 5, No. 7
sibility. In our studies on the interaction of radiation and oncogenic viruses,“-*’ it was demonstrated that radiation exposure alone, either total body or localized to the right leg, failed to induce a detectable increase in the frequency of sarcomas in the right leg. However, injection of graded doses of the Moloney strain of the sarcoma/leukemia virus complex, MSV/MLV, which had been passaged in vitro to reduce its leukemogenic potency, resulted in a linear relationship between injected virus dose and the yield of sarcomas (Fig. 1 upper graph). Exposure of the right leg to localized X-ray doses of up to 500 rad did not alter the yield of sarcomas induced by the virus injection, but total body irradiation did. Total body X-ray doses of 250 or 500 rad, given 1 month prior to the virus, converted the relationship of virus dose to sarcoma yield from a linear one to a curvilinear one, i.e. the exposures enhanced the yield of sarcomas in the high dose, but not in the low dose, range. Since local irradiation of the injection site prior to virus
60
/ c
/
/
9 f!? 0
0 rod 40
: v)
,” z
20
0
VIRUS
ALONE
/
TREATMENT
LEVEL
Fig. 1. Yield of MSV/MLV induced injection site sarcomas at 6-months as a function of virus dose and total body irradiation exposure. (Upper graph) = Sarcoma incidence vs virus dose in 4-month-old BALB/c mice given 0, 250 or 500 rad of X-rays, l-month earlier. (Lower graph) =Sarcoma incidence vs. graded treatment: MSVIMLV doses for treatments 1-5 were 0.1 ml of 1O-5 through 10-l dilutions of the stock virus; X-ray doses for the same were 100, 200, 300, 400, or 500 rad.
Intrinsic and extrinsic variables affecting sensitivity l J. M. YIJHAS
inoculation failed to alter the sarcoma yield, we interpret this result as indicating that non-target cell injury can convert a linear input of carcinogenic events into a curvilinear dose-response relationship. In this artificial example, we have compared the effect of a constant amount of non-target cell injury with no non-target cell injury on an increasing frequency of carcinogenic events. In the intact animal, the frequency of carcinogenic events and the level of non-target cell injury would increase in concert. To provide a closer simulation on the intact animal situation, we compared mice which had been given the lowest dose of X-rays, 100 rad, and the lowest dose of virus, with the animals given the next higher dose of X-rays and the next highest dose of virus, etc. Lower graph is a plot of the yield of sarcomas in these mice compared to mice given only the virus. Clearly, in this comparison, where the frequency of carcinogenic events and the non-target cell injury is increasing proportionately, non-target cell injury converts a linear dose response curve into one which fits aD + pD* kinetics. In this particular example, the non-target cell injury can be traced to immunosupbut undoubtedly, a variety of additional pression,*’ types can contribute in the intact animal. These observations do not deny the possibility that target cell injury itself can produce linear plus quadratic kinetics, but they do indicate that demonstration of such kinetics should not restrict one’s consideration to target cell populations only. The nature of target cell injury The in uitro transformation system is one for which it might be argued that the only cells which can contribute to yield are the target cells. In this system, normal cells are plated in petri dishes, exposed to radiation, and at a prescribed time following exposures the cultures are stained and examined for the presence of clones of cells which appear morphologically transformed, i.e. they are no longer subject to contact inhibition of growth.” Assuming, for the moment, that a morphologic hansformant in culture is equivalent to an induced cancer in vivo, we can ask whether the demonstration .of linear plus quadratic type curves in this system is necessarily reflective of the induction of the transforming event. Data obtained in these systems are expressed in terms of transformants per surviving cell in order to consider that with increasing dose the fraction of exposed cells which survives decreases.” This assumes that transformation and cell death are independent events, yet in none of the data reported does the number of transformants per survivor increase continually; both plateaus and declining yields at high doses have been reported.‘323’7 These observations suggest that the 2 events are not totally
1119
independent, which raises the possibility that yield of the transforming events is not solely the product of the kinetics of transforming injury, even in the low dose range. Whether an artifact or a true radiobiologic interaction, these observations suggest that both types of injury must be considered in interpreting these curves, especially since allowing time for repair before harvesting exposed cultures decreases cytotoxicity but enhances transformation.” Further, in vitro does not show the yield of somatic mutations a similar interaction at similar cytotoxicity levels (see Fig. 2, below). A second problem concerns the effect of dead cells on the ability to detect transformed ones. Studies conducted in viva have led to the proposal that the presence of dead cells in the area of a transformed cell could increase the likelihood that it would develop into a frank cancer.4 While the mechanism involved was never identified, it was thought that feedback stimuli which promoted growth were involved. More recently, however, a role for dead cells in enhancing the yield of in vitro transformants has been suggested by Klein.’ In her studies, addition of heavily irradiated cells to the culture increased the yield of transformants in both unirradiated and irradiated cultures alike. Although this effect does not occur in all tissue culture systems,‘*” it may be a source of error in at least some in vitro transformation systems. Following higher doses of radiation, cultures contain more dead cells per transformant and therefore might be subject to artifactual enhancement of the yield in the high dose range, i.e. the D* component would be overestimated. A third condition, which prevents us from interpreting in vitro transformation curves strictly in EXPRESSION TIME 140
P
r
(days)
DOSE
l4
(rod)
Fig. 2. Yield of HGPRTase mutants/lob surviving CHO-K, cells as a function of X-ray dose, using expression times of 4-14
days
before
selection in medium.
