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Mechanistic Pharmacokinetic Modelling of the Bioamplification of Persistent Lipophilic Organic Pollutants in Humans during Weight Loss Li Li, and Frank Wania Environ. Sci. Technol., Just Accepted Manuscript • Publication Date (Web): 24 Apr 2017 Downloaded from http://pubs.acs.org on April 24, 2017
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Mechanistic Pharmacokinetic Modelling of the Bioamplification of Persistent Lipophilic Organic
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Pollutants in Humans during Weight Loss
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Li Li* and Frank Wania
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Affiliations: Department of Physical and Environmental Sciences, University of Toronto Scarborough,
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1265 Military Trail, Toronto, Ontario, Canada, M1C 1A4
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Correspondence to: L. Li, Department of Physical and Environmental Sciences, University of Toronto
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Scarborough, 1265 Military Trail, Toronto, Ontario, Canada M1C 1A4. Telephone: (416) 287-5659. Fax:
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(416) 287-7279. E-mail:
[email protected].
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TOC Art
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Abstract
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Bioamplification means the liberation of persistent lipophilic organic pollutants (PLOPs) into blood
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from their storage in inert adipose tissue during rapid weight loss. Here, using a modified mechanistic
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pharmacokinetic model, we investigated how chemical properties and anthropometric parameters
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interact to influence the bioamplification of various PLOPs in humans. The model succeeds in
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reproducing literature documented weight loss-induced increments in human blood PLOP
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concentrations. We simulated the degree of bioamplification, as characterized by the bioamplification
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factor (BAmF), of hypothetical PLOPs with different combinations of partitioning and biotransformation
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properties at various rates of lipid loss. We also investigated how BAmF evolves with the duration of
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weight loss. Results show that bioamplification is expected to occur for any chemical with even
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moderate lipophilicity (logKOW>2 and logKOA>6) as long as the half-life for metabolic elimination is
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long relative to the time scale of relative lipid loss (e.g. exceeding 104 hours in the case of lipid loss of 3
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kg month-1 with an initial lipid mass of 40 kg). While BAmF of a chemical is time-variant, whether
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bioamplification occurs for a chemical or not is independent of the duration of weight loss. The
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successful application of such a simple model demonstrates that it is the lipid dynamics that
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predominantly govern the dynamics of PLOPs rather than vice versa.
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Introduction
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Humans are exposed to a variety of persistent lipophilic organic pollutants (PLOPs) of concern;
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prominent examples are polybrominated diphenyl ethers and polychlorinated biphenyls. Within the
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human body, PLOPs preferentially reside in adipose tissue such as subcutaneous and visceral fats1-3 and
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only a tiny fraction partitions into plasma/serum lipids (e.g., cholesterol, triglycerides, and phospholipids)
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and circulates throughout the body.1,
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toxicological effects in other organs and tissues such as reproductive organs and brain, and leads to slow
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elimination by limiting biotransformation by xenobiotic metabolizing enzymes and excretion via
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egestion.1, 5 However, such storage is not necessarily permanent – when an individual loses weight due
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to gastric surgery, exercise, a low-calorie-diet or disease progression, PLOPs stored in adipose tissue can
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be mobilized and released into the circulating fluids along with lipolysis.6 If the rate of mobilization
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exceeds the rate of elimination, the plasma/serum concentration of a lipophilic organic chemical is
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anticipated to amplify; this phenomenon, in particular when referring to animal studies, is called
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“bioamplification”.7 The essence of bioamplification is “solvent depletion”;7 namely, as adipose tissue
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(which can be viewed as solvent) is depleted, the chemical potential of PLOPs (as solutes) therein rises,
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creating a driving force for redistribution from adipose to other tissues.8
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Storage in adipose tissue prevents PLOPs from exerting
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A weight loss-induced increase in plasma/serum chemical concentration can be problematic as it has
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been linked with elevated adverse health outcomes such as endocrine disruption.9, 10 Bioamplification
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has even been hypothesized as one of plausible explanations for earlier epidemiological observations of
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elevated morbidity and mortality among post-weight-loss individuals.11, 12 Moreover, bioamplification
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during postpartum weight loss may elevate PLOP concentrations in breast milk, which could result in
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greater postnatal exposure of breastfed infants.13,
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cost-effective intervention to combat the global obesity epidemic,15 it is of tremendous interest to
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establish to what extent the negative consequences of bioamplification could counteract the health
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benefits of weight loss. The above reasons necessitate building a deeper understanding of the mechanism,
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influencing factors, and adverse outcomes of bioamplification.
