Calculating the SAR

The specific absorption rate (SAR) is a measure of the amount of electromagnetic energy absorbed in a lossy dielectric material. The SAR is a basic scalar field quantity that can be plotted on surfaces or within objects in HFSS. The HFSS>Fields>SAR Setting... command lets you specify the SAR setting. You have a choice ofIEC/IEEE 62704-4 Draft and Gridless.

For the IEEE/IEC STD 62704-4 we subdivide the model space into a grid of voxels properly aligned along the global coordinate system. The density and local SAR values are then mapped over the grid of voxels. Afterwards the two-pass average SAR algorithm is applied to the voxels. Since this two pass algorithm is very time consuming we try to use parallel processing as much as possible. The algorithm is divided into two phases so that the results of the time consuming phase can be reused when fields change.

For more details, see IEC "Determining the Peak Spatial Average Specific Absorption Rate (SAR) in the Human Body from Wireless Communications Devices, 30 MHz - 6 GHz: Requirements for Using the Finite-Element Method for SAR Calculations, specifically involving Vehicle Mounted Antennas and Personal Wireless Devices."

For Gridless, HFSS uses the following equation to calculate the SAR: s * E²/(2r).

where

• s = the material's conductivity. This is defined as: s_bulk+we₀e_rtgd
• r = the mass density of the dielectric material in mass/unit volume.

There are two types of SAR Field Overlay plots available in HFSS: local SAR, and average SAR. When calculating the local SAR, HFSS uses the equation above to calculate the SAR at each mesh point on an overlay plot. HFSS interpolates the values between the mesh points across the plot.

When plotting the average SAR, for each mesh point on the plot, HFSS reports the SAR averaged over a volume that surrounds that point. The volume is determined by the settings for the material's mass density and mass of the material surrounding each mesh point set in the Specific Absorption Rate Setting dialog box. When you use the Gridless method, the volume will not cross object boundaries. The IEEE/IEC method performs averaging over all tissues.

The Certification SAR quantity provided in the Fields Calculator is an efficient way to determine the peak spatial-average SAR. When computing the certification SAR using the Gridless method, HFSS assumes the peak spatial-average SAR is located on an object surface. HFSS therefore searches for the peak local SAR on the surfaces, and creates an averaging volume around that location, completely inside the object with an axis normal to the surface at the location of the peak value of the local SAR.

If the Average SAR method is IEC/IEEE 62704-4 Draft, then the IEC/IEEE 62704-4 Draft standard is followed. Voxel meshes are used, E fields, mass density and conductivity values are resampled onto the voxels first. Then the algorithm for IEC/IEEE 62704-1 is applied to calculate the psSAR. In order to reduce the computation time for the iterative resampling and SAR averaging, subregions with SAR hot spots are identified in a pre-scan. In these subregions, the psSAR is then calculated according to IEC/IEEE 62704-1. The maximum psSAR of all subregions is reported as the psSAR maximum. The psSAR is calculated on an initial voxel mesh according to the procedure defined in IEC/IEEE 62704-1. Then the computational domain shall be resampled with on a voxel mesh of half grid size. This procedure is repeated until the differences in psSAR from the previous iteration to the current iteration are less than 1%.

Average SAR Through Voxelization

To calculate the Average SAR, HFSS first subdivides the model space into a grid of voxels properly aligned along the global coordinate system. The density and local SAR values are then mapped over the grid of voxels. Afterwards, HFSS applies the two-pass average SAR algorithm to the voxels. Finally HFSS distributes the average SAR from the voxels back to the FEM mesh. Because this two pass algorithm is very time consuming, HFSS uses parallel processing as much as possible. The algorithm is divided into two phases so that the results of the time consuming phase can be cached and reused while fields change due to new combinations from edit sources.

HFSS progress messages are included here in parentheses and in red color.

1. Build the grid of voxels.
   1. If we have cached data, load the data. (2nd phase: Reading voxel data) Go to 3.
   2. Otherwise subdivide the model space into a grid of voxels and map density to voxels. See below for details on mapping. (1st phase: Mapping density to voxels...)

2. Collect information for all valid and unused voxels.
   1. Traverse all voxels to collect all valid voxels. For each valid voxel store the extends in one direction and the used ratio of the exterior voxels. See below for requirement for valid voxels. See Figures 1 and 2. (1st phase: 1st pass …)
   2. Traverse all valid voxels to collect all used voxels. (1st phase: 2nd pass ...)
   3. For the unused voxels find possible extends in the 6 directions, see Figure 3. For each unused voxel store an array of directions, extends and ratio of exteriors.
   4. Cache data from a and c.

3. Collect voxels needed for field plot and calculation (field geometry instance).
   1. Get overall elements for field geometry instance.
   2. Get all voxels that cover the nodes of these elements. (2nd phase: Collecting voxels containing elements)
   3. Classify these voxels as valid, used and unused. For each used voxel add all the valid voxels using it to the valid set.
   4. Collect all elements needed to get the data for all the voxels above. (2nd phase: Collecting involved elements)
   5. Map FEM local SAR to voxels. (2nd phase: Mapping data to voxels)

4. Calculate average SAR.
   1. Traverse all valid voxels. For each valid voxel collect average SAR and mark used voxels and propagate average SAR to used voxels. (2nd phase: 1st pass)
   2. Traverse all unused voxels. For each calculate the average SAR on possible directions and take the maximum. (2nd phase: 2nd pass)

5. Distribute average SAR to the FEM mesh from the voxels. For each element node take the SAR value from the voxel which contains this node. (2nd phase: Distributing fields)

This section describes how HFSS maps general data (mass density and conductivity) from FEM mesh to voxels. For each voxel:

1. Collect all intersecting tetrahedra and calculate data over these tetrahedra.
2. Cut each intersecting tetrahedron by this voxel. This gives a series of new smaller tetrahedra.
   1. For each new tetrahedron get data by interpolating over its parent (the original tetrahedron that it is cut from). Integrate the data to get the total over it.
   2. Add the contributions to get the total over the intersection of this voxel and this tetrahedron.

3. Now add the total from above for all intersecting tetrahedra. This gives the total over this voxel. Now take the average by dividing this total by the voxel volume.

A voxel is counted as tissue if its centroid lies in an FEM element with nonzero conductivity and the field value at this location is used for this voxel. The density at each voxel is the total tissue mass divided by voxel volume.

A voxel is valid if the following holds:

1. Expand a cubic volume centered at the voxel evenly in the six directions aligned along the global axis so that the enclosed tissue mass is within 0.0001% of the prescribed mass.
2. Less than or equal to 10% of the cube contains background material in volume.
3. None of the six faces is completely filled with background material.