Addressing Temporal Variability When Modeling Bioaccumulation in

presented provide guidance for understanding the dominant uptake/elimination processes and the time to approach steady state in relation to the pa...
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Environ. Sci. Technol. 2009, 43, 3751–3756

Addressing Temporal Variability When Modeling Bioaccumulation in Plants EMMA UNDEMAN,* GERTJE CZUB, AND MICHAEL S. MCLACHLAN Department of Applied Environmental Science, Stockholm University, S-106 91 Stockholm, Sweden

Received January 26, 2009. Revised manuscript received March 26, 2009. Accepted March 27, 2009.

Steady state models are commonly used to predict bioaccumulation of organic contaminants in biota. However, the steady state assumption may introduce errors when complex dynamic processes such as growth, temperature fluctuations, and variable environmental concentrations significantly affect the major chemical uptake and elimination processes. In this study, a strategy for addressing temporal variability in bioaccumulation modeling is proposed. Chemical partitioning space plots are used to show the time necessary for organic contaminants to approach steady state in plant leaves and roots as well as the dominant uptake/elimination fluxes of chemicals as a function of the contaminants’ physical chemical properties. The plots were produced with a novel nonsteady state model of bioaccumulation in plants, which is presented, parameterized, and evaluated. The first prerequisite identified for using a steady state model is that the duration of chemical exposure exceeds the time to approach steady state. Next, the dominant chemical transport processes for the chemical in question should be identified and the variability of parameters affecting these processes compared to the time to approach steady state. A major systematic variation in one of these parameters on a time scale similar to the time to approach steady state may cause an unacceptable deviation between the predicted and true chemical concentrations in vegetation. In such cases a nonsteady state model such as the one presented here should be used. The chemical partitioning plots presented provide guidance for understanding the dominant uptake/elimination processes and the time to approach steady state in relation to the partitioning properties of organic compounds.

Introduction Organic contaminants are taken up by plants from both air and soil (1-6). Fruits and vegetables constitute a considerable fraction of the human diet, and plants contribute a significant portion of human exposure to some organic contaminants (7-9). In addition, vegetation is consumed by herbivores, which can transfer the contaminants up the food chain and eventually to humans. This indirect exposure makes vegetation the dominant source of human exposure to many persistent organic pollutants (10). The use of mathematical models of organic contaminant bioaccumulation in vegetables and other crops facilitates the estimation of the direct or indirect human exposure. Since * Corresponding author e-mail: [email protected]. 10.1021/es900265j CCC: $40.75

Published on Web 04/14/2009

 2009 American Chemical Society

the development of the first multivector models in the late 1980s, a number of models with different levels of complexity have been developed (11-17). An example of the application of this kind of model is the European Union System for the Evaluation of Substances (EUSES) (18), which is recommended in the European Union for risk assessment of organic chemicals. Many plant bioaccumulation models described in the literature are steady state models, i.e., it is assumed that the chemical concentrations in the plant and in the surrounding media, as well as the environmental variables that affect chemical uptake and elimination, are constant over time (12-14, 17, 19). In reality, variables affecting plant exposure such as environmental concentrations, temperature, rainfall, and wind speed vary with time at different rates. In addition, plant tissues grow and change in composition, resulting in alteration of the plant’s capacity to store chemicals. Despite these simplifications, steady state models have proven to be useful in many cases, and they have been employed widely, for instance in the exposure assessment tool CalTOX (20). Unlike steady state models, nonsteady state models can account for the changes in environmental conditions, exposure concentrations, and plant properties, predicting the concentration in the plant at different time points during the plant’s lifetime. There are several examples of nonsteady state models (15, 16, 21, 22). However, most of these models account for only the variability in exposure concentrations. Many plant and environmental parameters are assumed to be constant, an approach which greatly reduces the requirements for information that would otherwise be required to parameterize a comprehensive nonsteady state model. In modeling the uptake of contaminants in plants, it is important to establish what kind of model is required and how to most appropriately and effectively parameterize it. One key consideration is the time scale for the response of the plant concentration to changes in system variables compared to the time scale for the variation in these variables. The aim of this study was to investigate these issues and how they are influenced by the physical chemical properties of the chemical under study. A strategy was developed for addressing time variability in environmental conditions and plant characteristics. First, a nonsteady state plant model applicable to both hydrophobic and hydrophilic neutral organic chemicals was assembled and evaluated for chemicals possessing different properties. Using the model, the time to approach steady state in a lettuce leaf was calculated for hypothetical persistent chemicals covering a chemical partitioning space defined by their octanol-air (KOA) and air-water (KAW) partition coefficients. In addition, the uptake and elimination processes dominating in various regions of the chemical partitioning space were identified. Using this information, a procedure was developed for choosing the appropriate kind of model (steady state or nonsteady state) and for parameterizing it.

