arxiv: 2604.18634 · v1 · submitted 2026-04-18 · 🧬 q-bio.QM

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Topological analysis of hemodynamic response to cardiac resynchronization therapy

Aina Ferr\`a Marc\'us , Carles Casacuberta , Josep Vives , Joan Guich , Gerard Amor\'os-Figueras , Jose M. Guerra

Authors on Pith no claims yet

Pith reviewed 2026-05-10 05:57 UTC · model grok-4.3

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keywords Mapper algorithmtopological data analysiscardiac resynchronization therapyhemodynamic responsebiventricular pacingswine modelself-connectivity indexendocardial versus epicardial

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The pith

Topological Mapper analysis finds basal pacing sites produce higher self-connectivity in hemodynamic responses than mid or apical sites during biventricular stimulation.

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

The study applies the Mapper algorithm to map distributions of four hemodynamic variables recorded during endocardial and epicardial biventricular pacing in a swine model of non-ischemic cardiomyopathy. It augments the resulting graphs with three new numerical indices that measure self-connectivity, scattering, and homogeneity. These measures detect statistically significant regional differences, with basal pacing yielding a self-connectivity index of 0.57 while mid and apical sites yield 0.14 and 0.24 respectively. Lateral endocardial stimulation further widens the separation between basal and non-basal patterns compared with epicardial stimulation. The approach demonstrates that topological tools can extract biologically interpretable distinctions in cardiac pacing effects from complex multivariate data.

Core claim

The Mapper algorithm applied to point clouds of hemodynamic variables generates graphs whose self-connectivity index reaches 0.57 for basal-region pacing but only 0.14 for mid-region pacing and 0.24 for apical-region pacing, with the differences statistically significant at p less than 0.01. Endocardial stimulation from lateral sites increases the separation between the basal and non-basal distributions relative to epicardial stimulation, revealing new quantitative distinctions across heart regions.

What carries the argument

The Mapper algorithm enhanced by quantitative indices that compute self-connectivity, scattering, and homogeneity directly from the colored graphs it produces.

If this is right

Pacing from basal left-ventricular regions consistently produces more internally connected topological structures in the hemodynamic variable space.
Lateral endocardial lead placement increases the topological contrast between basal and non-basal pacing effects compared with epicardial placement.
The self-connectivity index provides an objective, graph-based metric for ranking the hemodynamic impact of different CRT site combinations.
Topological indices can detect regional response patterns that remain hidden under standard summary statistics alone.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If the same topological signatures appear in human CRT patients, the indices could help select lead positions that maximize response homogeneity.
The observed basal-mid contrast may correspond to underlying differences in myocardial fiber orientation or local wall stress that future imaging studies could test.
Combining Mapper-derived indices with electrical activation maps might produce a joint optimization framework for multi-site pacing.

Load-bearing premise

The numerical indices extracted from Mapper graphs capture genuine biological differences in hemodynamic response distributions rather than depending on specific algorithm parameters or the swine model.

What would settle it

Re-running the Mapper construction on the same hemodynamic data with altered filter functions, cover parameters, or clustering methods and obtaining non-significant differences in self-connectivity between basal and mid/apical groups would falsify the central claim.

Figures

Figures reproduced from arXiv: 2604.18634 by Aina Ferr\`a Marc\'us, Carles Casacuberta, Gerard Amor\'os-Figueras, Joan Guich, Jose M. Guerra, Josep Vives.

**Figure 2.** Figure 2: Colored Mapper graph of the study dataset for a comparison between epicardial [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Figure 3: Colored Mapper graph using only epicardial points in the study dataset. Colors of vertices correspond to heart sites (red: basal; yellow: mid; blue: apical). 13 [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗

**Figure 4.** Figure 4: Colored Mapper graph using only endocardial points in the study dataset. Colors of vertices correspond to heart sites (red: basal; yellow: mid; blue: apical). Self-connectivity Scattering Homogeneity Basal 0.57 1.56 0.77 Mid 0.29 0.57 0.76 Apical 0.28 0.73 0.75 [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗

