Drinking Water and Health, Volume 8 Pharmacokinetics in Risk Assessment (1987) / Chapter Skim
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IV. Uncertainties: Integration with Risk Assessment and Resources
IV. Uncertainties: Integration with Risk Assessment and Resources
Pages 183-250
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PART IV Uncertainties: Integration with Risk Assessment and Resou roes
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Blau and W Brock Neely INTRODUCTION In the course of investigating the behavior of a chemical, the toxicologist normally doses a mammalian species and follows the movement and distribution of the chemical over a period of time.
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BLAU AND W BROCK NEELY chemical for a specific species to the elucidation of the fate and distribution in a variety of mammals, including man.
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PK Models Using SIMUSOLV 187 MODELING PROBLEM rPRIOR FACTS l | AND THEORIES ~ 1-' 1 NO /SUITABLE \ MODEL SELECTED,/ \/ YES ESTIMATE MODEL PARAMETERS < MODEL YES USE MODES PARAMETERS FIGURE 1 Sequential model-building procedure.
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BLAU AND W BROCK NEELY limits in the values predicted by the model, as well as confidence regions around the estimated parameters.
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The determination of these maximum likelihood estimates is a nontrivial task, except for the special case in which the models in Equation 1 are linear. Unfortunately, this situation does not occur with phenomenologically based models; consequently, it is necessary to apply estimation procedures (Bard, 19741.
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In addition, the state-of-the-art numerical integration techniques Lawrence Solver for Ordinary Differential Equations (LSODE) are being used to solve all the differential equations associated with the model (Hindmarsh, 19821.
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+ ei, (3) where the kj's are the individual rate constants, and the error ci is a constant fraction of the amount being measured.
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BLAU AND W BROCK NEELY considerable range.
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This is a package that has been developed at the Dow Chemical Co. to aid the nonmathematician in building and solving models containing systems of algebraic and ordinary differential equations.
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Assuming a first-order absorption of the oral dose from the gastrointestinal tract into the blood stream followed by a first-order elimination into the urine, the mass-balance equations describing Model A become: dmlldt = —kl2m1 dC21dt= kl2(ml/V2) —k20C2 duldt= k2oc2v2 (8)
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back into the blood generates a long clearance time into the urine pool (k32 ~ k201. The following set of differential equations describes this model: dm,,ldt = —karma dC21dt = k~2 m~lV2 + k32m31V2 k23C2—k20C2 dm31dt= k23V2C2—k32m3 duldt= k20C2V2, (9)
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Problem 2 Problem 2 demonstrates the ability of SIMUSOLV to examine the confidence regions around the rate constants. Metzler (1968)
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associated with the data for generating the uptake rate constant is very minimal (one datum point at 1 h from Table 31. This would indicate a strong suspicion that the confidence region around kl is very large.
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BLAU AND W BROCK NEELY TABLE 3 Sequential Blood ConcentrationTime Data Following an Oral Dose Time (h)
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Time (h) Parent Metabolite Parent Metabolite 0.82 0.175 0.822 1.0 1.87 7.23 1.2 0.166 1.14 1.4 0.126 1.15 2.0 0.109 0.860 3.23 15.53 2.4 0.09 0.648 2.9 0.083 0.601 3.0 4.02 21.15 3.38 0.070 0.382 3.92 0.059 0.403 4.0 4.59 25.88 4.42 0.051 0.304 5.18 0.035 0.252 6.0 5.77 32.4 6.35 0.015 0.143 8.0 6.3 34.9 8.3 0.0081 0.0636 10 0.0047 0.0332 12 6.65 37.06 12.4 0.0026 0.0065 24 6.92 38.7 24.57 0.0009 0.0065 48 7.3 40.29 72 7.38 40.77 The confidence region has now been reduced, and the new value for k1 is more reliable.
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BLAU AND W BROCK NEELY CONTOUR PLOT 0.0 kit 2.0 4.0 ,,'"o j,~35~0o$~"` L ~^,,~r 0 lo ,~/ 1 1 (9 ~ al 1 .o 1 1 1 0.021 0.024 0.027 0.030 0.015 0.018 k2 FIGURE 5 Linear confidence regions around kit and k2 for Model A using the data in Table 3.