Materials and Methods Model Development. A three compartment (leaf, root, fruit), fugacity based, nonsteady state, model of bioaccumulation in plants was developed for the exploration of vegetation as a vector of human exposure to neutral organic chemicals. The plant model was foreseen for integration in the exposure assessment model ACC-HUMAN (23). Several modeling strategies described in the literature served as the starting point (14, 17, 19, 24). The model structure is shown in Figure 1. It consists of a leaf, a fruit, and a root compartment, whereby the fruit compartment can be applied to either aerial VOL. 43, NO. 10, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 1. Structure of the plant model with the transport and transformation processes considered (described as the product of D values (mol h-1 Pa1-) and fugacities, f (Pa)). Key: A, S, R, L, F, xy, and ph refer to air, soil, root, leaf, fruit, xylem flow, and phloem flow, respectively; trans, part, rain, and diff stand for biotransformation, particle bound deposition, wet deposition of dissolved chemical, and diffusive exchange with the ambient medium, respectively. Note that the fruit compartment can stand in diffusive exchange with either air or soil depending on the fruit species. The broken arrow indicates the xylem flow into fruit from the root which may be present in some species. fruits or subterranean tubers. The leaf and fruit compartments exchange chemicals via diffusion with the ambient medium, i.e, air or soil. In addition, chemical uptake from air via wet and dry deposition of particle associated chemicals and wet deposition of dissolved chemicals, as well as from soil pore water via the roots is considered. Biotransformation is included as a further elimination pathway for all three compartments. Within the plant, the contaminants undergo advective transport from the root to the leaf and fruit compartment with the transpiration stream in the xylem, and from the leaf to the root and fruit compartment with the phloem flow. The model enables the user to define growth functions for the leaf compartment (linear, sigmoid, or exponential) and time dependent scenarios for the ambient chemical concentrations (periodicity of data optional) in air and soil. A limited time dependency for ambient temperature (monthly resolution) can also be accommodated. Temperature dependence of all partitioning coefficients is accounted for via the van’t Hoff equation, whereas complex interrelationship between environmental conditions and plant properties are not automatically accounted for; e.g., growth, transpiration, mass transfer coefficients, and biotransformation rates are specified/calculated independently of the model temperature. For a steady state solution of the model, constant values of time dependent parameters are used. A full description of the plant model and all parameter values is presented in the Supporting Information (SI). Model Evaluation. To assess the predictive ability of the nonsteady state plant model, it was evaluated for both a group of hydrophobic chemicals (polychlorinated biphenyls (PCBs, log KOW 5.66-7.19) in rye grass (Lolium perenne L.) leaves) and a hydrophilic chemical (sulfolane (log KOW -0.77) in cattail (Typha latifolia) roots and leaves) using experimental data provided in refs 25 and 6, respectively. A detailed description of the model evaluation is provided in the SI. Identification of Dominant Transport Processes and the Time Required to Approach Steady State. The appropriateness of the steady state assumption was assessed by comparing the time required to achieve 90% of the steady state chemical concentration in a plant compartment (t90 (d); for the derivation see the SI), with the variability of relevant environmental parameters. The relevance of an environmental parameter depends on whether the uptake or elimination process(es) affected by this parameter plays 3752

