SAR and B1

Specific absorption rate and the MRI transmit field from a 3D EM run on openEMS — setting it up, what the numbers are normalised to, the B1 convention, and reading the results.

A 3D view's openEMS setup can compute, at one or more frequencies, the specific absorption rate (SAR) in every lossy tissue it holds, the peak spatial-average SAR over cubes of 1 g, 10 g or any mass you name, the power the tissue absorbs, and for MRI work the transmit field B1+ and its counter-rotating part B1−. They come out as field plots on the 3D model, readouts in the setup editor, and scalars in the run's .npy.

SAR needs openEMS (see 3D EM). Palace does not write the per-cell data SAR is computed from, and a setup that names Palace alone is refused.

What the numbers are

• Local SAR in a cell is σ|E|²/(2ρ), in W/kg: the cell's conductivity, the peak amplitude of its electric field, and its density. Air has no density and no SAR.
• psSAR of a mass m is the largest average of local SAR over a cube holding m of tissue. A cube centred on each tissue cell is grown until it holds the mass; it counts only if less than 10 % of it is air and every one of its six faces touches tissue. A cell that is the centre of no such cube takes the largest average of a valid cube it lies wholly inside, and a cell inside none takes a cube grown outward from one of its own faces. This is why a cube at a surface is not simply clipped: a phantom's skin is where the peak usually is.
• Whole-region SAR (SARwb) is the region's absorbed power over its tissue mass.
• Absorbed power (Pabs) is ½σ|E|² summed over the tissue's volume.
• B1+ and B1−: the B1 convention, below.

Setting it up

In the EM Setup editor, an openEMS setup has a SAR and B1 group. Tick it, then:

In the .c3d or .cem this is the setup's Sar section; circuitrf reference em-setup lists every key.

Which cells are tissue. A solid is tissue when it is a dielectric with a conductivity above zero and its material states a density. A lossy material with no density in the region is refused, naming it: openEMS would write it as air and every SAR tool would then ignore it. Several of circuitRF's shipped tissues state no density, because no free source gives one; add one, with its source, to your own copy (see Materials). A board whose loss is a loss tangent has a conductivity of zero and is never tissue.

One frequency per tissue evaluation. A body tissue's εr and σ change with frequency, and an openEMS run sees each material as one constant pair over its whole band. circuitRF evaluates every frequency-dependent material once, at the first SAR frequency, so the SAR and B1 a run reports are valid at that frequency only. Two SAR frequencies with a frequency-dependent tissue are refused; make a second setup for the second frequency, or use a band sweep, which makes one setup per band for you.

What the group switches on. Cell-constant material (each FDTD cell takes the material at its centre), which cube averaging needs. It is slightly less accurate at a material's face, and the run says so. Unticking it in the openEMS options overrides the group.

Disk. Each SAR frequency and driven port writes a raw dump of the tissue's box, 36 bytes a cell, plus about 276 bytes a cell for B1's magnetic field while the run lasts. The run's notes and circuitrf explain estimate it before the run, and it is a warning above 4 GB.

Refused before any run: a SAR frequency outside the sweep; a setup with no lossy dielectric; a region that names no object; a non-driven problem; on a cylindrical grid, an averaging mass or the cross-check (a cube is a Cartesian grid's, so a cylindrical grid gives local SAR and B1 only).

Units and normalisation

The run's excitation is arbitrary and tiny, so every SAR, power and B1 number circuitRF shows is per 1 W accepted at the driven port: SAR divided by the accepted power, B1 divided by its square root.

The accepted power is ½Re(V I*) at the port at the SAR frequency, the same rule openEMS's own SAR tutorials use. A field plot can be drawn at another power: its Drive power in the Inspector takes one (250 mW, 30 dBm), referred to the accepted or to the incident wave, and SAR scales with the power, B1 with its square root.

The B1 convention

With the phasor convention b(t) = Re{B e^{jωt}}, B = μ0H, and B0 along +z, the transverse field splits into two circularly polarised parts:

B1+ = (Bx + j·By) / 2        B1− = (Bx − j·By) / 2

|B1+| is the part rotating counter-clockwise seen from +z (from +x towards +y), |B1−| the part rotating clockwise. This is exactly what openEMS's own MRI tutorials compute. Which of the two is the transmit field depends on the sign convention for precession, and the literature uses both; circuitRF takes openEMS's definition as it stands. B0 along −z swaps the two. For B0 along ±x or ±y the transverse pair is taken cyclically, (By, Bz) and (Bz, Bx).

The mean |B1+| is volume-weighted over B1 mean over's objects.

Reading the results

• The setup editor's readouts, after a run, per SAR frequency and driven port: psSAR per mass with the peak cube's centre and tissue, peak local SAR, whole-region SAR, absorbed, accepted (1 W, and the value as solved), radiated and the power budget when the setup has a radiation pattern, mass, mean |B1+| and the efficiency, and sar_calc's peak with the cross-check on. circuitrf em prints the same, one line per port.
• Field plots. Each run offers its SAR and B1 as two solutions of their own, labelled (SAR) and (B1), at the SAR frequency and port. The quantities are SAR (local), SAR1g, SAR10g and so on per mass, B1p and B1m. SAR is drawn over tissue only, so air is transparent; B1 is drawn over the whole box, because B1 is wanted in the air inside a coil.
  • Maximum-intensity projection (a SAR clip plane's Maximum-intensity projection box, or render --mip x|y|z): each line through the volume along the plane's axis carries its largest value, so one plane shows the hottest tissue wherever it lies.
  • The peak marker: the peak cube as a wireframe in the 3D view, and on a section its square, solid where the plane cuts it and dashed, with its distance, where it does not. Local SAR has no cube and is marked with a cross.
• The .npy gains a sar group, each cube over the SAR frequencies and the driven ports: psSAR1g, psSAR10g (per mass), SARwb, Pabs, Pacc, Mass, and with B1 B1pMean and SarEff; with a radiation pattern also Prad and PowerBudget, (absorbed + radiated) / accepted, which should lie a little under 1.
• The volumes (local SAR, each mass's average, B1+, B1−) are kept as float32 .npy arrays in the run folder, beside openEMS's raw dump, with their cell centres. Their names are in the run's sar<j>.json record.

Headless: circuitrf em view.c3d --setup <name> runs it, circuitrf explain view.c3d reports the group, the tissue each object is, ρ, εr and σ as the solver will see them and the disk estimate, and circuitrf render view.c3d --field <plot> -o out.png draws a SAR or B1 plot. MCP's run analysis=em and render do the same.

How it was checked

circuitRF rebuilt openEMS's own SAR and MRI tutorials from 3D-view objects and ran them on openEMS 0.37.0:

openEMS stops a run when its energy has decayed, checked on wall-clock time, so two runs of the same problem can stop at different steps; that alone moved the dipole's psSAR10g by 0.24 % between runs of the tutorial itself.

Related

• Co-simulation: parts as ports, and B1, SAR and the radiation pattern from a schematic with no new EM run.
• Tissues and phantoms: the materials and the bodies SAR is computed in.
• Voxel and mesh import: your own segmented anatomy.
• Phone SAR: placement against a phantom, band sweeps and reference values.