PBPK model for cadmium

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The text on this page is taken from an equivalent page of the IEHIAS-project.

The PBPK model for cadmium is based on the model of Kjellström and Nordberg (1978) and allows prediction of the invididual and population based exposure to cadmium from oral and inhalatory intake. The input parameters of the model are:

  • age and gender;
  • body weight;
  • iron status;
  • intake dose of cadmium from inhalation of particles, smoking, diet, drinking water, soil and house dust.

Inputs should be provided by year (age), allowing the model to predict age-dependent exposure. Some age-dependent inputs like body weight can be calculated based on auxiliary models. The output parameters of the model are:

  • concentration of cadmium in blood;
  • concentration of cadmium in kidney and kidney cortex;
  • excretion of cadmium in urine.

Model description


The purpose of the PBPK model for cadmium is to predict age-dependent internal doses of cadmium in different body compartments. It is therefore suited to link external exposure data to specific biomarker data and to interpret biomonitoring results in terms of exposure routes and pathways.

The model allows for predictions on an individual basis or and can be used to derive population based estimates of exposure. The model is age-dependent and is designed to take into account changing exposure conditions during a lifetime.


Fields of model:


Temporal resolution:

The model predicts an age-dependent exposure with a 1 year resolution.

Pollutants covered:



The population should be specified by the user. The model can be run for individuals, whose external exposure pattern is specified. Model results can be used to derive population based exposure characteristics.


The model includes standard values or approximation models for the required toxicokinetic parameters. There is no user interface provided with the model, but parameters can be mofidied in the source code itself. If the model is run at individual level, the required input is:

  • age & gender
  • iron status (serum ferritine level)
  • time dependent data (by year):
    • year
    • age
    • body weight
    • intake dose of cadmium from air
    • intake dose of cadmium from smoking
    • intake dose of cadmium from passive smoking
    • intake dose of cadmium from food
    • intake dose of cadmium from drinking water
    • intake dose of cadmium from soil and house dust.

The intake doses required by the model are calculated by an external exposure model. Some of the remaining inputs can be calculated based on auxiliary models (e.g., body weight based on Belgian population based growth curves).

In the current implementation, these inputs are provided in the form of a Matlab .MAT file, containing a "struct" variable listing these input values for all persons to be simulated.


Output of the model, as currently implemented, is:

  • predicted current urinary cadmium level
  • predicted current blood cadmium level
  • total current body burden of cadmium

The model code can be easily adjusted to provide more outputs, like age-dependent concentrations.

Output is generated in the form of Matlab data structures, which can be graphed afterwards.

Description of processes modelled and of technical details

=Description of the model

The cadmium PBPK model is based on the PBPK model published by Kjellström and Nordberg (1978, 1979), around which a model wrapper was implemented to enable the linkage to exposure doses from various pathways and to provide the required exposure metrics to enable comparison with biomonitoring data.

The core of the model consists of a set of differential equations representing the cadmium flows in the body as depicted in Figure 1.

Inhalatory intake distinguishes between the intake of cadmium for particles in outdoor and indoor air and intake of cadmium from smoking, because of differing deposition patterns in the respiratory system. Part of the inhaled dose is transferred to the gastrointestinal tract, where it is summed with intakes from diet, drinking water, soil and dust. Oral absorption calculations take into account the iron status of the person, as it is known that a low iron status leads to an increased absorption of cadmium.

Three blood compartments are distinguished. Blood cadmium is exchanged with liver, kidney and other tissues. Excretion takes place via faeces and urine.

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Figure 1: Scheme of the PBPK model for cadmium

A preprocessing module allows to generate individual age-dependent values for body weight, exposure factors (food intake, inhalation rate) based on the actual value. Age-dependent doses are generated by the external dose model, from estimated time profiles of environmental and food cadmium concentrations.

Technical details

The PBPK model is programmed in a Matlab environment. It is designed as an in-house model, part of the larger exposure assessment model for the cadmium study in the Northern Campine region.

Unit responsible for running and maintenance

The model was developed in the unit MRG (Enviromental Risk & Health) of VITO, the Flemish Institute for Technological Research.

Contact person

Arnout Standaert (arnout.standaert@vito.be).

Time required for a typical run

A one-person simulation takes 1-2 seconds.

Operating System

The code should run on any platform that runs Matlab: Windows / Linux / Mac OSX

Database type

Data are read from Matlab-based .MAT files, containing a "struct" variable listing the required input parameters per person.

Software requirements

The model is developed in Matlab and was run in Matlab version 2008b. It is likely to run on older versions too, but this hasn't been tested.

Degree of mastery

The model, as currently implemented, does not provide a user interface or usage guide. Model users should be at least somewhat familiar with Matlab coding to adapt the code for own needs.

Can modify/reprogram within platform


Model availability

The model code can be provided on request.


The PBPK model for cadmium is capable of predicting the individual internal exposure of cadmium and is therefore suitable for comparison with biomonitoring data. From this, it allows for the interpretation of biomonitoring data with regard to pathways and sources of exposure. It can therefore be used in site-specific assessments. The advantage of the model is also that it accounts for changes in exposure during a lifetime.

Limitations of the model are the uncertainties related to some of the toxicokinetic parameters, such as deposition in the respiratory system and absorbed fractions. The interindividual differences in toxicokinetic parameters are generally not accounted for (except for iron status).


  • Kjellström, T., Nordberg, G.F. (1978). A kinetic model of cadmium metabolism in the human being, Environmental Research, 16 (1-3), 248-269.
  • Nordberg, G. F., Kjellström, T. (1979). Metabolic model for cadmium in man, Environmental Health Perspectives, 28, 211 - 217.
  • Standaert, A. R., Van Holderbeke, M., Cornelis, C. (2008). Modeling Human Exposure to Cadmium and Arsenic in the Northern Campine Region Modeling Human Exposure to Cadmium and Arsenic in the Northern Campine RegionMoModeling Human Exposure to Cadmium and Arsenic in the Northern Campine Region Modeling human exposure to cadmium and arsenic in the Northern Campine Region, Epidemiology, 19 (6), S203-S203.

See also

Integrated Environmental Health Impact Assessment System
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