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a dominant role in the mass balance for the chemical in question. To this end, the dominant uptake and elimination processes were assessed as a function of chemical partitioning properties. The key physical chemical properties influencing bioaccumulation of persistent chemicals in plants are the partition coefficients between octanol and air (KOA) and air and water (KAW). Hypothetical, completely persistent chemicals were defined possessing log KOA and log KAW values ranging from 3 to 14 and -8 to 3, respectively. This is a range in which the majority of neutral organic pollutants are found. So called chemical space plots were generated in which the outcome of interest for each simulation was plotted as a function of these partition coefficients. Following the approach for chemical space calculations adapted in refs 26 and 27, the molecular mass of all chemicals was set to 100 g/mol, the heat of phase change between octanol and air, ∆UOA, to -80 kJ/mol, and that between air and water, ∆UAW, to 60 kJ/mol. The rate constants for degradation were set to zero. Lettuce was chosen for the model parametrization. This vegetable grows exponentially, which enables the use of a constant growth dilution factor (see below and section 3 in SI). Since lettuce is a leafy vegetable lacking a fruit, the volume of the fruit compartment was set to zero. The parameter values selected for the lettuce model are listed in Table S1. The soil and air compartments were assigned the same generic fugacity, i.e., it was assumed that a chemical equilibrium existed between the air and the soil. The absolute value of the fugacity has no impact on the end points calculated in this paper. The relevance of different chemical uptake and elimination processes was assessed by calculating the chemical flux for single uptake processes and comparing these with the total uptake or elimination flux. The calculations of both t90 and chemical uptake/elimination fluxes were done using the values of the parameters on the day of harvest of the fully grown lettuce.

Results and Discussion Evaluation. To demonstrate the model’s applicability to both polar and nonpolar neutral chemicals, it was evaluated for PCBs in rye grass and sulfolane in cattail. As shown in Figure S1, the predicted PCB concentrations in rye grass leaf tissue and sulfolane concentrations in cattail leaves and roots are within an acceptable range considering the level of uncertainty in the model parameterization and the field/experimental data. For rye grass the mean quotient of the PCB concentrations predicted with the model and the measured concentrations ranged from 0.5 to 0.9 for the different PCB congeners (standard deviation 0.2-0.7). For the cattail roots the mean quotient between the predicted and observed sulfolane concentrations was 0.6 with a standard deviation of 0.3. The predicted sulfolane concentrations in cattail leaves were on average 1.5 times greater than the observed concentrations with a standard deviation of 0.8. The accuracy of the model predictions lends confidence to the model’s applicability to both hydrophobic and hydrophilic chemicals. Dominant Uptake Process. Figure 2 shows the ratio of the chemical flux (mol h-1) from the dominant uptake process relative to the total flux from all uptake processes, predicted for a lettuce leaf. The ratio, expressed as a percentage, is plotted as a function of KOA and KAW. A region of high percentage indicates that a single process dominates uptake for chemicals possessing these partitioning properties. The chemical space plot contains three distinct regions with a high ratio, each indicating a different dominant process: (i) gaseous deposition to the leaf surface, the dominant process for volatile chemicals with low KOA and high KAW values, (ii) xylem mediated advection via the root, dominant for water-soluble compounds, and (iii) particle

