WebNIR

The dielectric behaviour of a lossy medium is described by the complex relative permittivity, whose real and imaginary parts are:

We put:

so that:

We specify ε as Relative permittivity and σ as Conductivity (S/m) in our tables. Conversely, from the complex permittivity we have the (equivalent) conductivity and the relative permittivity:

Exact formula

where:

and is the complex permittivity defined above.

Limiting cases

Perfect dielectric (σ → 0): the wave is not attenuated.

Perfect conductor (σ ≫ 2πfεε₀): the exact formula reduces to the classical skin depth.

Numerical verification

Exact formula, perfect-conductor approximation and value returned by the Tissue Properties server. The approximation holds if and only if σ ≫ 2πfε₀ε: at radio and microwave frequencies the condition is far from being met in tissues, and the approximation underestimates the penetration depth by a factor of two or more.

Exact formula

where is the free-space wavelength:

Limiting cases

Perfect dielectric (σ = 0): the wavelength is shortened by the square root of the permittivity.

Perfect conductor (σ ≫ 2πfε₀ε): the wavelength becomes 2π times the skin depth.

Numerical verification

Same tissues and frequencies as above. As for the penetration depth, the perfect-conductor approximation is far from accurate at these frequencies and overestimates the wavelength.

The small differences between the Exact and Server columns (fourth significant digit) come from the rounded value of the speed of light used in the spreadsheet check; the server uses .

The server knows 57 tissues, but only 41 of them are primary entries taken directly from the 1996 Gabriel report. The other 15 were added over the years to match the tissue list of the AFRL/HED anatomical model (the numerical phantom based on the Visible Human dataset used at Brooks Air Force Base) or as more readable aliases, and share the Cole-Cole parameters of an existing tissue, as Gabriel herself suggested in her notes (for instance Stomach (also oesophagus, duodenum and all upper digestive track) or Thyroid (thymus has a similar composition, expect similar properties)). Air and Vacuum are free-space placeholders (ε_r = 1, σ = 0).

The table gives, for each name accepted by the server, the denomination in the Gabriel report (the tissue whose parameters are used), the name and the numeric code in the AFRL/HED table (the code, 0–255, is the tissue index of the anatomical model) and the mass density where available. The Origin column reads Gabriel 1996 for the primary entries, = tissue for the entries that reuse the parameters of another tissue (identical Cole-Cole set, checked in the database) and IFAC for the placeholders. Hover a row for the note on its origin.

The density (g/cm³) does not enter the dielectric calculation: it is the mass density assigned to each tissue in the AFRL/HED table distributed with the server, useful for dosimetry (specific absorption rate). It is given for the 41 tissues that have an AFRL/HED entry and left blank elsewhere: no value has been estimated.

Sources: the Tissue denomination comparison page of the historical site (D. Andreuccetti, 2000–2013, 52 tissues), completed to the current 57, and the AFRL/HED tissue table distributed with the tpd server. The permission to use the Gabriel parameters was requested to the Brooks AFB authors in 1997.