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As weight loss is now recommended as a
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A number of lab and biomonitoring studies have documented bioamplification of PLOPs in both
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animals16-22 and humans.9, 10,
12, 23-28
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inconsistency. For example, Imbeault et al.10 observed statistically significant increases in human plasma
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concentrations for all compounds but β-hexachlorocyclohexane (HCH) during the same weight loss
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period. For the same compound, e.g., β-HCH, the increase can be significant in some studies24, 25 but not
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in others.9, 10 Lab and biomonitoring studies generally provide “snap-shots” of the dynamics of PLOPs at
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two specific temporal cross-sections before and after a weight loss event. As such, they provide only
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limited insight into pharmacokinetic processes occurring during a weight loss event, which hinders us to
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gain comprehensive understanding of how chemical and anthropometric factors interact in determining
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human bioamplification. To cope with this issue, process-oriented pharmacokinetic (PK) models
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incorporating parameters that account for chemical and anthropometric properties, can complement the
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experimental studies. However, while there indeed exist a few mechanistic PK modelling studies on the
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dynamics of PLOPs in response to periodical (or seasonal) change in body weight of animals like birds29,
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30
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model simulations”.7 Furthermore, bioamplification of PLOPs in humans has not yet been subject to PK
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modelling.
However, their findings are often plagued with variability and
and fish,31 few of them “were focused explicitly on interpreting bioamplification […] resulting from
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In this work, we use a one-compartment PK model to explore the factors that influence
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bioamplification of different chemicals in humans and thus may account for the observed variability.
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Specifically, we first evaluate the model performance by seeking to reproduce bioamplification
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observations reported in publications. With confidence in its predictive capability established, we
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investigate bioamplification using diverse combinations of lipid loss rates, chemical partitioning
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properties and biotransformation half-lives. Furthermore, we investigate how bioamplification changes
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with time during weight loss.
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Methods
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Model Equations 4
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The starting point of our PK model is the human module within the ACC-Human model32 (Equation
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1), which describes the dynamics of a chemical within the human body using fugacity notation:
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dm d (VH ⋅ Z H ⋅ f H ) = = EOH ∑ ( DuHi ⋅ f UHi ) + DreH f A dt dt i
− ( DmH + EOH DeH + DreH + DperH + DlH + DchH + DurH ) ⋅ f H
(Eq.1)
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m is the total amount of a chemical within the human body (in mol), which is the product of an
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“effective” body volume (VH in m3), a fugacity capacity (ZH in mol Pa-1.m-3) and a fugacity (fH in Pa); t is
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time (in h); DmH, DuHi, DeH, DreH, DperH, DlH, DchH and DurH are D-values (with units of mol Pa-1.h-1)
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representing chemical transfer via metabolism (or referred to as biotransformation), food uptake,
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egestion, respiration, percutaneous excretion, lactation, childbirth, and urinary excretion, respectively;
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EOH is the efficiency of gastrointestinal absorption of the chemical; and fUHi and fA are fugacity of the
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chemical in foods and air. These terms are calculated according to equations given in ref.32; they are
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gender-, age- and body-weight-dependent. To make the model geared toward bioamplification
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simulation, we make two simplifying assumptions:
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(I) Chemical uptake via diet and inhalation is negligible throughout the period of short-term weight
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loss, i.e.,
∑(D
uHi
i
⋅ f UHi ) = 0 and DreH f A = 0 . An individual losing weight often has a reduced
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intake of lipid-rich food12 which is the dominant route for non-occupational PLOP exposure in the
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general population.33 Meanwhile, a sensitivity analysis (Figure S1) indicates that omitting chemical
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uptake has a minor (less than a factor of 2) influence on calculation results, irrespective of chemical
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partitioning properties, when daily intake of a compound is below a certain level (e.g., 10-4
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mg-chemical kg-1-body-weight d-1 in the case of the absolute rate of lipid loss of 3 kg month-1).