6-thioglucose
containing
1120
Radiation
Oncology
0 Biology
0 Physics
terms of transforming injury, is that all cultures are scored at a single time post-irradiation. In uivo studies consistently indicate that as the dose of radiation is increased, the latent period for tumor development decreases.15 Depending on the specific time chosen for analysis, the shape of the dose-response curve can be altered. The earlier the time chosen for analysis, the more pronounced is the pDz contribution, but as the time chosen for analysis increases the curves approach linearity. Since the latent period before appearance of tumors in uivo is affected by a large number of variables which do not operate in vitro, we are not suggesting simply that these in viva observations can be used to criticize the in vitro data. To the best of our knowledge, however, this question has not been investigated systematically in vitro. Studies are currently in progress in our laboratory to determine whether in vitro transformants induced by high doses of radiation appear earlier than those induced by low doses. differ Since the kinetics of in vitro transformation widely depending on the target cells employed’,2,‘4~‘7 we are conducting these studies in 3 target cell types: BALB/c-3T3, C3H-lOTi and differentiated epithelial cells derived from the mouse lung. Although it is too preliminary to warrant analysis, we have obtained suggestive evidence that the time of analysis can affect curve shape in an analogous system, somatic cell mutation. Dr. Albert P. Li (in our laboratory) has studied the dose-response curve for radiation induced mutations at the HGPRTase locus in CHO-K, cells as a function of the time allowed for expression of the mutant phenotype. As shown in Fig. 2, the yield of radiation-induced mutations is a curvilinear function of dose when 4 days are allowed for expression of the mutant phenotype, but the shape of the curve approaches linearity as the time for expression is increased. Whether this reflects the type of mutations induced by low and high doses or a more complex interaction of mutant and non-mutant sub-populations is presently under study. While it would be tenuous to assume that a similar pattern will be observed in our transformation studies merely because mutation and transformation both involve derangement of the genetic information of the cell, these data indicate that such a possibility must be considered and that one need not invoke complex in viuo interactions to obtain such a result. From the data presented above, we conclude that demonstration of a dose-response curve which conforms to CXD+ pD* kinetics can result from target-cell or non-target cell injury, that it can be affected either positively or negatively by the concomitant killing of target cells, that it can be the product of dose dependency for the latent period required for expression, or that it truly reflects the kinetics of induction of the
July 1979, Volume 5, No. 7
transforming event. With all of these potential variables involved, we consider it unlikely that doseresponse curve analysis alone will help us to unravel the complexity of radiation carcinogenesis. Predictive value of the model Although the linear plus quadratic model does little to improve our understanding of the process of radiation carcinogenesis, it is possible that the model can be used as a means of predicting either the effects of extremely low doses of radiation which are beyond the possibility of direct analysis,* or the consequences of dose protraction. Since it is impossible to verify whether the predictions of the model are indeed valid in the extremely low dose range, we will address here the predictions of the model regarding the effects of dose protraction. As pointed out above, the PD’ component of the model indicated that multiple sub-effective hits can summate to produce cancer, and the aD term indicates that at least some single hit events can produce cancer by themselves. The effectiveness of single hits in producing cancer should be independent of the rate at which they are received; but the interacting sub-effective events should be heavily time dependent, since the first of a required series of events might be repaired before the others are received under conditions of low rates of accumulation. In the low dose range, the number of hits delivered to the cells is small and the likelihood of multiple event interaction within a cell is also small, i.e. low doses contribute to cancer yield primarily by the single hit, or aD, mechanism. In the high dose range, however, hit interaction becomes increasingly more likely and multi-hit events, as well single hit events contribute to the overall yield. Therefore, this model predicts that protraction of low doses would result in negligible reductions in carcinogenic yield, while protraction of larger doses would result in significant decreases. Although there are a number of experimental studies whose results conform to the predictions of this model,‘3,‘9 a growing body of data exists which not only fails to conform to the predictions of the model but suggests a pattern which is the reverse of expectation. At the simplest level of organization, in vitro transformation, the consequences of a 5 hr split between 2 equal doses, when compared to the respective single doses, are dependent on the total dose size, but not in accord with the predictions of the model. Fractionation of large total doses (> 150 rad) results in a reduced yield of transformants as predicted by the model. However, fractionation of low doses (< 150 rad) results in an enhanced yield. The modelI would predict similar yields from single and fractionated doses in the low dose range. Once this dose
Intrinsic and extrinsic variables affecting sensitivity 0