FIGURE 2. Plot of the dominant transport processes to lettuce foliage as a function of the chemicals’ KOA and KAW values at 25 °C. The model parameterization is given in the Supporting Information, Table S1. The colors indicate the percentage of the total uptake flux that is contributed by the dominant process on the day of harvest. The positions of a number of polychlorinated biphenyls (PCBs), sulfolane, hexachlorocyclohexanes (HCHs), polycyclic aromatic hydrocarbons (PAHs), dichloro-diphenyl trichloroethane (DDT), polychlorinated dibenzo-p-dioxins (PCDDs), polychlorinated dibenzofurans (PCDFs), phenol, phthalates, pesticides, and alkylated phenols in the chemical partitioning space are indicated. bound deposition (including wet and dry particle deposition), dominant for high KOA chemicals. Between the areas of single process dominance are regions where several processes make significant contributions to the compartment uptake. For the root (see Figure S4), the dominant uptake processes are advection in with soil pore water for chemicals with log KOW > 1 and phloem mediated uptake from the leaf compartment for chemicals with log KOW < 1 and log KAW < -6. The location of the boundary in Figure S4 is, however, dependent on the extent of passive diffusion across vessel membranes from the downward directed phloem flow to the xylem flowing in opposite direction, which is a highly uncertain parameter (see the more detailed explanation and equation describing this “xylem backflow” in the Supporting Information, Table S2). Chemicals with log KOA < 11 and KAW > -3 are mainly taken up in lettuce leaves by gaseous deposition to the leaf surface. Chemicals belonging to this region of the partitioning space include highly volatile compounds such as short chained alkanes and halogenated solvents (e.g., methane, CCl4), as well as semivolatile organic compounds (SOCs) including some PCBs, PCDDs, and PAHs (28). The gaseous concentration of the chemical in air and parameters affecting gaseous deposition velocities (e.g., wind speed) will have the greatest impact on uptake of these chemicals in the lettuce leaf. A change in chemical soil concentration will not affect the total bioaccumulation notably unless there is a much higher fugacity in soil than air. This is confirmed by research showing that plant uptake of SOCs such as PCBs is mainly from the atmosphere (29, 30). For hydrophilic chemicals of low log KAW (< -5) and low log KOW (< 4), chemical uptake occurs mainly via the roots (Figure 2). In this portion of the chemical partitioning space one finds chemicals such as sulfolane and many pesticides. They are highly mobile in the soil-plant system. In soil they partition readily into the soil pore water which quickly equilibrates with the fine roots. For these chemicals, the chemical uptake in the leaf will be controlled by the soil concentration and the transpiration streamflow.

