## Calculating SAR with Elmer

Numerical methods and mathematical models of Elmer
awarru
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### Calculating SAR with Elmer

I'm looking to switch my electromagnetic simulations from Ansys to Elmer at the moment, and one thing I am looking to get working is the calculation of SAR (specific absorption rate) for biomedical simulation purposes.

Is there anyone out there who has used Elmer and the electromagnetics solver to calculate SAR values? I saw that there were two past threads that mentioned it in passing (viewtopic.php?f=3&t=4045&p=14219&hilit=SAR#p14219, viewtopic.php?f=3&t=3992&p=14002&hilit=SAR#p14002) but it doesn't seem as though it was resolved.

From my understanding of SAR calculations, this would require generating a new 3D grid overlay after the electric field has been calculated for all tetrahedra, seeing which electric field point-values lie inside each cube from the new mesh and taking an average of those electric field values and using that value in the SAR equation. I haven't coded something like this myself before but if there is interest and it's feasible I would be interested in using/coding this sort of functionality for Elmer.

raback
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### Re: Calculating SAR with Elmer

Hi awarru

Correct me if I'm not mistaken but isn't the problem in SAR computation that the material response is nonlinear? This means that the solution must performed in a transient fashion using quite small timesteps. Then the explicit FDTD methods provide superior speed over FEM allowing to use much more detailed grids.

I guess SAR computation could be done using transient FEM simulations as well and computing SAR from the results directly. If you would solve the fields equations with FEM what would be the reason to interpolate the results into a uniform grid? To my understanding this would not improve the accuracy.

-Peter

awarru
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### Re: Calculating SAR with Elmer

I was relatively unaware of the exact algorithms used to calculate SAR until recently, so I've been going back over the standards and the literature on FEM calculations of SAR. It does appear that FDTD solutions to SAR were the first developed that were considered reliable from simulation, but nowadays FEM solutions for SAR calculations have been developed that work as well [1].

An E-field solution for every mesh element is necessary which comes by virtue of the already existing FEM solution for the E-field. The grid I was referring to was a reference to the SAR calculation algorithm that chooses a volume for each voxel based on a chosen mass (typically 1 or 10g). Within the mass you want to measure the SAR you would subdivide the volume into a set of voxels and calculate SAR using the straightforward formula:

SAR = integral(conductivity * |E|^2 / density dV)

There are many ways to subdivide the volume into voxels when calculating the SAR values, however there is a current IEEE standard (C95.3) and a standards committee working on methods of computational SAR calculation for FEM solvers specifically. The C95.3 standard is described briefly here: http://www.jpier.org/PIERB/pier.php?paper=12091502

I don't think I understand exactly what you are asking, what is the reason the solution must be performed in a transient fashion?

[1] Another paper that explains using FEM solvers to calculate SAR: http://www.jpier.org/PIER/pier.php?paper=12041105

raback
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### Re: Calculating SAR with Elmer

Hi awarru

It seems that my knowledge was a bit outdated. I thought that FTDT was used because of nonlinear tissue properties but perhaps it was used simply for the fact that it is the easiest method to code. The complexity of FTDT is a fraction of that of implicit FEM.

If there is no need for nonlinear treatment of materials then I don't see why Elmer would not be fit for the job. It seems that the VectorHelmholtz solver would be a natural starting point. Quickly reading I'm a little confused with the treatment of grad(div) term in (2) of [2]. Also they use nodal FEs and get in trouble with the internal BCs. I would think that use of edge elements would be favorable (as in VectorHelmholtz solver).

It would probably be quite easy to implement SAR computation as explained in [1]. However, I'm not too keen on their take on the integration. Why not use standard Gaussian integration over the sphere and close to the interface elements use more integration points? One could also smear down the step function at the interfaces is done in levelset methods. This would generate less numerical noise. That would also be simple to implement.

Given this additional info I would say that this would suite Elmer development quite nicely. There is an active electromagnetics community and this would extend the usability further to new application areas.

-Peter