IndusChemFate: A Cross-Chemical Physiologically Based Kinetic Model

Introduction

IndusChemFate is a Physiologically Based Kinetic (PBK) model, also known as a Physiologically Based ToxicoKinetic (PBTK) model, designed to estimate blood and urine concentrations of multiple chemicals and their metabolites given specific exposure scenarios. This implementation is a translation of the original Visual Basic code into R, preserving all the functionality of the original model while making it accessible as a web service through Jaqpot.

Original Model Credits

Full credit for the original IndusChemFate model goes to Frans Jongeneelen and Wil ten Berge. The model was developed as a software application in MS-Excel with Visual Basic code under contract LRI-HBM2.2-ITC-0172 for CEFIC-LRI. The original model and its scientific validation are published in the following references:

Reference 1:

Frans J. Jongeneelen; Wil F. Ten Berge. A Generic, Cross-Chemical Predictive PBTK Model with Multiple Entry Routes Running as Application in MS Excel; Design of the Model and Comparison of Predictions with Experimental Results. Annals of Occupational Hygiene 2011 55: 841-864.

Reference 2:

Frans J. Jongeneelen; Wil F. Ten Berge. Simulation of urinary excretion of 1-hydroxypyrene in various scenarios of exposure to PAH with a generic, cross-chemical predictive PBTK-model. International Archives of Occupational and Environmental Health 2011.

Example

A csv file is provided at the following Github Repo in the folder named Jaqpot_examples, as example on how to provide the input of the model.

Model Structure

The model contains 11 body compartments: Adipose tissue, Bone, Brain, Heart, Kidney, Intestine, Liver, Lung, Muscle, Skin, and Bone marrow. Blood is modeled as arterial and venous compartments. The model estimates chemical concentrations in each tissue, as well as in blood and excretory products.

Available Physiological Scenarios

IndusChemFate supports multiple physiological scenarios, which allows for simulations in different human subjects and experimental animals:

1. Normal man (in rest) - 70 kg male at rest
2. Obese man (in rest) - 80 kg male with increased adipose tissue at rest
3. Normal man (light work) - 70 kg male with increased cardiac output and ventilation
4. Obese man (light work) - 80 kg male with increased cardiac output and ventilation
5. Normal woman (in rest) - 60 kg female at rest
6. Obese woman (in rest) - 70 kg female with increased adipose tissue at rest
7. Normal woman (light work) - 60 kg female with increased cardiac output and ventilation
8. Obese woman (light work) - 70 kg female with increased cardiac output and ventilation
9. Normal child (in rest) - 16 kg child at rest
10. Obese child (in rest) - 20 kg child with increased adipose tissue at rest
11. Normal child (playing) - 16 kg child with increased cardiac output and ventilation
12. Obese child (playing) - 20 kg child with increased cardiac output and ventilation
13. Mouse (experimental study) - Standard 0.03 kg mouse model
14. Rat (experimental study) - Standard 0.3 kg rat model

Each scenario comes with its own set of physiological parameters, including body weight, tissue volumes, blood flows, cardiac output, and alveolar ventilation rates.

Exposure Routes

The model considers three main exposure routes:

1. Inhalation - Exposure to chemicals in ambient air, with possible respiratory protection
2. Dermal absorption - Through two pathways:
   • Direct contact with liquid or solid chemicals on the skin
   • Absorption of chemicals from the gas phase through the skin
3. Oral intake - Modeled as a bolus dose that enters the intestinal lumen

Multiple exposure routes can be simulated simultaneously. For workplace or environmental scenarios, the model can simulate exposures that repeat over specified time periods.

Elimination and Removal Mechanisms

The model includes several elimination pathways:

1. Metabolism - The model can simulate up to four sequential metabolites. Metabolism is described by Michaelis-Menten saturable kinetics with parameters Vmax (maximum velocity) and Km (Michaelis-Menten constant) for each tissue and each substance.

2. Urinary excretion - Renal clearance through glomerular filtration with possible tubular resorption, which is estimated based on the physicochemical properties of the compound.

3. Exhalation - Removal of volatile compounds through the lungs, governed by the blood:air partition coefficient.

4. Enterohepatic circulation - The model incorporates enterohepatic recirculation by defining a ratio of excretion to bile relative to excretion to the blood, which can extend the residence time of metabolites in the body.

Parameter Estimation with QSARs

The model uses Quantitative Structure-Property Relationships (QSPRs) to minimize the number of required input parameters:

1. Blood:air partition coefficients - Estimated using dimensionless Henry coefficient and octanol:air partition coefficient derived from vapor pressure, molecular weight, water solubility, and octanol-water partition coefficient.

