Document DvzJEraEjp83gb14xj7bjaZRN

Ammteric~ ~furD~~1ililllTil Tillll.5\tD.fum(t<e 1220 L Street, Northwest Washington,-DC..20005-4070 Tel202 682-8341 Fu 202 682-8270 e-mail mongillo@API.org Da11id A. llllongillo Manager, Health Sciences January 20, 1998 TO: -!FROiVl: Ben:Eene 1ias-Bt !Ferree ~David Mongillo RIE: RIESIEARCIHI GROUIP iVl!EIETDNG The Benzene Basic Research Group will meet the morning of Friday, February 13 in Houston at the Marriott Hotel following the Benzene dinnenneeting the night before. The purpose of the meeting will be to update the on-going benzene research activities and discuss plans for 1998/199.9. The meeting will begin at 8 am and last no longer than 3 hours. For planning purposes, please return the attached meeting .confirmation sheet. Two work products have been received recently for review. You should have received Tony Cox's report "A Biomathmatical Model of Hematotoxicity". Included in this mailing is AHF's draft "Evidence for DNA Reactivity of Benzene and Benzene Metabolites". Please call with any questions. An equal opportunny employer BP-00017712 0 Ameriicaum 1220 L Street, Northwest .-f\ -n\br(Q)!eum Wasllington, D.C. 20005-4070 lill1l5tiihullte 202-682-8000 J:o: Phone: Fax: -From: Company: Phone: Fax: E-mail: Vanessa Moore (202)682-8330 (202)682-8210 NO Benzene Basic Research Group Meeting Houston, Texas February 13, 1998 Please fax back to (202) 682-8270 no later than January 30. An equal cpponunity employer BP-00017713 . ~-:-::--~;_ ~- .. - !:("-""') I - . ' .L I COX ASSOCIATES, 1997. 503 Franklin Street, Denver, Colorado, 80218. 303-388-1778. TCoxDenver@aoG:cifu_ _ _:; JJW20 'S J / A ~~(Q)MA1'HIIEMA1rOICAl MIODIE:l OIF H~illiiATOl'O~OCDNj;~ !lo-lUlos AD1ltlhloD1ly Cox, J1r. I -r- .. ---1---.- -'~-:ia-- -,I -~-I-- -~-r--- .- !- - - .:.\______ Decemlbleir, H~SI' _ <;_~:!/;!_ ~~~t= AIBlS'fAAC1r f_.:_ ...I__/ . - ..;/>..' - ---I. :. - In the past decade, toxicokinetic and physiologically-based pharm~~:>k!ii~tic-J- .,:. (PBPK) moeels have been used extensively to-help clarify the dynamic'reLatiqns;-! between administered doses and biological responses, ranging <from--acut~-----.- f toxicity to chronic cancer risks. ~n the 1990s, researchers and modelers have;l___.; .II increasingly recognized the need to link PBPK models to pharmacodynamic models, representing the interactions between chemicals and cells, in order to better understand how time patterns of administered dose affect the risks of adverse health outcomes. This paper describes such a model, representing the effests on the hematopoietic-(blood-forming) system of myelotoxic agents such as metabolites of cyclophosphamide (CP) or benzene. The model consists of a set of physiological compartments representing hematopoietic progenitor cell, granulocyte-macrophage (GM)-committed stem cells, and more mature blood cells. These compartments are linked by nonlinear feedback control loops .and are susceptible to first-order cell-kiUing kinetics from cytotoxic metabolites. In contrast to earlier biomatt:lematical .models- of normal hematopoiesis and hematotoxicity, this model has been validated by testing its _predictions against experimental and clinical data for blood cell counts following administration of CP to mice, dogs, and humans. It successfully explains apparent anomalies and patterns in previously published data, including the fact that smaller cumulative doses can cause larger hematotoxic responses and that bone marrow toxicity may be disproportionately sensitive to exposure concentration but relatively insensitive to exposure duration. An intriguing prediction from the model is that sustained exposures to sufficiently- small concentrations of myelotoxic agents may tend to-j)mvoke a protective response, increasing rather than decreasing the numbers of CFU-GM and early hematopoietic stem -cells available to sustain hematopoiesis. KEY WORBS: Hematopoiesis, myelotoxicity. cyclophosphamide, pharmacodynamics, mathematical modeling, biologically-based risk assessment BP-00017714 COX ASSOCIATES, 1997. 503 Franklin Street, Denver, Colorado, 80218. 303-388-1778. TCoxDenver@aol.com UNTR.ODUJCT!ON Applied quantitative risk assessment seeks to answer questions such as the following. Suppose that a risk manager must choose among risk mitigation options (a)-(d) for protecting workers from a potentially hazardous airborne chemical in a manufacturing plant: (a) Reduce daily occupational exposure time from 8 hours to 4 hours. {b) Reduce 8-hour average workplace concentration by 50%. (c) Reduce weekly exposure from 5 days to 2.5 days. (d) Reduce yearly exposure from 50 to 25 weeks per year. Which option is most health-protective? By how much would each be expected to -Feduce the health risk due to occupational exposures? How well can these questions be answered without further specifying the options, e.g., -how- the 4 hours in option {a) are distribtited within the work day_, how the 25 weeks in option (d) are distributed within the year, -and so forth? This-paper shows how biomathematical, biologically-based risk assessment (BBRA) models can address such questions. Section 1 presents empirical evidence motivating the need for explicit dynamic models of dose-response relations. Using the chemotherapeutic and immunosuppressive drug cyclophosphamide (CP) as a detailed example, Section 2 develops a dynamic dose-response model for pre.djcting and explaining cytotoxic effects of chemicals on bone marrow and blood cell populations. Section 3 presents new results on empirical validation of the model with human clinical data ar:~d experimental animal data-. Section 4 discusses potential implications for risk assessment of chemicalleukemogens. 1. WIHJY !DYNAMIC IDOSE..RIESPONE MODElS? The need for explicit dynamic- models in quantifYing- dose-response relations is often implicitly denied in_applied risk assessments. Instead, "dose metrics", such a~ cumulative exposure or cumulative dose per unit body weight or per unit surface ar-ea, are commor}ly used -to equate- the risks of very different e~posure histories that map to the same value of the dose metric. This principle has been used to extrapoiate risks=-trom high to low doses and from one species 1 1 I BP-00017715 COX ASSOCIATES, 1997. 503 Franklin-Street, Denver, Colorado, 80218. 