How to simulate frequency-dependent conductivity of biological tissue using EM LF Electro Ohmic Quasi-Static solver?

[gotou]

Hello,
I’m currently working on a simulation involving electrical stimulation of biological tissue. I am using the EM LF Electro Ohmic Quasi-Static solver and varying the frequency to compare current flow in the tissue.

Since biological tissue conductivity is frequency-dependent, I would like to reflect this property in my simulation. Therefore, I have selected the IT'IS Database, rather than the IT'IS LF Database, to account for frequency-dependent changes in conductivity.

However, when I use the IT'IS Database, I receive a warning message recommending that I switch to the LF (low-frequency) version of the database.

How can I run a simulation where the tissue conductivity remains frequency-dependent, while still using the EM LF Electro Ohmic Quasi-Static solver?
If changing the solver is necessary to achieve this, I would appreciate any suggestions on which solver to use and how to proceed.

Any advice or insights would be greatly appreciated.
Thank you!

[bryn]

You can run an LF simulation with the normal (non-LF) database: just ignore the warning.

However, please note that the Gabriel Cole-Cole model (which is used in the standard IT'IS database) was primarily fitted using measurements above 1 MHz. For example, the conductivity of the skin is about 2 orders of magnitude smaller than the well-accepted value (see LF database).
I believe that at lower frequencies, there are currently not enough measurements in the literature to justify fitting a frequency-dependent model.

[gotou]

Thank you very much for your response.
I understand now that it's okay to ignore the warning, and that the Cole-Cole model in the standard IT'IS database is primarily fitted to measurements above 1 MHz.

I have a follow-up question:
Is there a recommended way to perform simulations with low-frequency currents (e.g., around 100 kHz)?

I couldn’t find a clear explanation in the manual regarding how to handle this frequency range, so I would really appreciate any guidance or suggestions you could provide.

Thanks again for your help!

[AntoninoMC]

Dear @gotou,
There is a fundamental misunderstanding here. The EM LF Electro Ohmic Quasi-Static solver, is frequency-independent. The complex part of the fundamental electro quasi-stati equation \nabla\cdot\tilde\epsilon\nabla\phi = 0 (see Sim4Life manual, "2.6.1.4 Choosing the Appropriate Low Frequency Solver") is not solved AT ALL, since it is assumed that you have chosen this solver after having evaluated that the condition $\sigma>>\omega \epsilon_r \epsilon_0$ is valid for all the tissues and materials in your simulation at the frequency of interest. How to quantify this condition is also explained in the manual. The frequency has not impact on your simulation at all when you choose this solver.

If you are unsure whether the condition $$\sigma>>\omega \epsilon_r \epsilon_0$$ applies, then you should consider to use the QS solver (not Ohmic-Current dominated) solver that solves the full complex equation. This solver uses both the conductivity and the permittivity and is frequency dependent. Please read the manual before running any further simulation if you have not clear which limitations apply to each solver: this is very important to proceed further.

However, as @bryn also pointed out, the problem is then to decide which dielectric properties should be used. I agree with his observation.
If your application uses sufficiently small frequencies, i.e. up to several tents of kHz, we suggest that you use the Ohmic current dominated solver in combination with the LF-IT'IS tissue properties.

If you want further help, you should mention the type of application (e.g. neurostimulation) and the frequencies of interest. We could suggest you further documentation and scientific literature.