ToxSci Advance Access originally published online on April 21, 2008
Toxicological Sciences 2008 104(2):250-260; doi:10.1093/toxsci/kfn080
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Published by Oxford University Press 2008.
A Physiologically based Pharmacokinetic Model for Intravenous and Ingested Dimethylarsinic Acid in Mice
National Health and Environmental Effects Research Laboratory, Office of Research and Development, U.S. Environmental Protection Agency, Research Triangle Park, North Carolina 27711
1 To whom correspondence should be addressed at US EPA, MD B143-01, Research Triangle Park, NC 27711. Fax: (919) 541-3680. E-mail: evans.marina{at}epa.gov.
Received February 12, 2008; accepted April 11, 2008
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONSUPPLEMENTARY DATAREFERENCES |
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A physiologically based pharmacokinetic (PBPK) model for the organoarsenical dimethylarsinic acid (DMAV) was developed in mice. The model was calibrated using tissue time course data from multiple tissues in mice administered DMAV intravenously. The final model structure was based on diffusion limitation kinetics. In general, PBPK models use the assumption of blood flow-limited transport into tissues. This assumption has historically worked for small lipophilic organic solvents. However, the conditions under which flow-limited kinetics occurs and how to distinguish when flow-limited versus diffusion-limited transport is more appropriate, have been rarely evaluated. One important goal of this modeling effort was to systematically evaluate descriptions of flow-limited compared with diffusion-limited tissue distribution for DMAV, using the relatively extensive pharmacokinetic data available in mice. The diffusion-limited model consistently provided an improved fit over flow-limited simulations when compared with tissue time course iv experimental data. After model calibration, an independent data set obtained by oral gavage of DMAV, was used to further test model structure. Sensitivity analysis of the two PBPK model structures showed the importance of early time course data collection, and the impact of diffusion for kidney time course data description. In summary, this modeling effort suggests the importance of availability of organ specific time course data sets necessary for the discernment of PBPK modeling structure, motivated by knowledge of biology, and providing necessary feedback between experimental design and biological modelers.
Key Words: physiologically based pharmacokinetic (PBPK) model; toxicokinetics; dimethylarsinic acid.
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INTRODUCTION |
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Dimethylarsinic acid (DMAV, cacodylic acid) is produced commercially for use as a nonselective herbicide, and is also the major metabolite formed from ingested or inhaled inorganic arsenic in both rodents and humans (ATSDR, 2007
; Hughes and Kenyon, 1998). In terms of metabolism, DMAV is initially reduced to dimethylarsinous acid (DMAIII) and then oxidatively methylated to trimethylarsine oxide (TMAO) (Cohen et al., 2006). When administered directly by the oral route, DMAV is excreted mainly in the urine of mice and humans. In mouse urine, parent, DMAIII, TMAO, and low levels of arsenic thiol compounds have been detected (Hughes et al., 2008). Because of its unique binding to rat hemoglobin, the rat avidly retains DMAIII for an extended period, much longer than mice or humans (Stevens et al., 1977; Vahter et al., 1984). DMAV not retained as DMAIII bound to hemoglobin in rats is extensively metabolized to trimethylated forms and excreted in urine (Adair et al., 2007; Cohen et al., 2006; Yoshida et al., 1997, 1998).
DMAV is a tumor promoter in mouse skin and lung (Yamanaka et al., 1996, 2000) and in rat urinary bladder, liver, kidney and thyroid gland (Yamamoto et al., 1995). DMAV is also a complete urinary bladder carcinogen in female rats via diet at levels in the range of 40–200 ppm (Arnold et al., 1999), and male rats via drinking water at levels of 50 and 200 ppm (Wei et al., 2002). The proposed mode of action for the carcinogenic effects of DMAV in rat bladder is cytotoxicity followed by regenerative proliferation. DMAIII has been proposed to be the active metabolite involved in this process (Cohen et al., 2006). The carcinogenic mode of action of a chemical is but one of the pieces needed in the risk assessment together with knowledge of differences in metabolism and disposition between species (Cohen et al., 2006).