303-388-1778. TCoxDenver@aol.com and strain to others. Uncertainties about the validity of the extrapolation are often equated to uncertainty about the most appropriate choice of dose metric. In conjunction with another widely used assumption - that excess risk at sufficiently low doses increases in approximate proportion to the dose metric - this dose metric approach provides a simple, clear method for assessing the risk cOnsequences of risk management options such as (a) - (d). For example, these principles imply that all four options reduce health risk equally at small concentrations. Different practitioners might debate which specific parametric risk model is most appropriate, e.g., logistic regression, probit, proportional hazards, linear relative risk, linear absolute risk, and so forth. Yet, the rankordering of risk management options and estimates of their relative quantitative efficiencies in reducing risk do not depend on such model differences. T-hey are fully determined by the assumptions of a dose metric and approximate low-dose linearity. This may create-an apparent consistency and robustness in the results of different specific parametric risk models, including all of those just listed, that is traceable to their common underlying methodological approach. To motivate a more complicated BBRA modeling approach, this section reviews data suggesting that the dose metric strategy of mapping time patterns of exposures to single numbers before evaluating their risks . is ultimately unsatisfactory. Despite its simplicity and robustness, the framework is inconsistent with experimental data that permit it to be tested, for some chemicals of practical interest. Specifically, stop-exposure experiments, in which different groups of animals are exposed to chemical carcinogens for different amounts of time, reveal results that seem to contradict the most basic tenets of appJied risk assessments based on dose metrics. For example: o Smaller cumulative doses can produce larger toxic and carcinogenic responses (e.g., Luke eta/., 1988a; Cox eta/., 1996). o Relatively small increases in concentration can dramatically-increase tumor incidence (e.g., Williams, 1993 for hepatocarcinogenesis; Melnick et at., 1990 for butadiene-induced lymphomas). o Extending durations of exposure may have little or no impact on tumor risks (Cox eta/., 1996 for isoprene-induced tumors at-several anatomic sites). 2 BP-00017716 COX ASSOCIATES, 1997. 503 Franklin Street, Denver, Colorado, 80218. 303~388-1778. TCoxDenver@aol.com o Sufficiently low exposure concentrations can have disproportionately small impacts, or even appear to have beneficial effects, prompting some investigators to speculate about biological hormesis (e.g., David and Srendsgaard, 1990). Table 1 illustrates some of these phenomena for isoprene (Cox et al., 1996). The following patterns are notable. o Doubling concentration (from 70 ppm to 140 ppm between exposure groups 3 and 5) increases liver adenomas from 0.29 to 0.44. But, doubling weeks of exposure (-fmm 40 to 80 between exposure groups 3 and 4) does not increase risk significantly at any site, and even appears to reduce it. This observation is not explained by competing risks of death from toxicity, as animals tolerated these concentrations. Nor is it explained -by saturation of carcinogenic response mechanisms, as higher concentrations produce much higher tumor yields. Thus, no dose-response theory that predicts that risk increases with cumulative exposure provides a useful model for these data. o Quadrupling exposure concentration from 70 ppm to 280 ppm while quartering exposure duration from 80 weeks to 20 weeks unambiguously increases tumor risk (compare exposure groups 4 and 6), even though cumulative exposures are identical. Thus, no risk model that uses cumulative exposure (area under curve, AUG) as a dose metric adequately describes these data.- o At higher concentrations, doubltng hours-per-day of exposure while halving weeks of exposure increases the risk of adenomas and liver carcinomas (compare exposure groups 10 and 11 ), even though cumulative exposures are identical. o Liver and lung tumors- (both adenomas and carcinomas) are only significantly elevated at concentrations- above 70 ppm. In this data set, 140 ppm is the smallest concentration for which significant increases were observed. Such observations challenge any dose-response modeLtbat uses a dose metric in which risk increases monotonically and/or symmetrically with exposure concentration and duration. BP-00017717 COX ASSOCIATES, 1997. 503 Franklin Street, Denver, Colorado;-80218. 303-388-1778. TCoxDenver@aol.com T ARILJE li: RJEl[J]L1!' OIF A 1l'OJP-1EXPOS1URE lEXJ?lEllUMlEN'Jl' IFOIFlJIOPRENE liN MA..JLJE R6C3Fl Ml!CJE t:iJ:m!P. l2/l!!1 ~ Liver Lung hr!iJJJ;?. adenomas adenomas Other adenomas Liver Lung Histio- carcinomas carcinomas sarcomas 10 0 8 0.22 0.22 -0.14 0.18 0 0 2 10 80 8 0.24 0.32 0.12 0.12 0.02 0.04 3 70 40 8 0.29 0.16 0.30* 0.22 0 0.04 4 70 80 8 0.30 0.08 0.18 0.18 0.04 0.04 5 140 40 8 0.44!* 0.20 0.28* 0.20 0.02 0.02 6 280 20 8 0.36 0.32 0.36* 0:24 0.06 0.16* 7 2200 80 4 0.42* 0.30 0.56* 0.30 0.06 0.1~* 8 2200 40 8 0.7* 0.59* 0.65* 0.37* 0.06 0.]41* Explanation: Columns 2-4 summarize the exposure factors defining each dose group. The remaining columns show the fraction of animals in each dose group that were found to have each tumor type at necropsy. Tumor incidence rates in bold and marked with an asterisk are significantly greater than in the control group (p < 0.05 by Fisher's Exact Test). Stop-exposure experiments for health end-points other than cancer show similar patterns. Genotoxic, cytogenetic, and cytotoxic responses are often sensitive to the time pattern of dose administration, rather than only to the AUC of administered dose (or of metabolites formed. For example, Table 2 summarizes experimental results for benzene, a relatively well-studied human leukemogen and animal carcinogen, for endpoints other than (and perhaps causally prior to) cancer. Benzene metabolites such as phenol, hydroquinone (HQ), and catechol synergize strongly in producing both cytog~netic a!ld cytotoxic damage. Since carcinogenesis is often postulated to arise from the combination of genotoxic and cytotoxic effects (e~g... Farris et a/:, 1997 for benzene; Williams et a/., 1993, for the hepatocarcinogefl DEN, Monticello and Morga11, 1994 for formaldehyde), it is not surprising that chemicals with strongly nonlinear dose-response patterns for genotoxic and cytotoxic effects may exhibit similar nonlinear patterns for tumors. 4 BP-00017718 COX ASSOCIATES, 1997. 503 Franklin Street, Denver, Colorado, 80218. 303-388-1778. TCoxDenver@aol.com if"ABLIE 2: ~IE~ILDLTS ON IBIEi\IIZIENIE IHEMATOTOX~C~lllf AND GENOTO~iCDTV RESULT IRE FERENC IE ema o ox1c1 y 1n mouse bone marrow , measured by reduction in CFU-GM per tibia bone marrow These examples demonstrate the need for dose-response models that do not satisfy the usual assumption that risk is an -increasing function of a dose metric that combines exposure concentration and duration in some simple, monotonic, and perhaps symmetric way. The fo"owing sections investigate the potential of BBRA models, which attempt to simulate key dynamic aspects of adverse health effects, to obtain more realistic and useful predictions. 5 BP-00017719  COX ASSOCIATES, 1997. 503 Franklin Street, Denver, Coloi'4clo, 80218. 303-388-{ 778. TCoxDenver@aol.com 2. MIETIHIOIDlS To assess how well BBRA-models can predict and explain phenomena such as those in Tables 1 and 2, we undertook the following three steps: -a) Construct a dynamic simulation BBRA model of .pharmacokinetics and cytotoxicity I cell kinetics for a well-studied leukemogen (CP). Mathematical models of pharmacokinetics and metabolism, hematopoiesis (blood formation), and hematotoxicity and myeJotoxicity (blood-poisoning and marrow-poisoning) were based on previously published data and modeling efforts for- CP, as-described below. They were combined and implemented in a continuous simulation model using the !THINKTM modeling environment. b) Validate the model's predictions with data from several species and agents. Model parameters -estimated primarily from canine data were used successfully to predict observed dynamic responses in humans, dogs, and mice exposed to CP. lnterspecies extrapolations were made by adjusting only two scaling parameters --a time scaling factor and a dose scaling factor - to account for differences in body weight and metabolism. Similar work has recently validated similar model predictions for effects of radiation- on humaR and canine hematopoiesis {Fiiedner eta/., 1996; Tibken et af., 1995). c) Apply the validated model to explain and predict the dynamic responses of specific cell populations to differeAt time patterns of dosing with hematotoxic agents. Dynamic responses were simulated for specmc hematopoietic progenitor cell populations (e.g., early CFU-GM) thought to be involved in chemically induced my-eloid leukemogenesis (Irons and Stillman, 1996). The meihods used to carry out each step are described next. The biomathematical model of hematotoxicity is described in Cox (1996), which-gives detailed model equations in an appendix. It is based largely OR- the model of Steinbach et af. (1980) with some simplifications and improved CP 6 BP-00017720 COX ASSOCIATES, 1997. 