dependency is taken into account, other and more limited studies fit the same anomalous pattern.2”7 At present, the basis of this enhanced yield of transformants in the low dose range has not been elucidated, but it is already apparent that the mode1 does not predict the effects of protraction in even the simplest of systems. As the level of organization becomes more complex, the failure of the model to predict the effects of dose protraction becomes more pronounced, even though the respective single dose curves fit D+ D2 kinetics. One of the most well documented models for the study of radiation induced neoplasms is the radiation-induced leukemia mode1 of Kaplan and co\Single doses of X-rays are relatively 1eagues.6 ineffective in producing this cancer, but if the total dose is divided into 4 weekly fractions, leukemia yields in excess of 80% are obtainable. Two factors which do not contribute to the single dose response yield would appear to be responsible for an increased yield of leukemias upon fractionation of large total doses: activation of prototype viruses by radiation, which has been shown to be more effective following low intensity exposures,‘6 and a quantitative overcompensation by the target cells, and possibly a qualitative increase in their susceptibility to the virus.20 Chronic radiation exposures constitute a final example of the inability of the mode1 to predict the effects of dose protraction. In the lung carcinoma system of the BALB/c mouse, single acute doses of gamma rays (41 rad/min) produce a dose-response curve which conforms to linear plus quadratic kinetics (Fig. 3 upper graph). Doses of up to 196 rad are on the ascending limb of the curve, indicating that cytotoxicity does not significantly diminish the yield of tumors. Yet when doses of this magnitude are delivered at low rates, the yield of induced lung carcinomas increases, at least down to dose rates of 14 rad/day. A similar pattern was observed in the lung adenoma system of the RF mouse.18 As predicted by the model, the diminished yield with decreasing dose rates is observed at lower dose rates. We conclude therefore that cancer yields which are primarily a function of the D term do not necessarily remain unchanged upon fractionation of the dose, and that yields which are the product, at least in part, of a D2 term do not necessarily decline upon dose fractionation. DISCUSSION In the foregoing, we have shown that we are unable with any degree of certainty to identify the types of injury which lead to D + D2 kinetics, or even the cells in which injuries occur. As a consequence, the predictions of the model are often in error. As pointed out above, we have addressed this particular mode1
J. M. YUHAS
1121
25 r
DOSE
RATE
(rod
/day)
Fig. 3. Yield of induced type II alveolar cell carcinomas in BALB/c female mice exposed to 13’Cs gamma rays. (Upper dose size; graph) = incidence vs acute (41 rad/minute) (Lower graph) = yield of carcinomas vs the dose rate at which a total dose of 196 rad was delivered. since it is the one employed most frequently, but the basic criticism applies to all other mathematical models which rest on similar simplifications. This evaluation or criticism of the model should not be interpreted pessimistically, however, since the intent was to be constructive. It would appear that 2 avenues are available for further development of models of this process. At one extreme, one could propose a mode1 which takes account of all of the complexities of the process and includes terms for immunosuppression, transformation, cytotoxicity. etc. While such a model would be biologically pleasing because of its completeness, it would be functionally useless; at our present state of knowledge, we cannot assign strict quantitative values to any one variable, much less to all of them. A more logical approach would appear to be to address the problem in a single system, develop a quantitative understanding of the cancers induced under both acute and protracted exposure conditions, and then identify the biological variables which account for these patterns. A true understanding of the factors involved in the radiation induction of cancer in even a single system would appear to be more valuable than a series of anecdotal observations in many systems.
Radiation Oncology 0
I122
Space models already as the different get cell effects, example,
Biology
0 Physics
does not permit us to present the 2 types of we are presently considering, but 2 points are apparent: injury to a population of cells, such lymphocyte, can have opposite effects in tumor systems,*’ and perturbation of a tarpopulation can lead to diametrically opposed depending on the endpoint studied. As an doubling the number of target cells in an
July 1979, Volume 5, No. 7
animal would increase its resistance to hematopoietic death, would not alter its sensitivity in mutagenesis assays, but would double its likelihood of developing cancer. Hopefully, through identification of the biological variables involved and through consideration of endpoint-dependent differences in response to these perturbations, more adequate models of radiation carcinogenesis can be developed.
REFERENCES 1. Borek, C., Hall, E.J.: Transformation of mammalian cells in vitro by low doses of X-rays. Nature 243: 450-453, 1973. 2. Borek, C., Hall, E.J.: Effect of split doses of X-rays on neoplastic transformation of single cells. Nature 252: 499-501, 1974. 3. Brown, J.M.: The shape of the dose-responses curve for radiation carcinogenesis: Extrapolation to low doses. Radiat. Res. 71: 34-50, 1977. 4. Casarett, G.W.: Pathogenesis of radionuclide-induced tumors. In, Radionculide Carcinogenesis, ed. by. Saunders C.L., Washington., D.C., (U.S. Atomic Energy Commission) 1973, pp. I-18,. 5. Clapp, N.K., Yuhas, J.M.: A suggested correlation between radiationinduced immunosuppression and radiogenie leukemia in mice. J. Nut1 Cancer Inst. 51: 12111215, 1973. 6. Kaplan, H.S., Brown, M.B.: A quantitative dose response study of lymphoid tumor development in irradiated C57 black mice. .I. Nat1 Cancer Inst. 13: 185-208, 1952. 7. Kellerer, A.M., Physical aspects of radiation sensitivity. Znt. J. Rad Oncol Biol Phys 5: 000-000, 1979. 8. Kellerer, A.M., Rossi, H.: The theory of dual radiation action. In Current Topics in Radiation Research, Vol. 8: North-Holland Public, Amsterdam. 85-158, 1972. 9. Klein, J.C.: Evidence against a direct carcinogenic effect of X-rays in vitro. .Z. NatZ Cancer Inst. 52: 111 l1116, 1974. 10. Klein, J.C.: The use of in vitro methods for the study of X-ray induced transformation. In Biology of Radiation Carcinogenesis, ed. by. Yuhas, J.M., Tennant, R.W., Regan, J.D., New York, Raven Press, 1976, pp. 301307. 11. Lappe, M.: Evidence for immunological surveillance during skin carcinogenesis: lnflammatory foci in imIn Immunological munologically competent mice. Parameters of Host-Tumor Relationships, Vol. I, ed. by. Weiss, D., Academic Press, 1971, pp. 52-65.
