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REVIEW 3 major objections 6 minor 82 references

NELM: Modern Open-Source Software for Multipurpose Impedance Spectra Analysis

T0 review · 3 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read NELM is a free, open-source MatLab/GNU Octave package for CNLS fitting of impedance spectra to arbitrary equivalent circuits, with Monte Carlo multistart stabilization and adaptive filtering, validated on RLC circuits, a silicon…

desk verdict Open-source impedance fitting package with real features and honest validation examples, but the universal RL-CPE+delay model needs identifiability checks before the physics claims carry weight. read the letter →

arxiv 2506.01997 v1 pith:7RSLWN6Y submitted 2025-05-19 physics.app-ph physics.comp-phphysics.data-an

Natalia A. Boitsova , Anna A. Abelit , Daniil D. Stupin This is my paper · ORCID
classification physics.app-phphysics.comp-phphysics.data-an
keywords impedancespectroscopyCNLSequivalentcircuitsconstantphaseelementadaptivefilteringMonteCarlomultistartbiosensingopen-sourcesoftware
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper introduces NELM, a free and open-source MatLab/GNU Octave package for electrical impedance spectroscopy analysis. Its central claim is that NELM can fit measured immittance spectra to essentially arbitrary equivalent circuits by complex nonlinear least squares, with user-chosen solvers, weights, immittance representations, Monte Carlo multistart stabilization, and an adaptive filtering mode for noisy time-domain data. The authors argue this matters because existing impedance analysis software is largely closed-source, dated, or limited to series/parallel circuits, and cannot handle delay exponents or high-resolution noisy spectra. They support the claim with demonstrations on RLC circuits, a silicon photodiode whose 0.7 V barrier potential is recovered, cultured-cell biosensing where cell-induced resistance changes are tracked, and a noise-immunity test at -6 dB signal-to-noise ratio.

What carries the argument

The engine is the CNLS working function $$$E^{2}$ = \frac{1}{L}\sum_{\ell=1}^{L} |Y_m(\omega_\ell)-$Y^{{ex}}$(\omega_\ell)|^2 W(\omega_\ell),$$ minimized by a switchable set of solvers, including simplex search, damped Newton-type refinement, coordinate and gradient descent, trust region, and homotopy methods. The workhorse model in most validations is the generalized RL-CPE circuit with delay exponent, $$Z = \left(R+i\omega L + \frac{1}{W(i\omega)^\$\alpha$}\right)$e^{{i\omega\tau}}$,$$ in which $1/(W(i\omega)^\alpha)$ is the constant-phase element modelling non-ideal capacitive behaviour and $e^{i\omega\tau}$ accounts for the time offset between voltage and current sampling; fixing the CPE exponent at unity reduces it to an RLC circuit, which is how the same model spans resonant circuits, photodiodes, and cell-covered electrodes. The adaptive filtering mode uses a separately implemented optimal linear filter, trained on the measured voltage and current sequences, to produce clean spectra before CNLS fitting. Making the model an anonymous function and generating Jacobians symbolically is what lets users define bridge circuits and custom models without touching the core solver.

What would settle it

Generate a synthetic impedance spectrum from a known equivalent circuit that contains an element the fitting model omits, such as a second RC time constant, and run NELM's CNLS with Monte Carlo stabilization on it. If the fit produces low residuals but recovered parameters that deviate from the known values, or if the Monte Carlo confidence intervals exclude the true values, then the claim that NELM reliably recovers physical parameters from real spectra would be weakened.

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Extended reading notes

Core claim

The paper's central claim is that NELM supplies a complete and flexible CNLS fitting pipeline: the user selects the immittance type, the weighting, the minimization solver, and the equivalent circuit, either from built-in models, by fixing parameters in the style of the classic CNLS construction method, or by generating a new model symbolically with automatic Jacobian computation. Around this core, NELM layers a Monte Carlo multistart that seeds parallel fits from the previous spectrum, a warming-up mode for the first spectrum, confidence intervals from both Monte Carlo statistics and linearized error analysis, and an adaptive filtering method that estimates spectra from noisy time-domain recordings. The validation results reported are that NELM recovers the ratings of RLC circuits, identifies the photodiode pn-junction as near-ideal and abrupt with a 0.7 V diffusion barrier matching the datasheet, detects a single cultured cell floating over a microelectrode as a synchronous rise and fall in fitted resistance while pseudo-capacitance stays stable, and, in the adaptive filtering test, recovers the parameters of a cell-like R-CPE circuit at -6 dB SNR where the FFT-based approach fails. The paper's position is that these demonstrations establish NELM as a general-purpose tool for semiconductor, electrochemical, and biosensing applications.