503 Franklin Street, Denver, Colorado, 80ZJ8. 303-388-1778. ICoxDeaver@aol.com pharmacokinetics based on experimental data (Sladek, 1988). In summary, it consists of the following components: 1. A linear comparlmental flow model (Jacquez, 1997) describing the pharmacokinetics and metabolism of CP in humans. The model structure and flow rate parameter values for CP are based on measurements in human patients (Cohen eta/., 1971; Sladek, 1988). 2. A nonlinear compartmental flow model- with feedback-control loops, describing_ the myelotoxicity and hematotoxicity of CP. This model has the following six main sequential compartments, describing the granulocytemacrophage (GM) lineage of the hematopoietic system: o Early stem cells and hematopoietic progenitor cells (HPCs) o Granulopoietic committed stem cells (e.g., CFU-GM) o Proliferative cells (myeloblasts, promyelocytes, -myelocytes) o Maturation pool o Bone marrow resen~_e o Peripheral blood granulocytes Partial differential equations (PDEs) describe the dynamics of the age-structured CFU-GM cell populations. These PDEs were approximated numerically by systems- of ordinary differential equations ODEs (10 serial subcompartments), to make the mean and variance of transit times conform to experimentally observed values in dogs (Steinbach et al., 1980). Nonlinear feedback loops, implicitly modeling the regulatory effects ofihe cytokine network,-f-eed back information (interpreted as strengths of regulatory signals) from blood cell population sizes to-control the following rate parameters: o Fraction of early HPCs-that differentiate iAstead of self-renewing; o Rate of recruitment of resting stem cells into active cycling; o Birth rates of CFU-GM and downstream--proliferative cells; o Release rate of mature granuloCf:es from the bone marrow reserve to the peripheral blood. These feedback control laws were described by smooth curves constructed to pass tbrotJgh experimental data points. Typically, the experimental data 7 BP-00017721 COX ASSOCIATES, 1997. 503 Franklin Street, Denver, Colorado, 80218. 303-388-1778. TCoxDen-ver@aol.com consisted of extreme values (e.g., maximal and minimal cell division rates observed under a variety of experimental conditions) with some intermediate data- points. An s-shaped function would then be used to interpolate among these observed values, with its parameters being estimated from experimental data by least squares. Most of the parameter values for the CP cytotoxicity and cell kinetics component were taken from previously published estimates based on a model of granulopoiesis in dogs (Steinbach et a!., 1980); see Cox (1996), for details and parameter values. The combined CP pharmacokinetics and hematotoxicity mod.el is a continuous simulation model of the standard form (van der Bosch and van der Klauw, 1994): dlt(t)/dt = {F[lt(t), [O;(t)] b(t) =g[x(t)] where x(t) is a state vector with components describing (a) the quantity of CP and its metabolites in each compartment of the pharmacokinetic model and (b) the number of cells in each compar:tment of the cell kinetics and cytotoxicity model at time t. lb(t) is a vector of rate parameters. Its components are constants for the pharmacokinetic model and are functions of the cell population sizes for the cell kinetics and cytotoxicity model. b(t) alse- includes cytotoxic parameters describing the rate of cell-killing of cycling_ HPCs and CFU-GM cells as a function of the concentration of toxic CP metabolites (specifically, phosphoramide mustard) in these marrow cell populations. The feedback laws determining lbl(t) from x(t) are symbolized by the vector function ~ and are detailed in Cox (1996). Initial values for cell population sizes were taken from published experimental data, as in Steinbach et a/. (1980), and starting values for CP in different compartments were- assumed to be zero. Given the initial conditions x(O) and -any specified dosing history, the above simulation model determines the resulting histories of CP and metabolite concentrations and fluctuations in hematopoietic cell populations. They may be salved for by numerical integration of the simulation model equations. 8 BP-00017722 COX ASSOCIATES, 1997. 503 Franklin Street, Denver, Colorado, 80218. 303-388-1778. TCoxDenver@aol.com Empirical validation of the BBRA hematotoxicity model for CP consisted of the following two major efforts: o Validation in humans: Using the model formulated above for dogs and a simple adjustment for interspecies dose conversion, predict the effects of repeated CP treatments on humans and compare the model predictions to published clinical data to assess its predictive validity for humans. o Validation in mice: Using the above- model and the same simple adjustment for interspecies dose conversion, predict the effects on hematopoiesis-(CFUGM and peripheral granulocytes) of single- and multiple injections of CP in mice. Then. test the predictions by carrying out the single- and multipleinjection experiments in mice. INTERSPECIES DOSE-RESPONSE CONVERSION Since humans have a larger body weight than dogs, their biological clocks are expected to run more slowly. The most parsimonious way of adjusting for this effect is to rescale the time axis, multiplying it by a constant greater than 1 to slow down predicted canine hematotoxic responses (e.g., decreases or increases in cell popuJation sizes) to predict the timing of corresponding human responses. Rather than using allometric arguments to estimate the scaling factor, which would introduce uncertainties about what power of body weights to use, it is simpler and more reliable to estimate it directly by comparing the results of analogous experiments in dogs and humans. Comparing the time course of peripheral white blood cells (WBCs) in canine model simulations following a single injection of CP (Steinbach et a/., 1980) to the time cmuse. reported for humans (Coggins et al., 1960) showed that the nadir occurs at approximately 11 days in humans compared to approximately 7.5 days in dogs. Jnus, predictions from the canine model are scaled by a factor of 11/7.5 = 1.47 along the time axis to obtain predictions for humans. The pharmacokinetics submodel is already developed from human data, and hence requires no rescaling,_ Also, -rescaling itsrelatively fast dynamics we~;~ld make little or no difference to the slower CPhematotoxicity submodel for most dosing scenarios. 