12. Leenhouts,
H.P.,
Chadwick,
K.H.:
An analysis
of
13.
14.
15.
16.
17.
radiation-induced malignancy based on somatic mutation. lnt. J. Radiat. Biol. 33: 357-370, 1978. Metalli, P., Silini, G., Castello, S., Covelli, V.: In Radiation Induced cancer, 1AEA-SM- 118/ 14, IAEA, 1969, pp. 277-289. Miller, R., Hall, E.J.: X-ray dose fractionation and oncogenic transformations in cultured mouse embryo cells. Nature 272: 58-60, 1978. Mole, R.H.: Carcinogenesis by ionizing radiation and lessons for other pollutants. In Radiation Research: Biochemical, Chemical and Physical Perspectives, ed. by. Nyggard, 0. Adler, H. Sinclair, W. New York, Academic Press, pp. 560-868, 1975. Tennant, R.W., Rascati, R.J., Lavelle, G.C.: Mechanisms in endogenous leukemia virus induction by radiation and chemicals. In Radiation-Induced LeukeNorthmogenesis, ed. by. Duplan, J.F., Amsterdam, Holland Pub]. Co, pp. 179-188, 1977. Terzaghi, M., Little, J.B.: Repair of potentially lethal radiation damage in mammalian cells is associated with enhancement of malignant transformation. Nature 253:
pp. 548, 1975. 18. Upton, A.C., Randolph, M.L., Conklin, J.W.: Late effects of fast neutrons and gamma rays in mice as influenced by the dose rate of irradiation. Induction of neoplasia. Radiat. Res. 41: 467-491, 1970. 19. Yuhas, J.M.: Dose response curves and their modification by specific mechanisms. In Biology of Radiation Carcinogenesis, ed. by. Yuhas, J.M., Tennant, R.W., Regan, J.D., New York, Raven Press, pp. 51-61, 1976. 20:Yuhas, J.M.: The dual role of the lymphocyte in radiation leukemogenesis, In Radiation-Induced Leukemia, ed. by. Duplan, J.F., Amsterdam, North-Holland Publ. Co, pp. 99-114, 1977. 21. Yuhas, J.M., Pazmino, N.H.: Relative contribution of target cell distrurbances and immunosuppression in radiation leukemogenesis: Model Studies with exogenous virus. Radiat. Res. 60: 104-114, 1976.
Sensitivity:
INTRINSIC
Facts and Models
AND EXTRINSIC VARIABLES AFFECTING RADIATION CARCINOGENESIS JOHN
Cancer Research and Treatment
M.
YUHAS,
SENSITIVITY
TO
Ph.D.
Center and Department of Radiology, Albuquerque, NM 87131, U.S.A.
University
of New Mexico,
Mathematical models relating observed yield of cancers vs administered radiation dose have become popular in recent years, especially as means of predicting hazards associated with exposure conditions which are beyond the realm of practical experimentation. While the validity of these predictions remains a controversy, these models, especially the cxD + PD’ model, have more recently been used to infer the mechanism(s) underlying the carcinogenic process. Through the analysis of simple experimental systems, we demonstrate in this report that aD + hD2 kinetics can result from injury to the cells which eventually develop into the cancer (target cells) or from injury to those cells which affect target cell survival. Further, these kinetics can fail to predict the consequences of dose protraction, largely due to the fact that transformation increases with dose, while survival decreases. The role of these models in helping to develop an understanding of mechanisms should be restricted, therefore, to the formulation of basic hypotheses which are subject to direct testing in the laboratory. Radiation carcinogenesis,
Linear plus quadratic model, Target cells
INTRODUCTION
forest because of all of the trees which are in the way, and it might be possible, that many of the potential variables are, in fact, of minor consequence, and sensitivity may be determined by one or a few key factors. If this is true, then development of a clear understanding of radiation carcinogenesis would proceed more rapidly, and this possibility forms the subject matter of this discussion. A particularly useful model in radiation carcinogenesis is the linear plus quadratic model, which can be fitted to most if not all, experimental data on the subject. As an example of mathematical models in general, we will examine this model in terms of the types of injury which can contribute to it, and in terms of its reliability in predicting the effects of dose protraction. The conclusions reached below, which are equally applicable to other purely mathematical models, are that linear plus quadratic kinetics can result from a variety of types of injury in different types of tissues, and that since this model does not take this complexity and variety into account it is often unable to predict the consequences of dose protraction.