Physiologically based pharmacokinetic (PBPK) modeling has become a preferred option for various types of extrapolation implemented in risk assessment. These forms of toxicokinetic extrapolations include interspecies (rodent to human), high to low dose, duration (acute to chronic) and from the average human to potentially susceptible subpopulations (Andersen and Dennison, 2001). A PBPK model for arsenic would be applicable for species extrapolation in animal models to humans, particularly as it relates to tissue dosimetry, where little or no data exists in humans (El-Masri and Kenyon, 2007).
One of the fundamental questions faced by a modeler at the start of a new physiological quantitative description is whether chemical distribution into tissues is best described as blood flow-limited or diffusion-limited. In most applications within toxicology, once the organs to be included in the model are selected, the assumption of blood flow-limited distribution of chemicals is the major factor affecting movement of chemical into the particular organ (Andersen and Dennison, 2001). However, the initial PBPK work started in the clinical therapeutics field made use of a diffusion description of distribution which included separation of the blood and tissue compartments by a capillary membrane (Lutz et al., 1980). The justification for this addition to model complexity was based on the data available and on the larger molecular size of the modeled drugs. In general terms, the implicit assumption has been made that blood flow is sufficient to describe most data sets for smaller environmental molecules with high lipophilicity. Despite wide application of the flow-limited description, there has been limited examination of the impact of increasing structure complexity to include a complete description of transport biology, or even a description of when this change may be necessary (Collins et al., 1999)
In this manuscript, we present a PBPK model for DMAV exposure that was developed using mouse time course data. The goals of this paper were: (1) to develop a PBPK model which incorporates current knowledge of the effects of DMAV exposure on physiological and biochemical processes in mice, (2) to use the existing set of data generated for the model to investigate the role of flow versus diffusion limitation on final model structure, and (3) to apply sensitivity analysis techniques to compare impact of model parameters on model predictions, and structures.
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METHODS |
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Experimental data
The experimental iv data used in model development and calibration have been described in detail elsewhere (Hughes and Kenyon, 1998
; Hughes et al., 2000). Briefly, [14C]-DMAV (1 µCi per animal) was administered intravenously (tail vein, 4 ml/kg) to adult female mice at doses of 0.6 or 60 mg/kg of elemental arsenic (As). These doses correspond to 1.11 or 111 mg/kg of DMAV, respectively. The mice were killed by cardiac puncture under CO2 anesthesia at 5-, 15-, 30-, 45-, 60-, 90-, or 120-min postinjection. There were four mice per time point for the two dose levels of DMAV administered. Blood, liver, lung, and kidney were removed from the animals. Blood was fractionated into plasma and red blood cells (RBCs) by centrifugation. The tissues and blood fractions were combusted and analyzed for radioactivity in a liquid scintillation spectrometer (Hughes et al., 2000). In a second experiment, mice were similarly treated with unlabeled DMAV and sacrificed over time. Tissues were removed, solubilized and analyzed for speciated arsenicals by hydride generation-atomic absorption spectrometry (HG-AAS) (Hughes et al., 2000).
Cumulative urinary elimination data were collected in mice administered [14C]-DMAV intravenously using the same dosing protocol described above (Hughes and Kenyon, 1998). Cumulative percent of the dose excreted in urine as DMAV-derived radioactivity was determined at 1-, 2-, 4-, 8-, 12-, and 24-h postdosing.