9 BP-00017723 COX ASSOCIATES, 1997. 503..Eranklin Street, Denver, Colorado, 80218. 303-388-1718. TCoxDenver@aol.com For mice, a contraction of the time axis must be made. Comparing experimental data on murine hematotoxic responses to CP injections (DeWys et at..., 1970) to human clinical data (Buckner eta/., 1972; Nissen-Meyer and Host, 1960) suggested that the time scale for hematopoietic responses in mice should be contracted by a factor of about 0.4 compared to humans. This estimated adjustment factor was used in making all predictions for mice. Mice have a higher ratio of surface area-to-volume than do dogs or humans. It is therefore to be expected that the number of mg/kg required to produce a given dynamic response in mice (e.g., a given depth of the nadir as a percentage of ...tl:!e normal level) will be different from the number of mg/kg required to produce the same response in humans. The required dose-scaling factor was estimated to be about 5, based on the observation that mouse responses to about 300 mg/kg appear to correspond-roughly to human responses to 60 mg/~g. appropriately speeded up. However, responses within each species to all sufficiently high single doses are similar enough to each other so that the exact correspondence between mouse and human dose scales is hard to identiPf from previously published data. Similarly, although it might in principle be desirable to account for differences between dogs and humans in the hematotoxic potency of CP, such adjustments make little practical difference in predicting human hematotoxic responses to the high levels of CP used in clinical trials. The hematotoxic response is approximately saturated, making detailed adjustments unnecessary. MODEL VALIDATION TESTS The complete CP model contains over 120 individual equations and formulas and over 20 parameter values (all with values fixed by experimental data). Thus, it would be impractical to attempt to validate its assumptions and implications by direct inspection. Instead, the following val~dation tests were performed. Testing face validity- and internal consistencv of the model. The model was cP.ecked by introducing deliberate errors into its equations_(e.g., using incorrect formulas or parameter values) and confirming that the-resulting outputs became unrealistic, e.g., unstable in the absence of any external perturbation from dosing. 10 BP-00017724 COX ASSOCIATES, 1997. 503 Franklin Street, Denver, Colorado, 80218. 303-388-1778. TCoxDenver@aol.com Such experiments revealed that the self-consistent dynamic behaviors exhibited by the model (specifically, homeostasis and a stable steady state) do not survive the intreduction-of obvious errors, increasing confidence that such errors have not been made. DescripUve validity of the BBRA model was established by checking that its predictions for HPC stem cells in bone marrow and for WBC counts after an injection of 15 mg/kg CP agree with experimental observations on dogs (Steinbach eta/., 1980). These same experimental data points had been used to estimate the model parameters, however, so this check only confirms the descriptive validity of the model, i.e., its aeility to explain a large number (over 70) data points with a much smaller number of parameters. It does not prove that other parameter values would not fit the same experimental data equally well but make different predictions outside the range of observed experimental conditions. Predictive validitY of the CP model was first assessed using human data. As described in the following section, the predictive validity of the human model was tested by simulating the outcomes of clinical experiments previously reported in the literature (Buckner eta/., 1972; Nissen-Meyer and Host, 1960) and comparing the model-predicted time courses of blood cell counts to corresponding clinically observed values. The human data sets and clinical trials used to test the model are quite different from the animal experiment data sets used to build it, thus providing a1air test of its ability to make useful predictions across these species and experimental conditions. The model's predictive validity was further tested through new experiments in male B6C3F1 mice, conducted at the University of Colorado Medical School in Denver b- Drs. R. Irons and W. Stillman. Table 3 summarizes the experimental design used. Five mice were sacrificed at each "x" and 50 mg/kg of CP was administered via Lp.-injection into surviving mice at each "D'". Rows 1-3 represent three treatment groups, receiving one, two, and three doses of CP, respectively, spaced 48 hours apart. Row 0 is the control group. This design was constructed based on simulation model results, which predicted large, testable differences in CFU-GM population sizes-on different days for these three dose regimens. 11 BP-00017725 COX ASSOCIATES, 1997. 503 Franklin Street, Denver, Colorado, 80218. 303-388-1778. TCoxDenver@aol.com Group 1 2 3 4 5 6 7 8 9 10 11 12 13 14 0 XX X XX X X X 1 D XX X 2D D,x X X - X X XX X 3D D D,x X X X X X D =administration of dose (50 mg/kg via i.p. injection) X= sacrifice of animals A pilot experiment consisting of a single injection on day 1 cmd a one-week follow-up with sacrifices on days 2, 4, and 7 confirmed that mice could tolerate 50 mg/kg and that CFU-GM and WBC counts looked approximately as predicted on these three days. Following sacrifice by cervical disloca~ion, mouse bone marrow was extracted, plated, and assayed for CFU-GM stem cells using a colonyforming assay . Following the validation tests, the BBRA hematotexicity model was applied to several different dose scenarios to determine whether it could help to explain the phenomena in-Tables 1 and 2. Scenarios examined included: 1. Stop-exposure experiments, .similar to those for isoprene and benzene in Tables 1 and 2, that allocate the same total administered dose according to different time patterns to determine which create the largest predicted hematotoxic effects on CFU-GM populations. 2. Continuous infusion experiments, inteneied to create internal dose profiles similar to those that might arise from sustained low-level exposures to an airborne leukemogen such as benzene. The model-based predictioRs for these dosing scenarios were used to draw inferences about dose-response relations that may help to explain some of the qualitative patterns noted in Tables 1 and 2 for other chemicals and end-points. 12 BP-00017726 COX ASSOCIATES, 1997. 503 Franklin Street, Denver, Colorado, 80218. 303-388-IJ78. TCoxDenver@aol.com . 3. RIESUl1"S Tbis section first presents the results of the model validation experiments, since validation should be an essential prerequisite for using models to explore substantive research issues. The validation tests generally support the predictive value of the model. Next, the model is applied to various dosing scenados to identify its implications for the dynamic properties of hematotoxicity doseresponse relations. 