This article is part of the monograph on Mathematical Modeling in Environmental Health Studies.
Address correspondence to R. Conolly, CIIT, Six Davis Dr., PO Box 12137, Research Triangle Park, NC 27709-2137 USA. Telephone: (919) 558-1330. Fax: (919) 558-1300. E-mail: rconolly@ciit.org
*Current affiliation: Boehringer-Engleheim Pharmaceuticals, Ridgefield, CT, USA
We thank P. Schlosser for helpful discussions, P. Schlosser and S. Borghoff for critical reviews of the manuscript, and B. Kuyper for editorial review. This research was funded by the member companies of the Chemical Industry Institute of Toxicology.
Received 16 February 2000; accepted 8 August 2000.
Formaldehyde inhalation leads to the formation of DNA-protein cross-links (DPX) in the nasal mucosa of rats and rhesus monkeys. Dose-response and time-course data on DPX concentrations in nasal mucosa have been collected for Fischer 344 (F344) rats and rhesus monkeys (
1-3). DPX are considered to be part of the mechanism by which the cytotoxic and carcinogenic effects of formaldehyde are exerted (
4,5), and DPX data have been used as a measure of tissue dose in cancer risk assessments for formaldehyde (
6,7). Given that DPX are a measure of delivered dose of formaldehyde and that DPX probably play a role in formaldehyde toxicity and carcinogenicity, an ability to accurately predict DPX concentrations as a function of the inhaled concentration of formaldehyde is desirable.
Casanova et al. (2) and Heck and Casanova (8) described a biologically motivated pharmacokinetic model for DPX. In their model, the inhaled concentration of formaldehyde was linked directly to DPX formation. This model incorporated sufficient biological information that successful extrapolation from rat to monkey was possible through adjustment of species-specific physiological factors. Hubal et al. (9) described a refined pharmacokinetic model that used an anatomically realistic computational fluid dynamics (CFD) model of the rat nasal airways (10) to provide predictions of site-specific flux of formaldehyde into tissue lining the nasal airway. Site-specific flux was then linked to DPX formation. The advantage of the model developed by Hubal et al. (9) was the use of the rich anatomical information embedded in the CFD models. Use of this anatomical information increases confidence in the extrapolation to the human case, where no DPX data are available for confirmation of model predictions.
The approach used by Hubal et al. (9) was to calculate average flux across the nasal epithelium of the rat, using estimates of nasal surface area and overall nasal uptake of formaldehyde. This average flux estimate was then used with DPX data for the pooled nasal mucosa to estimate the parameters of the tissue disposition model for formaldehyde. With the parameters so estimated, CFD model predictions of flux in a specific region of the rat nose--the high-tumor region--were then used with DPX data specific to that region to evaluate the predictive capability of the model. Acceptable predictions of the high-tumor data were obtained. This work was the first, albeit limited, quantitative demonstration of the role of site-specific flux as a determinant of site-specific DPX.
The goal of the present work was to refine the model of Hubal et al. (9) by a) use of an improved CFD model of the rat nasal airways; b) increased use of regional rat nasal DPX data; and c) extending the modeling approach to the rhesus monkey and human. The longer-range goal of this work was to maximize the use of scientific data in the prediction of human DPX values.
DNA-Protein Cross-Link Data
Casanova et al. (3) exposed male F344 rats to formaldehyde gas by inhalation 6 hr/day, 5 days/week, for 11 week plus 4 days at 0.7, 2, 6, or 15 ppm. On the fifth day of the twelfth week, the rats were exposed for 3 hr to 14C-formaldehyde at the same concentrations and were sacrificed immediately after cessation of exposure. A control group of rats was exposed only to room air prior to the exposure for 3 hr to 14C-formaldehyde. DPX were determined in the mucosal lining of the nasal lateral meatus (high-tumor site) and the medial and posterior meatuses (low-tumor site). The high-tumor and low-tumor designations refer to the incidence of formaldehyde-induced tumors found at these sites during a chronic exposure bioassay (11). Casanova et al. (2) exposed rhesus monkeys to 0.7, 2, or 6 ppm 14C-formaldehyde gas by inhalation for 6 hr. The monkeys were sacrificed immediately after the end of the exposure, and mucosal samples were taken from the anterior lateral walls and septum (ALWS), the nasopharynx (NP), and the middle turbinates (MT) of the nose.
