Drinking Water and Health, Volume 8 Pharmacokinetics in Risk Assessment (1987) / Chapter Skim
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VI. Applications of Mathematical Modeling
VI. Applications of Mathematical Modeling
Pages 351-428
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PART Vl Applications of Mathematical Modeling
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In any case, the uncertainties identified in risk assessments help to establish areas in which additional research would be useful. The intent of this paper is to broaden the awareness that pharmacokinetics and mathematical dosimetry models are useful tools in risk assessments of noncarcinogenic as well as carcinogenic effects.
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The incorporation of laboratory and field observations of adverse health effects, hazard information, and extrapolation methods to yield dose-response assessments is critical to the risk assessment process. The combining of these phases can be facilitated by the integrated physiologically based dosimetry modeling approach, illustrated schematically in Figure 2.
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The phases of the process that can be addressed by using an integrated physiologically based dosimetry modeling approach are contained within the dashed rectangle. Overall figure schematic is based on Figure 1-1 of NRC (1983)
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_ . and Design Experiments | Estimate Hu j an Toxicity ~ r | Risk Characterization 1 FIGURE 2 A schematic of the elements of an integrated physiologically based dosimetry modeling approach to estimating human toxicity that leads to one of the components of risk characterization.
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An application to ozone toxicological data is presented to illustrate the methodology of using mathematical dosimetry models to examine quantitative dose-response relationships. LOWER RESPIRATORY TRACT MATHEMATICAL DOSIMETRY MODELI NG In the papers presented in this volume, much attention is placed on the use of physiologically based pharmacokinetic models to provide a description of dose distribution following inhalation of a chemical compound.
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, so proper treatment of gas transport processes is not apparent. Experimental values for upper respiratory tract uptake of the inhaled gas, however, can provide appropriate boundary conditions for mathematically modeling delivered doses to LRT regions.
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HY~ An -- ' "'AS' UQUlD uea~c Use. LIQUID LINING FIGURE 3 The relationships between morphologies and their model representations.
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Compartmental diffusion coefficients and partitition coefficients, such as those used in physiologically based pharmacokinetic models, are also needed. Much of the above topic is discussed in detail elsewhere (Miller et al., 1985; Overton et al., 19871.
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Another example of sensitivity analysis demonstrating the importance of model parameters is concerned with the values of the liquid lining rate constants. Simulations show that the effect of increased chemical reactivity in the TB liquid lining is to increase the net airway doses in the TB region and to decrease the tissue dose throughout the LRT.
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Tissue dose is the predicted dose of the epithelial layer in the tracheobronchial region and of the air-blood barrier in the pulmonary region. Net dose is the total absorbed by the liquid lining, tissue, and blood compartments.
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Nasopharyngeal removal studies are currently being conducted, and when available, they will facilitate translation of the net and tissue dose curves of Figure 4 into delivered dose curves associated with exposure to O3. CRITICAL TOXICITY REFERENCE SYSTEM Data collection for the O3 analyses was accomplished by the CTR system (Smolko et al., in press)
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The basic criteria applied include a quantitative representation of effect, the use of a species appropriate for combination with the PBD model for 03, an adequate presentation of data, a statistical analysis of data, exposures to O3 only, a lack of variables that might confound results, and continuous exposures to a single concentration of O3. Other items to be considered when selecting studies concern both interpretive and technical quality.
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Because of the complexity and cellular diversity of the lung, toxicologically relevant lung dosimetry needs to be related to specific sites within the respiratory tract to achieve a better understanding of the tissue dose dependence on toxicity of inhaled pollutants. Direct measurement of tissue or cellular dose by radiometric, physical, or chemical means within specific segments of the lung is one approach to determining equivalent doses between species.
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and 10% (., solid line) upper respiratory tract removal is plotted.
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1976. Mass-transfer coefficient for sulphur dioxide and nitrogen dioxide removal in cat upper respiratory tract.
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I The sensitivity of the uptake of ozone in the human lung to lower respiratory tract secretions and exercise.
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Role of Pharmacokinetic Modeling in Risk Assessment: PerchIoroethylene as an Example Chao W Chen and Jerry N
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Pharmacokinetic analyses can range from very simple arithmetic operations, which are used to calculate the amount of the dose that is converted to some suspected or proven toxin, to complicated physiologically based pharmacokinetic (PB-PK) models.
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PK Modeling: Perchloroethylene 371 models may give information regarding the concentration of a putative toxin at a target tissue or cell. Most importantly, they can provide a description of the disposition of a compound over time rather than just at some predetermined endpoint.
