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Topological texture analysis of microscopy images of dynamic casein gelation and its relation to rheological properties

T0 review · 2 major / 2 minor · reviewed 2026-06-28 · grok-4.3

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Pith's one-line read TDA on STED images uses max-Betti-1 curves to track protein network loops during casein gelation matching rheology.

desk verdict Max-Betti-1 curves from TDA on the STED time series track the percolation point and sol-gel transition in these casein gels and line up with the rheology data. read the letter →

arxiv 2606.02048 v1 pith:UTZEJGPE submitted 2026-06-01 cs.AI cs.CVphysics.bio-ph

Zahra Tabatabaei , Diana Soto Aguilar , Jose C. Bonilla , Mathias P. Clausen , Jon Sporring This is my paper · ORCID
classification cs.AIcs.CVphysics.bio-ph
keywords topologicaldataanalysiscaseingelationSTEDmicroscopysol-geltransitionproteinnetworkrheologicalpropertiesmicrostructurefractal
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

This paper presents a toolbox that applies topological data analysis along with fractal and texture methods to time-lapse super-resolution images of sodium caseinate gels forming at different temperatures and acidifier levels. The key is using max-Betti-1 curves to follow the appearance and changes of closed loops in the protein structure. These curves identify an early dispersed phase, a rapid shift when the network connects, and later rearrangements, all aligning with the point where the material changes from liquid to gel in rheological tests. Other image measures back this up by showing complexity changes. The result is a way to see fine details of how the microstructure develops that are smoothed over in bulk property measurements.

What carries the argument

max-Betti-1 curves from TDA that track topological loops as measures of protein network interconnectivity

What would settle it

A mismatch between the timing of the sharp decay in the max-Betti-1 curve and the rheological measurement of the sol-gel transition in the same gelation experiment would indicate the correspondence does not hold.

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Extended reading notes

Core claim

The authors establish that max-Betti-1 curves from topological data analysis on STED microscopy images of dynamic casein gelation reveal a lag phase of dispersed aggregates, a sharp decay coinciding with network percolation and the sol-gel transition observed in rheology, and a post-gelation increase linked to network rearrangements.

Load-bearing premise

The assumption that max-Betti-1 curves directly and quantitatively reflect the network interconnectivity and mark the sol-gel transition without extra calibration or independent checks.

Editorial extensions

If this is right

  • The integrated methods detect structural changes at different GDL concentrations and temperatures.
  • DBC and MFP corroborate the TDA findings on complexity and heterogeneity.
  • The approach is more sensitive to microstructural details than bulk rheology alone.
  • Validation on simulated images supports reliability for experimental use in food science.

Reading between the lines

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

  • This topological tracking could extend to monitoring gelation in other protein or polymer systems.
  • Industrial processes might use such image-based metrics for quality control during gel formation.
  • Further work could test if these curves predict final gel properties like strength or texture.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 2 minor

Summary. The paper introduces an integrated computational toolbox combining Topological Data Analysis (via max-Betti-1 curves tracking loops in protein networks), Differential Box Counting (DBC), Multifractal Partition (MFP), and Local Binary Patterns (LBP) applied to time-lapse STED microscopy images of sodium caseinate gelation induced by GDL at 30°C/40°C and two concentrations. It claims these descriptors reveal a lag phase of dispersed aggregates, a sharp decay in max-Betti-1 at network percolation matching the rheologically observed sol-gel transition, and post-gelation increases due to rearrangements, with DBC/MFP corroborating changes in complexity and heterogeneity; the approach is validated on simulated fractal images and positioned as more sensitive to microstructural dynamics than bulk rheology, with code released.