The DPX data were obtained in units of picomoles per milligram DNA. For modeling purposes, units of picomoles per cubic millimeter tissue were desired. To convert picomoles per milligram DNA to picomoles per cubic millimeter tissue, the amount of DNA per milligram tissue, or DNA yield, was needed. This quantity was measured as 4.1 ± 0.5 µg/mg in rat nasal tissue (12) but was not measured in monkeys. The rat value of 4.1 µg/mg was assumed to be a reasonable estimate for DNA yield in monkey nasal tissue, and all DPX measurements were converted to picomoles per cubic millimeter tissue using the rat DNA yield value. A tissue density of 1 g/mL was assumed. The DPX data obtained from the rat and monkey experiments are shown in Table 1.
Tissue Thickness Measurements
Estimates for the thickness of nasal mucosa at high-tumor and low-tumor sites in the rat and at ALWS, NP, and MT sites in the monkey were made from measurements on histological slides of nasal cross-sections from control animals. In both species, mucosal thickness was measured as the distance from the air-tissue interface to the lamina propia at the bone, including nasal epithelial layers. The measurements of mucosal thickness were made at 20 
in rats and 4 in monkeys using an image analysis system (Image 1; Universal Imaging Corp., West Chester, PA, USA).
In rats, measurements were made on cross-sectional levels 3, 4, 5, and 6, as described by Méry et al. (13), using slides from five control animals. Mucosal thickness estimates representing the high-tumor region were made on the lateral walls at levels 5 and 6; the dorsal margin of the nasoturbinate at level 6; and the ventral margin of the maxilloturbinate at level 6. Mucosal thickness estimates representing the low-tumor region were made on the dorsal septum at levels 3 and 5; the mid-septum at levels 4, 5, and 6; the medial aspect of the nasoturbinate at levels 5 and 6; and the ventral septum at levels 5 and 6.
In monkeys, measurements were made on cross-sectional levels 2, 3, 5, 10, 11, and 12, as described by Kepler et al. (14), using slides from three control animals. Mucosal thickness estimates representing ALWS were made on the ventral and mid-lateral walls and on the ventral and mid-septum at levels 2, 3, 5, and 10. Mucosal thickness estimates representing the MT were made on medial and lateral aspects at levels 5 and 10, and estimates representing the NP were made on the dorsal, ventral, and mid-lateral walls at levels 11 and 12.
For each species, measurements from all animals were averaged for each region (high-tumor and low-tumor regions in rats; ALWS, MT, and NP in monkeys) separately. Thus, variation in mucosal thickness estimates represented a combination of differences in mucosal thickness among sites within each region and among individual animals.
Air-Phase Modeling
Regional flux of formaldehyde from inhaled air to the air-lining interface was estimated from steady-state CFD simulations of airflow and formaldehyde uptake that were conducted using three-dimensional, anatomically accurate reconstructions of the nasal passages of an adult male F344 rat and rhesus monkey. The models were constructed from tracings of airway outlines of the right nasal passages from the nostril to the nasopharynx from serial step-sections of embedded tissue specimens, as described by Kimbell et al. (15) and Kepler et al. (14), using in-house software (16) and the finite element mesh preprocessor of the CFD software package FIDAP (Fluent Inc., Lebanon, NH, USA). The locations of areas in which DPX were measured (2,3) were mapped into the rat and monkey CFD models, with the exception of the rat nasopharyngeal meatus, a portion of the dissected tissue that was included by Casanova et al. (3) in the low-tumor region for DPX measurement, but was not included in the rat CFD model.