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Note the large uncertainty in the confidence around the uptake rate constant.
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BLAU AND W BROCK NEELY CONFIDENCE INTERVAL PLOT 0.0 k1 2.0 <~2," 0.015 0.018 0.021 0.024 k2 0.027 0.030 FIGURE 7 Confidence region around k' and k' for Model A using the data in Table 3 with additional data taken at 0.5 and 0.75 h.
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SIMUSOLV was used to determine the maximum likelihood estimates shown in Table 5. Table 5 also shows the progressive improvement in the fit of the model in going from Model 1 to Model 3.
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BLAU AND W BROCK NEELY TABLE 5 Statistical Analysis Using SIMUSOLV on the Four Models Represented by Equations 10-13 and the Data in Table 5 Model 2 4 Maximum likelihooda 57.34 66.28 90.15 91.65 Parametersb kit 0.362 0.365 0.36 0.34 k24 6.85 5.08 17.37 17.15 k20 1.11 0.83 3.08 3.06 k40 1.37 2.68 2.96 3.14 k23 3.34 2.48 k32 0.069 0.047 v2 9.8 13.6 3.33 3.41 V4 4.19 3.19 Percent variation explained 98.79 98.77 98.76 98.75 aThe maximum likelihood function is expressed in natural logarithms.
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PK Models Using Sl MUSOLV 205 60 ~ 45 a)
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BLAU AND W BROCK NEELY Dunker, A
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PK Models Using SIMUSOLV 207 Statistical Summary Maximized Weighted Residual Weighted Likelihood Sum of Residual Function Squares Sum Standard Error of Estimate Percentage Variation Explained Weighting Parameters 97.667 0.00 36.88 3.668E - 04 Correlation Matrix kl2 1.000 0.1293 kl2 k2o Variance-Covariance Matrix kl2 k2o 1 .000 kl2 3.4559E—02 1.5384E - 03 4.0937E - 03 2.432E—02 6.057E—03 k2o aThis is the difference between the observed and calculated values multiplied by the weighting factor.
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An effective approach for interpreting empirical data relating to pharrnacokinetics is the development of predictive physiologically based pharmacokinetic models. These models utilize actual physiological parameters of the experiThe submitted manuscript has been authored by a contractor of the U.S.
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A chief advantage of the physiologically based model is that by simply changing the physiological parameters, the same model can be utilized to describe the dynamics of chemical transport and metabolism in mice, rats, and humans. DESCRIPTION OF THE MODEL The pharmacokinetic model used in the present study (Figure 1 and Table 1)
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Qalv Calv Qb Cart Qf Cart Q I Cart Ql Cart FIGURE 1 Diagram of the pharmacokinetic model used to simulate the behavior of inhaled PCE.
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for tissue groups or compartments I Liver (metabolizing tissue group) f Fat tissue group r Vessel-rich tissue group p Vessel-poor tissue group Blood flow rate to tissue group (liters blood/in)
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INTERSPECIES EXTRAPOLATION In this section, it will be determined whether the metabolic scaling factors described above allow for both interspecies extrapolation and doseroute extrapolation. To accomplish this, we will first determine metabolic parameters so that model predictions will reproduce rat data published by Pegg et al.
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Qalv 5.02 325.0 Blood flow rates (liters blood/in) Total blood flow rate Qb 5.02 325.0 Blood flow rate in liver I 1.26 81.3 Blood flow rate in fat Q5 0.45 29.3 Blood flow rate in vessel-nch tissues Or 2.56 165.7 Blood flow rate in vessel-poor tissues Qp 0.75 48.7 Tissue group volumes (liters)
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~ _ flu ~ ~ tr 1 0 O O LU c, ~ He LU con ~ 5 x UJ UJ o 1 10 ppm PCE EXPOSURE IN RATS FOR 6 h - · MODEL PREDICTIONS T EXPERIMENTAL DATA l WITH ERROR BAR I I l · ~ 0 8 16 24 32 40 48 56 64 72 POSTEXPOSURE TIME (fur) FIGURE 2 Percentage of PCE expired by rats following expsure to to ppm in air for 6 h.
