Environmental Health Perspectives, Volume 104, Supplement 6, December 1996
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Modeling Marrow Damage from Response Data: Evolution from Radiation Biology to Benzene Toxicity
Troyce D. Jones, Max D. Morris, and Jafar S. Hasan
Oak Ridge National Laboratory, Oak Ridge, Tennessee
Abstract
Consensus principles from radiation biology were used to describe a generic set of nonlinear, first-order differential equations for modeling toxicity-induced compensatory cell kinetics in terms of sublethal injury, repair, direct killing, killing of cells with unrepaired sublethal injury, and repopulation. This cellular model was linked to a probit model of hematopoietic mortality that describes death from infection and/or hemorrhage between 5 and 30 days. Mortality data from 27 experiments with 851 dose-response groups, in which doses were protracted by rate and/or fractionation, were used to simultaneously estimate all rate constants by maximum-likelihood methods. Data used represented 18,940 test animals: 12,827 mice, 2925 rats, 1676 sheep, 829 swine, 479 dogs, and 204 burros. Although a long-term, repopulating hematopoietic stem cell is ancestral to all lineages needed to restore normal homeostasis, the dose-response data from the protracted irradiations indicate clearly that the particular lineage that is critical to hematopoietic recovery does not resemble stemlike cells with regard to radiosensitivity and repopulation rates. Instead, the weakest link in the chain of hematopoiesis was found to have an intrinsic radioresistance equal to or greater than stromal cells and to repopulate at the same rates. Model validation has been achieved by predicting the LD50 and/or fractional group mortality in 38 protracted-dose experiments (rats and mice) that were not used in the fitting of model coefficients. -- Environ Health Perspect 104(Suppl 6):1293-1301 (1996)
Key words: benzene, radiation, marrow, stroma, stem cell, CFU-S
This paper was presented at Benzene '95: An International Conference on the Toxicity, Carcinogenesis, and Epidemiology of Benzene held 17-20 June 1995 in Piscataway, New Jersey. Manuscript received 16 January 1996; manuscript accepted 14 June 1996.
This research was sponsored by the Defense Nuclear Agency, Office of Radiation Environmental Modeling, Interagency Agreement DOE 0046-1539-A1 under Lockheed Martin Energy Systems, Inc. with the U.S. Department of Energy.
Address correspondene to T.D. Jones, Chemical and Biological Physics Section, Oak Ridge National Laboratory, Building 4500-S, MS 6101, PO Box 2008, Oak Ridge, TN 37831-6101. Telephone: (423) 574-6257. Fax: (615) 576-7651. E-mail: tdj@ornl.gov
Abbreviations used: CFC, colony-forming cell; CFU-F, colony-forming unit of marrow fibroblast; CFU-S, colony forming unit in the spleen; EPD, equivalent prompt dose of a radiation given in a pulse; LD50, dose that is toxic to 50% of the test population; MLE, maximum likelihood estimation; MSOD, many sets of data; SSOD, single set of data; TD, doubling time.
Introduction
An editorial in The American Statistician by A.S.C. Ehrenberg (1), derived from experiences with business and marketing, insightfully describes a belief that analysis of many sets of data (MSOD)
"seems to be the only way in which we can produce results that are generalizable, lawlike, and predictable--which in fact hold for many sets of data...our concern will be with deciding what the main effect is quantitatively, how to model it, how consistent it is, under what different conditions it does or does not occur, why it arises, how it links up with other findings, and how it can be used in practical applications and/or in the development of theory."
Although we have used such practices for nearly 20 years--in carcinogenic risk assessments, mathematical models of acute lethality, and marrow cell kinetics underlying radiation-induced hematopoiesis--we did not attempt to communicate those generalized ideas outside our particular areas of interest, nor have we stated the essential ideas so compactly.
For mathematical models of dose-response effects, historically there has been a near-total reliance upon finding a simple equation that will approximate a single set of experimental data (SSOD) when the numerical constants are fitted appropriately. Fits to other data sets, from similar experimental protocols, require additional statistical justification that the model is acceptable and require new fitted parameters. Although continued use of the same functional form usually produces some attempt to establish a biological interpretation of the underlying effects (i.e., a conceptual model), in general, such interpretations usually have no fundamental validity and ignore far more important biological factors than the few they are hypothesized to approximate; even for those few factors, there is a pronounced lack of generality for protracted-, fractionated-, or variable-rate exposure protocols. Results from such exercises are without substantial validity outside the ranges of experimental conditions used and have no basis in reality when extrapolated in terms of dose, dose rate, or test species/strain used.
