Case Study: Health Risks from Asbestos Exposures

Abstract

Can a single fiber of amphibole asbestos increase the risk of lung cancer or malignant mesothelioma (MM)? Traditional linear no-threshold (LNT) risk assessment assumptions imply that the answer is yes: there is no safe exposure level. This chapter draws on recent scientific progress in inflammation biology, especially elucidation of the activation thresholds for NLRP3 inflammasomes and resulting chronic inflammation as discussed in Chaps. 3 and 4, to model dose-response relationships for malignant mesothelioma and lung cancer risks caused by asbestos exposures. Similar to the model for respirable crystalline silica in Chap. 4, the modeling in this chapter integrates a physiologically based pharmacokinetics (PBPK) front end with inflammation-driven two-stage clonal expansion (I-TSCE) models of carcinogenesis to describe how exposure leads to chronic inflammation, which in turn promotes carcinogenesis. Together, the combined PBPK and I-TSCE modeling predict that there are practical thresholds for exposure concentration below which asbestos exposure does not cause chronic inflammation in less than a lifetime, and therefore does not increase chronic inflammation-dependent cancer risks. Quantitative examples using model parameter estimates drawn from the literature suggest that practical thresholds may be within about a factor of 2 of some past exposure levels for some workers. The I-TSCE modeling framework presented here explains some previous puzzling aspects of asbestos epidemiology, such as why age at first exposure is a better predictor of lifetime MM risk than exposure duration.

Appendices

Appendix 1: A Physiologically Based Pharmacokinetics (PBPK) Model for Asbestos Fibers in the Human Body

Figure 5.6 shows the structure of a systems dynamics model for the asbestos fiber PBPK model. The notation and model are adapted from DeStefano et al. (2017); details are given at www.tandfonline.com/doi/pdf/10.1080/17513758.2017.1355489 cf p. 368. For example, FL denotes free fibers in lung; ML denotes macrophages in lung that have not yet ingested a fiber; MI denotes macrophages that have ingested fibers (at least partly, as frustrated phagocytosis may block full ingestion) and await mucociliary clearance; FY, FB, FP, and FM denotes free fibers in the lymphatic system, blood, pleural cavity, and mesothelium, respectively, and AM denotes alveolar macrophages. These stocks, or compartments, of the fiber inventory are represented by rectangular boxes in Fig. 5.6. Flows among them, representing movement of fibers among compartments, are shown by thick arrows. Thin arrows represent information flows: the value of a variable is calculated from the values of the variables that point into it.

Fig. 5.6

Systems dynamics diagram for the PBPK model

Fibers flow among these compartments at rates indicated by the constants (e.g., pLY for clearance rate of free fibers in the lung by lymphatic removal) or determined by Michaelis-Menten parameters for saturable removal kinetics in the kidney (where the removal rate of fibers from blood by the kidney is given by the formula KB = k1*FB/(k2 + FB)) and lung (where the rate of uptake of free fibers by alveolar macrophages is given by the formula GLM = g1*FL*ML/(g2 + FL), expressing a maximum removal capacity of g1 fibers per unit time per macrophage). The recruitment rate of alveolar macrophages to the lung likewise follows saturable kinetics: it is given by the formula GI = gI1*FL/(gI2 + FL) when the lung is inflamed. Multiplying compartment contents by outflow rates gives the values of the outflows at each moment, corresponding to the thick arrows between compartments in Fig. 5.6. Summing the inflows and outflows for each compartment at each moment gives the rate of change of its contents, and these dynamics can be described by a system of ordinary differential equations (ODEs). DeStefano et al. (2017) give rough estimates for the parameter values and constants for both inflamed and normal tissues in humans, noting that the qualitative and quantitative dynamics of the system are determined primarily by the ratios of the different flow rates to each other, so that the exact numerical values, which in any case differ among individuals, are less important than the approximate values of their ratios. Table 5.2 lists the detailed equations and parameter and constant values for the PBPK model under normal conditions. DeStefano et al. (2017) (Table 5.1) also provide suggested modifications of these input values for fibrosis and chronic inflammation. However, our focus is on the normal case, as the transition to chronic inflammation locks in a high-ROS environment and changes the parameters of the TSCE model (Appendix 3), making the continued dynamics of fiber distribution less relevant for calculating cancer risks. Although experiments in rats exposed to many types of dusts and particles show that lungs become overburdened at high concentrations, impairing clearance of even low-solubility and relatively low toxicity particles by alveolar macrophages (AMs) (Borm et al. 2004, 2015), the rat lung appears to be unique in this regard, and relevance for human pathology is unclear (Warheit et al. 2016). The model in Table 5.2 focuses on PBPK dynamics for the healthy human lung prior to onset of chronic inflammation or fibrosis.