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In Figure 3, model predictions of expired air concentrations are compared with the empirical data of Pegg et al.
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Pharmacokinetic models provide a tool to quantitatively evaluate the effect of route of administration on dose to the target tissue. This effect must be evaluated on a chemical by chemical basis.
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The largest difference is a factor of three and occurs in the 500- to 10,000-mg/kg applied dose range. Figure 6 shows model predictions of total metabolized dose to the mouse lung following inhalation and oral administration.
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It has also been shown that it is possible to use pharmacokinetic models to investigate the effect of route of administration on dose to target tissue. Since pharmacokinetic models allow for a quantitative extrapolation of exposure data across species and between routes of administration, they provide a tool to quantitatively evaluate assumptions currently used in the risk assessment process.
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1987. Physiologically based pharmacokinetics and the risk assessment process for methylene chloride.
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1979. Partition coefficients of some aromatic hydrocarbons and ketones in water, blood and oil.
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This report will discuss the utility of using carcinogenDNA adduct levels as a measure of the biological dose in the risk analysis of carcinogenic data. EVIDENCE FOR USE OF DNA ADDUCTS AS A MEASURE OF BIOLOGICAL DOSE Considerable evidence has indicated that many mutagens and carcinogens react with cellular DNA either directly or following metabolic formation of reactive products.
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Thus, the extent of promutagenic damage induced by environmental chemicals and the capacity of the cell to repair such damage may be important factors in both initiation of malignant transformation and tissue specificity of many carcinogens. Various studies, both in vivo and in vitro, of carcinogen-DNA adducts in a known target tissue are a good measure of a biological dose for initiation of neoplasia.
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In any case, this does not detract from the use of adduct levels in the target tissue as a measure of biological dose of the carcinogen. The abovementioned results strongly imply that it is biologically more meaningful to relate tumor response to concentrations of specific DNA adducts in the target tissue than it is to relate tumor response to the administered dose of the chemical (Hoer et al., 19831.
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The dose- and time-dependent accumulation of adducts is required to construct a measure of biological dose. Adduct levels can be determined from direct measurements or, at least in theory, calculated a priori from physiologically based pharmacokinetic models.
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DOSE-RESPONSE RELATIONSHIPS - Dose-response relationships for carcinogen-DNA adducts have been determined for several chemicals. A plot of adduct levels divided by dose versus dose is one way to represent dose-response relationships, and this representation is especially useful for consideration of low-dose extrapolation.
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1985. Use of monoclonal and polyclonal antibodies against DNA adducts for the detection of DNA lesions in isolated DNA in single cells.
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pyrene: DNA adduct formation in vivo in the forestomach, lung, and liver of mice. Cancer Res.
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1985. Quantitative comparison of genetic effects of ethylating agents on the basis of DNA adduct formation.
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is a portion of the larger and more general effort of mathematical simulation of physical and biological phenomena. PK simulates certain aspects of the behavior of biological systems, and makes predictions about the future behavior of those systems, by solving systems of algebraic or differential equations.
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Recent progress in numerical analysis has yielded methods that can permit microcomputers to produce useful approximations, even to such complicated systems as the three-dimensional convection of reactive gases in the human lung. COMPUTER LANGUAGES USED IN PHARMACOKINETIC MODELS Any computer language can be used to simulate the distribution ot chemicals within the body or cells with time.
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These modern languages also encourage modular programming, in which each large task (such as simulating the evolution of the concentrations of a chemical toxicant in each of several human organs) is broken down into smaller tasks (such as reading a data base of organ descriptions, building a data structure for the simulation, approximating the evolution of a single organ for 1 s, stepping through the list of organs, stepping through time, and plotting the results)
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Many simulation languages, such as CSSL and ACSL, work by translating the simplified model description into a general purpose computer language such as FORTRAN. ACSL is being incorporated into a more TABLE 1 Popular Simulation Languages Language ACSL Description SCoP SIMNON ADSIM A language designed for modeling and evaluating the performance of continuous systems described by time-dependent, nonlinear differential equations.
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Because biological simulation has not yet developed to the stage where models can be constructed from a set of standard modules, SCoP lets the modeler write equations of any type, e.g. linear or nonlinear algebraic, ordinary, or partial differential equations.