Steady-state airflow simulations were conducted using FIDAP software, as described by Kimbell et al. (15) and Kepler et al. (17). Simulations were carried out at 0.576 L/min in the rat and 4.8 L/min in the monkey, flow rates equivalent to twice the estimated minute volume in each species. Simulations of regional uptake by nasal walls were also conducted, and flux of formaldehyde to nasal walls was calculated using FIDAP software, as described by Kimbell et al. (18). Predicted flux in the rat low-tumor region was adjusted as follows to account for nasopharyngeal tissue missing from the CFD model that was collected from exposed rats as part of the low-tumor region in which DPX were measured. The weight of tissue in the low-tumor region of the CFD model was estimated by multiplying surface area and tissue thickness to estimate tissue volume and assuming that the density of the tissue is equal to that of water. The difference between the estimated weight and the weight of tissue collected by Casanova et al. (3) was used to approximate the amount of missing surface area in the CFD model associated with the nasopharyngeal meatus. Formaldehyde concentration in air passing through this posterior portion of the rat nasal passages was expected to be low enough that flux in the nasophrayngeal meatus could be assumed to differ insignificantly from zero. Therefore, formaldehyde flux for a low-tumor region commensurate with the region dissected by Casanova and co-workers (3) was approximated by the amount of formaldehyde predicted to be taken up by the low-tumor region as defined in the CFD model divided by the adjusted surface area.
Tissue-Phase Modeling
The model used to describe the tissue disposition of formaldehyde and the formation of DPX was similar to that described by Hubal et al. (9). Briefly, after entering the tissue, formaldehyde is cleared by a saturable pathway, a separate first-order pathway, or by pseudo first-order binding to DNA. The saturable pathway represents enzymatic metabolism of formaldehyde, which is primarily by formaldehyde dehydrogenase (19), while the first-order pathway is assumed to represent the intrinsic reactivity of formaldehyde with tissue constituents. The pseudo first-order rate of binding of formaldehyde to DNA responsible for DPX formation was measured by Heck and Keller (20). No other routes of formaldehyde clearance are described in the model.
The model thus implicitly assumes that other potential routes of clearance, such as diffusion back across the tissue-air interface or into blood perfusing the respiratory epithelial tissue, are not quantitatively significant. These assumptions are based on the following considerations. a) Formaldehyde is highly soluble in water and reacts with tissue constituents. Quantitatively important desorption from tissue back into the air is thus judged to be unlikely. b) Heck et al. (21) and Casanova et al. (22) reported that inhalation of formaldehyde did not lead to measurable changes in the blood concentration of formaldehyde in F344 rats, rhesus monkeys, and humans. These findings do not preclude the possibility that some formaldehyde is cleared from the nasal mucosa by blood perfusion, but they do suggest that the amount cleared by perfusion, if any, is relatively small. The validity of these assumptions was further tested by the ability of the model to fit the DPX data, as described in "Results."
The rate of change of the concentration of formaldehyde in the mucosal tissue lining the nose of F344 rats or rhesus monkeys is defined by
[1]
where Cf is the concentration of formaldehyde in the tissue (pmol/mm3), flux is the flux of formaldehyde from air into tissue (pmol/mm2-min-ppm), thick is the mucosal thickness of the tissue (mm), ppm is the inhaled concentration of formaldehyde, Vmax is the maximum rate of formaldehyde clearance via the saturable pathway (pmol/mm3-min), Km is the concentration at which the enzyme is half-saturated (pmol/mm3), Kf is the first-order clearance rate constant (min-1), and Kb is the pseudo first-order rate constant for binding of formaldehyde to DNA to form DPX. The rate of change of the concentration of DPX is given by
[2]
where CDPX is the concentration of DPX (pmol/mm3), Kb is the pseudo first-order rate constant for binding of formaldehyde to DNA (min-1), and Kloss is the first-order rate constant for the clearance of DPX (min-1). The model was built with the graphical simulation tool SIMULINK, which is part of the MATLAB technical computing product family (The MathWorks Inc., Natick, MA, USA). Appendix describes the block form of the SIMULINK model.
The value of Kloss was determined by identifying the smallest value of this parameter consistent with the observation that DPX do not accumulate in the rat with daily exposure (3). The parameters Vmax, Km, and Kf were estimated by optimization against the DPX data (Table 1) using the fmincon algorithm from the MATLAB Optimization Toolbox, Version 2. The standard deviations of the parameter estimates were calculated from the Hessian matrix supplied by fmincon. The optimization involved minimization of the modified least squares cost function described by Steiner et al. (23):
[3]
where n is the number of data points, zI is the measured value of CDPX for the ith data, fI is the model-predicted value of CDPX for the ith data point, and 
is the heteroscedasticity parameter. Absolute error is defined = 0, while = 2 defines relative error. Here, = 2 was used for all optimizations.