The experimental data (mouse oral gavage) used for model evaluation have been described in detail elsewhere (Hughes et al., 2008). Briefly, mice were administered [14C]-DMAV (2 µCi per animal) by oral gavage (10 ml/kg) at the same dose levels administered via iv. Mice were then placed in individual metabolism cages to collect urine and feces until they were killed by cardiac puncture under CO2 anesthesia. Mice were euthanized at the following time intervals: 0.25-, 0.5-, 1-, 2-, 4-, 8-, 12-, and 24-h postdosing. There were four mice per time point for each dose level. Blood, liver, lung, kidney, and urinary bladder were harvested immediately, flash frozen in liquid nitrogen, and stored until analyzed for radioactivity as described above. In a second experiment, mice were similarly treated with unlabeled DMAV. One group of mice was sacrificed at 2-h postdosing. Tissues were removed, solubilized and analyzed for speciated arsenicals by HG-AAS. A second group of mice were held in metabolism cages for 24 h. The urine from these animals was collected and analyzed for speciated arsenicals by HG-AAS.
The data are presented in this paper as concentration in the different tissues in µg/l, as opposed to % of dose injected. In this way, we can directly match the output of the PBPK model with the experimental data. The data used for model development and evaluation was based on radioactivity, with no speciation of DMAV and DMAIII. The results from the speciated arsenic tissue analysis following iv administration of unlabeled DMAV detected only total dimethyl arsenic (DMA) at 2 h for the low dose and 8 hr for the high dose (see Fig. 6, Hughes et al., 2000). For these data, it was not possible to differentiate between DMAV or DMAIII in the samples. However, neither TMAO nor demethylated metabolites of DMAV were detected in tissues following iv administration. TMAO was detected in kidney, liver, lung and urinary bladder from the oral study with unlabeled DMAV using a more sensitive HG-AAS method (see Table 4 in Hughes et al., 2008). Tissue analysis was performed at 2 h (where maximum tissue levels were attained based on the results from the experiments with [14C]-DMAV). However, TMAO was only consistently detected at the high dose (111 mg/kg), with the highest levels in liver (approximately 10% of the total arsenic detected). TMAO levels in the other tissues were no more than half that detected in the liver. Again, it was not possible to speciate DMAV and DMAIII in these tissues, but total DMA was the predominant arsenical detected. The descriptor DMA will be used to signify the radioactivity derived from [14C]-DMAV. The use of this descriptor in the model development adequately represents DMA because tissue analysis results using HG-AAS for arsenic speciation showed the arsenic was predominately DMA. In urine, most of the detected radioactivity can be associated with DMA when given by iv route to mice. This is supported by findings from rat studies which are efficient methylators of DMAV (Cui et al., 2004; Suzuki et al., 2004).
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General model structure and parameterization
The tissue compartments used in the PBPK model include lung, liver, kidney, bladder, skin, gastrointestinal (GI) tract and residual body. Blood plasma and RBCs were included as separate compartments because this model will ultimately be extended to rats in order to evaluate the impact of species-specific differences in metabolism and disposition for orally ingested DMAV. Two different model structures were developed to evaluate the transport kinetics of DMA into body organs: flow-limited and diffusion-limited. The model structures are illustrated in Figures 1 and 2. Distribution in the flow-limited model is through blood flow mainly, whereas the diffusion-limited model includes an additional term to describe diffusion through a capillary membrane. The partition and permeability coefficients were estimated using tissue time course data after an intravenous injection in mice (Hughes et al., 2000
). The blood compartment included separate mathematical descriptions for RBCs and plasma in both flow- and diffusion-limited models, with distribution of DMA into tissues assumed to occur via the plasma. In terms of organ clearance, the model included metabolism of DMAV to TMAO in the liver and urinary clearance of DMA via the kidneys. Skin, lung, GI, bladder, and the residual body compartments were assumed to be nonmetabolizing organs.
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Organ DMA time course data points generated from a separate oral gavage data set obtained from Hughes et al. (2008)
, which were not used for parameter estimation, were used for model evaluation. This particular oral experimental design matched the initial doses given for the iv exposures.