For very lipophilic chemicals (log KOA > 11 and log KOW > 6), such as some PCDDs/PCDFs (Figure 2), partitioning to airborne particles and their deposition on the leaf surface is the dominant uptake route to the lettuce leaf. These results are in agreement with the work of McLachlan who concluded that particle bound deposition dominates for SOCs when log KOA exceeds 11 (31). For persistent chemicals with these partitioning properties, accumulation in the plant will be determined by the particle bound concentration of the chemicals in the atmosphere and the net deposition velocity of these particles to the vegetation. The assessment of the dominant uptake process is based on the assumption of equilibrium between air and soil. This is usually a good assumption, although there are occasions when a gradient in chemical potential (or fugacity) is present, e.g., at contaminated soil sites or after pesticide application. A higher fugacity in soil would shift the position of the contours delineating the xylem advection region in Figure 2 upward and to the right, with the magnitude of the shift proportional to the magnitude of this gradient (e.g., if the soil fugacity was 10 times higher than the air fugacity then the contours would shift approximately one log unit in KAW/ KOW). Dominant Elimination Process. Chemical elimination processes play an important role in determining contaminant concentrations in plants if these concentrations approach a steady state (steady state is per definition the situation when chemical uptake equals chemical elimination). Figure S3 shows the plot of dominant processes for elimination of persistent chemicals from lettuce leaves, excluding growth dilution. For the nongrowing leaves, diffusive release as a gas to air is the dominant process for most chemicals. Very water-soluble compounds (log KOW < 3, log KAW < -5) are an exception; they are eliminated primarily via the phloem flow. Note that the model applied to calculate phloem advection is highly uncertain. However, as shown in Figure 3 and explained in detail below, when the lettuce is growing (the normal case), growth dilution is the dominant elimination process in that portion of the partitioning space in Figure S3 where phloem flow is dominant. This suggests that under normal conditions the uncertainty in the description of phloem advection is of little consequence. The consequence of Figures 3 and S3 is that parameters related to gaseous elimination such as leaf temperature and atmospheric turbulence will be key in determining the concentrations of volatile chemicals that approach steady state in the lettuce leaf. For less volatile chemicals these parameters will have little influence; careful modeling of growth dilution will be required instead. In roots, watersoluble chemicals are removed via the xylem flow, whereas lipophilic chemicals are retained in the root. For these compounds growth dilution is the major elimination process. The transpiration rate will thus be an important parameter for hydrophilic chemicals, and estimation of growth dilution will be crucial for hydrophobic compounds that approach steady state. Time to Approach Steady State. The plant model was used to assess the time scale of bioaccumulation in vegetation by calculating the time, t90 (d), needed to approach 90% of steady state. The t90 values of the hypothetical chemicals were plotted as a function of KOA and KAW (Figure 3). Two scenarios were used: no growth dilution (kgrowth ) 0) and dilution due to fast exponential growth (panels A and B, respectively). These two scenarios represent two extremes and thus illustrate the expected range of possible t90 values. No or very slow growth is expected for ripening crops that have reached full size or plants growing under cold conditions, for example at high altitudes. Exponential growth is anticipated for some plant species growing in a warm humid VOL. 43, NO. 10, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 3. Chemical partitioning space plots showing the time, t90 (d), required to reach 90% of the steady state concentration in a lettuce leaf that is (A) not growing and (B) growing exponentially, both plotted as a function of the KAW and KOA value (at 25 °C) of the fully persistent chemical. The positions of a number of environmentally relevant chemicals are indicated; for the legend see Figure 2. climate under favorable conditions (e.g., light intensity, nutrient supply). When growth was not considered in the model simulations, t90 was strongly dependent on the compound’s physical chemical properties over the entire chemical partitioning space (Figure 3A). When growth was included, however, the influence of chemical partitioning properties was negligible for log KOA >7.8 and log KAW < -5 (Figure 3B). The t90 value for any chemical in the lettuce leaf is a function of the ratio between the chemical storage capacity of the leaf (expressed as a fugacity capacity, Zleaf, in fugacity modeling notation) and the overall rate of elimination of the chemical (expressed as ∑Delimination in fugacity modeling notation) (eq S12). It is the influence of the chemical partitioning properties on these two parameters that determines the shape of the t90 plot. The ∑Delimination excluding growth dilution varies by approximately 1 order of magnitude across the entire chemical partitioning space. This low variability is a consequence of the dominant elimination process, diffusive release to the atmosphere (see Figure S3), being largely governed by chemical diffusion in air, which is independent of chemical partitioning properties. The Zleaf values, on the other hand, range between 10-2 and 108 mol m-3 Pa1-. Consequently, the contours of the t90 plot for no growth (Figure 3A) resemble the shape of the analogous plot of Zleaf (see Figure S5). The time for a chemical to approach steady state in a plant is largely determined by Zleaf, or the plant/air partition coefficient. Zleaf is computed 3754