Table 5.2 Listing of PBPK model formulas and parameter values

Appendix 2: A Model of the Transition from Acute to Chronic NLRP3-Inflammasome-Mediated Inflammation

The mathematical model for the transition from acute to chronic inflammation is adapted from the inflammation submodel for respirable crystalline silica and lung cancer described in Chap. 4. This appendix recapitulates key aspects of that model. In brief, exposure can cause uninflamed cells in target tissues to become inflamed (e.g., undergoing pyroptosis) either directly, as when a macrophage interacts with a fiber; or indirectly if pro-inflammatory materials from nearby inflamed cells exceed the cell’s own NLRP3-inflammasome activation threshold and cause it to become inflamed. Although the spread of inflammation has been modeled and simulated in various ways, including deterministic ordinary differential equations (ODEs), stochastic (probabilistic) models, and agent-based models (ABMs), these multiple modeling approaches approaches converge on a conclusion that there is a tipping point, or threshold, for the fraction of inflamed cells (or sites, in a spatial model) (Gilroy and Lawrence 2008; Page 2018). Above this threshold, inflammation is self-sustaining, i.e., chronic, and will continue even if exposure stops; below, it is not, i.e., it remains acute and self-resolving once exposure stops.

This conclusion can be illustrated using a simple deterministic ODE model (as a mean-field approximation to an underlying probability model), as follows. Suppose that there are a large number of potential sites of inflammation (e.g., cells in a tissue); that the fraction of inflamed sites at time t is P(t); that a randomly selected site that is not yet inflamed and that does not directly interact with a fiber becomes inflamed if and only if more than k of its neighbors are inflamed, where k reflects its activation threshold; that direct interaction with fibers can also cause an uninflamed site to become inflamed; and that inflamed sites are resolved (i.e., cease to be inflamed) at some rate (possibly zero, for sites where fibers are lodged). A simple model for the dynamics of such a system is as follows:

$$ dP/ dt=f(P)\left(1-P\right)+c\left(1-P\right)- dP $$

(5.1)

where P is the fraction of sites that are inflamed; (1 − P) is the faction of sites that are not inflamed; c is the rate at which exposure directly causes uninflamed sites to become inflamed; d is the rate at which inflamed sites become uninflamed; and f(P) is the rate at which uninflamed sites become inflamed when the fraction of inflamed sites is P. Particle overload in the rat lung compromises the efficiency of phagocytosis, corresponding to a decrease in d (Borm et al. 2015). However, we shall focus on lower exposures and long averaging times in humans, for which the simplified approximate description of clearance of inflamed cells by a single rate constant yields useful insights into inflammation dynamics on a time scale of months to years or decades, despite its undoubted inaccuracies on short time scales. If a site has N neighboring sites, then the probability that at least k of these N neighbors are inflamed if the fraction of inflamed sites is P can be modeled (using a mean field approximation for the average case) as 1 − pbinom(k, N, P), where pbinom(k, N, P) denotes the cumulative probability that no more than k of the N neighbors are inflamed if each has probability P of being inflamed. The average rate at which the uninflamed site becomes inflamed due to proinflammatory effects from neighboring cells can be modeled as

$$ f(P)=a\ast \left(1- pbinom\left(k,N,P\right)\right) $$

(5.2)