A simple listing of all of the variables which can, at least theoretically, affect the sensitivity of mammalian cells and organisms to radiation carcinogenesis would occupy all of the space available for this discussion. Alternatively, we can examine the generalities which have been put forth to accpunt for the overall process. Given what is clearly a complex and varied problem, investigators have taken one of two approaches: development of mathematical models which ignore the underlying biological complexity in favor of precise quantification of the end result, or identification of single variables involved transformation, immunosuppression, etc.) (e.g. without regard to their relative importance or their interaction with other variables. We have suggested” that neither approach is entirely adequate, especially when one tries to predict qualitative aspects from strictly quantitative data and vice versa. We proposed, instead, that the logical study of radiation carcinogenesis requires both quantitative and qualitative information, and that both aspects must be investigated simultaneously or at least sequentially. Mathematical models, or more precisely dose response curves would serve as tools for the development of working hypotheses, which would then be tested in the hope of identifying the nature of the variables involved and their quantitative importance. Biologists are, however, often unable to see the
The linear PLUS quadratic The linear plus quadratic is of the form:
model model of radiation
Effect = crD + pD* 111
injury
1118
Radiation
Oncology
0 Biology 0 Physics
In the specific case being discussed here, effect is in terms of radiation-induced increases in the yield of cancers. While this model has been used by a number of authors, its formal inclusion in a model of radiation carcinogenesis can be traced to Kellerer and Rossi.* The microdosimetric considerations which led to the use of this model have been described elsewhere in this symposium by Kellerer.’ In brief, the “dual action theory” of radiation carcinogenesis argues that radiation exposure can produce cancer in one of two ways: through the production of single hit events, each of which is able in itself to produce the cancer; or, through the summation of multiple hits, each of which is unable to produce the cancer. These correspond to the olD and pD* terms, respectively. For sparsely ionizing radiation, such as X-or gamma-rays, which are the primary concern of the present report, the slope of the D2 term /3 is large, resulting in a curvilinear relationship between dose and yield of cancers. Beyond proposing that the linear and quadratic terms in the model had a microdosimetric basis, the original authors” made no further comments regarding the nature of the injury involved, its location, or the consequences of dose protraction. This model can, however, be fitted to many experimental data, and this, coupled with its reasonable microdosimetric basis, has increased its popularity dramatically. Quite often, however, the application of this model is made without regard to our limited understanding of it; assumptions are made regarding the cells and type of injury involved,‘* and predictions are made from it regarding the effects of dose protraction.3 We show below that oD+ pD2 kinetics can result from a variety of types and sites of injury, and that failure to take this into account makes the predictive value of the model poor in many instances.
Target cell us non-target cell injury We define target cells as those which can develop into the induced cancer, and non-target cells as any others. The question posed here is whether non-target cell injury can produce aD + BD2 kinetics even if the number of carcinogenic events bears a linear relationship to dose. If the only cells capable of producing these kinetics are target cells, then the value of in vitro transformation systems is markedly increased, but if both types of cells can, it is unlikely that the shape of the single dose curve will be predictive of the consequences of dose protraction. A number of systemic control mechanisms are logical candidates for non-target cell contributions, and certain published studies5,” are consistent with a role for them in determining dose-response curve shape. The clearest demonstration that non-target cell injury can affect curve shape, however, comes from experiments specifically designed to test this pos-
July 1979, Volume 5, No. 7
sibility. In our studies on the interaction of radiation and oncogenic viruses,“-*’ it was demonstrated that radiation exposure alone, either total body or localized to the right leg, failed to induce a detectable increase in the frequency of sarcomas in the right leg. However, injection of graded doses of the Moloney strain of the sarcoma/leukemia virus complex, MSV/MLV, which had been passaged in vitro to reduce its leukemogenic potency, resulted in a linear relationship between injected virus dose and the yield of sarcomas (Fig. 1 upper graph). Exposure of the right leg to localized X-ray doses of up to 500 rad did not alter the yield of sarcomas induced by the virus injection, but total body irradiation did. Total body X-ray doses of 250 or 500 rad, given 1 month prior to the virus, converted the relationship of virus dose to sarcoma yield from a linear one to a curvilinear one, i.e. the exposures enhanced the yield of sarcomas in the high dose, but not in the low dose, range. Since local irradiation of the injection site prior to virus
60
/ c
/
/
9 f!? 0
0 rod 40
: v)
,” z
20
0
VIRUS
ALONE
/
TREATMENT
LEVEL
Fig. 1. Yield of MSV/MLV induced injection site sarcomas at 6-months as a function of virus dose and total body irradiation exposure. (Upper graph) = Sarcoma incidence vs virus dose in 4-month-old BALB/c mice given 0, 250 or 500 rad of X-rays, l-month earlier. (Lower graph) =Sarcoma incidence vs. graded treatment: MSVIMLV doses for treatments 1-5 were 0.1 ml of 1O-5 through 10-l dilutions of the stock virus; X-ray doses for the same were 100, 200, 300, 400, or 500 rad.