The general domain of biologically based or conceptual models bifurcates into additional basic approaches. One pathway involves assumptions, either direct or indirect, that the important processes are known in terms of specific molecular/cellular effects, and simple factors and descriptive models can be written accordingly. When indirect assumptions are involved, it is often overlooked that the conclusions obtained from experiment-by-experiment evaluations of the models are mandated either by the constraints of the model or by limitations of the particular experiment used to estimate parameters. Subtle, indirect assumptions have the hazard of going unrecognized, perhaps even to the researchers themselves.
Our approach formulates generalized dose-response models in terms of generic processes: molecular effects, from a cell kinetics perspective, and descriptions of local and systemic reactions that may act through cell-to-cell and/or humoral-mediated effects involving hormones, chalones, or cytokines. The dosing schedules used for benzene experiments do not reflect adequate protocol-dependent variability to permit use of the MSOD approach to a degree that would provide insight into underlying biological mechanisms. In contrast, historical data from radiation biology do reflect those needed variations in experimental design. Those variations can be found at the molecular, cellular, organ, and organism levels, and all of those structural tiers have been considered to various degrees in model conceptualization, coefficient estimation, and model validation in our previous publications on radiation-induced hematopoiesis (2,3). Because our maximum likelihood estimations (MLE) have relied only upon lethality data from both short-term and long-term irradiations, those experiments, as summarized in Figure 1, serve as the database to evaluate the generic model in terms of cells critical to hematopoietic recovery (4,5).
Figure 1. Summary of data used from acute lethality experiments with protracted doses of ionizing radiations to determine the rate constants by maximum likelihood estimation techniques in the generic cell kinetics model of radiation-induced hematopoiesis.
Following is a brief description of how we have formulated a generic model for cell kinetics associated with radiation-induced hematopoiesis and how MSODs can be used to generalize the model and provide insight into the fundamental underlying mechanisms. As indicated in Table 1, the conceptual and mathematical models used for ionizing radiations, should also be relevant to considerations of benzene toxicity. Experimental data needed to estimate model parameters are fragmentary. Specifically, our intent was to use dogmatic terms and factors (or, as a minimum condition of acceptance those common to expert consensus) to approximate generic processes associated with marrow cell kinetics underlying acute lethality. Next, MLE methods were used to evaluate the numerical parameters of the models and their associated confidence bounds. This approach provides no direct cause-effect proof that the biologically based model is indeed correct in all details, but, because enormous sets of data, reflecting wide ranges of variability, can be fitted by a common set of evaluated parameters that are consistent with specific biological rate constants, it is obvious that the model is substantially correct in behavior and provides hypotheses that in turn may be validated or modified by further refinement of experimental design. In addition, we found it desirable to evaluate and test a cell kinetics model formulated in terms of those same nonspecific damage, repair, and repopulation processes as derived from colony-forming unit-spleen (CFU-S) experiments, in contrast to the parallel evaluation made from the generic model and animal lethality data (i.e., the underlying dependence on critical cells is not restricted to stem or CFU-S types of cells).
Materials and Methods
When animals are irradiated by acute protocols, death from infection and/or hemorrhage may occur between about 5 and 30 days postirradiation. The frequency of death can be described by a probit distribution function with fitted parameters composed of the LD50 and slope (i.e., slope = 
-1, which is the inverse standard deviation of the frequency distribution). The LD50 and may be for the particular radiation field of interest or for a standard or reference radiation if there is a realistic way of modeling the underlying degree of cytopenia from the exposure of interest and converting that level of effect back to an equivalent reference dose of the standard radiation associated with the LD50 and estimates. Depression of neutrophils and platelets are accepted as the proximate cause of death, but the contributing cause of death could be cytopenia of either the terminally differentiated cells themselves, ancestral cells, or ancestral-dependent lineages upstream in the direction of the undifferentiated pluripotent stem cells. Cytopenia of a critical lineage would result in either a deficiency of cells or cell-mediated cytokines. For generality, the weakest link (i.e., lineage) was treated generically and guided by MLE evaluations, in contrast to more restrictive assumptions. One major advantage of this approach is that only one (LD50, ) combination was required for a complex experiment involving different dose rates, exposure protocols, radiation sources, etc. (4,5). In short, only changes with respect to the strain, species, cage care, and conditions of observation required additional LD50 and values. One experiment in the analysis comprised 26 different LD50 protocols, but all were consistent with a common LD50 and associated with an "equivalent prompt dose."