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Such an intake level exceeds the realistic daily intakes of most PLOPs even for populations that are
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not dieting (e.g., ref.34, 35);
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(II) Only the fraction of chemical in blood is available for metabolism, which occurs in the liver alone:
ln 2 DmH = HLB′
⋅ Vblood ⋅ Z blood
(Eq. 2)
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whereby HLB′ (in h) is the total-blood-volume-adjusted biotransformation half-life (it is an
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“intrinsic” half-life36 and independent of weight change), Vblood the human blood volume which is
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height- and body-weight-related,37 and Zblood is the fugacity capacity of blood. In comparison with
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the original ACC-Human where DmH is related to the whole “effective” body volume (VH) and a
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whole body biotransformation half-life (HLB), this approach is more appropriate for
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bioamplification simulation because the smaller change in Vblood than VH during weight loss ensures
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a non-dramatic change in DmH, i.e., relatively stable hepatic clearance.
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Given f H =
m , the assumptions simplify equation 1 to: VH ⋅ Z H
dm m = − ( DmH + EOH DeH + DreH + DperH + DlH + DchH + DurH ) ⋅ dt VH ⋅ Z H
(Eq.3)
Thus, the lipid-normalized chemical concentration C (in molPLOP kg-1lipid) in the human body can be
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calculated by dividing the total chemical amount by the total lipid mass (Mlipid in kg) (Equation 4):
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dC d m = dt dt M lipid
D EOH DeH + DreH + DperH + DlH + DchH + DurH dM lipid + = − mH + ⋅C VH ⋅ Z H M lipid ⋅ dt VH ⋅ Z H
(Eq.4)
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Here, Mlipid includes both the lipids in plasma/serum and the whole body lipid pool (lipids in adipose
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tissue, liver, muscle, etc.). Since the lipid-normalized chemical concentration C is more often expressed
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on a mass basis (i.e., ngPLOP kg-1lipid), we do the same conversion throughout this paper.
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The model is coded using the Visual Basic for Applications (VBA) programming language.
Reproducing Observed Bioamplification Reported in the Literature
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In order to investigate whether Equation 4 is capable of reliably simulating realistic bioamplification
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situations, we sought to reproduce increments in lipid-normalized plasma/serum concentrations of
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PLOPs observed in study populations.9, 10, 12, 24-26 The observational data set comprises 91 measurements
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involving 20 compounds in 9 intentional weight loss events (see details in Supporting Information;
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Table S1). Here, event refers to the period between two subsequent measurements of a compound of
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interest. For example, multiple samplings after different durations (e.g., 3, 6 and 9 months after 6
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observation starts25) within the same observational cohort were classified as different events;
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simultaneous observations on male and female subgroups10 were treated as two events.