Physiological parameters for the model were either experiment-specific (e.g., body weight) or obtained from the literature (Tables 1 and 2). Details of chemical-specific parameter estimation for partition and permeation coefficients are described in the results section and presented in Tables 1 and 2, respectively. Although the present model includes saturable fecal clearance using a standard Michaelis-Menten equation to describe kinetics, we chose to set biliary maximal rate excretion to zero in this version of the model, because urine is the major route of excretion of DMAV in studies of mice (Hughes and Kenyon, 1998) and rats (Stevens et al., 1977; Suzuki et al., 2004). Metabolism of DMAV to TMAO was assumed to be first order (ktmao, /h) over the relevant range of exposure concentrations (12.5–200 ppm) based on rat data presented by Wei et al., 2002. Their results for TMAO concentration in urine (3–37 µg/ml) increased linearly with dose over the entire dose range. Urinary excretion was assumed to be constant across doses based on iv kinetic data in mice (Hughes and Kenyon, 1998). Using the assumption of first-order metabolism from DMAV to TMAO and dose independence for urinary excretion rates, an estimate for ktmao was derived from urinary excretion data for TMAO in mice (Marafante et al., 1987). Specifically, Marafante et al., (1987) reported that 3.5% of an oral dose of DMAV was excreted in urine in 48 h as TMAO. Hence, the first-order metabolic rate constant (ktmao) is approximated as –ln(c/c0)/t, where c is the urine concentration of TMAO at time = t, and c0 is the initial TMAO urine concentration. The calculation yields an estimate of 0.07/h [–ln(0.035)/48] for ktmao.
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Mathematical description of each organ
Rate equations for each compartment were obtained using the basic principle of mass balance conservation: the net amount of chemical in the organ must equal the sum of everything that comes in minus everything that leaves minus any amount that is converted by chemical reaction (e.g., metabolism). The simplest case for a PBPK modeler starting with a new chemical is to assume that flow-limited conditions apply for each body organ. For this type of model, one mass balance differential equation describes the chemical's distribution in each separate organ. As an example, the flow-limited lung equation is
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In cases when the blood flow-limited description is not sufficient to describe the experimental data, a capillary membrane can be added to describe separately mass conservation in the blood and tissue compartments. Using the lung again as an example, mass conservation in the lung blood leads to the following equation:
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Mass conservation in the lung tissue leads to the following equation:
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lu = permeability constant describing diffusion through the capillary membrane, l/h; Clu = total tissue concentration of DMA, µg/l; Plu = partition coefficient for DMA in lung tissue, dimensionless; VluT = lung tissue volume, l. Also, the definition for partitioning in this case becomes the ratio between DMA concentration staying inside the tissue, and the DMA blood concentration leaving the organ, which in this case equals capillary concentration. This paper will present a case for developing a PBPK model for DMA in the mouse by considering blood flow or diffusion-limited kinetics. All equations used are fully described in the Appendix (in Supplementary Data).
PBPK model implementation and software
The current PBPK model was implemented using Simulink (Mathworks, Natick, MA, version 6.4, 2006), a graphical user modeling software package. After pilot simulations were performed and the determination to use the general diffusion-limited case was made, both cases were simulated using the same general code. That is, the flow-limited version was adapted from the general model by setting all permeability coefficients ( parameters) to zero.
Blood, liver, kidney, and lung were fitted to a blood flow-limited model including binding in the venous compartment to RBCs. Subsequently, these same tissues were fitted to a diffusion-limited model which included a capillary membrane.