In the mathematical model, cells are compartmentalized into normal (N), injured (I), and killed (K) populations. Processes by which cells move among those populations are modeled by first-order, nonlinear equations. In an arbitrary volume of marrow, we call the numbers of normal, injured, and killed cells nN, nI, and nK, respectively. Initial conditions are nN = nO (normal before exposure), nI = 0 (no injury before exposure) and nK = 0 (no killing before exposure). The nO need not be estimated because only ratios of nN, nI, and nK relative to nO are used. The cellular component of the model is
In these equations, 
is the rate constant that mediates movement of cells from normal or injured states as indicated by the first subscript to the state indicated by the second subscript. D is dose given uniformly to marrow, and prime denotes the derivative of a cell count or dose (i.e., dose rate) with respect to time. Factors and terms of Equations 1 to 3 are given in Tables 2 and 3.Table 3.
The same functional form based on cellular damage, repair, and repopulation was evaluated from experimental studies on CFU-S cells as described in a previous reference (3). Damage constants were estimated from dose-rate data of Puro and Clark (6). The proliferation constant was estimated from an analysis of published values obtained from an extensive literature review. The repair constant was taken from the evaluation described above for the lethality database, but an additional normalization was required to adjust for the shorter cycle time of stem/CFU-S cells in contrast to the longer cycle for the critical cells.
Results
The two models of marrow cell kinetics involve a) cells that are critical to compensatory hematopoiesis with parameters estimated from MLE analysis of animal mortality data and b) CFU-S type stem cells with parameters fitted from in vivo and in vitro cell-survival studies. As described in previous publications (3,7), both models seem to preform remarkably well according to the foundations of their evaluations. Clearly, the point estimates and confidence intervals on estimated coefficients indicate that the two cellular models are distinct and do not merely provide dual estimates for a common lineage.
Thirty-four experiments have been analyzed previously by MLE methods to estimate cellular rate constants within the model and are not considered suitable for model validation considerations: 27 were used to evaluate the photon models (5) and 7 experiments were used to evaluate the neutron models. The lot, 72 experiments, resulted from an exhaustive literature review, and selection of the 38 experiments for model validation was based on a) dose protraction by rate or fractionation in mice or rats; b) mortality within 30 days from the end of the radiation treatments (studies were used if a few animals died from gastrointestinal damage because it was assumed that those same animals would have died from marrow depression at a later time; in contrast, studies were rejected if even a small number of animals died of marrow depression before the irradiation schedules were completed because the minimum effective dose could not be determined); c) no more than 60 days between successive dose fractions; d) equivalent handling of different phases of a particular experiment (e.g., uniform marrow doses and consistency in positioning the animals; confinement was needed to be sure animals actually received the planned dosage); e) adequate specifications of times or dose rates, and f) the experiment had to be reasonably successful at irradiating an adequate number of animals between the LD10 and the LD90. Overall, only about a half dozen studies were rejected.
The 38 experiments used to validate the model typically reported only LD50 values without giving the actual dose-response data. Although these studies were not useful for unbiased estimation of model constants, they do provide independent tests for model validation. The 12 doses rate studies ranged from 0.0008 to 4.74 Gy/min, and the 26 fractionation studies contained fractionations from 1.54 to 7 Gy given over periods ranging from hours to 8 weeks. Although the conversion of a protracted protocol to its prompt dose equivalence is cell-lineage dependent, that conversion for simple fractionated protocols will generally produce numerically similar estimates of the equivalent prompt dose (EPD), and it is not clear which lineage better explains the biology underlying acute mortality. In contrast, complex fractionation experiments and low dose-rate studies are sensitive to lineage-specific effects and result in different estimates for the EPD. These lineage-dependent EPD estimates clearly favor either a stem or a stromal cell type model. As seen in Figure 2, the results overwhelmingly indicate that a radioresistant, slowly repopulating cell is far more consistent with the biological processes underlying acute mortality, otherwise at least 50% of the distribution should be below the abscissa value of 1.0.
