Numerical calculations of induced currents

Both electric and magnetic fields induce currents in the body.

See also:

 

plot of calculated induced currents

The most accurate way to determine how much current is induced is to perform a numerical calculation. The body is split into millions of small elements called “voxels”. Each voxel is assigned a conductivity appropriate to the tissue type it forms part of. Then computers are used to calculate the current induced in each voxel.  In this example each voxel is a centimetre across but state-of-the-art these days is 2 mm or smaller.

Such calculations are performed by three main groups round the world:

  • Peter Dimbylow at the HPA
  • Maria Stuchly and group at University of Victoria
  • Om Gandhi and group at Salt Lake City
In the UK, the HPA and others tend to rely on the results of Dimbylow,and HPA's official advice on Application of the ICNIRP Exposure Guidelines uses these results.

Comparisons between the groups show that their results are fairly similar, nearly always to within a factor of two and often closer. When they apply their calculations techniques to the same models, results are even closer, within 2% or so. This gives confidence in the results. But all the groups use basically the same set of tissue conductivities which may not be very reliable. So all the results could easily be in error by another factor of two or so. National Grid are funding MCL to obtain better conductivity values.

Results can be expressed in various ways:

  • As the maximum induced current in any single voxel. But results for a single voxel are often unreliable as a consequence of the way the model represents curved shapes with cubical voxels
  • The average over a given organ
  • The maximum value when averaged over 1 cm2 in an organ. 1 cm2 is chosen because this is the area specified by ICNIRP in their exposure guidelines.

 

Results of numerical calculations

The following results are taken from the papers by Dimbylow for magnetic and electric fields. (These values are all for 50 Hz. Equivalent fields at 60 Hz are 5/6 of these values)

The current induced by a field depends on the direction of the field and, for electric fields, whether the body is grounded. These results are for the most sensitive conditions, ie the conditions where it takes the smallest external field to induce the given current.

To induce a current of 10 mA m-2 in the central nervous system requires:

  • A magnetic field of 1800 µT in a man or 2000 µT in a woman
    (this would be aligned side-to-side of the body and is in the retina)
  • An electric field of 48 kV m-1 in a man or 46 kV m-1 in a woman
    (this is a vertical field for a grounded person and is again in the retina)

These can be scaled to any other induced current. For example:

To induce a current of 2 mA m-2 in the central nervous system requires:

  • A magnetic field of 360 µT (for a man, the value for women is higher)
  • An electric field of 9.2 kV m-1 (for a woman, the value for men is higher)

For the whole body instead of just the central nervous system, to induce a current of 10 mA m-2 requires:

  • A magnetic field of 258 µT
  • An electric field of 5.9 kV m-1

See also

Reference levels in exposure guidelines

Exposure guidelines such as ICNIRP give investigation levels or reference levels. These are a guide to when further investigation is needed of whether the basic restriction is exceeded or not. They are not in themselves limits and it takes fields higher than the reference/investigation levels to exceed the basic restriction.

For example:

Basic restriction: 10 mA m-2 in the central nervous system
Magnetic fields
Electric fields

ICNIRP reference level: 500 µT
NRPB investigation level: 1600 µT
Field actually required: 1800 µT

ICNIRP reference level: 10 kV m-1
NRPB investigation level: 12 kV m-1
Field actually required: 46 kV m-1

 

Basic restriction: 2 mA m-2 in the central nervous system
Magnetic fields
Electric fields

ICNIRP reference level: 100 µT
Field actually required: 360 µT

ICNIRP reference level: 5 kV m-1
Field actually required: 9 kV m-1

* The Dimbylow calculations give a value of 9.2 kV m-1. HPA suggest 9 kV m-1 which includes a further small margin.