Sensitivity analysis
Sensitivity analysis has been primarily used in PBPK modeling to prioritize the impact of key model parameters (Clewell et al., 1994; Evans et al., 1994). The simplest sensitivity analysis provides answers to the question: If a known % change occurs in the model constants, what % change occurs in the model predictions? Although there are different ways to calculate sensitivity coefficients, we used normalized sensitivity coefficients described as the partial derivative of each variable of interest with respect to each model constant (parameter), normalized by both the variable and model parameter. In mathematical terms:
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The partial derivatives needed to calculate sensitivity coefficients were calculated using the Automated Differentiation (AD) algorithm written by Martin Fink, and available in MatlabCentral, (http://www.mathworks.com/matlabcentral/). Further theoretical details can be found in Dr J. A. David's dissertation (http://catalog.lib.ncsu.edu/web2/tramp2.exe/do_ccl_search/guest?setting_key=files&record_screen=record.html&*search_button=keyword&servers=1home&index=ckey&query=1998319).
The AD sensitivity method presented in this paper is similar in concept to the normalized sensitivity coefficient calculations used in Simusolv© (1993) in previous modeling efforts. The present code calculates normalized sensitivity coefficients over time, for each model parameter and predicted variable defined by the modeler. The AD sensitivity method numerically approximates the analytical solution for each partial derivative over time, increasing our confidence in the sensitivity calculations. We believe this is the first time that such a comprehensive sensitivity analysis has been applied to a diffusion-limited model. For the flow-limited case, we analyzed 8 model variables and 25 input constants. For the diffusion-limited case, we analyzed 14 model variables and 43 constants. Plots for each partial derivative were generated and evaluated.
Parameter estimation
After initial visual fits using the iv data set, optimizations were performed with Simulink's Response Optimization (Mathworks) software using the Simplex Search method. The Simplex Search method is a numerical technique based on the Nelder-Mead search methodology used to optimize a parameter defined within an ordinary differential equation.
The partition coefficients were estimated for the flow-limited iv model first, where by definition, the diffusion constants are set to zero. Individual tissue time course concentration data was used to estimate partition coefficients, using the area under the curve method (Gallo et al., 1993; Vahter et al., 1984). Once the flow-limited model was developed, simulations were compared with tissue time course data for model evaluation. Next, the diffusion-limited structure was used for parameter estimation. Both the partition and diffusion coefficients were allowed to vary during the optimization using the diffusion-limited structure. The partition coefficients obtained for the diffusion-limited case were not significantly different from the ones obtained in the flow-limited case.
Statistical index for goodness of fit.
A statistical index for comparison of experimental data to simulations was adopted from Krishnan et al. (1995) and coded in Matlab. This index was used for comparison of experimental data and simulation results. The index was then calculated for each available time course data set for both flow and diffusion-limited PBPK models. If there are N number of data points, then the index is
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RESULTS |
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Intravenous Route—Model Calibration
In this section, we show the ability of the two different structures of the PBPK model (flow-limited vs. diffusion-limited) to predict the experimental data. Figures 3, 5, 7, 9, and 10 show results for the iv exposure at both doses of DMAV in tissues. The parameters that were varied for each organ included partition and permeability coefficients, in addition to kidney clearance for the cumulative amount excreted in urine. The parameters estimated from the model are summarized in Table 1.
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After testing the flow-limited case, the diffusion-limited model was applied. The same kidney clearance value obtained for the flow-limited case was assumed to be the same for the diffusion-limited case (Table 1). The parameters that were varied for each organ included partition and permeability coefficients. These results are summarized in Table 2. Figures 3, 5, 7, 9, and 10 show the results for the diffusion-limited cases. Visually, and as a whole, the diffusion-limited model fit the experimental data better than the flow-limited model. Both models fit some organs better than others. In general, the diffusion-limited case resulted in lower statistical indices when compared with the flow-limited case (Table 3, Supplementary Data). As discussed in Krishnan et al. (1995)
the lower statistical indices (lower numerical value) are a direct quantitative measure of improved fits with data.