The mathematical analysis in Chap. 4 established that Eq. (5.1) with f(P) specified as in Eq. (5.2) has two stable equilibria, one at a low value of the inflammation fraction P (equal to zero if c = 0, e.g., in the absence of exposure) and the other at a higher value of P. Between them is an unstable equilibrium level—a tipping point threshold. Initial values of P below the threshold will decline to the lower equilibrium value, while initial values of P above the threshold will increase to the higher equilibrium value. Figure 5.7, the key points of which have been discussed in Chaps. 3 and 4, illustrates this behavior by showing P(t) trajectories starting from different initial inflammation fractions P(0) (expressed as percents, between 0 and 100) on the vertical axis. Time is on the horizontal axis. (The units of time are left unspecified, since the qualitative behavior shown does not depend on the choice of time units, which are the reciprocal units of the rate constants.) The trajectories in Fig. 5.7 assume that no further exposure occurs to cause direct inflammation, so that only indirect effects (i.e., inflammation caused by existing inflammation) are shown. In this case, the lower equilibrium value is P = 0 and the upper equilibrium value is P = 0.5 = 50%, denoted by E on the vertical axis. More generally, if ongoing exposure is nonzero (as is plausibly the case for biopersistent fibers), then the lower equilibrium value increases with c, the potency of ongoing exposure. Trajectories that start below the threshold T correspond to acute inflammation (declining to the lower equilibrium level, which is 0 in the absence of further exposure), while trajectories that start above T correspond to chronic inflammation and approach level E. Of course, as Fig. 5.7 illustrates, the time between onset of chronic inflammation and convergence to the chronic inflammation equilibrium level of inflammation may be long for trajectories that start very close to the threshold T, where creation and resolution of inflamed units are in balance, but this is an unlikely circumstance, and in any case is unlikely to persist if exposure to fibers continues.

Fig. 5.7

A family of P(t) inflammation trajectories starting from different initial inflammation levels on the vertical axis (numbers show percent of units inflamed). Time is on the horizontal axis. Time units are left unspecified here; they are the inverse of the units for the rate parameters a and d. For these trajectories, k = 2, N = 3, d = 0.2, and a = 0.4. Time (nominal units, e.g., months or years, depending on rate constants). For human inflammation, a time scale of weeks to months is plausible

Such bistable, or tipping point, behavior is common in models where it becomes easier for unchanged units to change as the fraction of already-changed units increases (Page 2018). As previously noted (Cox 2019), “The existence of such a threshold is robust to many modeling details. It occurs in a wide variety of stochastic models that allow for realistic complexities such as heterogeneity in the thresholds for different units, or heterogeneous and time-varying numbers of neighbors for different units. The key feature driving the occurrence of bistability and a threshold between 2 basins of attraction for extinction versus self-sustaining activation of units in such models is that a unit is more likely to become activated when more of its neighbors are activated. This interdependence is realistic for phenomena ranging from spread of forest fires to epidemics, and we believe that it is also realistic for NLRP3- mediated spread of pyroptosis and lung inflammation.”

For biopersistent fibers, as opposed to crystalline silica particles, the preceding model can be extended to consider the spatial distribution of fibers lodging in target tissues over time. If they are very biopersistent, such fibers may never be cleared, and may act as sources for ongoing local inflammation. If enough of them accumulate in proximity to each other, then all or most of the surrounding tissue may become inflamed. Agent-based models (ABMs) of the evolution of spatial patterns of inflammation can be obtained by modifying and reinterpreting spatial models of segregation in populations (Schelling models) (Hatna and Benenson 2015; Kaul and Ventikos 2015; Page 2018). In a Schelling model, people are of two types and a person moves away from a neighborhood if the number of neighbors of opposite type exceeds a threshold. This can be modified (by not requiring the number of units of each type to be conserved or replaced units to be relocated) and reinterpreted as a model of inflammation in which a unit of one type (inflamed or not inflamed) is replaced by a unit of the opposite type if the number of its neighbors of opposite type exceeds a certain threshold. Biopersistent fibers lodged in tissue correspond to people who never move. In such spatial models, there are typically still tipping points, so that neighborhoods tend to end up being either entirely inflamed or not. However, the final pattern of inflammation need not be all-or-nothing: inflamed and uninflamed regions may co-exist (Page 2018). This is consistent with the qualitative pattern in Fig. 5.7, in which an initial inflamed fraction greater than the tipping point T will spontaneously evolve to the new equilibrium fraction E.