Load-bearing premise

The load-bearing premise is that the simple model circuits chosen for the test systems actually represent the physics of those systems, so the fitted values, such as the 0.7 V photodiode barrier or the cell-induced resistance change, are real properties and not artifacts absorbed by the model.

Editorial extensions

If this is right

  • Users of impedance spectroscopy gain a free alternative to closed packages for fitting arbitrary equivalent circuits, including bridge topologies and delay-exponent terms that series/parallel-only tools cannot represent.
  • Batch time-series data, such as long cell-culture or corrosion experiments, can be fitted with warm starts from the previous spectrum and Monte Carlo multistart, reducing the impact of local minima on long runs.
  • The adaptive filtering mode makes CNLS fitting practical on spectra recorded at negative signal-to-noise ratios, which matters for implantable and wearable bioimpedance sensors.
  • Because models and solvers are user-extensible and the code is open, the package can be adapted to new equivalent circuits or new minimization protocols by modifying settings files rather than rewriting the analysis core.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If NELM is adopted, impedance analyses become more reproducible: the settings files, model definitions, and fixed parameters together form an explicit record of the analysis, which the paper does not highlight as a sharing feature.
  • The warm-start plus Monte Carlo multistart recipe is a general remedy for drift-prone time-series fitting and could transfer to other spectroscopies that suffer the same local-minimum and noise problems.
  • The adaptive-filtering result implies that visual fit quality is not a reliable success criterion: spectra can look well approximated while parameter estimates are wrong, so future EIS studies should report parameter uncertainties and the noise-handling method used.
  • The symbolic model generator suggests a broader reach than electrochemistry: any system whose response can be written as an immittance-like transfer function could in principle be fitted with the same core, making NELM a general immittance-fitting platform rather than an EIS-only tool.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper introduces NELM, a free, open-source MatLab/GNU Octave package for complex nonlinear least-squares (CNLS) analysis of impedance spectra. It describes the package architecture, data-loading and model interfaces, built-in equivalent-circuit models, multiple minimization solvers, Monte-Carlo multistart stabilization, confidence-interval estimation, symbolic model construction via Make_Model, and an adaptive-filtering (AF) noise-reduction routine. Validation is demonstrated on factory-rated RLC circuits, a BPW 20 RF silicon photodiode (yielding a barrier potential of 0.7 V), HeLa cell detachment monitored on a multielectrode array, and a Lapicque-circuit noise-immunity test comparing AF with FFT. The central claim is that NELM provides a modern, flexible, open alternative to EC-Lab, ZView, and LEVM that reliably recovers physical equivalent-circuit parameters from experimental impedance spectra.

Significance. If the parameter-recovery claim holds, NELM is a valuable open-source contribution: it supports bridge circuits, arbitrary user-defined equivalent circuits, symbolic Jacobian generation, parallel Monte-Carlo initialization, and AF noise reduction, and it is demonstrated on four distinct application classes against external reference values (factory-rated components, a manufacturer's C-V plot, and nominal Lapicque element ratings). The GitHub distribution and example data support reproducibility, and the software addresses genuine limitations of existing packages. However, the validation is at proof-of-concept level, and the central identifiability question for the delay-exponent model used in most demonstrations is not addressed; the quantitative reliability claims therefore need additional support before they can be accepted.

