SCIRun User Mailing List

## Re: [SCIRUN-USERS] Total current going through the TDCS Mickey Mouse model

• From: Tomasz Moszkowski <tmoszkowski@gmail.com>
• To: Jess Tate <jess@sci.utah.edu>
• Cc: "scirun-users@sci.utah.edu" <scirun-users@sci.utah.edu>
• Subject: Re: [SCIRUN-USERS] Total current going through the TDCS Mickey Mouse model
• Date: Sat, 17 Sep 2016 13:39:00 +0000

Hello Tate,

thank you very much for your reply! Exactly how you described it, the values that I received were varied greatly depending on where the plane was situated. Basically the further from each electrode I got, the smaller the measured current. The closer to one of the electrodes, the greater the amount of current (it got pretty close to the set value of 2 A). I think I know what the problem is: basically if you map your current density onto the elements of a plane, sometimes the geometry of the plane does not change (for very small changes in comparison with the resolution of the mesh) but the interpolated current values do. Because the area of each element stays the same, the resulting current is different. At first I extracted an isosurface from a separate mesh that was the size of the original mesh but with a higher resolution. I think that the mapped values got somehow duplicated because of the difference in resolutions of both meshes thus yielding different current values. Also, if one varies the resolution of the mesh, the measured current also varies greatly. Thus I guess that in order to solve this, one should measure the current close to one of the electrodes (of course, as you said, making sure that the plane separates the sinks from the sources and does not coincide with the electrode). I guess that this is not the best way to validate the accuracy of your model, since it depends on many factors: resolution, mapping method etc.

A comment on the selection of the plane: I tried several methods to pick a proper plane out. The first is to simply get a plane located between the source and the sink making sure that it is parallel to one of the planes of the reference system and map only the component of the current density which is perpendicular to this plane. Another way was to pick any plane and project the current density onto the plane normal. The third way was to pick an isosurface of the electric potential and map the magnitude of the current density onto this surface (the isosurfaces of a field are surfaces with equal value of the field and thus the gradient of the field is normal to every point on the isosurface. One does not need to project the values, just get the field magnitude). Of course all of these methods are prone to error of the mesh resolution and the mapping method.

I guess that the most accurate method of measuring current is the one I mentioned earlier: verifying that the TDCS matrix multiplied by the solution vector yields the RHS vector and the set current values.

THank you very much for your help! If I try other methods of measuring current inside the model (e.g. from calculating the total power dissipation inside the model), I will let you know of the results! In the meantime I wish you all a great weekend.

All the best,
Tomasz Moszkowski

pt., 16.09.2016 o 22:58 użytkownik Jess Tate <jess@sci.utah.edu> napisał:
Hi Tomasz,

The method that you described will give you an estimate of the total current assuming each step is done correctly.  However, it is subject to numerical errors and the resolution of the mesh of the model as well as the plane will make some difference in this estimation.  You will need to make sure that the plane separates all sources from all sinks and it is best if it is perpendicular to the current direction (or that the vector normal is parallel).  I think that you were talking about the plane normal vector that is parallel, which is correct, but if the plane itself is coincident or parallel with the electrodes, that is a problem.  One thing that you should also consider when comparing the estimated current the applied current is the electrode impedance, which is modeled in the TDCS example and is set as a parameter in one of the CreateMatrix modules (in SCIRun 4.7).

How different are the values that you are getting from what you are expecting?

cheers,
Jess

On Sep 16, 2016, at 2:33 AM, Tomasz Moszkowski <tmoszkowski@gmail.com> wrote:

Hello everyone,

I would like to ask you for help. I would like to validate a model that I am working on by calculating the current that is flowing through a simple model. For this purpose I use the Mickey Mouse TDCS model supplied in SCIRun 4.7. I would like to confirm that the flowing current that I measure equals the values given in the settings of the model (the RHS of the linear set of equations). My procedure:
1. Calculate the current density within the model (nothing out of the ordinary here: -gradPhi*sigma)
2. Map the normal component of the current density onto a plane that is a cross-section of the entire model. To simplify the problem I just picked a vertical plane parallel to both electrodes.
3. Multiply the normal component of the current density from the plane by the areas of the elements of the plane to get the flowing current per plane element
4. Sum all such "unit" currents to get the total current flowing between the two electrodes.

As you can imagine, the values that I get by doing this are off from the values set to the input of the model and it is not just a matter of scaling. When I multiply the solution matrix by the TDCS matrix, the RHS that I get equals the one that I set into the model, so here everything is fine. I tried to study the maths behind the TDCS model from:

 P. Hua, Eung Je Woo, J. G. Webster, and W. J. Tompkins, “Finite element modeling of electrode-skin contact impedance in electrical impedance tomography,” IEEE Trans. Biomed. Eng., vol. 40, no. 4, pp. 335–343, 1993.

Current shunting along the electrodes was mentioned in the paper. Could it be that some current set into the electrodes simply does not get through into the model? Or am I making some sort of a mistake that has been oblivious to me so far?

I would really appreciate any help!

Kind regards,
Tomasz Moszkowski

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