3.1 JRIESW..iS Of MODEL VAUIDlATiONS FOR HI!JMANS Buckner eta/., (1972) report clinical data for nine human cancer patients administered 60 mg/kg of CP each via infusion, and for seven patients each given 120 mg/kg CP as two 60- mg/kg infusions spaced one day apart. The CP model was used to predict the time courses of WBCs for these groups of patients. Figure 1 shows the model predictions (top panel) and the observed data (bottom panel) for both groups. Figure 2 shows a similar-comparison of predictions with clinical data from an earlier study (Nissen-Meyer and Host, 1960) in which patients were administered doses of 60 mg/kg of CP on four consecutive days. Figure 1 shows that the simulation results from the model provide a useful approximation to the empirically observed results. In both the simulation and the clinical data, the WBC time courses are not significantly different between the 60 mg/kg and the 120-mg/kg groups for the first week following exposure. They begin to separate in the second week, with severe leukopenia persisting for over 4 days in the 120 mg/kg group before noticeable recovery begins, compared to an earlier recovery in the 60 mg/kg group. This basic match-between predictions and observations-is reassuring, especially given the high interindividual variability indicated by the range bars in the experimental data. Figure 2 similarly sl'lows that model predictions (tap panel) approximately match oaserved data (bottom panel) throughout the duration of observations for a clinical trial in which CP v.~s administered on four consecutive days (Nissen-Meyer and Host, 1960). Again, given-the approximations made in the CP hematotoxicity model (e.g., in scaHng 13 BP-00017727 COX ASSOCIATES, 1997. 503 Franklin Street, Denver, Coloradc,80218. 303-388-1778. TE:oxDenver@aol.com the dose and time axes from dogs to humans), the match between model predictions and clinical observations is encouraging. Figures 3a and 3b present-the main results of the validation experiments in mice. Figure 3a shows predicted vs. actual results for CFU-GM time courses in the single-injection pilot experiment. (Peripheral granulocyte-macrophage counts were also predicted, and provide even better matches to observed values than- CFU-GM. Since the bone marrow CFU-GM responses are both more volatile and hence harder to predict, and also more relevant to leukemia induction, they are the focus of this summary.) Similar to the human data, the fit between predicted and observed values, while not perfect, is close enough to be useful in understanding the approximate magnitude and timing of changes in cell counts over time. Figure 3b shows the e~;~tcome of the multiple-injection experiment described in Table 3. The three panels, a, b, aAd c, show the observed (squares) and predicted (ciFs!es) average values of CFU-GM for mice sacrificed on different days-in each of the three treatment g~oups. (Straight-line extrapolations and interpolations are sketched among the data points. In the middle panel, for dose group 2, these segments are not connected for days 5 and 6 because their locations are uncertain.) Mean values of CFU-GM counts among all animal sacrificed in each treatment group on each sacrifice day are shown. All plotted values are expressed relative to the control group values, i.e., 1 is the no-effect level. There is enough experimental variabUity between replicates so that an exact match between predicted and observed value.s would not-be expected in any single experiment. For example, the left~ost panel of Figure 3b repeats the single-injection dose regimen in Figure 3a,_yet produces a different time course of observed relative CFU-GM counts in bone marrow. However, the predicted time courses areJ3imilar to the observed ones in key_ r:espects of the approximate magnitudes and timings of changes in CFU-GM counts. The largest discrepancies (e.g., at the left ends of the curves in Figure 3b) can be explained by noting that the CFU-GM compartment is predicted to be highly volatile over this time interval-;- with population sizes c!:langing dramatically from hour to hour. Indeed, tile experiment design in Table 3 was chosen to produce just such, 14 I BP-00017728 COX ASSOCIATES, 1997. 503 Franklin Street, Denver, Colorado, 80218. 303-388-1778. TCoxDenver@aol.com large, fast variations so that they could easily be detected. The rough agreement between predicted and observed values in terms of magnitude, direction of change, and approximate timing of peaks and of recovery (starting to return to pre-exposure levels) is reassuring, despite the experimental variability. 3.3 IRESiUlTS OfF MOIDIEl AI?PUCATHOi\l$ The model validation results summarized in Figures 1-3 suggest that the BBRA model of hematotoxicity provides usefu1 predictions in novel situations, e.g., for humans and for multiple-dose experiments. Confidence in its predictions is further bolstered by independent investigations reported by other researchers (Fliedner eta/., 1996; Tibken and Hofer, 1995), who also used a modified version of the Steinbach eta/. (1980) model to predict CFU-GM responses in dogs and humans exposed to radiation. That model, which is similar to ours, also produced predictions that match observations fairly closely. These results and the new model validation experiments reported above prov~de empirical support for applying the BBRA model to predict CFU-GM and --Peripheral granulocytemacrophage responses to situations for which data are not yet available. Figures 4 through 6 show results from three sets of simulation experiments performed using the CP model for humans. The first set (Figure 4) consists of infusions of CP representing alternative concentration-duration-frequency combinations with the same -product (total AUC of administered CP) but with different time patterns of administration (AUCs per unit time). The second group (Figure 5) examines the predicted effects of different durations of exposure te-a constant low concentration. (The concentration for the 480-hour dosing scenario is higher in Figure 5 than in Figure 4.) The-third set (Figure 6) shows simulated responses to long-term infusions of different low concentrations of CP. Such simulation experiments allow detailed examination of the-predicted- effects of different combinations of CP concentration and timing on stem cell dynamics. Early CFU-GM cells, i.e., those in the -first of the ten subcompartments in- the proliferative portion of the model, are-examined in the top panel of each of Figures 4 through 6, as this is a plausible starting location for the events leading to AML (-Irons and Stillman, 1996). The bottom panels show corresponding predictions for peripheral granulocyte-macrophage time courses, which are easier and less expensive to observe experimentally. 15 BP-00017729 COX ASSOCIATES, 1997_ 503 Franklin Street, Denver, Colorado, 80218. 