Modeling the In Vivo Case with In Vitro Nanotoxicity Data

Abstract

As more in vitro nanotoxicity data appear in the literature, these findings must be translated to in vivo effects to define nanoparticle exposure risk. Physiologically based pharmacokinetic (PBPK) modeling has played a significant role in guiding and validating in vivo studies for molecular chemical exposure and can develop as a significant tool in guiding similar nanotoxicity studies. This study models the population dynamics of a single cell type within a specific tissue. It is the first attempt to model the in vitro effects of a nanoparticle exposure, in this case aluminum (80 nm) and its impact on a population of rat alveolar macrophages (Wagner et al. 2007, J. Phys. Chem. B 111:7353–7359). The model demonstrates how in vitro data can be used within a simulation setting of in vivo cell dynamics and suggests that PBPK models should be developed quickly to interpret nanotoxicity data, guide in vivo study design, and accelerate nanoparticle risk assessment.

Currently, there is a lack of data characterizing nanotechnology’s effects on biological systems. The technology has numerous possible benefits to society, but the risks involved still need to be characterized (Dreher 2004; Colvin 2003). Nanotoxicology is a young field, and, compared to the advance of nanotechnology, it is far behind (funding and research) in adequately supporting the technology (Roco 2003). Thousands of new nanomaterial product ideas are being developed, but, as seen in the National Institute of Occupational Safety and Health (NIOSH) strategic plan and current literature concerning nanotoxicology, only a few types of materials are being characterized, usually carbon based materials and titanium oxide (NIOSH Strategic Plan 2005). Tools are needed to expedite the characterization of nanotechnology’s impact on complex biological systems.

Physiologically based pharmacokinetic (PBPK) modeling has used in vitro data to parameterize whole-system models for decades (metabolic coefficients, dermal permeability coefficients, tissue/blood partition coefficients, etc.). The concept was introduced in the classic Ramsey and Andersen paper of 1984 and then quickly applied to many risk assessment scenarios such as nursing infant risk through a lactating mother’s occupational exposure (Shelley et al. 1989). These models mechanistically consider whole tissue systems as they are linked together dynamically by blood flows, allowing simulation of target tissue concentrations of primary exposure chemicals and metabolites resulting from environmental concentrations. Simple, classical reaction kinetics are assumed as well as reasonable simplifying assumptions such as instantaneous equilibrium in most tissue groups. When indicated, more complicated diffusion kinetics are employed as in the case of bronchial tissue absorption modeled by Shelley et al. in 1996.

Toxic responses seen during in vitro nanotoxicity studies include cytoskeletal dysfunction in macrophages (Moller et al. 2005), oxidative stress in liver cells (Hussain et al. 2005), and macrophage phagocytosis response to nanoparticle exposure (Renwick et al. 2001; Lundborg et al. 2001; Guang et al. 2005). Ultimately, one must find meaning in data collected in vitro as it may apply to in vivo risk analysis. This is typically pursued through modeling the in vivo case in a mechanistic sense while using batch or time series in vitro data to parameterize the dynamic in vivo model in time. For example, in vitro exposure of alveolar macrophage to 80-nm aluminum particles (Wagner et al. 2007) has revealed a mild toxicity to cell viability (LD₅₀ of ~250 μg/ml after 24 h) and a much more significant toxic effect in macrophage function (~90% function loss after 24 h with only a 25 μg/ml exposure). These data, along with reasonable initial assumptions, gives a starting point for exploration of the in vivo case.

Accordingly, an initial simple model of alveolar macrophage dynamics under aluminum nanoparticle exposure is constructed. The structure would apply to any tissue system but, in this case, conceptually applies to alveolar macrophage in alveolar tissue because related in vitro data used macrophage cells harvested from such tissue. Within this context, a mechanistic model would need to employ the concept of interstitial transport of nanoparticles away from the alveolar epithelial region of interest as a mechanism of nanoparticle disappearance as presented in Oberdörster et al. (2005). This transport would be a passive “diffusion-like” process that would be first order in particle concentration, with the first-order coefficient varying with particle size, shape, surface chemistry, etc. Because the first-order coefficient for interstitial dispersion is unknown, values of 0.01 and 0.1 per day are used to indicate possible effects on model results when this mechanism is considered (these values provide a good discernable range of effects). The model serves two primary purposes:

1. It demonstrates the dynamic, systemic, mechanistic view required to meaningfully interpret nonsystemic, nondynamic in vitro data.