Intrinsic and extrinsic variables affecting sensitivity l J. M. YIJHAS
inoculation failed to alter the sarcoma yield, we interpret this result as indicating that non-target cell injury can convert a linear input of carcinogenic events into a curvilinear dose-response relationship. In this artificial example, we have compared the effect of a constant amount of non-target cell injury with no non-target cell injury on an increasing frequency of carcinogenic events. In the intact animal, the frequency of carcinogenic events and the level of non-target cell injury would increase in concert. To provide a closer simulation on the intact animal situation, we compared mice which had been given the lowest dose of X-rays, 100 rad, and the lowest dose of virus, with the animals given the next higher dose of X-rays and the next highest dose of virus, etc. Lower graph is a plot of the yield of sarcomas in these mice compared to mice given only the virus. Clearly, in this comparison, where the frequency of carcinogenic events and the non-target cell injury is increasing proportionately, non-target cell injury converts a linear dose response curve into one which fits aD + pD* kinetics. In this particular example, the non-target cell injury can be traced to immunosupbut undoubtedly, a variety of additional pression,*’ types can contribute in the intact animal. These observations do not deny the possibility that target cell injury itself can produce linear plus quadratic kinetics, but they do indicate that demonstration of such kinetics should not restrict one’s consideration to target cell populations only. The nature of target cell injury The in uitro transformation system is one for which it might be argued that the only cells which can contribute to yield are the target cells. In this system, normal cells are plated in petri dishes, exposed to radiation, and at a prescribed time following exposures the cultures are stained and examined for the presence of clones of cells which appear morphologically transformed, i.e. they are no longer subject to contact inhibition of growth.” Assuming, for the moment, that a morphologic hansformant in culture is equivalent to an induced cancer in vivo, we can ask whether the demonstration .of linear plus quadratic type curves in this system is necessarily reflective of the induction of the transforming event. Data obtained in these systems are expressed in terms of transformants per surviving cell in order to consider that with increasing dose the fraction of exposed cells which survives decreases.” This assumes that transformation and cell death are independent events, yet in none of the data reported does the number of transformants per survivor increase continually; both plateaus and declining yields at high doses have been reported.‘323’7 These observations suggest that the 2 events are not totally
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independent, which raises the possibility that yield of the transforming events is not solely the product of the kinetics of transforming injury, even in the low dose range. Whether an artifact or a true radiobiologic interaction, these observations suggest that both types of injury must be considered in interpreting these curves, especially since allowing time for repair before harvesting exposed cultures decreases cytotoxicity but enhances transformation.” Further, in vitro does not show the yield of somatic mutations a similar interaction at similar cytotoxicity levels (see Fig. 2, below). A second problem concerns the effect of dead cells on the ability to detect transformed ones. Studies conducted in viva have led to the proposal that the presence of dead cells in the area of a transformed cell could increase the likelihood that it would develop into a frank cancer.4 While the mechanism involved was never identified, it was thought that feedback stimuli which promoted growth were involved. More recently, however, a role for dead cells in enhancing the yield of in vitro transformants has been suggested by Klein.’ In her studies, addition of heavily irradiated cells to the culture increased the yield of transformants in both unirradiated and irradiated cultures alike. Although this effect does not occur in all tissue culture systems,‘*” it may be a source of error in at least some in vitro transformation systems. Following higher doses of radiation, cultures contain more dead cells per transformant and therefore might be subject to artifactual enhancement of the yield in the high dose range, i.e. the D* component would be overestimated. A third condition, which prevents us from interpreting in vitro transformation curves strictly in EXPRESSION TIME 140
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Fig. 2. Yield of HGPRTase mutants/lob surviving CHO-K, cells as a function of X-ray dose, using expression times of 4-14
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terms of transforming injury, is that all cultures are scored at a single time post-irradiation. In uivo studies consistently indicate that as the dose of radiation is increased, the latent period for tumor development decreases.15 Depending on the specific time chosen for analysis, the shape of the dose-response curve can be altered. The earlier the time chosen for analysis, the more pronounced is the pDz contribution, but as the time chosen for analysis increases the curves approach linearity. Since the latent period before appearance of tumors in uivo is affected by a large number of variables which do not operate in vitro, we are not suggesting simply that these in viva observations can be used to criticize the in vitro data. To the best of our knowledge, however, this question has not been investigated systematically in vitro. Studies are currently in progress in our laboratory to determine whether in vitro transformants induced by high doses of radiation appear earlier than those induced by low doses. differ Since the kinetics of in vitro transformation widely depending on the target cells employed’,2,‘4~‘7 we are conducting these studies in 3 target cell types: BALB/c-3T3, C3H-lOTi and differentiated epithelial cells derived from the mouse lung. Although it is too preliminary to warrant analysis, we have obtained suggestive evidence that the time of analysis can affect curve shape in an analogous system, somatic cell mutation. Dr. Albert P. Li (in our laboratory) has studied the dose-response curve for radiation induced mutations at the HGPRTase locus in CHO-K, cells as a function of the time allowed for expression of the mutant phenotype. As shown in Fig. 2, the yield of radiation-induced mutations is a curvilinear function of dose when 4 days are allowed for expression of the mutant phenotype, but the shape of the curve approaches linearity as the time for expression is increased. Whether this reflects the type of mutations induced by low and high doses or a more complex interaction of mutant and non-mutant sub-populations is presently under study. While it would be tenuous to assume that a similar pattern will be observed in our transformation studies merely because mutation and transformation both involve derangement of the genetic information of the cell, these data indicate that such a possibility must be considered and that one need not invoke complex in viuo interactions to obtain such a result. From the data presented above, we conclude that demonstration of a dose-response curve which conforms to CXD+ pD* kinetics can result from target-cell or non-target cell injury, that it can be affected either positively or negatively by the concomitant killing of target cells, that it can be the product of dose dependency for the latent period required for expression, or that it truly reflects the kinetics of induction of the