Rather than seeking to develop an ABM or other model of the detailed dynamics of the spatial distribution of inflammation within a target tissue over time, we will make the simplifying approximation that the tissue can be modeled as a set of patches, within each of which a tipping point model for chronic inflammation, similar to the one in Fig. 5.7, holds. Each patch becomes chronically inflamed if and only if at least some critical number K of fibers are lodged in it; K is its tipping point, and once it is passed, inflammation spreads in the patch until some final spatial equilibrium configuration is reached. We do not model the details of the spatial configuration, but simply call the patch chronically inflamed (while acknowledging that the spatial density of inflammation may increase somewhat if further fibers arrive).

In this simplified patch approximation, a key question is how the fraction of chronically inflamed patches increases over time. The PBPK model in Appendix 1 can be interpreted as providing the average or expected cumulative number of fibers lodged in target tissues (lung and mesothelium) over time, but it provides no information about their spatial locations within the target tissues. However, the theory of Poisson processes implies that if the average arrival rate of fibers is λ fibers per patch unit time (with arrivals modeled as a Poisson process), then the random time for a patch to accumulate K fibers has a gamma distribution with parameters K and 1/λ, implying a mean time of K/λ and a variance of K/λ². (These formulas can be generalized if the arrival rate is time-varying, so that the Poisson process is non-homogeneous.) For example, if a single lodged fiber were enough to chronically inflame a patch (K = 1) and the average arrival rate is λ = 0.25 lodged fibers per patch-year, then the mean time until the onset of chronic inflammation in the patch is K/λ = 1/0.25 = 4 years, and the standard deviation is (K/λ²)^0.5 = K^0.5/λ = 4 years. On the other hand, if K = 8 and λ = 2, then the mean time until the patch becomes inflamed is 4 years and the standard deviation is 1.4 years. If K = 16 and λ = 4, then the mean time until the patch becomes inflamed is 4 years and the standard deviation is 1 year. Table 5.3 summarizes these and other calculations showing how the standard deviation of the random time at which chronic inflammation begins decreases as K increases, holding the mean time fixed at 4 years. These numbers illustrate an important general principle: for any given mean time until the onset of chronic inflammation in a patch the more lodged fibers are needed to initiate chronic inflammation in the patch (i.e., the larger is K), the smaller is the standard deviation of the actual (random) time until onset of inflammation around its expected value. If K is large, the time at which chronic inflammation begins will be very close to its expected value, K/λ. The coefficient of variation, i.e., the ratio of the standard deviation to the mean, of this random time, approaches zero. This follows from the theory of sharp transitions in random processes (Cox Jr. 2006; Motwani and Raghavan 1995). Therefore, even if there are many patches, all of them will tend to undergo the transition to chronic inflammation at around the same time if many fibers are required to initiate chronic inflammation in each patch. Since counts of asbestos fibers greater than 5 micrometers long in the lungs of patients with LC or MM are typically on the order of millions to hundreds of millions of fibers per gram of dry tissue weight (Gilham et al. 2016; Churg 1982; Tuomi et al. 1989; Rödelsperger et al. 2001), this large-number assumption for K seems plausible.