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The collected observational data are on the population level (see Supporting Information; Table S1)
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and do not contain information on the inter-individual variations in anthropometric parameters and
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chemical concentrations. Here, we used a Monte Carlo simulation to construct an individual-specific
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dataset with inter-individual random variations in the reported (i) gender, (ii) age, (iii) body weight (both
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before and post the event), and (iv) the initial lipid-normalized blood concentration of target compounds
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at the beginning of the event, as information on their variations is available in almost all 91
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measurements. Combination of variations in the four variables leads to variations in all terms on the
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right hand of Eq. 4 because the latter are gender-, age- and body-weight-dependent. For each weight loss
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event, we ran 1000 Monte Carlo iterations, each of which represents a hypothetical individual. For a
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given hypothetical individual, we randomly assigned its gender according to the published fraction of
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male subjects (male %; see Supporting Information; Table S1) in the observation population, and
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sampled its age, body weight and lipid-normalized chemical concentrations based on the respective
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population-level statistics given in the literature. Given that the population-level statistics are presented
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in different forms in the literature, we assumed that a variable was either normally distributed if mean
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and standard deviation were reported, or triangularly distributed if median (or mean) and range (or
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percentile interval) were reported. Furthermore, we made the following pharmacokinetics-related
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assumptions:
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(I) Lipid-normalized PLOP concentrations in plasma/serum are the same as in adipose tissue. This
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assumption is reasonable for PLOPs because the lipid content is the predominant determinant
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controlling the partitioning of a lipophilic compound between different tissues,38,
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residence time within the human body is sufficiently long for a persistent compound to reach
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equilibrium between the lipids in different tissues. Previous biomonitoring studies show
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mean/median lipid-normalized PLOP concentrations in the two matrices to be within a factor of
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4,40-42 which is much smaller than the variability range of the lipid-normalized PLOP concentrations
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themselves. Meanwhile, we do not discriminate between different types of adipose tissues although
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we recognize that weight loss can affect PLOPs behavior differently in subcutaneous and visceral
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fats;12
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(II) Given that either plasma or serum measurements are available in the literature, we do not
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discriminate whether a concentration refers to that in plasma or serum. This assumption, which has
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also been adopted in other PK modeling studies such as Verner et al.,43 is justifiable because earlier
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analytical studies have demonstrated the equivalence of the two concentrations for various PLOPs;44,
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45
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(III) Since the total lipid mass Mlipid before and after weight loss is not available in most measurements,
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we calculate Mlipid from the total body fat mass Mfat by assuming that lipids constitute 83% of total
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body fat.46 Unless reported in the literature, Mfat is calculated as the product of body weight and
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body fat percentage (BF%). The BF% is further calculated using an empirical regression47 that
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correlates BF% with the body mass index (BMI, defined as body weight divided by squared height
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in kg m-2), age, and sex. Height is age-related (built-in in ACC-Human) and is assumed to be
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constant during weight loss;
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(IV) During the weight loss, an individual’s body weight changes linearly.
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At each Monte Carlo iteration, we simulated the increment in lipid-normalized PLOP concentration
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(∆Cmodelled) in response to weight loss. The modelled results of the 1000 hypothetical obese individuals
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were then statistically summarized and compared with the published observed increments.
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For PLOPs used for the model evaluation, partitioning coefficients at 25 °C were taken from the
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literature48-51 or calculated using the EPI SuiteTM software. Internal energies (∆UOA, ∆UAW, ∆UOW) for
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adjusting the cited partitioning coefficients to normal body temperature (37 °C) were calculated based
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on the method in ref.52 Derivation of HL′ from HLB is detailed in Text S1 of Supporting Information. B
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The HLB estimates of PLOPs other than β-HCH were derived using the quantitative structure-activity
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relationship (QSAR) in ref.53 The HLB estimate of β-HCH was calculated from the observed total
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elimination half-life (HLT)54 using the “1-CoPK model” method in ref.,53 because the QSAR fails to 8
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provide isomer-specific estimates to discriminate isomers with slow (β-HCH, HLT=7.2 – 7.6 yrs54) and
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fast (γ-HCH, HLT=26 h55) elimination.
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Investigating Factors Influencing Bioamplification
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The “bioamplification factor (BAmF)” is defined as the ratio of lipid-normalized chemical concentrations after (Cafter) and before (Cbefore) weight loss (Equation 5):7
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BAmF = Cafter / Cbefore,
(Eq. 5)
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We used the model to calculate BAmF for hypothetical chemicals with octanol-air partitioning
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coefficients log KOA ranging from 0 to 12 and octanol-water partitioning coefficients log KOW from 0
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and 12. Internal energies of phase transfer of these hypothetical chemicals were again calculated using
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the
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total-blood-volume-adjusted biotransformation half-life HLB′ ranging from 1 h to infinite, and (ii)
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absolute rate of lipid loss of either 1.5 kg month-1 (representing the range of 0.5 – 1 lb week-1 weight
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loss recommended for overweight patients15), 3 kg month-1 (representing the range of 1 – 2 lb week-1
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recommended for obese patients15), or 6 kg month-1 (representing the range of 110 – 220 lb over a period
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of 6 to 12 months recommended for severely obese patients who receive bariatric surgery15). All other
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parameters were the same as in our above efforts reproducing literature reported increments. BAmF
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values after n months of weight loss (BAmFn) are displayed in a chemical partitioning space defined by
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log KOA and log KOW.