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as the volume weighted sum of separate Z values of the different leaf constituents (water, lipid, protein, carbohydrates, and air). Above a log KOW value of about 3, the lipid fraction in leaves is the dominant sorbing matrix, and consequently Zleaf is proportional to KOA (see Figure S5). Below a log KOW of 2, water is the dominant sorbing matrix, and Zleaf is proportional to KAW. Figure 3A can be summarized as follows. The leaf compartment has low fugacity capacity for highly volatile chemicals (high KAW and low KOA) values. Since the chemical storage capacity of the leaf is small, gaseous elimination to the atmosphere enables the leaf to approach the steady state concentration within minutes to hours. The low KOW chemicals show increasing t90 with decreasing KAW, t90 ranging from a minute for log KAW > -1 to over 100 days for log KAW < -6. This is due to the increase in Zleaf with decreasing KAW. The Zleaf for chemicals reaching the leaf via particle bound deposition (high KOA and high KOW) is high, which means that the gaseous elimination to the atmosphere, the dominant elimination process in the model, is very slow in comparison, and t90 exceeds 104 days. The extreme t90 values are, however, unrealistically long because elimination processes such as particle erosion and cuticle shedding (32) were not considered in the model. In the second scenario, growth dilution shortens the time needed to approach steady state in the leaf compartment for high KOA or low KAW chemicals to ca. 30 days (Figure 3B). For chemicals with these partitioning properties, growth dilution is the fastest elimination pathway. Mathematically, t90 becomes independent of physical chemical properties when this elimination pathway dominates ∑Delimination, since Zleaf in DGrowth cancels out Zleaf in the numerator of the t90 equation (eq S12). Intuitively, this result makes sense because growth dilution is not connected to chemical properties. The size of the plateau of growth controlled t90 in Figure 3B depends on the growth rate; slower growth will reduce the size of the plateau and increase the t90 value. Comparing Figure 3A and B shows that plant growth may lower t90 by several orders of magnitude. It is thus theoretically possible for all chemicals to approach steady state within the lifetime of a fast growing plant, but only if the exposure and the relevant environmental parameters are constant. The influence of temperature on plant bioaccumulation and time to approach steady state may be substantial. Cold weather implies slow growth and thus a higher chemical concentration in the plant and a longer t90 due to the reduced elimination rate. Low temperature also influences the temperature sensitive plant-air partition coefficient, KPA, resulting in higher KPA. Since leaf uptake is only weakly affected by temperature (molecular diffusivities are not strongly temperature dependent) and the elimination is inversely proportional to KPA, low temperatures may lead to significantly higher bioconcentration factors. Application of Results. The t90 maps and the maps of the dominant processes can be used for assessing the type of model (steady state or nonsteady state) required for bioaccumulation calculations and for parameterizing the models. A procedure is outlined in the following. The first prerequisite for using a steady state model is that the chemical exposure time is long enough for steady state to be approached. If the time period of chemical exposure exceeds t90 of the chemical, then steady state is possible. Assuming an exposure duration of more than 30 days, this condition would be fulfilled for a lettuce plant after 30 days of growth for all persistent chemicals (Figure 3B), and a steady state model would be appropriate if further conditions are also satisfied (see below). Next the dominant chemical transport processes should be identified. The concentrations in the plant are governed by the dominant uptake process and the dominant elimina-

