Mathematical modelling consists in building a mathematical representation of reality that attempts to explain the behaviour of some aspect of it, based on simplifying assumptions (hypotheses). The mathematical representation usually consists in a set of variables and a set of equations that establish relationships between these variables. The mathematical model can serve several purposes: answer a variety of what-if questions, understand the relationships between variables, extrapolate past data to derive meaning, etc. Models are typically used when it is either impossible or impractical to create experimental conditions in which scientists can directly measure outcomes. However, even when experiments are possible, obtaining a good mathematical model is usually very interesting, as it can provide insights into the internal workings of a system that direct measurements cannot.

In EMF research, a large effort is underway to construct mathematical models to calculate electric and magnetic fields generated by electrical devices (powerlines, transformers, engines, electronic circuits, furnaces…). Recently, researchers have been trying to extend such models to compute electromagnetic fields inside living organisms (from the cellular level all the way to the whole human body). Such models of the human body cannot usually be solved using a “pencil and paper” approach: they require the use of computers, which break the body into many simple geometrical shapes (for example little cubes), in which mathematical equations are solved.

Modelling is of major interest in defining guidelines and recommendations for limiting the exposure of the public to electromagnetic fields. For example, recent guidelines intend to avoid internal electric fields greater than 0.02 V/m for the public and 0.1V/m for workers (see pages Standards). Modelling allows to predict the magnitude of such internal electric fields in full-size phantom models or partial body models exposed to various external sources (magnetic fields, electric fields, contact currents…). Modelling is also pertinent in in vitro and in vivo studies to accurately assess the distribution of fields in cells and animals, according to the exposure system. It is a principal tool in assessing the biological dose resulting from EMF exposure.

In brief...

Advantages of modelling studies

  • Easily reproducible virtual “experiments”
  • Cheaper than laboratory experiments
  • Ability to test many variations
  • Non invasive

Limitations of modelling studies

  • Potentially wrong if based on bad simplifying hypotheses
  • Potentially wrong if bad input data

The first limitation must be addressed by validating the mathematical model with repeatable laboratory experiments. Lack of agreement between theoretical mathematical models and experimental measurements often leads to important advances as better theories are developed. To try to mitigate the second limitation, probabilistic (stochastic) mathematical models are developed, which analyze the sensitivity of results with respect to uncertainties on the input data.

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