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Accurate & Consistent SAR Results

Recommendations for grid alignment.

XFdtd's algorithm for computing specific absorption rate (SAR) is derived from and compliant with the international IEC/IEEE P62704-1/D4 standard [1], which requires that dielectric volume averaging be enabled on the tissue material part and SAR be defined only on voxels consisting entirely of tissue. These requirements exclude some cases, which are addressed by additional guidelines for applying the standard using XF.

XF project setup recommendations help users generate a computational grid in cases involving partially filled voxels in order to obtain consistent, accurate SAR values.

Two corrective actions may help resolve project issues:

Specific Absorption Rate

Raw SAR is defined at a point as

\begin{equation} SAR = \frac{\sigma |E|^2}{2\rho} \end{equation}

where $\sigma$ is the electrical conductivity, $E$ is the complex electric field, and $\rho$ is the density.

In a discretized computational space, raw SAR is defined at the center of each regular cuboid, or voxel, using the values $\sigma$, $\rho$, and $E$. The raw SAR values and corresponding voxel densities are then post-processed for one-gram and ten-gram averaged SAR values.

In discretized computational space for the finite-difference time-domain (FDTD) method, SAR is based on voxels defined by the Yee cells.

IEC/IEEE Standard Considerations

The standard sets the following regulations on SAR usage:

Enabling dielectric volume averaging on the tissue material part affects how the fields are computed during the simulation, but does not affect the definition, density, or voxel conductivity of the SAR computation.

SAR is only computed on voxels consisting entirely of tissue. When a tissue material is not completely aligned with the Yee cells, such as a cylinder discretized by a uniform grid, the partial tissue voxels are not addressed by the standard and are excluded from XF's SAR computations.

XF Project Setup

XF's grid defines the FDTD Yee cells, which in turn define the voxels. XF's computational grid creates the twelve Yee cell (voxel) edges, from which the complex electric field, $E$, is derived. This value is used to locate the raw SAR value at the middle of the voxel. Consistent, accurate SAR values are therefore dependent upon a grid that accurately represents the geometry, particularly at the surface and near-surface regions where SAR is the highest.

XF 7.8.0 and later versions discard partially filled voxels, using only the voxels specified in the standard's computational directives. SAR is calculated using materials in and on the Yee cells that are each categorized as a tissue and have non-zero density and electrical conductivity. Users can check the tissue material option in the material editor to create a phantom, or part with tissue assigned to it.

There are some recommendations for generating the computational grid:

Customer Example

A customer ran a set of simulations in XF 7.7.1 that produced unexpectedly high raw and one-gram averaged SAR results. They shared the project seeking insight into the source of the problem, as well as possible solutions.

The phone was located at multiple distances—0 mm, 1 mm, 2 mm, 5 mm, 10 mm—above the flat phantom. The phone was axis aligned, but the phantom was tilted due to the camera pushing out the top, back portion the phone. The SAR results contained high spikes rather than decreasing regularly as the distance between the phone and phantom increased.

Original Grid, XF 7.7.1 0 mm 1 mm 2 mm 5 mm 10 mm
Max Raw SAR (W/kg) 45.886 252.748 5.261 150.586 4.637
Max 1g Averaged SAR (W/kg) 3.443 5.856 2.597 7.243 1.017

An inspection of the grid revealed that relatively large cell sizes were used at the surface of the phantom and the percentage fill of the surface voxels varied significantly.

Two project changes resolved the issues, but most users will find that either one or the other is sufficient. The first change is preferred because it does not increase the cell number or run time, and the second option is one to consider if the first does not correct the problem. The first change attached a manual fixed point to the phantom's surface where the maximum SAR value was expected. This caused a grid line to align with the surface, producing fully filled voxels to include in the evaluation. The attachment also ensured proper alignment at the phantom's surface as its distance from the phone increased.

This particular project's tilted phantom required a manual fixed point rather than automatic fixed points. In the image, we can see that the fixed point generated a grid line at the phantom's surface below the bottom of the phone. The same grid line created a partially filled voxel at the top of the phone, but that area is of less concern because of its lower SAR values.

The second change added a grid region of smaller cells around the phantom's surface. This decreased the size of the voxels, generating more fully filled voxels closer to the surface. The impact on this project was minor due to the phantom's slight tilt, but would be notable when applying these guidelines to projects with curved phantoms.

This process revealed some needed changes, and XF's SAR algorithm was modified to discard partially filled voxels. XF 7.8.0 uses only voxels for which the standard provides clear computational directives, unlike previous versions that evaluated partially filled voxels. The end result was expected behavior with SAR values decreasing as separation increased.

Updates Applied, XF 7.8.0 0 mm 1 mm 2 mm 5 mm 10 mm
Max Raw SAR (W/kg) 8.947 6.367 5.039 2.634 1.315
Max 1g Averaged SAR (W/kg) 3.604 2.974 2.469 1.548 1.035

Reference

  1. International Electrotechnical Commission (IEC) and the Institute of Electrical and Electronics Engineers (IEEE), IEC/IEEE P62704-1/D4, Determining the Peak Spatial-Average Specific Absorption Rate (SAR) in the Human Body from Wireless Communication Devices, 30 MHz - 6 GHz - Part 1: General requirements for using the Finite-Difference Time-Domain (FDTD) method for SAR calculations, 2016.