Oral Route—Model Evaluation
In this section we show the simulation fits combined with experimental data gathered from different tissues following oral exposure to low (1.11 mg/kg) or high (111 mg/kg) doses of DMAV. The ability of the two different versions of the PBPK model: (flow vs. diffusion limited) was tested statistically using the same index described by Krishnan et al. (1995). Figures 4, 6, 8, 11, and 12 show the results for both oral doses. The results shown were obtained by using the same parameters as listed in Tables 1 and 2 and estimated using the iv data. Due to stomach absorption, one additional parameter estimated in the oral exposure model is the absorption proportionality constant from the stomach, kabs (/h). Only kabs was optimized using the oral data set, whereas other parameters were fixed to values obtained with the iv data set. The final optimized value for kabs in both cases was 0.5 /h.
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As for the iv case, the diffusion-limited model statistical indices were calculated after the flow-limited simulations were finished. The resulting shapes of the diffusion-limited and flow-limited curves are very different, and continue to become farther apart from each other as time progresses. These individual organ results were plotted using the log of the tissue concentration (Figs. 3–13).
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Sensitivity Analysis
Results for the iv sensitivity analysis for both flow- and diffusion-limited iv exposures are shown in Figures 14 and 15. For the flow-limited case, we looked at the results of 8 model variables and 25 model constants, for a total of 200 plots. For the diffusion-limited case, we looked at the results of 14 model variables and 43 constants, for a total of 602 plots. We present here the results summarizing a small subset of model parameters for both flow- and diffusion-limited iv. The sensitivity analysis for both structural cases studied illustrates the importance of collecting data at early experimental time points.
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The only constant present in both models was RBC binding, which was examined for impact during early experimental time points. Very small differences were noted between the two model structures (i.e., flow vs. diffusion), due to the inclusion of the same constant in both model structures.
For the flow-limited model, sensitivity coefficients for kidney clearance gradually decreased to a minimum of –1 during the first 5 h, and then increased to zero (Fig. 14). These results suggest the relative importance of early time points in experimental design for maximum parameter identifiability in comparison to data. For the diffusion-limited model, sensitivity coefficients for most permeability coefficients examined were zero for the time course examined (Supplementary Data). The one exception found was the kidney, where normalized sensitivity coefficients were close to one, particularly at early time points (Fig. 15).
Statistical Analysis
The results for the index calculations across different structures and exposure routes are calculated for every model simulation. Results are given in a table in Supplementary Materials (Table 3). For the iv route, the diffusion-limited indices calculated for each organ were smaller than flow-limited indices, except for the lung, where index values were similar. These results were consistent for both the low and high experimental concentrations analyzed. The statistical analysis increases our confidence in stating that the diffusion-limited case resulted in better fits when compared with the flow-limited description (Krishnan et al., 1995).
For the oral route, the lower diffusion-limited statistical indices calculated for each organ are consistently smaller than their flow-limited counterparts. For the highest oral concentration simulated, there was no consistent pattern across indices between the two model structures. Therefore, the higher oral dose was not as helpful in distinguishing between the two different model structures examined in this paper.
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DISCUSSION |
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The overall goal of PBPK modeling is to mathematically describe the distribution of a chemical or drug once inside the body. In the past, PBPK model development has included increased levels of complexity in describing transport from blood to organ with physiological information such as blood flow, organ volume, protein binding in plasma, and the presence of a capillary membrane (Bischoff et al., 1971
). Although there are precedents in the literature for adding a capillary membrane when describing chemical transport between blood and tissue, complexity is often reduced to minimize the number of estimated parameters by assuming that blood flow drives all transport into each organ (Kohn, 1997; Levitt, 2002). This simplifying assumption of blood flow limitation has worked well for lipophilic drugs (Bjorkman, 2003) and solvents (Andersen, 1995). In most clinical studies, it would be impossible to obtain tissue time course data for all organs included in a PBPK model. Using animal models, we have the advantage of being able to gather tissue time course data for several organs of different species and routes of exposure. Just as this is important for drug delivery, accurate description of environmental contaminants is important for risk assessment applications. The final form of the model and the predicted shape of the concentration time course data will play a role in calculations such as areas under the curve, a potential dose metric for risk assessment purposes, which is also dependent on the particular mode of action chosen for a particular toxic effect.