Significance. If the reported alignment between max-Betti-1 transitions and independent rheological measurements holds under quantitative scrutiny, the work supplies a practical multi-descriptor framework for quantifying evolving network interconnectivity in soft-matter systems, with direct relevance to food science and materials characterization. The validation on simulated fractals and public code repository strengthen reproducibility and allow extension to other dynamic imaging datasets.

major comments (2)
  1. [Abstract and Results] Abstract and Results: the central claim that max-Betti-1 curves 'directly and quantitatively correspond' to the sol-gel transition and network percolation rests on visual coincidence with rheological data, yet no correlation coefficients, timing offsets with error bars, or statistical tests across replicates are reported; this absence is load-bearing because the claimed sensitivity advantage over bulk rheology cannot be evaluated without such metrics.
  2. [Methods] Methods: the extraction of max-Betti-1 from STED time series (including filtration, persistence diagram construction, and any image preprocessing or thresholding) is described at a high level only; without explicit parameters or pseudocode, independent reproduction of the reported lag-phase and decay features is not possible, undermining the toolbox's utility as a 'robust quantitative tool'.
minor comments (2)
  1. [Abstract] Abstract: the phrase '30 {\deg}C' should be rendered as standard degree symbol for readability.
  2. [Discussion] The manuscript would benefit from a table summarizing the four descriptors (TDA, DBC, MFP, LBP) and the specific microstructural features each is sensitive to, to clarify their complementary roles.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help strengthen the quantitative rigor and reproducibility of the work. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract and Results] Abstract and Results: the central claim that max-Betti-1 curves 'directly and quantitatively correspond' to the sol-gel transition and network percolation rests on visual coincidence with rheological data, yet no correlation coefficients, timing offsets with error bars, or statistical tests across replicates are reported; this absence is load-bearing because the claimed sensitivity advantage over bulk rheology cannot be evaluated without such metrics.

    Authors: We agree that the current manuscript presents the alignment between max-Betti-1 transitions and rheological data primarily through visual inspection without accompanying quantitative metrics. In the revision we will add Pearson and Spearman correlation coefficients computed between the normalized max-Betti-1 curves and the storage modulus G' across all biological replicates, report mean timing offsets with standard deviations at the identified percolation points, and include appropriate statistical tests (e.g., paired t-tests or Wilcoxon tests) to evaluate whether the observed transitions differ significantly from the rheologically determined gel points. These additions will allow direct assessment of the claimed sensitivity advantage. revision: yes

  2. Referee: [Methods] Methods: the extraction of max-Betti-1 from STED time series (including filtration, persistence diagram construction, and any image preprocessing or thresholding) is described at a high level only; without explicit parameters or pseudocode, independent reproduction of the reported lag-phase and decay features is not possible, undermining the toolbox's utility as a 'robust quantitative tool'.

    Authors: We acknowledge that the Methods section currently provides only a high-level overview of the TDA pipeline. In the revised manuscript we will expand this section with the precise filtration parameters (e.g., Vietoris-Rips or cubical complex settings), persistence-diagram construction details, image-preprocessing steps (denoising, intensity normalization), and any thresholding values used. We will also include pseudocode for the max-Betti-1 extraction routine and deposit the full implementation in the existing public repository with version-tagged scripts that reproduce the reported curves. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity identified

full rationale

The paper presents an empirical application of TDA (via max-Betti-1 curves), DBC, MFP, and LBP to STED time-lapse images of casein gelation, with direct comparison to independent rheological measurements of the sol-gel transition. No equations, fitted parameters, or self-citations are described that would reduce the reported topological transitions or percolation points to quantities defined by the same data or prior author work. The toolbox is validated on simulated fractal images before experimental use, and the central claims rest on external corroboration rather than internal redefinition or self-referential fitting. This is a standard non-circular empirical study.

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

Abstract-only view supplies no explicit free parameters, axioms or invented entities; the toolbox applies established computational descriptors to new image data.