Figure 2. Journal publications have described LD50 estimates for protracted irradiations of mice and rats. The dose protractions were achieved by using low-dose rates and/or dose fractionations. Because the dose-response mortality data for these studies were not published, these experiments have not been used in our modeling efforts, hence these 38 experiments provide 343 LD50 values and serve as a good database for model validations. The two cell-kinetics models, i.e, one for the critical cells [rate constants determined by maximum likelihood estimation (MLE) methods] and the CFU-S-based rate constants, were used to predict the equivalent prompt dose associated with each protracted LD50 estimate. For each experiment, a number of protracted irradiations were studied as part of the experimental design (an average of 343/38 = 9 per experiment). For the perfect model all different dose protractions will yield the same estimate for the EPD. But because the EPD is lineage-specific, the two models will make contrasting predictions for protrated protocols. For simple protracted irradiations, either model should model the EPD accurately, and there may not be enough complexity in the experimental design to demonstrate the difference in the two models. However, for low dose rates and/or complex fractions, the two models will predict strikingly different EPDs, and one will have a smaller variance within a particular experiment. If the two are statistically equal, then 50% of the cumulative distributions shown should be <1.0. As shown, the MLE-based model reduces the variance of the experiment-specific EPD distributions by factors typically ranging from 1.5 to 5. These comparisons were based on the 50% level of response, and the gain is usually larger if data on the tails of the distribution function are available. Clearly, this exercise supports the idea that the critical cell for radiation-induced hematopoiesis is radioresistant and repopulates slowly, perhaps like the experimental data for marrow stroma or CFU-F cells.
The recovery to normal tissue homeostasis in the model is not dependent on the insult, either physical or chemical, that caused the injury. Instead, the recovery associated with repair of sublethal cellular injury and repopulation are formulated completely in terms of biologically related concepts involving populations of cells, length of the mitotic cycles, mitotic delay in G2, etc. Thus, although the injury used to stimulate the recovery shown in Figure 3 was due to ionizing radiations, other insults such as chemical and/or surgical ablation of the marrow used to create similar injury may, in principle, be compensated for according to recovery aspects of Figure 4. Of course, insults that have a long biological half-life, activate different mechanisms, or are associated with toxicity to nonhematopoietic organs may not necessarily act in the manner shown.
Figure 3. The models based on CFU-S data and the maximum likelihood estimation analysis of mortality data (labeled "mouse stroma") were used to predict the time required for repopulation to 95% of normal tissue homeostasis from cytopenia ranging from surviving fractions of about 0.001 to 0.95. These estimates are driven by the injury to the lineages indicated and are not linked to the specific factors of the insults that resulted in cytopenia below normal tissue homeostasis.
Figure 4. Doubling times for CFU-S cells in mice were computed for compensatory repopulation as described in Table 2 and the text. The vectors are used to indicate ranges as estimated from the experimental data described in Table 4.
Benzene is highly mobile inside the body and for simplicity may, like ionizing radiations, be expected to act primarily upon cells present in the body at the time of exposure. For example, Rickert et al. (8) found the benzene half-times in different organs of male Fischer-344 rats to be 48 min over the first 9 hr of exposure to 500 ppm by inhalation. A plot of benzene expired in air was biphasic with t1/2 times of 42 min and 13.1 hr. The fraction retained with the longer half-time is less than 5% of the exposure and therefore is 1 or 2 times the 13.1-hr half-life (i.e.,
13.1-26.2 hr) is still shorter than the typical cell cycle for most multipotent cells and their supportive stroma (3).
In regard to benzene-induced neoplasia, nine experiments comprised six different routes of administration, rats and mice as test species, treatment times in the general intervals of 2, 4, 12, and 24 months, plus variations in biological end point, dose, and dose rate. Obviously, the data grid is much too sparse to permit estimation of numerical coefficients even if the appropriate functional form of a biologically based dose-response model were known.
In regard to acute mortality from benzene toxicity, 15 experiments reflected 6 different routes of administration, seven test species, and exposure times ranging from minutes to 7 hr. In some regards, this data grid is more sparse than the neoplasia data, and in addition these data provide nothing useful to view/model the effects of dose protraction.