Previously published PBPK models for inorganic arsenic kinetics in rabbits, hamsters and mice have included a final submodel for DMA in a series that includes sequential models for arsenate, arsenite, monomethylarsonic acid (MMAV) and DMAV (Gentry et al., 2004; Mann et al., 1996). In all of these models, DMA tissue distribution was modeled as diffusion-limited. The Gentry et al. (2004) mouse model was based upon the Mann et al. (1996) hamster/rabbit model. Gentry et al. (2004) chose to use the same permeability coefficients for DMA, but re-estimated the partition coefficients for the mouse based on DMAV-derived radioactivity present in tissues 24 h after iv administration (Hughes and Kenyon, 1998). This re-estimation resulted in partition coefficients for DMA that are 10-, 2000-, and 5000-fold lower in the mouse model of Gentry et al. (2004) for liver, lung and kidney, respectively, compared with the same partition coefficients in the hamster/rabbit model of Mann et al. (1996). Gentry et al. (2004) did not offer an explanation for their choice to retain the values for the permeability coefficients and re-estimate the partition coefficients. To our knowledge, there does not appear to be data in the literature that provide a basis to conclude that partition coefficients would be more likely to change across species compared with permeability coefficients. In our model development effort for DMA, we made maximal use of extensive tissue time course data following iv administration of DMAV to mice (Hughes et al., 2000) that was not used in Gentry et al. (2004), together with sensitivity analysis, to both evaluate the need for diffusion-limited tissue transport and to provide greater accuracy in parameter estimation. The validity of this approach is supported by the ability of our model to successfully simulate an entirely separate data for DMAV administered orally without adjustment of the parameters (Hughes et al., 2008).
The model described in this paper also differs from other published models because of its intended risk analysis application, i.e., the model can be extended to both rats and humans to conduct cross-species dosimetry comparisons. The purpose of such comparisons is that it will allow evaluation of the hypothesis that pharmacokinetic differences between rats and mice account for the greater sensitivity of the rat to DMAV-induced bladder cancer, and to extrapolate between rodents and humans. Therefore, our mouse model includes an explicit erythrocyte compartment because binding to hemoglobin is significant in the rat compared with the mouse (Lu et al., 2004). This model also includes a bladder compartment (target organ) and metabolic clearance of DMAV to TMAO which was not incorporated in any of the published models for inorganic arsenic. Inclusion of metabolic clearance is critical for three reasons: (1) metabolism of DMAV to TMAO is quite extensive in rats (Adair et al., 2007), (2) there is compelling evidence that metabolism is necessary for DMAV-induced bladder cytotoxicity and cancer in rats (Cohen et al., 2006), and (3) DMAIII is an obligate intermediate in production of TMAO. It would be optimal if the DMA model were to distinguish between DMAV and DMAIII in tissues because DMAIII is believed to be the causative metabolite for DMAV-induced bladder tumors in rats (Cohen et al., 2006). However, current analytical technologies are not sufficient to distinguish between DMAIII and DMAV in solid tissues and even when measured in urine, careful sample preservation and handling are required to ensure the stability of trivalent arsenical metabolites.