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PK Modeling: Perchloroethylene 373 TABLE 2 Disposition of [~4C] PCE Radioactivity for 72 h After Inhalation Exposure for 6 h by Sprague-Dawley Rats and B6C3F1 Mice mg Eq./animal Drug Ratsa Micea disposition 10 ppm 600 ppm (10 ppm)
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PK Modeling: Perchloroethylene 375 TABLE 6 Tumor Incidence and the Corresponding Metabolized Dose for B6C3F1 Mice in NTP (1985) Inhalation Bioassay, Calculated by PB-PK Model Daily metabolized dose (mglkgl day)
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PK Modeling: Perchloroethylene 377 TABLE 8 Daily Amounts (mg) of Total Metabolites in Male and Female Mice Exposed to PCE by Inhalation According to the NIP Bioassay Pattern In males (0.035 kg bw)
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PK Modeling: Perchloroethylene 379 TABLE 12 Risk at a Unit Dose of 1 ~g/liter in Water or 1 ~g/m3 in Air With and Without the Use of PB-PK Modeling Without PB-PK modeling Based on inhalation data Medium Based on gavage data With PB-PK modeling Based on Based on inhalation Method 2a Method 2b gavage data data NEa NE 1.5 x 10-7 NE Water (1 1lg/liter)
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for cells at different stages: normal, initiated, or transformed. The ultimate goal is to construct a biologically based dose-response function and a physiologically based pharmacokinetic model that estimates target dose under any exposure pattern.
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One possible explanation for this is that the percentage of body fat is greater in humans than in rodents. FUTURE DIRECTIONS We believe that we have demonstrated here the utility and advantages of using physiologically based pharmacokinetic modeling in exposure and risk assessments.
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Describing and modeling exposure at such sites requires a greater understanding of mechanisms of action but ultimately can result in reducing some uncertainties that are inherent in present risk assessments. Subcellular models have already been formulated for the purpose of exposure assessments (Blancato and Bischoff, 1985; Gehring and Young, 19781.
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1986. Physiological pharmacokinetic modeling of cis-dichlorodiamineplatnium (II)
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PK Modeling: Perchloroethylene 385 APPENDIX: CONSTRUCTION OF PB-PK MODELS Description of the PB-PK Mode' for inhaled PCE PCE in vapor form in air is readily absorbed through the lungs into blood by first-order diffusion processes. Pulmonary uptake of PCE is largely determined by the ventilation rate, duration and concentration of exposure, solubility in blood and body tissues, and metabolism.
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Tissue Group 1 °a Qt Cart Qf .4 Cart Q can Cart Q Cart I m ~ Metabolites Km FIGURE A- 1 Diagram of the physiologically based pharmacokinetic model.
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Qp Blood flow rate to poorly perfused tissue group (liters/min) Via, Vf, Vr, and Vp Volumes of tissue groups (liters)
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The tissue:blood coefficients for humans are assumed to be identical to those of rats. METABOLISM RATE CONSTANTS, Vm AND Km Rats The constants Vm and Km were estimated by least-square optimization by using the system of differential equations and data from a metabolism
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PK Modeling: Perchloroethylene 389 study by Pegg et al.
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Development of Multispecies, Multiroute Pharmacokinetic Models for Methylene Chloride and I, I, I-TrichIoroethane (Methyl Chloroforms Richard H Reitz, Richard ]
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Considering all these factors, it is clear that risk estimations based upon animal data contain large areas of uncertainty. Physiologically based pharmacokinetic (PB-PK)
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Multispecies, Multiroute PK Models 393 Obviously, it would be useful to understand the reason for the different results obtained in the different studies. PB-PK analysis can be used in conjunction with biochemical studies to provide a single hypothesis that is consistent with all of these results.
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Multispecies, Multiroute PK Models 395 TABLE 1 Comparison of Average Daily Values of Dose Surrogatesa and Tumor Incidences in Lung and Liver Tissues of Female B6C3F1 Mice in Two Chronic Bioassays of Methylene Chloride Inhaled Inhaled Drink Tissue Control (2,000 ppm)
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For example, it is obvious that the values chosen for the human metabolic rate constants affect the levels of the dose surrogates calculated by the model. The rate constants for the MFO pathway in humans were estimated from existing in vivo human data as described elsewhere (Andersen et al., 19871.
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MC concentrations in fat, (4) MC concentraTABLE 2 Parameters Used in the Physiologically Based Pharrnacokinetic Model for Methylchloroform Parameter Human Rat 1 Rat 2 Mouse 1 Mouse 2 Body weight (kg)
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. Computer predictions are shown as solid lines, while actual data are given as open circles (1,500 ppm)
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Multispecies, Multiroute PK Models 399 TABLE 3 Comparison of Values for Selected Parameters in Young Rats and Young Mice as Predicted by the Models and Observed by Schumann et al.
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The physiologically based model predicted that MC would be eliminated from the mouse much more rapidly than from the rat. This is consistent with the data of Schumann et al.