303-388-1778. TCoxDenver@aoLcom DISCUSSION OF MODEL PREDiCTIONS Figure 4 shows predicted time courses of cell population sizes when the same total dose of CP is administered over three very different time intervals: 8, 120, and 480 hours. Since administered concentrations are inversely proportional to dosing durations, the AUC per day is far higher in the 8-hour dosing regimen than in the 480-hour regimen. The top panel in Figure 4 shows the effects on the earfiest of the CFU-GM compartments. The 8-hour administration leads to a profound initial depression in CFU-GM cells, followed by a rapid rebound and overshoot as a result of over-compensating proliferation. It is plausible that such a pattern may create a higher risk of leukemia than the other dosing scenarios. Tile reasoning is that the deep nadir is typicall accompanied by a premature transition into active cycling of normally GM-CSFnonresponsive stem cells (Irons and- Stillman, 1996; Irons eta/., 1992). Theimmediately following proliferation may therefore amplify a stem cell population that has just been enriched with stem cells that are espeeially susceptible to malignant transformation to acute myeloid leukemia (or its predecessor, myelodysplastic syndrome, MDS) (List and Jacobs, 1992). Such cells will not have had a chance to undergo a long period of detection and repair or elimination (e.g., via apoptosis) of somatically heritable damage, thus maximizing the potential for .leukemic transformation. Figures 5 and 6 may be interpreted s1milarfy. In Fig!Jre 5, extending- the duration of dosing while keeping the dose rate constant increases the predicted magnitude of post-exposure proliferation much less than proportionally to the duration. Instead, partial compensation occurs during dosing, with the number of early CFU-GM cells approaching a stressed-equilibrium level that is somewhat higher than normal. The nadir is not very low (i.e., the normal stem cell population- is not much depleted) and the recovery period is eomparatively lengthy. Thus, the post-dosing proliferation may be expected -t0 occur in a population that has not been as greatly enriched with at-risl< stem cells as in the first scenario of Figure 4. Indeed, if repair or elimination of inappropriately recruite-d stem cells and their pregeny takes place at a fast enough rate, then the 16 l BP-00017730 COX ASSOCIATES, 1997. 503 Franklin Street, Denver, Colorado, 80218. 303-388-1778. TCoxDenver@aol.com 240-hour exposure (leading to a zenith of proliferation about two weeks after dosing begins) might plausibly be more risky than the 480-hour exposure. Finally, the simulation experiments in Figure 6 predict that various characteristics of the early CFU-GM respond non-monotonically to CP concentration in simulations of sustained infusions. (Other simulation experiments confirm this result for shorter-term experiments in which two brief infusions are separated by different amounts of time.) The dynamics in Figure 6 suggest that the relation between concentration and risk may be more complex than the peripheral blood response in the lower panel suggests. Specifically, suppose that susta~ned depression of CFU-GM stem cells below their normal equilibrium level leads to an ongoing recruitment of less mature upstream stem cells (at least in the presence of leukemogenic metabolites). Then the qualitative response patterns in the top panel of Figure 6 suggests that higher concentrations lead to higher risks for administered concentrations above a certain threshold (as indicated by the transition from curve 4 to curve 5). Below that critical concentration, however, increases in administered concentration simply lead to a larger normal stem cell population, without recruitment of less mature stem cells. In summary, the main lessons from Figures 4 through 6 are as follows: 1. The simulation model predicts that the same total dose of CP administered over 8 hours instead of 120 or 480 hours creates a larger hematotoxic effect -and perhaps to a larger leukemia risk, if-the preceding speculations are accurate. 2. Doubling the duration of exposure (e.g., from 240 hours to 480 hours in Figure 5) less than doubles the simulated hematotoxic response (and any associated risk of leukemia). 3. Hematotoxic response (e.g., as indicated by height of zenith) is not a simple monotonic function of concentration (see Figure 6). If other organ systems and stem cell populations undergo similar feedback-control processes in responding to chamisal carcinogens, -then similar qualitative characteristics might be expected for the dynamic dose-response relations. 17 BP-00017731 COX ASSOCIATES, 1997. 503 Franklin Street, Denver, Colorado, 80218. 303-388-1778. TCoxDenver@aol.com Table 4 summarizes recent findings for several chemicals that suggest the following c0mmon pattern: When cytotoxicity-mediated cell proliferation plays an essential role in experimentally observed carcinogenesis, the dose-response pattern is typically non-linear at low doses and may exhibit hormesis. The BBRA model described in this paper offers a detailed explanation/prediction of this pattern in terms of the predicted dynamics of bone marrow stem celi (CFU-GM) responses to myelotoxic agents such as CP. cess ns ue o benzene exposure may be nonexistent or negative at sufficiently low doses." PBPK and hematotoxic models both support this nonlinear pattern. enzene exposure may increase s-MDS/Ieukemia risk by cytotoxic action on HPC and .normal stem cell po~l.llations followed by compensating proliferation. s1mu a 1on mo e predicts that at low concentrations, benzene increases stem cell counts in the bone marrow, instead of reducing them. OX, . See also Farris eta!., 1997 and Cronkite eta/., 1989. e mec amsm o carcinogenesis of TCE ... is nonlinear: very high doses, sufficient to cause cellular necrosis, are necessary." e no near~ observed in formaldehyde-induced rodent nasal cancer is consistent with a highconcentration effect of regenerative cell proliferation ... a 1gnancy anses . om repeated.cycles of necrosis and regeneration with the ultimate emergence of hyperplasia and then neoplasia." e concen a iOn- dependent increases in cell proliferation correlated strongly with the tumor response curve" on ceo an Morgan, 1994. See also Monticello et a/., 1996 and Lutz, 1991. 18 BP-00017732 COX ASSOCIATES, 1997. 503-Franklin Street, Denver, Colorado, 80218. 303-388-1778. TCoxDenver@aokom CONCLUSIONS The qualitative predictions about leukemia risks suggested for Figures 4 through 6 will remain no more than informed speculations until explicit modeling and empirical validation show whether they .are correct. Yet, the time patterns of hematopoietic responses generated by the CP model predict several phenomena that are inconsistent with simpler dose-response models but that occur in -practice. These include o Responses that increase less than proportionally when exposlolre durations are increased while holding administered concentration constant. o Nonmonotonic relations between concentration and response, suggesting that the relation between concentration and response may be different at very low concentrations. than it is at higher concentrations. o Response patterns that depend not only on the total dose (AUC of administered dose), but also on how the it is administered over time. Specifically, reducing exposure duration while proportionally adjusting exposure concentration can lead to larger responses (deeper nadir, higher and quicker zenith)for the same-total administered doses. These simulated phenomena are consistent with some of the complexities obse:ved in real dose-response patterns from stop-exposure experiments, as mentioned in the introduction. The results in Figures 4 through 6 suggest possible explanations for the anomalies in terms of nonlinear stem cell dynamics in response to cytotoxic stress. . Although the CP model is specific to hematopoietic cell populations and leukemogenesis, it is tempting to speculate that similar nonlinear dynamics and feedback control-ioops may help to explain the observed anomalies in other experimental systems, such as those in Table 4. In addition to predicting specific response patterns, the CP model provides potentially useful qualitative insights into the dynamics of hematopoietic responses. For example, simulation experiments in which two doses are separated by different amounts of time show that the hematopoietic system I 19 BP-00017733  COX ASSOCIATES, 1997. 