2. Tissue:blood partition coefficients - Estimated based on the lipid and water content of tissues and the octanol:water partition coefficient of the chemical.

3. Dermal permeation - Skin permeation parameters including permeation coefficients through the stratum corneum are estimated using physicochemical properties of the substance.

4. Renal clearance - Tubular resorption is estimated based on the octanol:water partition coefficient using a sigmoid model.

Different QSAR algorithms are applied for human subjects versus experimental animals (rat and mouse), reflecting physiological differences between species.

Mathematical Model: Ordinary Differential Equations (ODEs)

The model is constructed as a system of ordinary differential equations (ODEs) that describe the rate of change of chemical mass in each compartment over time. Each tissue compartment is described by a mass-balance equation accounting for:

1. Blood flow into and out of the tissue
2. Partitioning between blood and tissue
3. Metabolism within the tissue
4. Special processes for specific tissues (e.g., excretion in kidneys)

The system is solved numerically to provide time-course predictions of chemical concentrations throughout the body.

Parent Compound and Metabolites Representation

The model can simulate the parent compound and up to four sequential metabolites:

• Parent compound: Denoted with index 0 (e.g., M_Liver_0, C_Blood_0)
• First metabolite: Denoted with index 1 (e.g., M_Liver_1, C_Blood_1)
• Second metabolite: Denoted with index 2 (e.g., M_Liver_2, C_Blood_2)
• Third metabolite: Denoted with index 3 (e.g., M_Liver_3, C_Blood_3)
• Fourth metabolite: Denoted with index 4 (e.g., M_Liver_4, C_Blood_4)

Metabolite Formation in the ODE System

The metabolism of the parent compound and subsequent metabolites is incorporated in the tissue mass balance equations. For each tissue (i) and substance (j):

1. The parent compound (j=0) is metabolized according to:

   dM_i_0 = ... - (Vmax_i_0 * VolCmp_i * C_i_0)/(Km_i_0 + C_i_0)
   

2. For metabolites (j=1 to 4), both formation from the previous substance and further metabolism are included:

   dM_i_j = ... - (Vmax_i_j * VolCmp_i * C_i_j)/(Km_i_j + C_i_j) + (Vmax_i_(j-1) * VolCmp_i * C_i_(j-1))/(Km_i_(j-1) + C_i_(j-1))
   

The stoichiometric yield of each metabolic step is implicitly modeled by specifying different Vmax values for the removal of a parent compound versus the production of a specific metabolite.

Required User Input

To run a simulation with the IndusChemFate model, users need to provide the following information:

Basic Scenario Parameters

• Physiological scenario - Selection from the 14 available scenarios
• Body weight (optional) - If different from the default for the selected scenario
• Skin temperature - For estimating dermal absorption and evaporation

Chemical Properties

For the parent compound and each metabolite:

• Molecular weight (g/mol)
• Density (mg/cm³)
• Vapor pressure (Pa)
• Log octanol:water partition coefficient at pH 7.4 (blood pH)
• Water solubility (mg/L)

For the parent compound only:

• Log octanol:water partition coefficient at pH 5.5 (skin pH)

Metabolism Parameters

For each potential metabolic pathway:

• Vmax - Maximum metabolism rate (μmol/kg tissue/hour)
• Km - Michaelis-Menten constant (μmol/L)

These can be specified for each tissue and for each transformation (parent to first metabolite, first to second metabolite, etc.)

Excretion Parameters

• Tubular resorption - Can be user-specified or estimated by the model
• Enterohepatic recirculation - Ratio of biliary excretion to blood excretion

Exposure Scenarios

• Inhalation exposure:
  • Concentration in air (mg/m³)
  • Exposure times and durations
  • Respiratory protection factor (if applicable)
• Dermal exposure:
  • Deposition rate (mg/cm²/hour)
  • Exposed skin area (cm²)
  • Exposure times and durations
  • Dermal protection factor (if applicable)
• Oral exposure:
  • Bolus dose (mg/kg body weight)
  • Administration times
  • Intestinal absorption rate (1/hour)

Simulation Parameters

• sim.start: initial simulation time point
• sim.start: final simulation time point
• sim.step: simulation time step

Model Output

The model provides time-course predictions for:

• Concentrations of the parent compound and metabolites in all tissues
• Venous and arterial blood concentrations
• Alveolar air concentrations
• Urinary excretion and concentrations
• Dermal absorption parameters (if applicable)
• Mass balance information

These outputs can help assess internal exposure, target tissue concentrations, and biomarker levels for various exposure scenarios, supporting risk assessment and biomonitoring strategies.

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This R implementation of IndusChemFate maintains the functionality of the original model while providing a more accessible platform through the Jaqpot web service, allowing users to simulate chemical kinetics without specialized software.