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Results and discussion
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Capability of the model to reproduce literature-reported bioamplification
empirical
relationships
in
ref.52
We
tested
different
combinations
of
(i)
the
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Figure 1 plots the modelled increments in lipid-normalized PLOP concentration (∆Cmodelled) against
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the increments derived from measured data reported in the literature.9, 10, 12, 24-26 Compound-specific
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modelled and measured increments are also presented in numeric form in Table S1 in Supporting
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Information. The modelled mean/median increments are significantly correlated with measurements (r =
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0.80, p < 0.05). The root-mean-square deviation (RMSD) between logarithmical measured and modelled
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pairs, i.e.,
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RMSD =
1 n 2 ( log ∆Cmeasured − log ∆Cmodelled ) ∑ n i =1
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is calculated to be 0.31 (6 pairs with non-positive measured increments are excluded because the real
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logarithm is undefined for non-positive real numbers, see Table S1 in Supporting Information). That
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RMSD is less than 1 means simulations and measurements are generally within an order of magnitude,
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i.e., much smaller than the variability associated with the measured data (denoted as the error bars).
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Recent studies highlighted the complex interactions between the dynamics of PLOPs and lipids
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during weight loss. For instance, a negative feedback loop has been suggested, whereby a weight
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loss-induced increase in PLOP concentrations may trigger weight gain, or at least decelerate weight loss,
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due to the “obesogenic” effect.56, 57 Meanwhile, the induced expression and activation of xenobiotic
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metabolizing enzymes (e.g., cytochrome P450)27 is believed to enhance the hepatic biotransformation,58
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which would constitute a positive feedback loop. That our simple one-compartment PK model
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performed well in explaining the observations, despite ignoring all of these feedbacks, strongly suggests
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that it is the lipid dynamics that predominantly govern the dynamics of PLOPs rather than vice versa.
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Since epidemiological studies are often plagued with misinterpretations or misclassifications when
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involving multiple complicated and variable loops,59 such a simple model helps to recognize the essence
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of bioamplification, which could be particularly useful for future investigations on the adverse health
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outcome of PLOP bioamplification.
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Influences of chemical properties and lipid loss rate on bioamplification
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Figure 2 displays the calculated BAmF3, i.e., the BAmF at the end of a 3-month weight loss
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treatment, as a function of partition properties under different scenarios of biotransformation half-lives
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(horizontal panels in Figure 2) and absolute rates of lipid loss (vertical panels in Figure 2). In order to
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discuss and understand the results displayed in these plots, it is helpful to introduce a number of
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additional parameters. Specifically, we can define: 10
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(i) a metabolic elimination rate kelim,metab = DmH / (VHZH), and the corresponding metabolic elimination half time HLelim,metab = ln2 / kelim,metab; (ii) a non-metabolic elimination rate kelim, non-metab =
EOH DeH + DreH + DperH + DlH +DchH + DurH VH ⋅ Z H
, and the
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corresponding non-metabolic elimination half time: HLelim,non-metab = ln2 / kelim,non-metab. Here, kelim, non-metab
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is a function of the chemical partitioning properties log KOA and log KOW (see Supporting Information;
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Figure S2).
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(iii) a rate describing the mobilization of PLOPs due to lipolysis, which corresponds to the relative
dM lipid
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rate of lipid loss: kmobil = −
234
mobilization: DLelim,non-metab = ln2/ kmobil.