The DMAV model is also relevant to the issues associated with inorganic arsenic exposure and toxicity. Exposure to inorganic arsenic in drinking water is known to cause cancer of the bladder and other organs in human populations (Yoshida et al., 2004). However, conventional lifetime bioassays with inorganic arsenic and its pentavalent metabolites (MMAV and DMAV) have generally not shown convincing evidence of cancer in rodents with one notable exception. This exception is induction of bladder tumors in rats, but not mice, exposed to DMAV in lifetime bioassays (Arnold et al., 2006). Because DMAV is a metabolite of inorganic arsenic, a question may arise to its involvement in tumor production in humans exposed to inorganic arsenic. Additionally, the possibility of direct exposure of humans to DMAV exists because of its use as a herbicide and its presence in certain seafood (Borak and Hosgood, 2007). Differences in response between humans and rodents, and between rats and mice, when exposed to inorganic arsenic or its metabolites (MMAV and DMAV) highlights the importance of evaluating the impact of pharmacokinetic differences between species. The quantitative impact of pharmacokinetic differences in tissue levels of DMA, either from direct exposure or as a metabolite of inorganic arsenic, is an important factor to consider in interspecies extrapolation for the risk assessment of either inorganic arsenic or DMAV. The model described in this paper can be linked to the risk assessment of either inorganic arsenic or DMAV by extending it to both rats and humans to conduct cross-species dosimetry comparisons.
In this work, differences in the shape of the simulation curves are visually apparent between the flow- and diffusion-limited model structures. The diffusion-limited simulation more closely approximated the experimental data. Both flow- and diffusion-limited models provided close predictions for the iv data after the first hour. Simulations using both model structures diverge at earlier time points. This is expected, because diffusion or flow limitation affects the distribution and disposition of the chemicals in tissues. Later phases of the data time points are more influenced by clearance (metabolic and/or urinary). Therefore, the behavior of both models in comparison to data was consistent with biological processes.
One important question related to application of regression techniques to calculate model parameters is how to quantify the ability to estimate the desired parameters. One of the standard tools used to answer this question is local sensitivity analysis. Sensitivity analysis is related to model structure and formulation. Once a model is constructed, simulations of output variables (such as tissue concentrations) are conducted using various levels of input parameters. A sensitivity coefficient is obtained as the ratio of output (e.g., tissue levels) to input (e.g., blood flow rate) change. Hence, sensitivity analysis can be conducted in the absence of data to identify the impact of parameter variability on output simulations based on model structure and assumptions. In general, the higher the sensitivity coefficients, the higher the ability to estimate the input parameter when data is present. In this manner, sensitivity analysis can lead to improved experimental design by helping prioritize key input parameters in a model (Clewell et al., 1994; Evans et al., 1994)
To our knowledge, this is the first time that both sensitivity and goodness of fit analyses have been applied to a diffusion-limited PBPK model. Because diffusion increases the complexity and number of model parameters, the sensitivity analysis concentrated on possible identifiability issues for permeability coefficients. The one exception to this rule was the kidney, where the permeability coefficient was identifiable at early time points. Both types of analyses, goodness of fit and sensitivity analysis, showed how the diffusion-limited structure increases our confidence in the overall fits with the experimental data. Although goodness of fit does not include time course dependencies, sensitivity analysis does include the impact of experimental time. The current sensitivity analysis confirms how the diffusion-limited structure improves the time course description when compared with a flow-limited structure, particularly when early experimental time points are available.
In summary, a PBPK model was developed to describe the tissue disposition of administered DMAV in mice utilizing data that allowed evaluation of the impact of differing assumptions concerning transport of DMA into tissue. The results of the diffusion-limited model consistently provided an improved fit over flow-limited simulations when compared with tissue time course experimental data. This modeling effort shows the importance of collecting time course data from different exposure scenarios and from different tissues.
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SUPPLEMENTARY DATA |
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Supplementary data are available online at http://toxsci.oxfordjournals.org/.
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ACKNOWLEDGMENTS |
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This manuscript has been reviewed by the National Health and Environmental Effects Research Laboratory, U.S. Environmental Protection Agency and approved for publication. Mention of trade names and commercial products does not constitute endorsement or recommendation for use.
We would like to thank Dr Karen Yokley for invaluable help with the mathematical editor used to prepare the manuscript, and Drs David Thomas, Miles Okino, Mike DeVito, and Linda Birnbaum for helpful comments during the preparation of this manuscript. We would also like to thank Mr Christopher Eklund for editorial contributions.
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