Table 5.3 Standard deviations for different pairs of K and λ values giving a mean time of years to initiation of chronic inflammation

The net result of these modeling considerations is the very simple conclusion that chronic inflammation in a given patch of target tissue begins when the cumulative burden of fibers embedded in that patch reaches a certain threshold; moreover, this is likely to occur in multiple patches at approximately the same time. The exact time is a random variable, with a gamma distribution if the fiber arrival process is a Poisson process with constant intensity; and the exact spatial distribution of chronically inflamed locations, as revealed by ABM modeling, may be complex (Kaul and Ventikos 2015). But these details and complexities can be ignored if the goal is to integrate the inflammation model with the PBPK model, which only produces rough average fiber count estimates. Thus, the onset of chronic inflammation can be characterized, to a useful first-order approximation, as the time needed for a sufficient number of fibers to accumulate in target tissues to trigger the transition from acute to chronic inflammation. If this critical number of fibers is denoted by F*, then the time until chronic inflammation is triggered will be approximately the time for the PBPK model, driven by the exposure history, to deliver F* fibers to the target tissue.

A rough order-of-magnitude estimate for F* can be derived by considering a worker who eventually develops MM or LC after a 40-year career of exposure to asbestos. Such a worker might accumulate roughly 1–10 million long (>5 μm), thin fibers per year per gram dry weight of lung tissue (Gilham et al. 2016; Churg 1982; Tuomi et al. 1989; Rödelsperger et al. 2001). If chronic inflammation is caused after roughly 4 years, i.e., 10% of the way into the 40-year exposure, then the cumulative number of fibers per gram dry weight of lung tissue that triggers chronic inflammation would be about F* = 100,000 to 1 million. This simple estimate ignores sources of inter-individual variability, such as differences in pharmacokinetic parameters, or gene polymorphisms which might readily account for a several-fold difference in vulnerability to asbestos exposure, as measured by outcomes such as pleural thickening or signs of fibrosis (Kukkonen et al. 2011, 2014). It also ignores uncertainty about when chronic inflammation actually begins (e.g., at year 2 or 8 or 16 instead of 4). However, even with such uncertainty and variability, the simple baseline estimate of F* as being between a few hundred thousand and a few million long, thin fibers per gram dry weight of lung tissue suggests that a single fiber lodged in lung or mesothelial tissue has effects that are orders of magnitude too small to trigger chronic inflammation.

Appendix 3: Two-Stage Clonal Expansion (TSCE) Models of Lung Cancer (LC) and Malignant Mesothelioma (MM) Risk

Both LC and MM, as well as numerous other malignancies, have been modeled using two-stage clonal expansion (TSCE) models of carcinogenesis in which normal stem cells undergo an initial mutation to become initiated (premalignant) cells; this pool of initiated cells proliferates via clonal expansion (promotion), i.e., increased net growth rate of initiated compared to normal stem cells; and initiated cells may then undergo a second mutation or transformation to yield fully malignant cells (Tan and Warren 2011; Zeka et al. 2011). Once a malignant cell is formed, it and its clonal progeny may acquire other hallmarks of carcinogenesis (e.g., angiogenesis, metastasis), yielding observed tumors after a latency period. Exposure to a carcinogen such as asbestos—or to the products of chronic inflammation caused by exposure, such as ROS—can increase cancer risk by increasing one or more of the first mutation rate, the second mutation rate, or the net proliferation rate of initiated cells.

Figure 5.8 shows the structure of a systems dynamics model for one proposed MM TSCE risk model, taken from Tan and Warren (2011). Table 5.4 lists the model formulas and parameter values. Similarly, Fig. 5.9 shows a TSCE systems dynamics diagram for LC risk, building on the baseline (no-exposure) model of McCarthy et al. (2012) with a step increase in the net proliferation rate of initiated (pre-malignant) stem cells when chronic inflammation begins. Table 5.5 list its equations.