major comments (3)
  1. [Sec. 6.1, Eq. (4)] The silicon-photodiode validation checks only the derived barrier potential (0.7 V) and the observation that the CPE exponent is close to unity; the individual fitted parameters R, L, W, alpha, tau and their uncertainties are not reported. Because e^{i omega tau} rotates the impedance phase linearly in frequency, tau can trade off against both alpha (which changes phase slope) and L (which rotates the high-frequency impedance) over the 10 Hz to 40 kHz band. A biased W with a compensating tau could still produce a plausible linear C-V curve. Please report the fitted parameters with confidence intervals and correlations, and include a comparison with tau fixed at zero; without this, the claim that NELM recovers the physical junction capacitance is not established.
  2. [Sec. 6.2] The HeLa cell conclusion, that the electrode resistance rises while pseudo-capacitance remains stable during cell detachment, rests on the same RL-CPE-with-delay model of Eq. (4). No confidence intervals, time-resolved parameter trajectories, or alternative fits with tau fixed are shown, so one cannot exclude the possibility that adjustments in tau or alpha absorb part of the cell-induced impedance change. The authors should quantify the stability of the CPE parameters, show the resistance trace with error bars, and demonstrate that the observed response is not an artefact of parameter trade-off before attributing it specifically to cell resistance.
  3. [Secs. 4.2, 6.1, 6.2] NELM already includes both Monte-Carlo-based and Jacobian-based confidence-interval machinery, and the AF test in Sec. 6.3 reports 99.9% intervals over 10 experiments. Yet the RLC, photodiode, and HeLa validations report no parameter uncertainties or correlations at all. To substantiate the reliability claim for Eq. (4), at least one of these validation studies should include a full parameter report (best values, MC scatter or Jacobian confidence intervals, and a correlation matrix), ideally accompanied by a synthetic-data recovery test with known parameters. Without this, the absence of uncertainty reporting is a load-bearing gap, not merely a presentation issue.
minor comments (6)
  1. [Eq. (2)] The Hermitian-conjugation symbol is missing in the typeset normal equations: the expression 'J +J' should read J^dagger J and J^dagger F; as printed the equation is not mathematically valid.
  2. [Sec. 6.3, Fig. 7] The lower panels (c)-(e) are described only as 'Lower panels'; the text should state explicitly which panel shows which element rating to make the figure self-contained.
  3. [Throughout] The program name is spelled inconsistently as 'EC-lab' and 'EC-Lab'; please standardize.
  4. [Sec. 4.2] The sentence 'we does not use build into MatLab method MultiStart' should read 'we do not use the built-in MatLab MultiStart method'.
  5. [Sec. 5.2, Table 2] The text refers to 'asimplde_DRT.m' and 's implde_DRT.m' while Table 2 lists 'Simple_DRT.m'; please verify the actual file name in the distribution.
  6. [Abstract, Sec. 4.3] The abstract claims 'artificial intelligence' and the text calls AF 'AI-based adaptive filtering,' but the implemented AF method is a Wiener least-squares filter; this wording overstates the AI content.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper validates NELM on external benchmarks, and self-citations are implementation references rather than derivation inputs.

full rationale

The central content of the paper is a software description and a set of application demonstrations, not a theoretical derivation that reduces to its own inputs. The validation cases use independent points of reference: factory-rated RLC components, a digitized manufacturer CV curve for the BPW 20 RF photodiode, a Lapicque circuit with explicitly specified reference ratings for the AF noise-immunity test, and the published Giæver-Keese model for the HeLa cell experiments. The RL-CPE model with delay exponent, Eq. (4), is presented as a fitting ansatz, not derived from NELM, and the fitted parameters are then compared with external values. The one internal consistency check, where resonance peak position and height are recomputed from the NELM fit output in Sec. 6.1, is a sanity check rather than an independent prediction, and it is not load-bearing for the software's overall capability claim. The adaptive-filtering method originates in the authors' prior work (Ref. [12]) and the Monte-Carlo stabilization in Ref. [30], but the AF demonstration in Sec. 6.3 benchmarks the method against a known circuit with known element values, so the self-citations are not unexamined inputs that force the conclusion. No equation is shown to equal its own input, and no fitted parameter is renamed as a prediction. Identifiability concerns about trade-offs among tau, alpha, and L in Eq. (4) are correctness or uncertainty issues, not circularity. Overall, the derivation chain is self-contained against external benchmarks, and the paper warrants a non-circularity finding.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

NELM is a fitting tool, so the ledger is mostly model and method assumptions. No physical entities or hidden fitted constants are introduced: the EC parameters fitted in the examples are the intended outputs of the analysis. The key unproved premises are the adequacy of the chosen equivalent circuits, the reliability of the CNLS solvers, and the validity of the self-cited adaptive-filtering framework.