The parameters of the F344 rat model were estimated by simultaneously optimizing against the DPX data for the low-tumor and high-tumor regions using region-specific values for flux and tissue thickness. Separate parameter estimations were also conducted for the low-tumor and high-tumor regions to allow an evaluation the robustness of the rat parameter estimates obtained with the three combinations of low-tumor and high-tumor data.
The value of Kf identified by optimization of the rat model was used unchanged for the rhesus monkey model, as this parameter was assumed to represent inherent reactivity of formaldehyde with tissue constituents. Similarly, the value of Kb measured by Heck and Keller (20) for the rat was used unchanged for the monkey, as this parameter was assumed to represent a thermodynamic property of formaldehyde. The value of Kloss used for the monkey was also not changed from the rat value, as no data were available to suggest how the scaling might otherwise be done. The remaining parameters, Vmax and Km, were estimated by simultaneous optimization against the DPX data for the ALWS, MT, and NP regions of the monkey nose (Table 1).
Using the measured values for tissue thickness (Table 2) during optimization gave visually poor fits to the data. Because the standard deviations of the measured tissue thickness were relatively large fractions of the mean values, a Monte Carlo approach was used to allow variation in tissue thicknesses while estimating parameter values. At each iteration of the Monte Carlo approach, uniformly distributed random numbers were used to select new tissue thicknesses within one standard deviation of the mean measured values. For the ALWS and MT regions, the mean measured value was used as the lower bound on tissue thickness, while one standard deviation above the mean was used as the upper bound. For the NP region, one standard deviation below the mean was used as the lower bound, and the mean was used as the upper bound. These constraints were used to improve the efficiency of parameter identification given the fits obtained using the measured tissue thicknesses. In other words, anticipating the directions in which the tissue thicknesses would have to change to improve the fits was possible by visual inspection of the optimal fit to the DPX data obtained using the measured thicknesses. One thousand Monte Carlo iterations were used with simultaneous optimization of the model against the DPX data for the ALWS, MT, and NP regions at each iteration.
A human version of the model was developed by scale-up of parameters from the rat and monkey models. Human nasal mucosal tissue thickness was assumed to be 0.375 mm, which is the arithmetic average of the optimal thicknesses for the three regions of the monkey nose identified as described above. The human value of Vmax was assumed to be related to the rat and monkey values according to the general allometric scaling equation
Vmax = a 
BWb [4]
where BW denotes body weight (kg). The parameter b is obtained from the Vmax estimates and body weight data for rats and monkeys according to
[5]
Given b, a is calculated by rearrangement of Equation 4. With the values of a and b obtained in this manner from the rat and monkey data, Equation 4 was used to calculate the human Vmax, assuming that BWHUMAN was 73 kg. The value of Km estimated for the monkey was used unchanged for the human model, as were the values of Kb and Kloss used for the rat and rhesus models. Rat or monkey parameter values were used unchanged for the human model when no information was available to indicate how these values should be scaled.
To compare the predictions of the DPX model for the rat, monkey, and human cases, a series of dose-response simulations were run from 0.1 to 20 ppm for 3-hr inhalation exposures. Flux inputs to the model were calculated by dividing the range of fluxes predicted by the rat, monkey, and human CFD models for the combined respiratory and olfactory epithelia into 20 equally spaced intervals (flux bins) (18). The fluxes for the middle two flux bins were averaged to obtain a species-specific flux used for the comparative dose-response simulations.
All simulations were conducted on a 400-MHz Pentium II desktop computer (Dell Computer Corp., Round Rock, TX) or a 366-MHz Pentium II laptop computer (Dell). Both computers used MATLAB and SIMULINK with Windows NT 4.0.
Good fits to the F344 rat DPX data for the low-tumor and high-tumor regions were obtained (Figure 1). The optimal values obtained by simultaneous fitting to the low-tumor and high-tumor regions for
Vmax, Km, and
Kf, respectively, were 1,008 ± 9.5
10
-6 pmol/min/ppm, 70.8 ± 7.4
10
-6 pmol/mm
3, and 1.08 ± 2.1
10
-7 min
-1. Prior to optimization, the value of
Kloss was fixed at 6.5
10
-3. This is the minimum value that provides essentially complete loss of DPX in 18 hr after 6 hr of exposure to 15 ppm, as was observed by Casanova et al. (
3). The values of all parameters are provided in Table 2. Fitting only to the high-tumor data provided identical best estimates of the parameter values, although the estimated variances differed somewhat (data not shown). Fitting only to the low-tumor data provided very similar, though not identical, estimates (data not shown).