Fig. 5.8

Systems dynamics diagram for a TSCE model for MM caused by asbestos (Tan and Warren 2011)

Table 5.4 Listing of TSCE model formulas and parameter values for MM model in Fig. 5.8

Fig. 5.9

Systems dynamics diagram for an I-TSCE model

Table 5.5 Listing of TSCE model formulas and parameter values for LC model in Fig. 5.9

These two models are essentially conceptually different. In Fig. 5.8, internal doses (tissue burdens) of asbestos fibers act directly on the initiation and promotion rates, causing them to increase by amounts that increase with the internal doses. (The specific modeled dependences, taken from model T2 of Tan and Warren (2011), are as follows:

$$ \mathrm{Initiation}\ \mathrm{mutation}\ \mathrm{rate}:v={v}_0+{v}_1{d}^{v2}=2\mathrm{E}-7+0.007\ast d $$

$$ \mathrm{Promotion}\ \mathrm{rate}:y={y}_0+{y}_1{d}^{y2}=0.042+1\ast {d}^{0.097} $$

$$ \mathrm{Progression}\ \mathrm{rate}:\kern0.62em mu={v}_0 $$

where d is a measure of internal dose of fibers.) By contrast, in Fig. 5.9, exposure and internal dose determine the time at which chronic inflammation begins; it is then the chronic inflammation state, rather than the internal dose of fibers per se, that increases subsequent cancer risks. (Figure 5.9 follows the notation in Chap. 4, with v in Fig. 5.8 renamed as a1, y as g, and mu as a2 for the initiation, promotion, and progression rates, respectively.)

Which approach better describes observations? They make different testable predictions. The model in Fig. 5.8 implies that risk increases with increasing accumulation of fibers throughout an exposed individual’s life, but the model in Fig. 5.9 implies that, to the contrary, accumulation of fibers increases risk only by bringing about the onset of chronic inflammation, and becomes irrelevant thereafter. (Intermediate possibilities can be imagined, such as that continued fiber accumulation leads to more intense inflammation, but these two cases are the simplest and are empirically relevant, as discussed next.) Empirically, it appears that, once a sufficient quantity of asbestos (or similar carcinogens such as erionite) has been inhaled, it can cause MM decades later in a susceptible individual, even in the absence of further exposure (Carbone et al. 2012). Additional exposure does not appear to significantly increase future risk, or to reduce the latency period until MM develops (Carbone et al. 2012; Frost 2013). These observations favor the model in Fig. 5.9 over that in Fig. 5.8, so we use this “inflammation-mediated TSCE” (I-TSCE) model structure for MM as well as for LC, for which it was originally developed. To quantify an I-TSCE model for MM, we use the base (zero-dose) values from model T2 of Tan and Warren (2011), of a1 = a2 = 2E-7 for the initiation and progression rates (assuming 1E5 normal stem cells initially in the mesothelium) and g = 0.042 for the promotion rate if dose is zero. (For LC, the corresponding values are a1 = a2 = 1.4E-7 for the initiation and progression rates and g = 0.075 for the promotion rate.) Following onset of chronic inflammation, g increases relatively quickly; we approximate this as a step increase, of a size chosen to match the observation that sustained high exposure to asbestos starting from an early age can cause MM in up to 5% of individuals over a lifetime (e.g., by age 90) (Carbone et al. 2012). This corresponds to about a 3.5-fold increase in promotion rate g; this appears to be the main effect of asbestos exposure on carcinogenesis in TSCE models (Zeka et al. 2011, Table 5.2). Table 5.6 lists formulas and parameter values for the MM I-TSCE model. The two-stage clonal expansion (TSCE) modeling framework is undoubtedly only a relatively simple approximation to a more complex multistage clonal expansion (MSCE) process. However, it has provided useful empirical fits to several different data sets for asbestos-related cancer risks in past literature (e.g., Zeka et al. 2011; Tan and Warren 2011) and is adequate for the limited purposes of showing how inflammation-related changes in its transition rate parameters (Bogen 2019) can explain the main features of age-specific hazard rates for these data sets. Developing more realistic and detailed multistage clonal expansion models for asbestos-induced cancers appears to be a useful topic for future research. When such models become available, they can be used in place of the TSCE model in Table 5.4.

Table 5.6 Listing of I-TSCE model formulas and parameter values for MM model