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transforming event. With all of these potential variables involved, we consider it unlikely that doseresponse curve analysis alone will help us to unravel the complexity of radiation carcinogenesis. Predictive value of the model Although the linear plus quadratic model does little to improve our understanding of the process of radiation carcinogenesis, it is possible that the model can be used as a means of predicting either the effects of extremely low doses of radiation which are beyond the possibility of direct analysis,* or the consequences of dose protraction. Since it is impossible to verify whether the predictions of the model are indeed valid in the extremely low dose range, we will address here the predictions of the model regarding the effects of dose protraction. As pointed out above, the PD’ component of the model indicated that multiple sub-effective hits can summate to produce cancer, and the aD term indicates that at least some single hit events can produce cancer by themselves. The effectiveness of single hits in producing cancer should be independent of the rate at which they are received; but the interacting sub-effective events should be heavily time dependent, since the first of a required series of events might be repaired before the others are received under conditions of low rates of accumulation. In the low dose range, the number of hits delivered to the cells is small and the likelihood of multiple event interaction within a cell is also small, i.e. low doses contribute to cancer yield primarily by the single hit, or aD, mechanism. In the high dose range, however, hit interaction becomes increasingly more likely and multi-hit events, as well single hit events contribute to the overall yield. Therefore, this model predicts that protraction of low doses would result in negligible reductions in carcinogenic yield, while protraction of larger doses would result in significant decreases. Although there are a number of experimental studies whose results conform to the predictions of this model,‘3,‘9 a growing body of data exists which not only fails to conform to the predictions of the model but suggests a pattern which is the reverse of expectation. At the simplest level of organization, in vitro transformation, the consequences of a 5 hr split between 2 equal doses, when compared to the respective single doses, are dependent on the total dose size, but not in accord with the predictions of the model. Fractionation of large total doses (> 150 rad) results in a reduced yield of transformants as predicted by the model. However, fractionation of low doses (< 150 rad) results in an enhanced yield. The modelI would predict similar yields from single and fractionated doses in the low dose range. Once this dose
Intrinsic and extrinsic variables affecting sensitivity 0
dependency is taken into account, other and more limited studies fit the same anomalous pattern.2”7 At present, the basis of this enhanced yield of transformants in the low dose range has not been elucidated, but it is already apparent that the mode1 does not predict the effects of protraction in even the simplest of systems. As the level of organization becomes more complex, the failure of the model to predict the effects of dose protraction becomes more pronounced, even though the respective single dose curves fit D+ D2 kinetics. One of the most well documented models for the study of radiation induced neoplasms is the radiation-induced leukemia mode1 of Kaplan and co\Single doses of X-rays are relatively 1eagues.6 ineffective in producing this cancer, but if the total dose is divided into 4 weekly fractions, leukemia yields in excess of 80% are obtainable. Two factors which do not contribute to the single dose response yield would appear to be responsible for an increased yield of leukemias upon fractionation of large total doses: activation of prototype viruses by radiation, which has been shown to be more effective following low intensity exposures,‘6 and a quantitative overcompensation by the target cells, and possibly a qualitative increase in their susceptibility to the virus.20 Chronic radiation exposures constitute a final example of the inability of the mode1 to predict the effects of dose protraction. In the lung carcinoma system of the BALB/c mouse, single acute doses of gamma rays (41 rad/min) produce a dose-response curve which conforms to linear plus quadratic kinetics (Fig. 3 upper graph). Doses of up to 196 rad are on the ascending limb of the curve, indicating that cytotoxicity does not significantly diminish the yield of tumors. Yet when doses of this magnitude are delivered at low rates, the yield of induced lung carcinomas increases, at least down to dose rates of 14 rad/day. A similar pattern was observed in the lung adenoma system of the RF mouse.18 As predicted by the model, the diminished yield with decreasing dose rates is observed at lower dose rates. We conclude therefore that cancer yields which are primarily a function of the D term do not necessarily remain unchanged upon fractionation of the dose, and that yields which are the product, at least in part, of a D2 term do not necessarily decline upon dose fractionation. DISCUSSION In the foregoing, we have shown that we are unable with any degree of certainty to identify the types of injury which lead to D + D2 kinetics, or even the cells in which injuries occur. As a consequence, the predictions of the model are often in error. As pointed out above, we have addressed this particular mode1
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25 r
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/day)
Fig. 3. Yield of induced type II alveolar cell carcinomas in BALB/c female mice exposed to 13’Cs gamma rays. (Upper dose size; graph) = incidence vs acute (41 rad/minute) (Lower graph) = yield of carcinomas vs the dose rate at which a total dose of 196 rad was delivered. since it is the one employed most frequently, but the basic criticism applies to all other mathematical models which rest on similar simplifications. This evaluation or criticism of the model should not be interpreted pessimistically, however, since the intent was to be constructive. It would appear that 2 avenues are available for further development of models of this process. At one extreme, one could propose a mode1 which takes account of all of the complexities of the process and includes terms for immunosuppression, transformation, cytotoxicity. etc. While such a model would be biologically pleasing because of its completeness, it would be functionally useless; at our present state of knowledge, we cannot assign strict quantitative values to any one variable, much less to all of them. A more logical approach would appear to be to address the problem in a single system, develop a quantitative understanding of the cancers induced under both acute and protracted exposure conditions, and then identify the biological variables which account for these patterns. A true understanding of the factors involved in the radiation induction of cancer in even a single system would appear to be more valuable than a series of anecdotal observations in many systems.