|
Figure 1. Simulation of F344 rat nasal mucosal DPX data obtained at the end of a 3-hr inhalation exposure to formaldehyde gas. The differences in the predictions of the low-tumor and high-tumor areas were obtained by site-specific tissue thickness and formaldehyde flux estimates.
|
Good fits to the rhesus monkey data were also obtained using the Monte Carlo parameter estimation approach, as described in "Methods" and shown in Figure 2. The tissue thicknesses providing the best fit to the data were 0.540, 0.312, and 0.271 mm for the ALWS, MT, and NP regions, respectively. The optimal values of Vmax and Km were 94.8 ± 1.9 10-5 pmol/min/mm3 and 4.35 ± 1.0 10-5 pmol/mm3, respectively (Table 2).
|
Figure 2. Simulation of rhesus monkey nasal mucosal DPX in the ALWS, MT, and NP regions. Differences in the predictions between regions are accounted for by site-specific tissue thickness and flux estimates (see "Methods").
|
Finally, the predicted DPX dose response for the human case was compared to the predicted dose responses for the rat and monkey (Figure 3). An arbitrary inhalation exposure scenario of 3 hr was used, and formaldehyde concentrations were varied from 0.1 to 20 ppm. Flux inputs for this comparison were selected as described in "Methods." The results of this comparison are interesting, in the sense that the predicted DPX dose-response curves for the three species are similar, in spite of the significant interspecies differences in nasal anatomy, breathing rates, and parameter estimates, particularly the estimate of Vmax.
|
Figure 3. Log-log plot of nasal DPX predictions at the end of a simulated 3-hr inhalation exposure to formaldehyde gas for the F344 rat, rhesus monkey, and human. Fluxes into tissue were 19.6, 35.4, and 16.5 pmol/mm2/min/breath for the rat, monkey, and human, respectively (see "Methods").
|
Tissue samples from the nasal passages of rats and rhesus monkeys used for measurement of DPX by Casanova et al. (
3) consisted of nasal epithelium and mucosal tissue removed from the underlying bone and cartilage (
2,3). Because DNA from the combined nasal epithelium and mucosa in each region was analyzed, estimates of mucosal tissue thickness were used in formaldehyde disposition modeling. This is in contrast to the use of epithelial layer thickness by Hubal et al. (
9) based on the assumption that most of the DNA in the dissected DPX samples was located in the epithelial layer.
Visually excellent fits to the F344 rat DPX data for the high-tumor and low-tumor regions were obtained (Figure 1). Moreover, fitting only to the high-tumor data provided identical best estimates of the parameters, and fitting only to the low-tumor data provided similar estimates. These results show that, given the current model structure, estimates of site-specific flux formaldehyde into tissue and of mucosal thickness at the same sites are sufficient to predict the tissue concentration of DPX.
Confidence in the parameter estimates obtained for the rat model could be increased if a better characterization of the rate of DPX loss were available. As described above, the value of this parameter was fixed to ensure complete disappearance of DPX within 18 hr after the end of exposure to 15 ppm formaldehyde, as was seen by Casanova et al. (3). A time course study of postexposure DPX levels at several formaldehyde exposure concentrations would be required to provide a more robust estimate of this parameter.
The assumption that the tissue compartment is well mixed is an additional source of uncertainty in the current rat model. Schlosser et al. (24) reported in preliminary form a pharmacokinetic model for DPX that describes the diffusion of formaldehyde from the air-tissue interface into the tissue and uses data describing the distance of the nuclei in the nasal epithelial cells from the air-tissue interface. This new model may be able to identify whether the assumption of a well-mixed tissue compartment in the current model is justified.