The cytotoxicity of colony-forming cells (CFC) and CFU-S cells is often linked to benzene toxicity. Seven publications described a rather limited variety of measurements for CFC and CFU-S cells, treated by inhalation and subcutaneous injection, at different concentrations, and concentration rates, for various periods of time, and a wide range of postexposure assay times. Those data are summarized in Table 4. The benzene experiments currently available are inadequate for development of biologically based models, except for drawing of some fragmentary conclusions such as those listed in Table 5.
From Tables 2 and 3, compensatory repopulation by a particular cell is modeled by NNMFNN. The doubling time, TD, associated with a particular surviving fraction can be estimated by TD = ln(2)/( NNMFNN) and is shown in Figure 4 for a of 0.00022 min-1. The vectors shown in Figure 4 are estimated doubling times from experimental data of Uyeki et al. (9) and Cronkite et al. (12,13).
Discussion
In this paper, benzene-induced hematopoietic toxicity is viewed in the broader context of the spectrum of exposures that are pancytotoxic and induce compensatory hematopoiesis during or as a consequence of injury. Chlorambucil, chloramphenicol, chloroquine, cyclophosphamide, diethylamide, griseofulvin, ethylene oxide, ionizing radiations, lysergic acid, melphalan, methoxypsoralen, phenylbutazone, procarbazine, phosphorothioic acid triethylenetriamide, 7,12-dimethylbenz[a]anthracene, 2-acetylaminophenanthrene, N,N'-2,7-fluorenylenebisacetamide, N-2-fluorenylacetamide, 1-methyl-1-nitrosourea, and N-isopropyl-
-(2-methylhydrazine)-p-toluamide hydrochloride have been associated with leukemia in humans or animals. Several publications have concluded that injury to both hematopoietic stem cells and their cellular/cytokine-mediated environment can be important to acute mortality and leukemogenesis. A number of experimental studies have found that all marrow-derived lineages can be regenerated from only one cell alone surviving pluripotent stem cell, whereas a stroma of strong functional integrity is required to support that regeneration. The importance of stem and stromal lineages, especially as potentially related to benzene toxicity, has been discussed previously (16-25).
In 1961, Cronkite (26) concluded that any agent which produces marrow aplasia is a "putative leukemogen." Later, Adamson and Seiber (27) noted that
It is possible that a given proportion of individuals who develop bone marrow depression as a consequence of chemical exposure may ultimately develop ANLL [acute nonlymphocytic leukemia] regardless of which agent produced the marrow toxicity, and indeed all of the chemicals which have been implicated as leukemogens can be myelosuppressive. Nevertheless, there are also chemicals which are potent depressants of bone marrow function but that have not been associated with human ANLL.
Harigaya et al. (17) proposed that the role of benzene may be more of a promoter by forcing the pluripotent stem cells (that have been exposed to leukemogenic initiating agents before benzene exposure) to undergo compensatory hematopoiesis. Because of existing data and simple, well-established dosimetry models, the quantitative considerations, as described here, have been limited to exposures involving ionizing radiations, and the relevance to benzene toxicity is implied by analogy of molecular-, cellular-, and organ-based processes.
Figure 5. Scheme based on consenus principles from radiation biology and from the results of our many model evaluations and validations. Clearly, the supporting stromal tissues and their cytokine-mediated control of compensatory hematopoiesis are obligatory to recovery from toxic injury.
As illustrated in Figure 5, our generic model of radiation-induced compensatory hematopoiesis has led to a strongly supported hypothesis that cell-to-cell contact and/or cytokine-mediated processes between stomal and stem cells establish both the radiosensitivity and proliferation kinetics of the cells that are critical to hematopoietic recovery (28,29). Although that hypothesis is well supported by a large array of stromal cell experiments, it is still contested by some, based on the belief that survival of hematopoietic stem cells is both necessary and sufficient for rescue from hematopoietic syndrome. In contrast, the model evaluations described in this paper indicate that even though stem cell survival is necessary, the rate-limiting considerations seem to be associated with a more radioresistant and more slowly repopulating critical cell that is consistent with characteristics measured for marrow stroma and CFU-F type lineages.
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