503-Franklin Street, Denver, Colorado, 80218. 303-3 88-1778. TCoxDenver@aol.com response smoothes rapid transients in exposure inputs. In other words, it responds slowly enough (on a time scale of days to weeks) so that closely spaced doses (on a time scale of hours to days) creat~ essentially the same impact as a single combined dose. Thus, for example, if it is desired to constrain dosing so that both the depth of the initial nadir of WBCs and the height of the subsequent peak are minimized, then increasing the duratioil of the recovery period between the two successive doses from 1 day to 4 days would make relatively little difference. Allowing a week or 10 days instead of 4 days between successive doses would make a relatively large difference. ~rr summary, the type of dynamic dose-response model developed here for CP may be -useful in designing exposure regulations and guidelines that are more truly protective of human health than are standards based on AUC or, even more simplistically, on concentration. Guidelines that take into account the importance of exposure timing might be less burdensome than some current standards that assume (incorrectly, if the simulation experiments reported in Figure 4 are an accurate-guide) that long-duration, low-concentration exposure-scenarios are "equivalent" in risk to brief, high-concentration exposures. The dynamic simulation approach described in this paper can help to quantify the extent to which realistic dynamic dose-response patterns are likely to differ from those predicted by simpler dose-metric models. 20 BP-00017734 COX ASSOCIATES, 1997. 503 Franklin Street, Denver, Colorado, 80218. 303-388-1778. TCoxDenver@aol.com REFERENCES Buckner, C.D., R.. Rudolph, A Fefer, R.A. Clift, R.B. Epstein, D.O. Funk, P.E. Neiman, S.J. Slighter, R. Storb, and E.O. Thomas, 1972. High--dose cyclophosphamide therapy for malignant disease: Toxicity, tumor response. and the effects of stored autologous marrow. Cancer, 2S, 357-365. Butterworth, Byron E., J.L. Larson, R.B. Conolly, S_J. Berghoff, G.L. Kedderis, and D.C. Wolf. 1994. Risk assessmenUssues associated with chloroforminduced mouse liver tumors. GilT Activffies 14, 2. Calabrese, E.J., L.A. Baldwin, and H.M. Mehendale. 1993. G2 subpepulation in rat liver induced into mitosis-by low-level exposure to carbon tetrachloride: An- adaptiv-e response. Toxicology and Applied Pharmacology. 1211, 1-7. Chen, H_, D.A. Eastmond, 1995. Synergistic increase in chromosomal breakage within the euchromatin induced by an interactiGn of the benzene metabolites phenol and hydroquinone in mice. Carcinogenesis, 16(8):1963-1969. Chen, H., D.S. Rupa, R. Tomar, D.A. Eastmond, 1994. Chromosomal loss and breakage in mouse bone marrow and spleen cells exposed to benzene in vivo. Cancer Research, 54:3533-3539. Clewell RJ, Gentry PR, Gearhaft JM, Allen BC, Andersen ME, 1995. Considering pharmacokinetic and mechanistic information in cancer risk assessments for environmental contaminants: .e,xamples with vinyl chloride and trichloroethy~ene. ChemospheTe; 31(1 ):2561-2578 Coggins, P.R., R.G. Ravdin, and S.H. Eisman. 1960. Clinical evaluation of a new alkylating agent: Cytoxan (Cyclophosphamide). Cancer, 13, 1254-1260. Cohen L.L., J.Y. Jao, and W.J. Jusko. 1971. Pharmacokinetics of cyclophosphamide in man, British Journal of Pharmacology. 43:677-68. Cox, L.A., Jr., M.G. Bird, and L. Griffis. "Isoprene cancer risk and the time pattern of dose adminstration." Toxicology, 113,263-272, 1996. Cox, L.A., Jr-., Reassessing benzene risks using internal doses and Monte-Carlo uncertainty analysis. Environmental Health Perspectives, 104, Supplement 6, December. 1996. Cronkite EP, DrewRT, lnoueT, Hirabayashi-Y, BullisJE, 1989. Hematotoxicity and carcinogenicity of inhaled benzene. Environmental Health Perspectives, 82, 97-108. Davtd, J.M. and D.J~ Srendsgaard. 1990. "lJ-shaped dose-response curves: Their occurrence and implieations for risk assessment." J. Toxicology and Environmental Health, 30, 71 - 83. DeWys, W.O., A. Goldin, and N. Mantel, 1970. "Hematopoietic recovery after large doses of cyclophosphamide: Correlation of proliferative state with sensitivity: Cancer Research, 30. 1692-169-7. 21 BP-00017735 COX ASSOCIATES, 1997. 503 Franklin Street, Denver, Colorado, 80218. 303-388-1778. TCoxDenver@aolocom Farris GM, Robinson SN, Gaido KW, Wong BA, Wong VA, Hahn WP, Shah RS, t997. Benzene-induced hematotoxicity and bone marrow compensation in B6C3F 1 mice. Fundam Appl Toxicol; 36(2): 119-129 Fliedner TM; Tibken B; Hofer EP; Paul W, 1996. Stem cell responses after radiation exposure: A key to the evaluation and prediction of its effects. Health Phys (G2H), Jun; 70 (6): 787-97 Golden RJ, Holm SE, Robinson DE. Julkunen PH. Reese EA. 1997. Chloroform Mode of Action: Implications for Cancer Risk Assessment. Regul Toxicol Pharmaco/1;26(2):142-155 Green, J.D., C.A. Snyder, J. LoBue, B.D. Goldstein, R.E. Albert, 1981a. Acute and chronic dose/response effect of benzene inhalation on the peripheral blood. bone marrow: and spleen cells of CD-1 male-mice. Toxicology and Applied Pharmacology, 59:204-214. Green, J.D., C.A. Snyder, J. LoBue, B.D. Goldstein, R.E. Albert, 1'981b. Acute and chronic dose/response effect of inhaled benzene on multipotential hematopoietic stem (CFU-S) and granulocyte/macrophage progenitor (GM-CFUC) cells of CD-1 male mice. ToxicologyandApplied Pharmacology, 59:204-214. Irons, RD .. W.S. Stillman, D.B. Colagiovanni, and V.A. Henry. 1992. "Synergistic -action of the benzene metabolite hydroquinone on myelopoietic stimulating activity of granulocyte/macrophage colony-stimulating factor in vitro," Proceedings of the National Academy of Sciences USA, 89-;- 3691-3695. Irons R., and W. Stillman. 1996. The process of leukemogenesis. Environmental Health Perspectives, 104t, Supplement 6, December, 1239-1247. Jacquez, J.A., 1997. Compartmental Analysis in Biology and Medicine, 3ro Edition. Wiley, 1997. List, A.F., and A. Jacobs. 1992. Biology and pathogenesis oJthemyelodysplastic syndromes. Seminars in Oncology. 19(1 }: 14-24. Luke, C.A., R.R. Tice, R.T. Drew, 1988a. The effect-of exposure regimen-and duration on benzene-induced_ bone marrow damage in mice. I. Sex comparison on DBA/2 mice. Mutation Research, 203:251-272. Luke, C.A., R.R. Tice, R.T. Drew, 1988b. The effect of exposure regimen and duration on benzene-induced bone marrow damage in mice. II. Strain comparisons involving B6C3F1, C57BI/6 and -G>BA male mice. Mt:Jiation Research, 203:273-295. Lutz U, Lugli S, Bitsch A, Schlatter J, Lutz WK,-t997. Dose Response for the Stimulation of Cell Division by Caffeic Acid in Forestomach and Kidney of the Male F344 Rat. Fundam Appl Toxicol; 39(2t1'31-137 -Lutz WK, 1991..Dose-response relationships in chemical carcinogenesis: from DNA adducts-te tumor incidence. Adv Exp Med Bioi; 283:151-156 22 BP-00017736  COX ASSOCIATES, 1997. 503 Franklin Street, Denver, Colorado, 80218. 