Electrode-Tissue Impedance Parameter Extractor

You send a tiny, harmless electrical test signal into an electrode and measure how it pushes back at different speeds. This tool looks at that response and works out four numbers describing what's happening where the electrode meets the tissue, plus how much to trust each answer.

Technical description: Randles-CPE parameter recovery (Rs, Rct, Q, α) from an impedance spectrum. A neural-network estimate is refined by local nonlinear least squares, entirely client-side.

Ground-truth parameters

Drag these to invent a scenario. The tool builds a spectrum from your settings, then tries to work the same four numbers back out from that spectrum alone, so you can see, side by side, how close it gets.

The plain resistance of the tissue and fluid around the electrode: a fixed obstacle to current, like a length of wire. It doesn't change no matter how fast the test signal wiggles.

Range 1 kΩ–50 kΩ: supported by real fitted values — Abidian & Martin 2009, 4.2–8.9 kΩ [2]; Nimbalkar et al. 2018, Rsol=4.4 kΩ [4]. Exact endpoints are an engineering judgment call, not literature-pinned.

10000

How hard it is for charge to actually cross from the electrode into the tissue. Low means an easy, leaky contact. High means a tight, resistant contact that charge struggles to cross.

Range 10 kΩ–10 MΩ: narrower than the real fitted spread [1][2] — real devices range from 3.34 kΩ [4] up to 97 MΩ [5] across gold/graphene/TiN/glassy-carbon neural microelectrodes. Treat this as a moderate-impedance electrode class, not a literature-pinned outer bound.

316000

How much the electrode surface behaves like a tiny capacitor, storing charge, rather than a plain resistor. Rougher, larger, or more porous surfaces tend to store more, giving a bigger number here.

Range 1×10-9–1×10-6 S·sα: close to, but slightly narrower than, the real measured spread of 6.7×10-10 to 1.25×10-6 S·sα [5] — minor, acceptable undercoverage.

3.16e-8

How close to textbook-ideal that capacitor-like behavior is. Close to 1.0 means a smooth, clean capacitor. Lower means a rougher, less uniform surface that behaves more sloppily.

Range 0.5–0.999: the upper portion (0.87–1.0) is directly supported by real measurements [2][4][5]. The 0.5 floor sits slightly below the lowest directly measured value (0.55 [2]), per the general CPE-modeling convention (α∈[0,1]) rather than a literature-pinned bound.

0.75
Phase 1 hand-checked cases:

Three specific scenarios checked by hand during development, so you can confirm at a glance that the tool is working correctly.

Real instruments never give a perfectly clean reading. Turn this on to add realistic random wobble to the generated spectrum, and see how well the tool still recovers the right answer.

Nyquist

A shape-based fingerprint of the spectrum. Each dot is one test frequency. A smooth, rounded arc usually means a clean, well-behaved electrode; a squashed or odd shape can point to a messier or less certain fit.

Measured (your data)Model's best-fit curve

Bode

The same data laid out directly against frequency. Top: how big the signal's resistance is at each frequency. Bottom: how much the signal's timing shifts at each frequency.

Measured (your data)Model's best-fit curve

References

Parameter ranges above are grounded in these sources where marked; gaps and extrapolations are flagged explicitly rather than presented as fully literature-derived. Full detail, including what was checked and what remains unverified, is in this project's PHASE1_NOTES.md and README.md.

  1. Cogan, S.F. (2008). "Neural Stimulation and Recording Electrodes." Annu. Rev. Biomed. Eng. 10:275–309. DOI. Used for order-of-magnitude support of the Rct range (in vivo 1 kHz total impedance, 50 kΩ–1 MΩ, not a decomposed Rct value).
  2. Abidian, M.R. & Martin, D.C. (2009). "Experimental and theoretical characterization of implantable neural microelectrodes modified with conducting polymer nanotubes." Biomaterials 29(9):1273–1283. PMC2692518. Direct Rs, Rct, Q, and α measurements on real gold neural-probe sites (four polymer coatings).
  3. "Electrode impedance analysis of chronic tungsten microwire neural implants: understanding abiotic vs. biotic contributions." PMC4021112. Consulted as a candidate source for an α-vs-implant-time relationship; it does not report CPE exponent values per timepoint, so it does not support that claim. Listed for transparency, not as a source for a number used here.
  4. Nimbalkar, S., Castagnola, E., Balasubramani, A., Scarpellini, A., Samejima, S., Khorasani, A., Boissenin, A., Thongpang, S., Moritz, C. & Kassegne, S. (2018). "Ultra-Capacitive Carbon Neural Probe Allows Simultaneous Long-Term Electrical Stimulations and High-Resolution Neurotransmitter Detection." Scientific Reports 8, 6958. DOI. Modified Randles-CPE fit on a glassy-carbon microelectrode: Rsol=4.4 kΩ, Rct=3.34 kΩ, Y0 (Q)=4.07×10-11 S·sα, α=0.87.
  5. Greenhorn, S., Coizet, V., Dupuit, V., Fernandez, B., Bres, G., Claudel, A., Gasner, P., Warnking, J.M., Barbier, E.L. & Delacour, C. (2024). "Ultrathin, flexible and MRI-compatible microelectrode array for chronic single units recording within subcortical layers." arXiv:2402.04389. Real fitted resistances and CPE coefficients across flexible gold/graphene and rigid TiN/graphene-on-sapphire neural microelectrodes: resistances from about 0.7 MΩ to 97 MΩ, CPE coefficients from about 6.7×10-10 to 1.25×10-6 S·sα.