RF Safety

Computational Dosimetry

Q: How fine must the FDTD mesh be for SAR computation at 6 GHz?

The cell edge must resolve both the wavelength in tissue and the shallow penetration depth. At 6 GHz the wavelength in high-water tissue such as muscle is roughly 7 to 8 mm and the penetration depth is only about 8 mm, so the surface power deposition gradient is steep. A common rule is at least 10 cells per wavelength in the highest-permittivity tissue, which gives a 0.7 to 0.8 mm cell. For peak spatial-average SAR over 1 g or 10 g, finer 0.5 mm cells near the skin surface are typical because the 10 g averaging cube spans only about 21.5 mm per side and the field decays sharply across it. The Courant stability limit then forces a time step of about 1 ps, requiring tens of thousands of time steps to reach steady state.

Q: Why are voxel body models used instead of homogeneous phantoms?

Homogeneous liquid phantoms, such as the SAM head shell, give a conservative compliance estimate but cannot capture the layered skin-fat-muscle-bone structure that redistributes internal fields and creates local hot spots. Voxel models segmented from MRI data, such as the Virtual Family models Duke, Ella, Billie, and Thelonious, assign frequency-dependent permittivity and conductivity to 80 or more tissue types. This lets a solver compute organ-specific and 1 g or 10 g peak spatial SAR, model children and pregnant anatomy that no physical phantom covers, and evaluate exposure geometries that the robotic SAR probe in a phantom tank cannot physically reach.

Q: What tissue dielectric data drives a computational dosimetry model?

Each voxel is assigned a relative permittivity and conductivity at the operating frequency, almost always from the Gabriel parametric Cole-Cole model fitted to measured tissue data spanning 10 Hz to 100 GHz. For example muscle at 2.45 GHz has a relative permittivity near 52.7 and conductivity near 1.74 S/m, while low-water fat is near 5.3 and 0.10 S/m. Mass density per tissue, typically 900 to 1100 kg/m3, converts the dissipated power density into mass-normalized SAR. Because conductivity rises with frequency, the same incident power produces shallower but more intense surface heating in the millimeter-wave bands, which is why power density rather than SAR becomes the compliance metric above about 6 GHz.

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Numerical electromagnetic simulation applied to anatomically detailed body models to predict the internal RF field and specific absorption rate that a person experiences from a transmitter. Where a robotic probe in a liquid phantom cannot physically reach an organ or resolve a layered tissue interface, a solver, most often the FDTD method, discretizes the body into millions of voxels, each tagged with frequency-dependent permittivity and conductivity, and computes the dissipated power density everywhere. The result yields whole-body and peak 1 g or 10 g spatial-average SAR figures used to demonstrate compliance with FCC, ICNIRP, and IEEE C95.1 exposure limits, and to model populations such as children and pregnant anatomy that no physical phantom represents.

Category: RF Safety

Typical solver: FDTD / FEM

SAR averaging mass: 1 g or 10 g

How Numerical Models Replace the Probe

Physical SAR measurement scans an isotropic E-field probe through tissue-simulating liquid inside a shaped phantom shell. That approach is the regulatory reference for handset compliance, but it is slow, limited to the geometries a robot arm can reach, and blind to the layered skin-fat-muscle-bone structure inside a real body. Computational dosimetry removes those constraints by solving Maxwell's equations directly inside a digital human. The body is segmented from MRI scans into a voxel grid, each voxel assigned the relative permittivity and conductivity of its tissue type at the operating frequency, and a full-wave solver propagates the incident field through the model until a steady state is reached.

The dominant engine is the finite-difference time-domain (FDTD) method because its structured Cartesian grid maps cleanly onto voxel data and it handles broadband sources in a single run. The local SAR in each voxel follows from the time-averaged dissipated power per unit mass, σ|E|² divided by twice the tissue density. Mass-normalized averaging over a 1 g or 10 g contiguous cube then produces the peak spatial-average SAR that the FCC (1.6 W/kg over 1 g) and ICNIRP (2 W/kg over 10 g) limits reference. Above roughly 6 GHz the fields no longer penetrate deeply, so the compliance metric transitions from SAR to incident or absorbed power density, and the relevant voxels collapse to a thin surface layer.