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Statistical and plotting routines are either incorporated into simulation languages or can be used as general utilities once the PK model has been solved and the results of the prediction obtained. Commercially available packages such as SAS/GRAPH~ Microsoft Chart or LOTUS 1-2-3~ can be used with computer files generated by the PK model program to provide a visual display of the mathematical relationships.
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The model maintains a physiometric data base for each of several animal strains and species, including blood flow rates, organ masses, capillary or plasma volumes, etc., for each animal. For each new chemical the investigator must choose which organs or parts of organs to represent with separate compartments and which to aggregate together.
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iINHALE: _< E L N o o o S D Or ~ LUNG , LYMPH NODE S _ A SPLEEN ~ R B E L R O L | LIV E R | . | GUT - 1 ,<3 ~ E it' ~ r E S T E it KIDNEY _ ~ t u R N r MU SC L E I | OTHER | FIGURE 1 A generic multicompartmental model for distribution and metabolism of xenobiotic compounds in mammals.
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o 2 4 TIME (HOURS) 6 FIGURE 2 Simulated amount of nickel in the kidneys following an intravenous injection of 13 ,ug.
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200 190 180 1 70 '60 450 1 40 130 1 20 ~ ~ o c, 100 Z go So 70 60 z 50 40 30 20 0 o o i, 6 2 4 TIME (HOURS) FIGURE 3 Simulated amount of nickel in the lung following an intravenous injection of 13 leg.
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, 2 4 Tl ME (HOURS) FIGURE 5 Simulated amount of nickel in the blood following an intravenous injection of 13 log.
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1,241 1,522 947 237 61 1,795 1,241 338 947 237 61 1,795 846 846 175 175 5,640 5,640 Kidney Liver Gut Spleen Testes Carcass Arterial blood Arterial blood Arterial blood Arterial blood Arterial blood Arterial blood Arterial blood Muscle Lung Arterial blood Venous blood Lung Venous blood Venous blood Liver Liver Venous blood Venous blood Kidney Liver Gut Spleen Testes Carcass Muscle Venous blood Venous blood Lung Lung Arterial blood aMost compartments contain both a tissue (mass) and blood (capillary volume)
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pyrene dial epoxide, and the reaction of benzo(a) pyrene dial epoxide with glutathione and nuclear DNA to form covalent adducts.
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The integrated form of the Michaelis-Menten equation is used to describe the enzymatic reactions. To increase the precision of measurement TABLE 3 Equations Describing Benzotaypyrene, Glutathione, and Sulfite Metabolism and DNA Adduct Formation = k3[gssg]
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PDNA adduct formation in the presence of sulfite or sulfur dioxide is mostly due to the inhibition of the glutathione S-transferase pathway by the sulfite metabolite GSSO3H. Using this model and a simple calculation of the intracellular sulfite concentrations that are likely from exposure to sulfur dioxide concentrations used in three studies of the cocarcinogenicity of sulfur dioxide with
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polyaromatic hydrocarbons (Laskin et al., 1976; Pauluhn et al Pott and Stober, 1983) , we can predict that a marked increase in DNA adducts occurred in the study done by Pauluhn et al.
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Simulation Resources 245 _ _ 30o At L' 20o At a m ~ 10cn o // / l / I I / I / I i/ / Laskin ot al.
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Training in simulation is available from the NBSR and other NIH simulation resources at two levels. Introductory classes are designed for researchers with little or no background in computer usage or programming.
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The selection of physiological parameters for PK models is a particularly critical area in which comparisons of different values may prove especially useful. As better physiological values are amassed, they can be stored in data tables in a form useful for modeling.
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At present, ACSL, CSSL, SIMNON, ADSIM, SCoP, and SCoPFIT are available as simulation languages on NBSR and are accessible through TOXIN. Should user demand
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Development of special data bases for physiological parameters can be achieved. Much of our knowledge of organ blood volumes, flow rates, and gross anatomy are gained from tracer techniques.
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1985. Glutathione S-Sulfonate, a sulfur dioxide metabolite, as a competitive inhibitor of glutathione S-transferase, and its reduction by glutathione reductase.
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