assumptions (5)
  • domain assumption The RL-CPE equivalent circuit with delay exponent e^(i*omega*tau) in Eq. (4) adequately represents the RLC circuits, the BPW 20 RF photodiode, and the HeLa cell-electrode system.
    Used for all validation fits except the AF noise test in Sec. 6. If this model omits a relevant process, the extracted R, L, W, alpha, and tau values could fit the data while not corresponding to the claimed physical quantities.
  • domain assumption The adaptive filtering impedance spectroscopy theory from Ref. [12] is correct for noise-immune spectrum reconstruction.
    The noise-combat demonstration in Sec. 6.3 relies entirely on this self-cited theory; the paper does not re-derive or independently verify it.
  • domain assumption Monte Carlo multistart with warm-up initialization stabilizes the CNLS fitting and avoids local minima.
    The batch processing workflow in Sec. 4.2 and Fig. 2 assumes that randomized restarts around the previous best fit are sufficient to keep the fit process stable.
  • domain assumption The AF training sequences are long enough relative to filter order to avoid overlearning.
    The paper itself states in Sec. 6.3 that the AF theory assumes infinite length and that sufficient length is needed to prevent interpolation; no quantitative guidance is given.
  • domain assumption The model m-functions return correct admittances and Jacobians.
    Jacobian-based confidence intervals and CNLS solvers in Sec. 4.1 and 4.4 depend on accurate Jacobian evaluation; no unit tests or independent checks are shown.

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Cite this review

Pith. "Pith review of NELM: Modern Open-Source Software for Multipurpose Impedance Spectra Analysis." pith.science (2026). https://pith.science/paper/7RSLWN6Y

@misc{pith2026250601997,
  author       = {Pith},
  title        = {Pith review of: NELM: Modern Open-Source Software for Multipurpose Impedance Spectra Analysis},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7RSLWN6Y}},
  note         = {Machine review of arXiv:2506.01997}
}
read the original abstract

Nowadays electrical impedance spectroscopy (EIS) has become an advanced experimental technique with a wide range of applications: from simple passive circuits diagnostics to semiconductor high-end device development and breakthrough technologies in bio-sensing. Although hardware for EIS today is well developed, the EIS analysis software is mainly custom, old fashioned, i.e. it is limited by features, does not utilize the progress in the modern computer science and hardware, and is usually implemented in close-source code or written on outdated programming languages, which causes slow progress in field of the EIS and complicates researchers attempts of development in EIS autonomous devices, such as implants. In this article, we introduce a free and open-sourced MatLab/GNU Octave package for EIS analysis called NELM, which provides powerful equipment tools for matching experimental impedance data with theoretical equivalent circuits. Our software has an user friendly interface and supports different formats of input data, fitting programs, and impedance models. In addition, we have developed NELM with implementation of the latest progress in computation science such as symbolic calculations, parallel computing, and artificial intelligence. The abilities of NELM were validated by its applications in the different fields of science, such as semiconductor studies, bioimpedance and electrochemestry, which demonstrated high-efficiency of the proposed software package and showed that it is a promising tool for solving actual problems in electronic industry, biosensorics, and healthcare technologies.

Figures

Figures reproduced from arXiv: 2506.01997 by the authors.

Figure 1
Figure 1. Architecture of the NELM engine. To provide the program flexibility NELM has: data loading interface, which convert the data in arbitrary format to the MatLab complex column￾array by anonymous function @Get_Spectrum_Func; model loading interface, which evaluate by anonymous function Channels.Model the EC immittance; the structure options, which define the approximations process settings; the main universal approxima… view at source ↗
Figure 2
Figure 2. NELM Software Block Diagram. Here ⃗r is a random vector, MC is Monte-Carlo, CI is confidence intervals. 8 [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Screenshots of NELM software. (a) MatLab editor window in which the NELM shell code is open, and a message prompting to continue the previously started CNLS processing of spectra; (b) window for selecting an equivalent circuit for data processing. 9 [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Screenshots of NELM software (continued). (a) [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]
Figure 5
Figure 5. Figure 5: Kaleidoscope of the NELM applications for various scientific tasks. (a) and (b) Iden [PITH_FULL_IMAGE:figures/full_fig_p027_5.png]
Figure 6
Figure 6. Figure 6: The demonstration of the NELM applicability for the cell biophysics research. In this [PITH_FULL_IMAGE:figures/full_fig_p030_6.png]
Figure 7
Figure 7. Figure 7: Demonstration of the AF impedance spectroscopy noise immunity. Here green dots are corresponds to the experimental [PITH_FULL_IMAGE:figures/full_fig_p033_7.png]

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Pith tools

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