The fits to the rhesus monkey DPX data for ALWS, MT, and NP regions of the nasal epithelium were also good (Figure 2). These results were obtained when site-specific flux predictions, provided by the CFD model, were combined with a Monte Carlo approach to the estimation of tissue thickness and formal parameter estimation. Perhaps the major uncertainty in the rhesus model is the tissue thickness estimates used for the ALWS and MT regions. The DPX data for the ALWS and NP regions (Table 2) are inversely correlated with the fluxes for those regions, as predicted by the CFD model (Table 2). If tissue thickness in the two regions were the same, the model would predict a greater concentration of DPX in the ALWS region. With the current model structure, the only adjustable parameter that can reconcile the predicted fluxes with the measured DPX values is the tissue thickness. The Monte Carlo procedure thus predicted that the mucosal thickness in the ALWS region is considerably greater than that in the MT. Although this result is satisfying in the sense that a good simulation of the data was obtained, greater confidence in the model would be possible if a better characterization of tissue thicknesses in the ALWS and MT regions were available. Fixing mucosal thickness estimates against data, rather than estimating them using the Monte Carlo approach, would provide a more rigorous test of the ability of the current model structure to predict the observed data. Another possibility that might be explored in future work is that there may be regional variations in Vmax. The current model assumes that the value of Vmax is constant throughout the nasal mucosa.
The rate of first-order clearance of formaldehyde estimated against the rat data was used unchanged for the rhesus model. This reflects our assumption that this parameter describes the innate reactivity of formaldehyde with tissue constituents--a thermodynamic behavior that would not be expected to vary significantly across species. However, if some of the clearance of formaldehyde from nasal epithelial tissue is due to blood perfusion, then the first-order parameter may describe clearances due to both perfusion and reactivity. In this case, some scaling of the parameter across species would be justified. The currently available data and model development, however, do not allow this issue to be resolved.
The availability of DPX data for both the F344 rat and the rhesus monkey were used as the basis for predicting parameter values for a human DPX model (see "Methods"). The uncertainties inherent in the rat and rhesus monkey models, as discussed above, thus carry over to the human model. In addition, the uncertainty associated with the specific assumptions used in the construction of the human model should be recognized. First, we assume that the pharmacokinetic mechanisms of DPX formation and clearance are qualitatively similar for the rat, rhesus monkey, and human. Second, the body-weight scaling of Vmax, as defined by the rat and rhesus DPX and body-weight data, is assumed to predict the human Vmax. Third, the rhesus estimate of Km is assumed to be appropriate for use in the human. These assumptions were all necessary due to the lack of human data. Obtaining such in vivo human data is not likely for both ethical and practical reasons. In vitro experiments with human nasal epithelial cells might provide some indication of whether the estimated parameter values are, in fact, valid.
Finally, it should be noted that, in aqueous environments, free formaldehyde is in equilibrium with its hydrate, with the hydrate being the predominate form. Because the reactivity of the hydrate differs from that of free formaldehyde, a model that included the hydration reaction would have a different set of formaldehyde-specific parameter values. Although the structure of such a model arguably would be more realistic, it would also be more complex and would include a number of additional parameters requiring statistical optimization. The available data did not support this more complex approach. We view the current model as an iterative refinement of previous models and expect that future models will contain additional refinements as more, relevant data become available.
In summary, this work showed that a relatively simple, well-mixed model of formaldehyde disposition in the nasal epithelium is capable of accurately predicting measured DPX values. Essential inputs to the tissue model were site-specific flux predictions provided by anatomically realistic CFD models for the nasal airways of F344 rats and rhesus monkeys, and site-specific mucosal epithelial thickness estimates measured in F344 rats and rhesus monkeys. A number of uncertainties associated with the model were discussed, and additional research that could reduce these uncertainties was identified.
SIMULINK models are written as block diagrams. The DPX model consists of several block diagrams in a hierarchical relationship. The apical block (Figure A1) consists of two subsystem blocks. One subsystem block describes formaldehyde dosimetry in the mucosal tissues of the nose and the kinetics of DPX formation and loss, while the second subsystem block keeps track of simulated time and controls exposure to formaldehyde. These two subsystem blocks are connected by a summation block that adds their respective outputs, and an integrator that returns the tissue concentration of formaldehyde to the first block. Expanded views of the subsystem blocks are provided in Figures A2-A4.
|
Figure A1. Apical block of the SIMULINK DPX model.
|
Figure A2. Expanded view of the exposure control block that is embedded in the apical block.
Figure A3. Expanded view of timing block that is embedded in the exposure control block. u, input from previous block.
Figure A4. Expanded view of formaldehyde clearance and DPX kinetics block that is embedded in the apical block.
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Last Updated: October 9, 2000