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Cite this review

Pith. "Pith review of Topological texture analysis of microscopy images of dynamic casein gelation and its relation to rheological properties." pith.science (2026). https://pith.science/paper/UTZEJGPE

@misc{pith2026260602048,
  author       = {Pith},
  title        = {Pith review of: Topological texture analysis of microscopy images of dynamic casein gelation and its relation to rheological properties},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UTZEJGPE}},
  note         = {Machine review of arXiv:2606.02048}
}
read the original abstract

We propose a novel computational toolbox that integrates Topological Data Analysis (TDA), Differential Box Counting (DBC), Multifractal Partition (MFP), and Local Binary Patterns (LBP), applied to time-lapse super-resolution STED microscopy images of sodium caseinate gelation induced by glucono-delta-lactone (GDL) at 30 {\deg}C and 40 {\deg}C and two GDL concentrations (1.8% and 3.5% w/v). TDA tracked topological loops, closed ring-like structures reflecting protein network interconnectivity, via max-Betti-1 curves, which revealed a lag phase of dispersed aggregates, a sharp decay coinciding with network percolation and the rheologically observed sol-gel transition, and a post-gelation increase corresponding to network rearrangements. These topological transitions were corroborated by DBC and MFP as these methods were able to resolve changes in structural complexity and spatial heterogeneity. The toolbox was validated on simulated fractal images prior to experimental application. Together, these descriptors provided sensitivity to subtle microstructural transitions that bulk rheology captured as averaged bulk mechanical responses. This integrated approach provides a robust quantitative tool for characterizing complex microstructure in food and material science with evolving microstructural dynamics. Code is available at https://github.com/Zahratabatabaei/Delifood_CV_paper.git

Figures

Figures reproduced from arXiv: 2606.02048 by the authors.

Figure 1
Figure 1. Topological background and cubical complex pipeline used for persistence-based analysis. As it is mentioned above, TDA captures the topological descriptor of the network. For further investigation of intensity-based variations, fractal analysis was employed using DBC, which quantifies grayscale structural complexity. Fractal dimension Typically, a Fractal Dimension (FD) analysis uses a binarized image, which yields … view at source ↗
Figure 2
Figure 2. Quantitative descriptors extracted from the simulated fractal dataset. (a) Max-Betti-1 per image, where the frame index corresponds to the 30 simulated images and the y-axis shows the maximum number of loops. (b) DBC results as roughness increases from 0.70 to 1.00. (c) Generalized dimension D(q) as a function of moment order q for selected time points (Time 16–30). (d) Temporal evolution of the spectrum width ∆D, r… view at source ↗
Figure 3
Figure 3. Topological evolution and corresponding STED micrographs of sodium caseinate gelation under different GDL concentrations and temperatures. The trends observed in the max-Betti-1 graphs are consistent with protein aggregation processes. As the pH decreases in the system due to the hydrolysis of GDL into gluconic acid, casein proteins (αs1,αs2,β,κ) aggregate into small and reversible 10/20 [PITH_FULL_IMAGE:figures/fu… view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Topological max-Betti-1 curves (solid lines) and rheological parameter storage modulus (G’) (dashed lines) over pH at 30 °C (blue) and 40 °C (orange), with GDL concentration of 1.8% or 3.5%. formation aligns with the microstructure undergoing topological organization. …
Figure 5
Figure 5. Figure 5: STED micrographs of the evolution of NaCas gels in the rearrangement phase, after the gel point and until the end of aggregation (1h). System gelation induced by either 1.8% (a) or 3.5% (b) glucono-δ-lactone (GDL) with acidification at 30 °C (first row) and 40 °C (seco…
Figure 6
Figure 6. Figure 6: Fractal dimension via either DBC method (a) or via MFP method (b) over pH, at 30 °C (blue) and 40 °C (orange), with GDL concentration of 1.8% or 3.5%. Red vertical line marks the percolation point obtained via max-Betti-1 minimum. regular intensity surface than a unifo…
Figure 7
Figure 7. Figure 7: Entropy (a) and standard deviation (b) via the local binary pattern method, and storage modulus (G’) over pH, at 30 °C (blue) and 40 °C (orange), with GDL concentration of 1.8% or 3.5%. Red vertical line marks the percolation point obtained via max-Betti-1 minimum. Acc…

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    Cipelletti, L., Manley, S., Ball, R. & Weitz, D. Universal aging features in the restructuring of fractal colloidal gels.Phys. review letters84, 2275 (2000). 19/20 Supplementary Data Figure S1.Simulated set of the fractal images by increasing the roughness from 0.7 to 1. 20/20

    2000

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Reviewed June 28, 2026 · model on record in the stance chip above.