Validation matters: a model is only credible after the solver, the tissue dielectric library, and the mesh are benchmarked against canonical cases such as a homogeneous sphere or a measured flat phantom. Established voxel families, including the IT'IS Virtual Family models Duke, Ella, Billie, and Thelonious, ship with verified segmentation so that engineering teams compare like with like.

Governing Equations

Local (point) SAR:
SAR = σ|E|² / (2ρ) W/kg

Equivalent thermal form:
SAR = c_p × (dT/dt)|_t=0 W/kg

Mass-averaged spatial-peak SAR:
SAR_avg = ( ∫_V σ|E|² dV ) / ( 2 × ∫_V ρ dV ), mass(V) = 1 g or 10 g

FDTD stability (Courant limit, 3-D):
Δt ≤ 1 / ( c × √(1/Δx² + 1/Δy² + 1/Δz²) )

Where σ = tissue conductivity (S/m), E = peak internal field (V/m), ρ = mass density (kg/m³), c_p = specific heat (J/kg·K), c = speed of light, Δx/Δy/Δz = cell dimensions. Example: muscle at 2.45 GHz, σ ≈ 1.74 S/m, ρ ≈ 1090 kg/m³, |E| = 60 V/m → SAR ≈ 2.9 W/kg.

Solver and Phantom Comparison

Method / Model	Type	Typical cell or detail	Best frequency range	Strength	Limitation
FDTD	Numerical (time domain)	0.5 to 2 mm voxel	100 MHz to 10 GHz	Broadband, voxel-native	Staircasing at curved interfaces
FEM	Numerical (frequency domain)	Conformal tetrahedra	Single frequency, resonant	Smooth boundaries, fine detail	Costly per frequency point
MoM	Numerical (surface)	Surface mesh	Antenna-to-body coupling	Efficient for open radiators	Hard for inhomogeneous interiors
SAM head shell	Physical, homogeneous	Single liquid	300 MHz to 6 GHz	Regulatory reference	No internal tissue structure
Virtual Family voxel	Numerical, anatomical	80+ tissue types	Up to 100 GHz	Organ-specific SAR, all ages	Needs validated dielectric data

Common Questions

Frequently Asked Questions

How fine must the FDTD mesh be for SAR computation at 6 GHz?

The cell must resolve both the in-tissue wavelength and the shallow penetration depth. At 6 GHz the wavelength in muscle is about 7 to 8 mm and the penetration depth only about 8 mm, so deposition is steep. Using 10 cells per wavelength in the highest-permittivity tissue gives a 0.7 to 0.8 mm cell, refined to 0.5 mm near the skin because the 10 g averaging cube spans only about 21.5 mm per side. The Courant limit then sets Δt near 1 ps, needing tens of thousands of steps to converge.

Why are voxel body models used instead of homogeneous phantoms?

A homogeneous liquid phantom such as the SAM shell gives a conservative number but cannot capture the layered skin-fat-muscle-bone structure that redistributes fields and creates local hot spots. MRI-derived voxel models like Duke, Ella, Billie, and Thelonious tag 80+ tissue types with frequency-dependent properties, enabling organ-specific and peak 1 g or 10 g SAR, child and pregnant anatomy no physical phantom covers, and geometries a robotic probe cannot reach.

What tissue dielectric data drives a computational dosimetry model?

Each voxel gets a relative permittivity and conductivity from the Gabriel Cole-Cole parametric model fitted to measured data spanning 10 Hz to 100 GHz. Muscle at 2.45 GHz sits near ε_r = 52.7 and σ = 1.74 S/m; low-water fat near 5.3 and 0.10 S/m. Per-tissue density of 900 to 1100 kg/m³ converts power density to mass-normalized SAR. Because σ rises with frequency, millimeter waves heat a thinner surface layer, so power density replaces SAR above about 6 GHz.

Related Terms

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