tion process. For the lettuce example, the dominant uptake and elimination processes for a persistent chemical with a log KOA of 7 and a log KAW of -2 would be gaseous deposition and gaseous elimination, respectively, while for a persistent chemical with a log KOA of 12 and a log KAW of -4 the dominant processes would be particle bound deposition and growth dilution. The key parameters affecting these processes are the focus of the following considerations. The time scale of variability of these key parameters should now be compared to the t90. If no systematic variation over a time period of t90 prior to the desired end point was observed, average values of these parameters may be used. If this is the case for all key parameters, and the exposure time criterion outlined above is fulfilled, then a steady state model is appropriate. Note that short-term fluctuations in key parameters will not influence the steady state concentration notably if the variations are stochastic and fast compared to t90. Systematic variations in the key parameters (e.g., an increasing chemical concentration in the atmosphere over time) may preclude averaging and should be evaluated for their impact on model predictions. This also applies to nonsystematic variations with a period similar to t90. If the magnitude of the systematic variation is small compared to the desired accuracy of the model result, then a steady state model using an average value of the parameter may be suitable. For instance, if the chemical concentration in the atmosphere increases gradually by 10% over t90 while the desired accuracy of the predicted leaf concentration is a factor of 2, a steady state approach can be pursued. However, an increase of a factor of 4 would indicate that a nonsteady state model that takes into account the variability of this parameter should be employed. Note that parameters that do not strongly influence the dominant processes need not be considered. It is also worth noting that the accuracy requirements for a model will depend on the model application. High accuracy may be required in, e.g.. human exposure assessment, whereas for other purposes a less accurate measure of the plant concentration is sufficient. For instance, models are used for ranking chemicals for priority setting and chemical life cycle assessment. A correct rank ordering of chemicals is the model performance criterion for this application. The ranking of chemicals for their relative bioaccumulation may also depend on how well the model accounts for the temporal variability aspects. A steady state model may incorrectly rank a chemical that has a long t90 and a high steady state concentration (and thus never approaches steady state) compared to a compound that quickly approaches a constant concentration at a lower steady state level. Growth dilution is frequently the dominant elimination mechanism, and hence the variability in the growth rate is of importance for the procedure described above. Since the growth rate in the model is expressed as a fraction of the current compartment volume, a constant model growth rate is equivalent to exponential growth (see Supporting Information, section 3). Hence, only in plants that have experienced exponential growth over the time t90 prior to the time point of interest will the model growth rate have been constant. In other cases the deviation from exponential growth must be considered. The growth rate at different time points should be assessed. Depending on the variability in the growth rate and the desired accuracy of the model, it may be necessary to use a nonsteady state model that treats the growth rate as a variable. Figure S6 shows that the choice of growth scenario affects model output up to a factor of 4 in lettuce leaves depending on the chemical partitioning properties. To summarize, steady state models cannot be used if the length of exposure to the chemical is less than t90 or if there

is a large variation in a key parameter with a period similar to or longer than t90. Another limitation of steady state models is that the steady state solution implies that uptake and elimination processes are linearly related to the plant volume. Processes that are not linearly related to plant volume (e.g., particle deposition) will thus introduce an error in the steady state solution if they contribute significantly to the uptake and elimination processes. The hypothetical chemicals in this analysis were assumed to be fully persistent. While many semivolatile organic contaminants of concern are known to be very persistent in plants (31), many pesticides are degraded rapidly (33). For nonpersistent chemicals, the rate of elimination in Figure 3 can be compared with the rate of transformation. A transformation half-life equal to the t90 implies that this elimination process, if included, would contribute half of the total elimination and thus reduce t90 by half. Incorporating this into Figure 3B would result in the magnitude of t90 in the plateau region dropping by a factor of 2 and the KAW and KOW values delineating the limits of the plateau increasing by a factor of 2. The t90 of volatile chemicals would not be influenced, as they are eliminated very rapidly irrespective of metabolism. The maps of the dominant transport processes and the t90 maps illustrate the importance of considering a chemical’s physical chemical properties before deciding to use a steady state model to describe its bioaccumulation in plants. The plots also provide guidance in identifying the parameters that need to be carefully described in the model and they indicate which time span should be considered when choosing average values of time variable parameters such as environmental concentrations and temperature. This knowledge can also be applied to experimental work, e.g., to determine which parameters to measure and the appropriate frequency of sampling. The procedure presented here to identify the dominant uptake and elimination processes, and thereby the key model parameters, has some similarities to a model sensitivity analysis. However, by identifying the dominant processes, this procedure allows the user to also do a targeted evaluation of the strengths of the modeling approaches used to describe these processes. Hence it helps the user to go beyond examining parameter uncertainty and address issues of model uncertainty.

Acknowledgments Financial support from the European Chemical Industry Council Long-Range Research Initiative and the European Union (GOCE-CT-2007-037017) is gratefully acknowledged.

Supporting Information Available All model equations and parameters. This material is available free of charge via the Internet at http://pubs.acs.org.

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