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In view of the fact that apparently identical animal studies of toxicity and/ or carcinogenicity often differ between themselves by more than a factor of 2, the consistency of the PB-PK model seems remarkable. Furthermore, the fact that this consistency extends across a variety of endpoints, including end-exposure blood levels, total amounts metabolized, and tissue concentrations, suggests that this technique offers considerable promise in understanding and predicting interspecies differences in the delivery of internal dose to various organs.
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. Computer predictions are shown as solid lines, while actual data are given as open circles (350 ppm)
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Multispecies, Multiroute PK Models 403 be administered to animals in their drinking water are limited. Because small quantities of these materials are sometimes found in human drinking water supplies, however, it would be useful to have a procedure for predicting their toxicity from studies conducted by another route.
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Multispecies, Multiroute PK Models 405 TABLE 4 Comparison of Values for Selected Parameters for Disposition of MC in Old (approximately 18.5 months) Rats and Old Mice as Predicted by the Models and Observed by Schumann et al.
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These data offer encouragement that pharmacokinetic models may play an important role in understanding and predicting the toxicity of materials found in drinking water based on studies conducted by another route.
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. Other investigators have noted this phenomenon, and have found it necessary to increase the relative percentage of fat when constructing pharmacokinetic models in older animals (Lutz et al., 19771.
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Many uncertainties certainly remain in the risk assessment process, but risk assessments that properly consider the role of physiologically based pharrnacokinetics should be significantly more reliable than those that do not. REFERENCES Ahmed, A
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1984. A physiologically based de-description of the inhalation pharmacokinetics of styrene in rats and humans.
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The principal organs containing the compound are shown in Figure 1. Transport of MTX across the capillary and cell membranes of the liver, kidney, and skin is rapid, so that equilibrium ratios of tissue to plasma concentrations (plasma con410
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Methotrexate: Pharmacokinetics and Toxicity 41 1 1 I PLASMA, ASP 1 , SPLEEN QL~ C]
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As a consequence initial delivery of MTX to these organs is membrane transport limited rather than blood flow limited. MTX is cleared from the body through both biliary and urinary routes.
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and punne biosynthesis. Binding of drug prevents this enzyme from allowing continued production of DNA precursors, resulting in a cessation of DNA synthesis and, if continued long enough, in cell death.
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, fecal transit time (kF) , bile residence time art, and MTX reductase dissociation constant Aft.
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reported a Michaelis constant of 70 EM for excretion of MTX into bile; however, saturation is not observed in the mouse when plasma concentrations are in substantial excess of this value (D.
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Remaining parameters such as membrane transport constants (k, K) and metabolism rate constants for hydroxylation and polyglutamation are still other quantities that require species-specific work.
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The bone marrow concentrations are total tissue concentrations and are thus an average over the extracellular and intracellular regions. These concentrations are nonzero and dose scalable at short times because equilibration between plasma and the extracellular space is essentially instantaneous, and saturability only occurs during transport from the extracellular to intracellular space.
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to the target enzyme dihydrofolate reductase. This is exhibited in Figure 3, in which total MTX concentrations in rat bone marrow (extracellular MTX + intracellular MTX)
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The solid lines represent model simulations with saturable transport. SOURCE: Dedrick et al.
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The area under the bolus curve is about 2 orders of magnitude greater than that under the infusion curve, yet toxic response is greater with infusion. The principal correlate with response is the length of time that dihydrofolate reductase and, consequently, DNA synthesis are strongly inhibited.
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An inhibition time virtually identical to that above was observed, a period of about 30 h. Further indication of DNA synthesis inhibition time as an appropriate measure of toxicity comes from observing the trend in lethality if, at a fixed infusion rate, infusion times are lengthened.
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To predict toxic response from a given dose and schedule, the pharmacokinetic model of MIX must be coupled to the inhibition of DNA
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In the mid-1970s, this was accomplished very simply by observing that recovery of DNA synthesis occurred when MTX plasma concentrations, as measured by a competitive binding assay, fell below 10-8 M (Chabner and Young, 1973~. Figure 8 shows that recovery in
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. bone marrow was a strong function of this pseudo-threshold following bolus dosing from 5 to 350 mg/kg.
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Under long-term infusion or closely spaced multiple bolus conditions, however, cells have much more time to produce polyglutamates and attain inhibiting levels of these compounds. Under these circumstances, MTX pharmacokinetic models need to be expanded to include polyglutamation kinetics, and intracellular MTX polyglutamate concentrations, rather than plasma concentrations of parent compound, need to be correlated with levels of DNA synthesis.
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1981. Characteristics of membrane transport of methotrexate by cultured human breast cancer cells.
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Methotrexate: Pharmacokinetics and Toxicity 427 Zaharko, D
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