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Rainbow trout PFAS PBK
Rainbow Trout PFAS Physiologically Based Kinetic (PBK) Model
Overview
This model simulates the uptake, distribution, and elimination of per- and polyfluoroalkyl substances (PFAS) in rainbow trout (Oncorhynchus mykiss) following dietary exposure. It is a Physiologically Based Kinetic (PBK) model, meaning it describes how a chemical moves through the body based on realistic anatomical and physiological information — blood flows, organ sizes, and tissue-specific chemical affinity — rather than purely statistical relationships.
The model can simulate five PFAS compounds: PFOS, PFOA, PFBS, PFHxS, and PFNA.
Model Structure and Compartments
The model represents the fish body as a network of interconnected compartments, each corresponding to a tissue or physiological space. Chemical mass is tracked in each compartment over time and moves between them via blood circulation, bile flow, urinary excretion, and dietary absorption.
Tissue Compartments
| Compartment | Description |
|---|---|
| Arterial blood | Oxygenated blood delivering PFAS to tissues |
| Venous blood | Blood returning from tissues to the gills |
| Gills | Primary site of blood oxygenation; PFAS exchange with circulation |
| Liver | Central metabolic organ; receives blood from both arterial supply and viscera; source of bile secretion |
| Viscera | Abdominal organs (gut wall, mesentery); primary site of dietary absorption |
| Gut lumen (absorbable fraction) | Ingested PFAS available for absorption into the viscera |
| Gut lumen (bile fraction) | Bile-derived PFAS returned to the gut; only eliminated via feces |
| Kidney | Filters PFAS from blood; handles urinary excretion and reabsorption |
| Urine storage | Urinary bladder; temporary storage before voiding |
| Muscle | The largest tissue by mass; slow distribution kinetics |
| Skin | Peripheral tissue with direct routing of venous blood to kidney |
| Carcass | Remaining body mass (bone, connective tissue, etc.) |
Elimination Routes
- Urine: PFAS filtered at the kidney, partially reabsorbed, and excreted via the urinary bladder.
- Feces: Unabsorbed dietary PFAS and bile-derived PFAS eliminated through the gut.
- Enterohepatic circulation: A fraction of PFAS secreted into bile is reabsorbed from the gut back into the viscera, prolonging tissue retention.
Physiological Basis
Organ volumes and blood flow fractions are taken from Vidal et al. (2019), measured in rainbow trout. Cardiac output scales with body weight and is corrected for water temperature using an Arrhenius function, with reference values from Barron et al. (1987) at 6, 12, and 18 °C. Chemical-specific parameters (protein binding, urinary clearance, intestinal absorption fractions) are sourced from Sun et al. (2022), Cao et al. (2022), and Goeritz et al. (2013).
Training Data and Parameter Estimation
The model was calibrated against experimental data from Falk et al. (2015), who exposed rainbow trout to PFAS-contaminated food under controlled laboratory conditions. The experimental design consisted of:
- 28-day dietary uptake phase: fish fed food spiked with 500 µg PFAS/kg at 2.6% of body weight per day.
- 28-day depuration phase: fish returned to clean food.
- Tissue samples collected at days 7, 14, 28, 31, 35, 42, and 56.
- Tissues measured: liver, blood, skin, muscle, gills, kidney, and carcass.
- Five substances tested in parallel: PFOS, PFOA, PFBS, PFHxS, PFNA.
Fitted Parameters
Parameter estimation was performed using the Subplex (NLOPT_LN_SBPLX) derivative-free optimization algorithm. The objective function was the PBK Objective Function (PBKOF), which measures the geometric mean fold-error between model predictions and observations across all tissues and time points. A score of 1.0 is a perfect fit; values between 0.5 and 2.0 are generally considered acceptable.
The final PBKOF score across all five substances was 0.625, indicating good agreement between model predictions and experimental observations.
Three parameters were estimated as common across all five PFAS (reflecting shared physiological processes):
| Parameter | Description | Fitted Value |
|---|---|---|
| Ku | Intestinal absorption rate constant (1/h) | 1.467 |
| CLU_coef | Urinary clearance scaling coefficient | 5.72 × 10⁻⁴ |
| Cl_feces | Fecal elimination rate constant (1/h) | 1.306 |
Seven tissue-to-blood partition coefficients were estimated separately for each substance, reflecting the different affinity of each PFAS for each tissue:
| Tissue | PFOS | PFOA | PFBS | PFHxS | PFNA |
|---|---|---|---|---|---|
| Liver | 1.569 | 2.004 | 1.741 | 1.698 | 0.803 |
| Muscle | 0.113 | 0.037 | 0.139 | 0.043 | 0.065 |
| Kidney | 0.440 | 0.851 | 0.763 | 0.361 | 0.246 |
| Skin | 0.272 | 0.319 | 0.224 | 0.293 | 0.234 |
| Gills | 0.229 | 0.343 | 0.277 | 0.154 | 0.220 |
| Carcass | 0.107 | 0.180 | 0.116 | 0.041 | 0.114 |
| Viscera | 3.699 | 0.564 | ~0 | ~0 | 1.275 |
How to Use the Model
The model requires a small set of inputs that describe the fish and the exposure scenario. No programming knowledge is needed.
Selecting the Substance
Choose which PFAS compound to simulate: PFOS, PFOA, PFBS, PFHxS, or PFNA. Each compound has its own chemical properties and fitted partition coefficients, so only one substance is simulated per run.
Fish Body Weight
Provide the body weight of the fish in grams. The model was calibrated on fish weighing between 314 g and 808 g, which represents the validated range. If a weight outside this range is entered, the model will automatically use the nearest boundary value to ensure predictions remain within the calibrated domain.
Defining the Exposure Scenario
The exposure is described by two paired lists:
- Dose (
admin.dose): the amount of PFAS ingested at each feeding event, in micrograms (µg). - Time (
admin.time): the time of each feeding event, in hours from the start of the simulation.
This flexible format allows you to simulate a wide range of exposure scenarios. For example:
- Single acute dose: one entry in each list representing a single exposure event.
- Repeated daily feeding: 28 entries with doses spaced 24 hours apart, mimicking a dietary uptake experiment.
- Variable intake: different dose values at each time point to reflect changing food contamination levels or feeding rates over time.
The two lists must always have the same number of entries.
Simulation Time Window
Set the start time, end time, and output time step (all in hours) to define how long the simulation runs and how finely the results are reported.
Model Outputs
The model returns time-series predictions of PFAS concentration (µg/g tissue) in all compartments, as well as the total mass of PFAS in each compartment (µg). These can be used to estimate tissue residues at any time point during or after exposure.
References
- Falk, S. et al. (2015). Bioconcentration of perfluoroalkyl acids in rainbow trout. Environmental Toxicology and Chemistry.
- Vidal, A. et al. (2019). Physiologically based toxicokinetic modelling of PFAS in rainbow trout. Science of the Total Environment.
- Barron, M.G. et al. (1987). Cardiovascular parameters in rainbow trout. Journal of Fish Biology.
- Sun, M. et al. (2022). Urinary and fecal elimination of PFAS in fish. Environmental Science & Technology.
- Cao, X. et al. (2022). Enterohepatic circulation of PFAS in fish. Environmental Health Perspectives.
- Goeritz, I. et al. (2013). Intestinal absorption fractions of PFAS. Archives of Toxicology.
- Grosell, M. et al. (2000). Biliary secretion in teleost fish. Journal of Experimental Biology.
- Nichols, J.W. et al. (1996). Physiological model for gill uptake of organic chemicals in fish. Environmental Toxicology and Chemistry.