303-388-1778. TCoxDenver@aol.com Melnick, R.L., J.E. Huff, J.H. Roycroft, B.J. Chou, and R.A. Miller, 1990. "Inhalation toxicology and carcinogenicity of 1,3-butadiene in B6C3F1 mice following 65 weeks of exposure". Environmental Health Perspectives, 86, 27-36. Monticello TM, and Morgan KT, 1994. Cell proliferation and formaldehydeinduced respiratory carcinogenesis. Risk Analysis,14(3):313-319. Monticello TM, Swenberg JA, Gross EA. Leininger JR. Kimbell JS, Seilkop S, Starr TB. Gibson JE, Morgan KT, 1996. Correlation of regional and nonlinear formaldehyde-induced nasal cancer with proliferating populations of cells. Cancer Res 1;56(5):1012-1022 Moolgavkar, S., A. Dewanji, and D.J. Venzon. 1988. A stochastic two-stage model for cancer risk assessment. I. The hazard function and the probability of tumor. Risk Analysis. 8(3): 383-392. Nissen-Meyer R, Host H, Kjellgren K, Mansson B, Norin T . 1985. Short perioperative versus long-term adjuvant chemotherapy. Recent Results Cancer Res; 98:91-98 Portier, C.J., 1990. Utilizing biologically based models to estimate carcinogenic risk. In S.H. Moolgavkar (ed), Scientific Issues in Quantitative Cancer Risk Assessment. Birkhauser. Boston. Scheding, S., M. Loeffler, S. Schmitz, H-J. Seidel, and H.E. Wichmann; 1992. Hematotxic effects of benzene analyzed by mathematical modeling. Toxicology. 72, 265-279. Steinbach, K.H., H. Rattler, G. Pabst, and T.M. Fliedner, 1980. "A mathematical model of canine granulocytopoiesis". Journal of Mathematical Biology, 10: 1-12. Steinberg and DeSesso, 199.3. Regul Toxicol Phannaco/;18:137-153 Sladek, N.E. 1988. Metabolism of oxazaphosphorines. Pharmacology and Therapeutics. 37: 301-355. Tibken 8; Hofer EP. 1995. A biomathematical model of granulocytopoiesis fer estimation of stem cell numbers. Stem Cells, May; .13 Suppl 1 -2-83-9 Valberg, P.A.. .and AY. Watson, 1996. Analysis of diesel-exhaust unit-risk estimates derived from animal bioassays. Regulatory Toxicology and Pharmacology 2.4: 30-44 van der Bosch, P.P.J., and A.C. van der Klauw. 1994. Modeling, Identification, and Simulation of Dynamical Systems. GRC Press. Boca Rotan, -Florida. Williams, G.M., R. Gebhardt, H. Sirma, and F. Stenback, 1993. "Non-linearity ofneoplastic conversion induced in rat liver by low exposures to diethylnitrosamine." Carcinogenesis.14, 10, 2149-2156. 23 BP-00017737 FIGURJE '1: -M:O.DEL PREDICTIONS vs. CLINICAL OBSER-VATIONS FOR l'WO ADMINISTERED DOSE HISTORIES t: po1ipllornl 1>101 1: 2.00011l Model Predicllon --~ U: 1.0Clot0 \\__,~,;:?./ f: 0.00!------.r------,-E:::..::..::::=~:::;:.:.---~,8 0 Days 9 201 , 15 ' ... 10 Ee e ~'.)..... 0.... 6 ~ 0 ~~ 2 !Experimenial Daia {Budmer el a!., 1972) 0 () ~ 6 8 10 I~ 1<1 16> 18 Days Model PredicUons (top) and Experimental Data (boUom) nnon WBC Time Courses Human Pa-tients foltowing 60 and 120 -mg/kg of CP BP-00017738 FIGURE 2: t\fODEL PREDICTIONS vs. CLI.\"ICAL OBSERVATIONS FOR A FOUR-DA \' ADMI\'ISTERED DOSE HISTORY 1: patiphornl blood 1; 3.008<!-10 2: <1.00 . \1: 1.508<~-1~. 2: 2.00 2: doso ralo Model Prediction 22 12,000 10.000 e.ooo u ~ 6,000 -4,000 2,000 ~~ ~6 246 E>tperimental Data (Nissen-Meyer and Host. 1960) 500,000 400.000 lOO.OOO 200,000 a";' ~ re 0: 100,000 II -10 12 14 Days 16 18 20 22 Modei Predictions (top) and Experimental Data {bottom) on WBC Time Courses in Human Patients following 60 mg/kg for !Four (4) Days-' BP-00017739 @COX ASSOCIATES, 1997. 503 Franklin Street, Denver, Colorado, 80218. 303-388-InB. TCox.Denver@aol.com ModeJPrecfrctions (top) vs. Actual (mi~dle) and Comrol (bottom) for 50 mglkg Mean CFU-GM Values -1..8e6 _ _ _ _ _ _ _ oo::~~-14'\1.6e6 .. . .. J?redic.ted.time...... .. .... ..... 1.4es- ~~t1~ 1.2e6 II) Q) ::1 1e6 '1ij > 8e5 6e5 4e5 .. ): - \..~ . GM~-:~.e:.: .;I ~~!~~:. J --------~->~ ../ ... .. -'"''"' -0. -- ..... :.... . . ---- "\., ""'. '\: 2e5 ... Day2 Day4 DAY Day7 -o-- -GROUP CY 0 GROUP Control -<>-- GROUP CP Mode! FIGURE 3b: Predicted vs. ActUJal CFU~GM Values IVll NHce Afiefl' 01'1le, Two, ano11ihree CP lnjeciions P~redictedvs: Observed ... CF-U-GM CtfUiits for {a)-1, (b) 2.-a.n. d (c) 3 CP injections .. . . .. . . .0 . . ..; . . . . :. . ~ . .; . .: . ; . . :. . : -~- . ! 0 <>i "0' DOSE: (a) Group1 of*, 0q PREDCFU . [}- OBSERVED BP-00017740 FIGURE 4: SHORT, JB[HGH-CONCENTRATliON DOSING MAXIMIZES STEM CJEJLL RESPONSE FOR A GIVEN TOTAL AJDMINISTJERJED DOSJE (AUC) eCFUGM1 ': t.oo..-.oa 2:Cf\J GM 1 -3: CFU Gt.l1 1: 5.008+07 I: 0.00 I a? 0.00 C3raph l 1: peripheral blood 1: 2.00u10 -~480bt .~3 ===1==2~~3-=-- 240.00 IIAO.OO Hourn 720.00 10:28 PU 060.00 1115/94 2: per;plletal blood 3: pet19heraJ blOOd I : o.oo+-----...o....v------r----,--..-----...., 0.00 240.00 4110.00 720.00 &J 1 Graph 2: P:.ge I Houru 10:2G PM H/5194 Explqnation:.. This figure shows the effects on early CFU-GM stern cells (top panel) and peripheral WBCs (bottom panel) of different administered dose histories corresponding to the same total administered dose (AUC). Administering the dose over 8 hours instead of 480 hours leads to a deeper nadir followed more inunediately by a more extensive proliferation. According to the hypothesized model of leukemogenesis described in Section 4, this response pattern maximizes leukemia risk. BP-00017741 JFKGURE 5: LONGER EXPOSURE PERKODS DO NOT CREATE P.ROPOJRT!ONALLY GREATER l!USJKS I:CFIJGIIH 1: I.Ooo ..os 2:CFU GM f 3:CFU GM I 4:CFUOM 1 w: s.ooot ~~~ 1~!:-l;:0se~;;:._'---2-~l~~--4-~-- o.oo1: o.oo,~-----....------.....-------.------ .2~0.00 480.00 720.00 960.00 'if~ Grapl\:.1 Houro 3:24 PM 1116.194 1: perlpl'leral blood I: 2.00u10 :il: parfpherill blco<i ~: paripheral blood 1: 1.00(1 .. 10 dSO.OO. Houru 720.00 3:24 PM f)GO.OO 11~'96 E.xplanarion: This figure shows the effects on early CFU-GM stem cells (lop panel) and peripheral WBCs (bonom_pane!) of applying the same concentration (AUC per day) for different amounts of time. Administering the dose over 480 hours. instead of 48 hours leads to no deeper a nadir, but delays the post-exposure compensating proliferation. Alt-hough the proliferation is more pronounced whe.n it occurs. the initial nadir may not be deep enough to recruit many "immature" stem cells; moreover, the increased level of (presumably predominantly normal) stem cells in the interim and the increased opportunity for DNA repair and other damage-control processes to operate may make the longer-duration exposure less hazardous. Even wilhout these speculative hypotheses. the response of CFU- GM cells (e.g., nad1r1 zerurh. AUC. etc.) for the 480-hour exposure ace less than I0 times as great as the correspancling responses for the 48-hour exposure BP-00017742 FIGURE 6: HEMATOPOIETiC RESPONSE KS A NONMONOTONIC FUNCTIO~ OF CONCENTRATION KN SUSTAINED LOWLEVEL J:\FUSIONS 1: CFIJ Gld 1 t ; 1.0aa..08 2;CFUGAA 'i :t:CFUGM I 4: CJ'UGY I 5: CFU Ga.! I 1: I: o.oc~1~.o-o---------,-s~~o.-oo---------3-soT.-oo---------5-4~o'.o_o________72-o~.oo a ? 0Graph 3 Hours 2;41 PM 7/11194 I: peripheral blood 2: peripheral blood 3: peripheral blood 4: periphetal blOOd S: peripheral biCo<l 1: 2.00&+10 t: ------~-----2--------- 30.01----Jlg/ltg-day --3-----31-- 0.02 .,g.lllg~y E.t:planation: This figure shows the effects on early CRJ;;GM stem cells (top panel) and peripheral WBCs (bottom_panel) of different administered dose concentrations sustained throughout the simulation. Hematopoietic responses-such as the zenith, A UC. and 'stressed equilibrium levels ofCFU-GM cells fliSC increase and then decrease as a function of concentration. (This nonmonotonic pattern also occurs in finite-duration exposures.) BP-00017743