1. Model Overview
   This computational framework is a multi-compartmental, perfusion-based Physiologically Based Pharmacokinetic (PBPK) model designed to simulate the Absorption, Distribution, Metabolism, and Excretion (ADME) of eleven distinct Per- and Polyfluoroalkyl Substances (PFAS).

The model integrates human-specific physiological parameters with chemical-specific physicochemical and biochemical properties to predict the time-course of PFAS concentrations in systemic circulation and target tissues. It is particularly optimized to capture the complex renal handling and enterohepatic recirculation characteristic of the PFAS class.

1. Physiological Architecture
   The virtual human organism is represented by a series of anatomically and physiologically distinct compartments, interconnected by the systemic blood circulation.

Tissue Compartments: The model explicitly simulates 14 tissue compartments: Plasma, Rest of Body, Adipose, Brain, Gonads, Heart, Lung, Muscle, Skin, Spleen, Pancreas, GI Tract, Liver, and a highly detailed Kidney sub-compartment.

Physiological Parameters: Tissue volumes and regional blood flows (as fractions of cardiac output) are parameterized using established literature (e.g., Brown 1997, ICRP 2002, Davies 1993). Allometric Scaling: Physiological flow rates, Glomerular Filtration Rate (GFR), and transporter maximum velocities $V_{max}$ are scaled allometrically based on body weight $'BW^{0.75}'$ and $BW^{-0.25}$, allowing for inter-individual scaling. Hematocrit and Free Fraction: Tissue:blood partition coefficients are adjusted for hematocrit to reflect plasma partitioning. Furthermore, distribution and clearance processes are strictly driven by the unbound (free) fraction of the chemical in plasma, reflecting the assumption that only free PFAS can cross biological membranes or be filtered. 3. Chemical-Specific Parameterization The model currently supports 11 PFAS, including long-chain (e.g., PFOA, PFOS, PFNA, PFDA, PFHxS), short-chain (e.g., PFHpA, PFBA, PFHxA, PFBS), and emerging alternatives (e.g., DONA, HFPO-DA/GenX).

Each chemical is parameterized with specific:

Molecular weights (MW).

Plasma free fractions $f_u$. Tissue:plasma partition coefficients $PC$ across all 10 solid tissues. In vitro transporter kinetics $V_{max}$ and $K_m$ for renal uptake and efflux. 4. Mechanistic ADME Processes 4.1. Absorption Oral exposure is simulated via the Gastrointestinal (GI) tract compartment. The model incorporates first-order absorption kinetics $k_{abs}$ from the GI lumen into the systemic circulation via the hepatic portal vein. Unabsorbed chemical is transitarily passed to the feces compartment $k_{unabs}$.

4.2. Distribution

Distribution to peripheral tissues is modeled as perfusion-limited. Assuming equilibrium between plasma and tissue, the tissue concentration is governed by regional blood flow and the tissue:plasma partition coefficient. The pancreas partition coefficient is estimated as the arithmetic mean of the GI tract and spleen.

4.3. Hepatic Clearance and Enterohepatic Recirculation

The liver compartment receives blood from both the hepatic artery and the portal vein (from the GI tract and spleen). PFAS is cleared from the liver into the bile via a first-order biliary excretion rate $k_{bile}$. The biliary compartment empties directly into the feces pseudo-compartment, implicitly modeling enterohepatic recirculation, a critical pathway for the prolonged retention of certain PFAS.

4.4. Renal Clearance (Mechanistic Kidney Model)

Unlike standard PBPK models that use a simple first-order clearance rate for the kidney, this model features a mechanistic, sub-organ kidney model to accurately capture the unique renal retention of PFAS. The kidney is divided into Kidney Blood, Proximal Tubule Cells (PTC), and Filtrate.

Glomerular Filtration: Only the free (unbound) fraction in plasma is filtered into the filtrate compartment based on the GFR.

Basolateral Uptake: Chemical in the kidney blood is actively taken up into the PTC via basolateral transporters (e.g., OATs). This is modeled using Michaelis-Menten kinetics, scaled by the basolateral Relative Activity Factor (RAF), PTC cellularity, and protein content. Apical Efflux/Reabsorption: Chemical within the PTC can be transported back into the blood (reabsorption) or secreted into the filtrate via apical transporters. This is also modeled via Michaelis-Menten kinetics using apical $V_{max}$, $K_m$, and RAF. Urinary Excretion: Chemical remaining in the filtrate is excreted into the urine via a first-order rate constant. Note: This mechanistic representation of basolateral uptake and apical reabsorption is critical for accurately simulating the extremely long biological half-lives and chain-length-dependent renal clearance observed in PFAS toxicokinetics.

1. Exposure Scenarios
   The model supports multiple exposure routes to accommodate various toxicological study designs:

Oral Bolus: Discrete dosing administered directly into the GI lumen in units ug.

Continuous Oral Exposure: A zero-order input rate into the GI lumen, simulating continuous environmental or dietary exposure (e.g., contaminated drinking water) in unit ng/kg BW/timescale. 6. Model Outputs and Mass Balance The ODE solver generates time-course data for:

Concentrations: Total and free concentrations in plasma, and total concentrations in all peripheral tissues (reported in mass/volume tissue).

Amounts: Absolute mass of the chemical in every compartment, including cumulative excretory masses (urine and feces). Mass Balance Verification: The model continuously calculates the total mass in the system (tissues + excreta) to ensure strict mass balance closure, verifying that no mass is lost or artificially created during numerical integration.