# How to convert RF absorption rate (SAR) values to electric field values?

I'm currently reading a bunch of journal articles that describe biological effects of electromagnetic fields. They often refer to the field in terms of specific absorption rate (SAR) values (W/kg). I would like to figure out what electric field and/or magnetic field strength inside tissue that corresponds to (either RMS or peak to peak).

An example of such an article is http://www.sciencedirect.com/science/article/pii/S0006291X15003988

I assume the dielectric properties of tissue would be required for this. These are available for example from http://niremf.ifac.cnr.it/tissprop/htmlclie/htmlclie.php

The example article uses 0.04 W/kg SAR at 900MHz. Dielectric data for muscle at that frequency is:

To simplify things the field strength can be assumed to be uniform throughout.

If use the example above, by relative permittivity and loss tangent, one can get the imaginary part of the dielectric constant, see below: https://en.wikipedia.org/wiki/Dielectric_loss

once know the permittivity, the refractive index can be easily caculated, and if the material is not a gain media, then imaginary part for the refractive index is always positive. you can double check the data with the penetration depth. see: https://en.wikipedia.org/wiki/Penetration_depth

E=E0*e^(-z/(2*l)), where l is the penetration depth. you will get the E field for depth z if you know the incidence E field(E0). For E field on other direciton, your information is not enough.

Specific absorption rate (SAR) in your question is most likely to be one average value( otherwise it has to be a funtion of a lot of paramters, such as position, organ et.al).Generally it's a volum integration,see: https://en.wikipedia.org/wiki/Specific_absorption_rate

If we assume the issue is not magnetic , to simplify at depth z,
Absorbed Energy=conductivityE^2=conductivityE0^2*e^(-z/l)
Total absorbed energy would be the integration for above with depth.

You have to know another parameter(the thickness of the sample,h) to do the integration, finally: The total energy=conductivityE0^2(hl)(1-e^(h/l))
And the total power is the time average for the total energy,if E0 is a sine wave of time,then total power would be the half of above.

And you also need to know the total mass(M) for your sample, now:
SAR=the total power/M=1/2*conductivityE0^2(hl)(1-e^(h/l))/M

Now we can retrieve the initial E field(E0), and can get the E field for depth z. The general process would be like this, when more parameter were provided, you may be able to modify it to a more accurate version.

• Wilson - Thank you! I'm following this along to a point. Yes, tissue is not a gain medium, and I see how you get the E field at depth from the field at the surface. The part I can't figure out is: the incident field strength is specified in terms of absorbed power per unit weight of tissue; how do I convert that to E field that would cause that much power to be absorbed? Assume (for simplification) tissue with density 1g/cm^3 in a uniform field, and with the dielectric properties I posted. – Alex I Nov 17 '17 at 9:45