2. It demonstrates the nature and extent of assumptions required to put forward such a view and, therefore, where further research is required to use in vitro data on a cell line to gain insight into tissue system dynamics.

METHODS

In vitro macrophage viability and functional data were presented by Wagner et al. in 2007. The homogenous and highly responsive rat alveolar macrophages (NR8383 line) were maintained in F12K medium supplemented with 20% fetal bovine serum (FBS) in 1% penicillin and streptomycin and grown in a humidified incubator at 37°C and 5% CO₂ atmosphere on a layer of rat tail collagen. Once adequate in vitro macrophage populations were reached, they were dosed with various Al nanoparticle concentrations. Viability was determined using a colorimetric assay adapted from Carmichael in 1987, which measures mitochondrial function in the cell to determine its metabolic activity or viability. The assessment of the cells’ ability to function was adapted from a study done by Paine et al. in 2001. This assay assesses the cells’ ability to phagocytose latex beads after a nanoparticle exposure.

The model developed here simulates the population dynamics (including toxic effects and functional viability) of a single cell type within a specific tissue. It is a system of mechanistically derived ordinary differential equations in time with significant simplifying assumptions to stand up an initial working model for demonstration. The primary state variables are macrophage population, nanoparticle concentration, and macrophage phagocytosis function level. The following assumptions and simplified modeling approaches are employed:

1. It is assumed that 80-nm aluminum particles are small enough to reach alveolar air space with concentration similar to that in the breathing zone. It is also assumed that these particles have a settling velocity that overcomes aerosol diffusion and, therefore, have a deposition rate during exposure that can be calculated, yielding an initial deposited “concentration” in alveolar tissue. The model asserts an initial value on an arbitrary scale (the value “5” producing recoverable effects, the value “35” destroying macrophage functionality, and the value “250” reducing the macrophage population to one-half). The scale is conceptually indexed to units of μg/ml corresponding to experimental concentrations in vitro.

2. The macrophage population is assumed to have a first-order growth rate that is overcome by limiting factors as the population approaches an asserted healthy steady state value of 5000 on the arbitrary population value scale. Limiting factors could include an increased death rate due to limiting resources, chemically mediated signals that shut down cell division or cell immigration to the tissue when homeostasis conditions are reached, or other unknown factors. The assumption of a mechanistic approach to an ideal healthy steady state is considered reasonable. This mechanism remains active throughout the model simulation even when competing mechanisms such as toxicity are also active.

3. The model mechanisms of cell death and loss of macrophage function are parameterized to reflect the degree of effect seen in vitro. Specifically, the value of the first-order death rate due to nanoparticle exposure yields a macrophage population of one-half the healthy steady state value after a reasonable time when the initial nanoparticle “concentration” is 250 μg/ml (similar to the demonstration of an LD₅₀ at a nanoparticle concentration of 250 μg/ml in vitro). Similarly, a nanoparticle “concentration” about one order of magnitude less yields a functional loss of about 90%, similar to the in vitro observation of 10% functionality at a nanoparticle concentration of 25 μg/ml. In vitro observation clearly distinguishes these two effects (cell death and loss of cell function). The mechanisms of these two effects are not elucidated. Nonetheless, the two processes must be mechanistically represented in the model. They are clearly two separate mechanisms as one (functionality) is effective at an aluminum nanoparticle concentration one order of magnitude below the other (cell death). The model employs a mechanism of approach to normal function for all cells that is always active and is competitive with any toxic effect that reduces function. Therefore, upon reduction of nanoparticle concentration, all surviving macrophage cells can recover to full function. (The function reduction effect is first order in nanoparticle concentration.) Cell death, on the other hand, can only be repaired by cell division and multiplication in an environment of nanoparticle concentration that does not fully counteract that population growth. Cell death by nanoparticle effect is also first order in nanoparticle concentration.

4. Functionality per cell is measured on a scale of 0 to 1 with 1 being healthy function. Overall phagocytosis capacity is the cell functionality times the cell population, thus measured on an arbitrary scale of 0 to 5000 like cell population. Depletion of nanoparticles is by phagocytosis (and possible interstitial transport). These processes are parameterized in the model to yield reasonable results over the time horizon of the simulation. These coefficients have no basis in collected data for this modeled case and are simply asserted.