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does not permit us to present the 2 types of we are presently considering, but 2 points are apparent: injury to a population of cells, such lymphocyte, can have opposite effects in tumor systems,*’ and perturbation of a tarpopulation can lead to diametrically opposed depending on the endpoint studied. As an doubling the number of target cells in an
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animal would increase its resistance to hematopoietic death, would not alter its sensitivity in mutagenesis assays, but would double its likelihood of developing cancer. Hopefully, through identification of the biological variables involved and through consideration of endpoint-dependent differences in response to these perturbations, more adequate models of radiation carcinogenesis can be developed.
REFERENCES 1. Borek, C., Hall, E.J.: Transformation of mammalian cells in vitro by low doses of X-rays. Nature 243: 450-453, 1973. 2. Borek, C., Hall, E.J.: Effect of split doses of X-rays on neoplastic transformation of single cells. Nature 252: 499-501, 1974. 3. Brown, J.M.: The shape of the dose-responses curve for radiation carcinogenesis: Extrapolation to low doses. Radiat. Res. 71: 34-50, 1977. 4. Casarett, G.W.: Pathogenesis of radionuclide-induced tumors. In, Radionculide Carcinogenesis, ed. by. Saunders C.L., Washington., D.C., (U.S. Atomic Energy Commission) 1973, pp. I-18,. 5. Clapp, N.K., Yuhas, J.M.: A suggested correlation between radiationinduced immunosuppression and radiogenie leukemia in mice. J. Nut1 Cancer Inst. 51: 12111215, 1973. 6. Kaplan, H.S., Brown, M.B.: A quantitative dose response study of lymphoid tumor development in irradiated C57 black mice. .I. Nat1 Cancer Inst. 13: 185-208, 1952. 7. Kellerer, A.M., Physical aspects of radiation sensitivity. Znt. J. Rad Oncol Biol Phys 5: 000-000, 1979. 8. Kellerer, A.M., Rossi, H.: The theory of dual radiation action. In Current Topics in Radiation Research, Vol. 8: North-Holland Public, Amsterdam. 85-158, 1972. 9. Klein, J.C.: Evidence against a direct carcinogenic effect of X-rays in vitro. .Z. NatZ Cancer Inst. 52: 111 l1116, 1974. 10. Klein, J.C.: The use of in vitro methods for the study of X-ray induced transformation. In Biology of Radiation Carcinogenesis, ed. by. Yuhas, J.M., Tennant, R.W., Regan, J.D., New York, Raven Press, 1976, pp. 301307. 11. Lappe, M.: Evidence for immunological surveillance during skin carcinogenesis: lnflammatory foci in imIn Immunological munologically competent mice. Parameters of Host-Tumor Relationships, Vol. I, ed. by. Weiss, D., Academic Press, 1971, pp. 52-65.
12. Leenhouts,
H.P.,
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K.H.:
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radiation-induced malignancy based on somatic mutation. lnt. J. Radiat. Biol. 33: 357-370, 1978. Metalli, P., Silini, G., Castello, S., Covelli, V.: In Radiation Induced cancer, 1AEA-SM- 118/ 14, IAEA, 1969, pp. 277-289. Miller, R., Hall, E.J.: X-ray dose fractionation and oncogenic transformations in cultured mouse embryo cells. Nature 272: 58-60, 1978. Mole, R.H.: Carcinogenesis by ionizing radiation and lessons for other pollutants. In Radiation Research: Biochemical, Chemical and Physical Perspectives, ed. by. Nyggard, 0. Adler, H. Sinclair, W. New York, Academic Press, pp. 560-868, 1975. Tennant, R.W., Rascati, R.J., Lavelle, G.C.: Mechanisms in endogenous leukemia virus induction by radiation and chemicals. In Radiation-Induced LeukeNorthmogenesis, ed. by. Duplan, J.F., Amsterdam, Holland Pub]. Co, pp. 179-188, 1977. Terzaghi, M., Little, J.B.: Repair of potentially lethal radiation damage in mammalian cells is associated with enhancement of malignant transformation. Nature 253:
pp. 548, 1975. 18. Upton, A.C., Randolph, M.L., Conklin, J.W.: Late effects of fast neutrons and gamma rays in mice as influenced by the dose rate of irradiation. Induction of neoplasia. Radiat. Res. 41: 467-491, 1970. 19. Yuhas, J.M.: Dose response curves and their modification by specific mechanisms. In Biology of Radiation Carcinogenesis, ed. by. Yuhas, J.M., Tennant, R.W., Regan, J.D., New York, Raven Press, pp. 51-61, 1976. 20:Yuhas, J.M.: The dual role of the lymphocyte in radiation leukemogenesis, In Radiation-Induced Leukemia, ed. by. Duplan, J.F., Amsterdam, North-Holland Publ. Co, pp. 99-114, 1977. 21. Yuhas, J.M., Pazmino, N.H.: Relative contribution of target cell distrurbances and immunosuppression in radiation leukemogenesis: Model Studies with exogenous virus. Radiat. Res. 60: 104-114, 1976.