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M lipid ⋅ dt
, and the doubling time of blood chemical concentration due to
Note that while kelim,metab, kelim,non-metab and kmobil are labeled “rate constants”, they are time variant as lipid is lost (as discussed later). Substituting these rate constants into Equation 4, we get:
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dC = ( kmobil − kelim,metab − kelim,non-metab ) ⋅ C dt
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Equation 6 echoes the earlier understanding7 that the change of lipid-normalized chemical
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concentration depends on two competing processes: the “source”, i.e., the mobilization of PLOPs from
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adipose tissues into the bloodstream (i.e., kmobil) and the “sink”, i.e., the elimination of PLOPs from
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blood (i.e., kelim = kelim, metab + kelim, non-metab). Mathematically, bioamplification will occur (BAmF > 1)
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when kmobil – kelim > 0, or DLmobil < HLelim, which provides a quantitative basis for the statement by Daley
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et al.21 that “[b]ioamplification can be defined as the special case where the partition capacity (or
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fugacity capacity) of an animal’s tissues decreases faster than chemical can be eliminated.”
(Eq.6)
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Under all scenarios displayed in Figure 2, more lipophilic chemicals (i.e., with larger log KOW and
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log KOA, in the upper right corner) are prone to possess higher BAmF3 values (Figure 2). Specifically,
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bioamplification occurs (i.e. BAmF3 > 1) (Figure 2b,c,d,f,g,h,k,j,l), for compounds with log KOW > 2 and
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log KOA > 6, which coincides with the part of the partitioning space in which non-metabolic elimination
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is inefficient (HLelim, non-metab >104 h; see Supporting Information; Figure S2). This finding agrees well 11
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with a conclusion drawn from animal studies that “for terrestrial food webs, chemicals that possess a log
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KOW > 2 and a log KOA > 6 should be regarded as having a high bioamplification potential”.7 Soluble
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chemicals with a log KOW 2 and log KOA > 6 varies a lot among scenarios, in the remaining part of the partitioning space
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BAmF3 remains almost the same under all scenarios.
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At the contour lines indicating BAmF3 =1 mobilization and elimination processes are in balance and
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no change in contaminant concentration occurs. Mobilization prevails in the region BAmF3 >1 (upper
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right in Figure 2) while elimination prevails in the region BAmF3 5 and
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log KOA > 6) are almost constant (Figure 2), because their non-metabolic elimination half times (HLelim,
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non-metab
=104 – 106 h) far exceed mobilization doubling times (DLmobil = 103.5 – 104 h, assuming that an
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individual with an initial total lipid mass of 40 kg loses 1.5 – 6 kg lipid per month) and thus the
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mobilization process is the dominant determinant for bioamplification. The finding that PLOPs share
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similar BAmF values is also borne out in observations in human monitoring studies.10, 24 For instance,
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Chevrier et al.24 observed similar percent increments between 10% and 20% in plasma concentrations of
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14 of 17 detected chemicals after weight loss in a 39-individual population. This is also true for animal
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studies. For example, the depletion of yolk lipids during hatching was observed to amplify PLOP
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concentrations in hatched Chinook salmon larvae, with the BAmF between fresh eggs and larvae
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increasing when log KOW exceeded 5.5 “until it reached an asymptote at log KOW values exceeding 7”.20
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Raising the absolute rate of weight loss (moving from top to bottom in Figure 2) increases the
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BAmF3 value for all chemicals in the partitioning space because of elevated mobilization. This
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simulation explains an earlier finding that for most compounds the increment in plasma chemical
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concentration is significantly positively correlated with the reduction in body weight.12, 24 The increment
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is more profound for the most lipophilic PLOPs (upper right corner in Figure 2) because of inefficient
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non-metabolic elimination (see Supporting Information; Figure S2). As the BAmF3 increases, the
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contour line of BAmF3 =1 slightly moves towards the bottom left, which means that the faster lipid is
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lost the more chemicals will exhibit bioamplification.