5. Other model coefficients shown in Figure 1 and listed in Table 1 are given values that are reasonable when compared to established values of similar coefficients in similar systems of biological populations. This criterion is also modified to accommodate empirical data gathered from the in vitro experiments in the referenced work upon which this model is based. Coefficient value ranges are also chosen to provide a comparison of model output dynamics when certain processes are more or less dominating to illustrate the importance of certain processes and their inclusion in future research proposals. These coefficients are not well established in the literature and are asserted for demonstration in presenting the importance (or lack thereof) in certain processes over others in prioritizing future efforts.

The system of differential equations that define the model with its parameter values are given in Table 1. The model was implemented using the differential equation solver STELLA, version 8.0 (formerly distributed by High Performance Systems). The STELLA modeling diagram (or flow diagram) is seen at Figure 1.

RESULTS AND DISCUSSION

The model output in Figure 2 demonstrates the limited growth dynamics of macrophage cells starting at an arbitrary low value and climbing to the arbitrarily established steady state of 5000. This dynamic behavior arises from the model mechanism that is continually active throughout all simulations even though all remaining simulations start at an initial value of 5000. Thus, during and after disturbance of this pattern (by a toxic effect, for example), this mechanism will always provide a stabilizing force that attempts to return to the homeostasis value of 5000.

Figure 3 shows an initial population value of 5000 with an initial nanoparticle value of 250 μg/ml. Note that the population falls to one-half its initial value and fails to recover over time, whereas the nanoparticles remain at a high level (with interstitial dispersion turned off; Figure 3a ). These dynamics are dictated by the very high toxic effect on functionality at this agent concentration. Near-zero functionality destroys phagocytosis and prevents agent (nanoparticle) depletion. The agent continues to exert toxicity at a near constant rate (near constant concentration), continually inhibiting functionality. This toxicity competes with the cell’s mechanism of growth and recovery, holding the population at a steady state one-half its healthy value. This view of in vivo dynamics demonstrates the power of this kind of mechanistic, dynamic modeling technique in exploring the complexity of in vivo effects implied by in vitro observations. Figure 3b and c demonstrate how these dynamics change when interstitial dispersion is considered (dispersion coefficient of 0.01 and 0.1 per day, respectively).

The more interesting case of lower agent concentration is seen in Figure 4 where 25 μg/ml has little effect on cell viability but significant (yet recoverable) effect on function. Note the slight disturbance of pure first-order depletion of agent when function is inhibited, followed by complete first-order removal of agent after agent concentration falls low enough for function to recover. These kinds of observations have far-reaching implications for risk assessment. For example, only a small increase in agent concentration over that displayed in Figure 4 (from 25 to 35 μg/ml) completely inhibits the system’s ability to recover (Figure 5), perhaps requiring clinical treatment to remove agent or restore function. Without treatment, recovery begins to appear at about 50 days. Figure 5b again demonstrates the same dynamics when the significant effect of interstitial dispersion is turned on (coefficient 0.01 per day). Smaller concentrations, like that shown in Figure 6a (33 μg/ml; no interstitial dispersion), suggest a period of time after exposure when the subject may be immunologically compromised until macrophage function is restored. Further exploration of initial agent concentration can suggest exposure action levels below which recovery mechanisms in vivo are sufficient to prevent significant effect (Figure 7; agent concentration = 10 μg/ml, no interstitial dispersion).

CONCLUSIONS

This simple model demonstrates one approach to interpreting in vitro data on nanoparticle exposure to one cell line. It identifies and suggests the importance of research directions to make the tool more valuable. Questions needing exploration are

1. Where interest is focused on risk to a specific tissue group or cell line, what are the normal homeostatic cell population dynamic mechanisms, and what are the recovery kinetics upon damage in vivo?

2. For nanoparticles, what are the routes of entry for various particle composition and size, and what are various distribution and reaction kinetics required for a PBPK analysis to determine delivery to the target tissue?

3. In the target tissue, what are the measurable toxic indicators that are comparable to in vitro cell toxicity indicators as they vary with agent concentration?

Aspects of questions 2 and 3 are addressed in the recent review article by Nel et al. (2006).

Nanoparticle effects in complex biological systems can be studied using mechanistic modeling techniques, and these techniques can develop as fast as PBPK modeling developed for molecular chemical exposures. Nanoparticle toxicity research must transition quickly from only in vitro studies to studies that include more systemic and mechanistic approaches for insight into the in vivo context.