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As expected, increasing resistance to metabolic elimination (moving from left to right in Figure 2)
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increases BAmF3 for all chemical partitioning property combinations. The increase in BAmF3 is most
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prominent for the highly lipophilic chemicals in the upper right of the partitioning space. As indicated by
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the prevalence of green and yellow shadings in Figures 2a, 2e and 2i, readily degradable chemicals with
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a HLB′ < 10 hours (equivalent to an HLelim,metab of 2 and log KOA > 6) are quite different depending on whether HLB′ is 1 or 10 hours (equivalent to
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an HLelim,metab of 103 or 104 hours) (Figures 2a, b, e, f, i, and j), but are fairly similar for HLB′ of 100
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hours (equivalent to an HLelim,metab of 105 hours) or infinite (Figures 2c, d, g, h, k, and l), which suggests
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that the BAmF3 of PLOPs is no longer sensitive to HLB′ if HLB′ is sufficiently long. Here is the
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explanation: Given that their HLelim,non-metab values are around 104 – 106 hours (see Supporting
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Information; Figure S1), most PLOPs cannot be efficiently eliminated from humans via non-metabolic
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elimination; thus, biotransformation dominates total elimination if HLelim,metab is shorter than 104 hours,
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hence rendering the BAmF3 of the lipophilic chemicals highly sensitive to the HLelim,metab. This
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conclusion implies that an accurate HLB′ value is crucial for quantifying bioamplification for
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non-persistent compounds.
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Temporal evolution of the bioamplification factor
300
The BAmF changes with time because both mobilization and elimination are dynamic as weight loss
301
proceeds (Figure 3). As indicated by Eqs 4 and 6, on the one hand, while we assume the absolute rate of
302
lipid loss
dM lipid
dt
to be constant over the period of weight loss, the relative rate
dM lipid
M lipid ⋅ dt
keeps
303
increasing as Mlipid decreases, which means that mobilization (kmobil) accelerates. On the other hand, as
304
lipid is lost, the total effective volume (VH) and the Z-value (ZH) of an individual decrease, which
305
accelerates both metabolic and non-metabolic elimination (kelim). Accelerated elimination in leaner
306
individuals is supported by earlier observations, e.g., the decreasing yearly “decay rate” of
307
polychlorinated dibenzo-p-dioxins and dibenzofurans against increasing BF% in an occupationally
308
exposed population (N = 48).60
309
The deduction in Text S2 in Supporting Information indicates that both the mobilization (kmobil) and
310
elimination (kelim) rates are roughly proportional to the reciprocal total lipid mass (Mlipid), thus the loss of
311
a given amount of lipid will increase the absolute values of both rates by the same factor. Hence, if the
312
absolute values of the two rates are not equal, the one with a larger initial absolute value will increase
313
more; the accumulation of larger increments further enlarges the difference between the two rates. As
314
such, we can predict that: (i) if a compound falls into the elimination-dominated part of the partitioning
315
space and has a BAmF below 1 at the start of lipid loss, the BAmF will keep decreasing throughout the
316
entire weight loss period, i.e., BAmF1 > BAmF3 > BAmF6 (Figure 3a); (ii) if a compound falls into the
317
mobilization-dominated part of the partitioning space and has BAmF above 1 at the start of lipid loss, the
318
BAmF will keep increasing throughout the entire weight loss period, i.e., BAmF1 < BAmF3 < BAmF6
319
(Figure 3c); and (iii) the BAmF will remain almost unchanged if its initial value is close to 1 (Figure 3b).
320
This implies that, while the value of the BAmF is time-variant, whether a chemical is able to bio-amplify
321
in humans or not is independent of the length of weight loss. If bioamplification does occur, the longer
322
the weight loss duration the larger the observed BAmF.
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323
From Equation 6, it is clear that the derivative of the BAmF curve, i.e., the change in BAmF per unit
324
of time (∆BAmF/∆t), relies not only on the relative importance of the two rates kmobil and kelim, but also
325
on the time-dependent lipid-normalized chemical concentration C. When elimination dominates (Figure
326
3a), the concentration declines with time, which in turn decelerates the decline in BAmF and BAmF
327
asymptotically approaches 0 (a negative-feedback-loop-like correlation); in contrast, when mobilization
328
dominates (Figure 3c), the concentration keeps increasing as lipid is lost, which further accelerates the
329
increase in BAmF (a positive-feedback-loop-like correlation). Therefore, the time-dependent BAmF
330
curves in both cases are concave and have increasing derivatives.
331
Implications for future studies
332
The success of a modified and well-parameterized one-compartment PK model to simulate
333
bioamplification of PLOPs in humans has profound implications for future studies. For example, it can
334
serve as a simple and fast predictive tool for batch screening chemicals for their bioamplification
335
potential. For specific compounds (e.g., 2,3,7,8-tetrachlorodibenzo-p-dioxin) more sophisticated PK
336
models with additional physiological details (e.g., induction of a hepatic binding protein, and diffusion
337
limitation for movement of chemical between blood and tissue) will be required.58
338
Second, while we focused here on intentional weight loss, the model can be applied to investigate
339
the dynamics of PLOPs in the human body during unintentional, in particular illness-related, weight loss,
340
as well as its association with obesity-related disease. Such a simulation could help to avoid potential
341
confounders or reverse causation in developing exposure-outcome association in epidemiological
342
studies.61 For instance, future modelling studies may clarify whether high concentrations of PLOPs
343
observed in diagnosed diabetics are really epidemiological evidence of the endocrine disruptive effects
344
of the PLOPs, or just due to rapid bioamplification during the pathological weight reduction in the
345
pre-diagnostic phase of pre-existing illness.62
346
Finally, while we deemed ongoing dietary or respiratory exposure negligible during the short-term
347
simulations presented here, it could be included in long-term studies so as to assess its contribution to
348
the chemical burden in human. Such a simulation could help to elucidate the “apparent” 15
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bioamplification of non-persistent chemicals (e.g., bisphenol A, triclosan and phthalates) due to ongoing
350
exposure,63, 64 and to explore differences in “cross-sectional body burden versus BMI trends” of diverse
351
PLOPs due to their distinct emission histories and cumulative external exposures.59, 65
352
Acknowledgement
353
We thank Dr. Jon A. Arnot for QSAR calculation of whole-body biotransformation half-lives in humans.
354
Funding was provided by the Natural Sciences and Engineering Research Council of Canada.
355
Supporting information
356
The Supporting Information is available free of charge on the ACS Publications website at DOI:…
357
Text describing deduction of the total-blood-volume-adjusted biotransformation half-life, and the
358
approximate dependence on total lipid mass of mobilization and elimination rates; tables listing
359
literature-reported bioamplification measurements; and figures depicting results of sensitivity analysis,
360
and the chemical space of non-metabolic elimination half-life.
361
References
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Figure Legends
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Figure 1 Comparison between measured and modelled increments in blood concentrations of PLOPs.
545
Dots represent means (if means were reported in the cited literature) or medians (if medians were
546
reported in the cited literature) of the increments, and error bars represent semi-interquartile range
547
(intervals between the 75th and 25th percentiles) of the increments (reported in the cited literature
548
or converted from the data in the literature). Dashed diagonal lines denote agreement between
549
measurements and model within a factor of 10. Results for mirex9,24 cannot be displayed because
550
their measured increments are negligible.
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Figure 2 The bioamplification factor (BAmF) of hypothetical chemicals as a function of partitioning
554
coefficients (log KOW and log KOA), absolute rate of lipid loss (in kg month-1), and
555
total-blood-volume-adjusted biotransformation half-life (in h).
556
557
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Figure 3 Time courses of bioamplification factor (BAmF), elimination (kelim = kelim, metab + kelim, non-metab)
559
and mobilization (kmobil) rates of hypothetical chemicals (a) falling in the elimination-dominated
560
partitioning space (log KOW = log KOA = 4.45), (b) with equal elimination and mobilization rates
561
(log KOW = log KOA = 5.45), and (c) falling in the mobilization-dominated partitioning space (log
562
KOW = log KOA = 6.45). An initial total lipid mass of Mlipid = 40 kg and a lipid loss rate of 3 kg
563
month-1 was applied.
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