read the original abstract

Objective: The Mapper algorithm is a qualitative method in topological data analysis that constructs graphs from point clouds by combining dimensionality reduction and clustering techniques. The aim of this study is to apply Mapper, together with novel quantitative indices, to compare the effects of biventricular pacing from the left ventricular epicardium versus the endocardium in a swine model of pacing-induced non-ischemic cardiomyopathy. Methods: The distributions of four hemodynamic variables from a previous study on endocardial and epicardial cardiac resynchronization in an experimental swine model of nonischemic cardiomyopathy were analyzed using the Mapper algorithm, enhanced with numerical indices quantifying self-connectivity, scattering, and homogeneity of the resulting colored graphs. Results: Statistically significant differences were observed between pacing from basal regions versus mid or apical regions, with the following self-connectivity index values: basal $0.57$; mid $0.14$ ($p < 0.01$); apical $0.24$ ($p < 0.01$). Endocardial stimulation at lateral sites increased the contrast between the distributions of basal versus mid or apical data, when compared with epicardial stimulation. Conclusions: Topological analysis using the Mapper algorithm, enhanced with quantitative statistical measures, revealed new and biologically plausible significant differences in pacing effects across heart regions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper runs Mapper on existing swine CRT hemodynamic data and adds three new indices that flag basal vs mid/apical differences, but the methods are too thin to tell if those differences hold up.

read the letter

The core of this work is straightforward: they take four hemodynamic variables from a prior swine non-ischemic cardiomyopathy study, feed the point clouds into the Mapper algorithm, and define three new indices (self-connectivity, scattering, homogeneity) on the resulting graphs. The reported numbers show basal self-connectivity at 0.57 versus 0.14 mid and 0.24 apical, with p<0.01, plus a note that endocardial lateral pacing increases contrast over epicardial. That is the actual new piece—an application of Mapper plus these indices to distinguish pacing regions in this model.

Referee Report

3 major / 2 minor

Summary. The manuscript applies the Mapper algorithm from topological data analysis to distributions of four hemodynamic variables obtained from a swine model of pacing-induced non-ischemic cardiomyopathy. It introduces three novel quantitative indices (self-connectivity, scattering, and homogeneity) computed on the resulting colored graphs and reports statistically significant differences in the self-connectivity index between basal (0.57), mid (0.14, p < 0.01), and apical (0.24, p < 0.01) pacing regions, with endocardial stimulation at lateral sites producing greater distributional contrast than epicardial stimulation.

Significance. If the reported differences prove robust, the work illustrates how topological methods can extract regional and stimulation-mode distinctions in CRT hemodynamic responses that may be missed by conventional statistics. The swine-model findings could help guide site selection in clinical resynchronization, and the quantitative indices represent a methodological step toward making Mapper outputs more interpretable. However, the absence of parameter-sensitivity checks and basic experimental details substantially weakens the immediate biological or clinical implications.

major comments (3)

[Methods] Methods: The exact mathematical definitions and computational formulas for the self-connectivity, scattering, and homogeneity indices are not supplied. Because the central claims rest entirely on the numerical values of these indices (e.g., basal self-connectivity = 0.57), readers cannot reproduce the numbers or evaluate their dependence on Mapper parameters.
[Results] Results: No sample size (number of animals or total hemodynamic measurements per pacing condition) is stated, the statistical test underlying the p < 0.01 values is unspecified, and no correction for multiple comparisons is mentioned despite the use of three indices and multiple regional contrasts.
[Methods] Methods: No sensitivity or robustness analyses are presented for Mapper hyperparameters (filter functions, number of intervals, clustering resolution) or for the preprocessing steps applied to the four hemodynamic variables. The reported regional differences and endocardial-versus-epicardial contrast therefore cannot be distinguished from possible artifacts of the chosen configuration.

minor comments (2)

[Abstract] Abstract and Methods: The four hemodynamic variables are never named; listing them explicitly would improve reproducibility.
Figure legends: Color scales and graph-construction parameters should be stated so that the colored Mapper graphs can be interpreted without reference to the main text.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed and constructive feedback on our manuscript. We address each of the major comments below and have made revisions to improve the clarity and reproducibility of the work.

read point-by-point responses

Referee: [Methods] Methods: The exact mathematical definitions and computational formulas for the self-connectivity, scattering, and homogeneity indices are not supplied. Because the central claims rest entirely on the numerical values of these indices (e.g., basal self-connectivity = 0.57), readers cannot reproduce the numbers or evaluate their dependence on Mapper parameters.

Authors: We agree that the precise mathematical definitions of the indices are necessary for reproducibility. In the revised manuscript we have added an explicit subsection in Methods that supplies the formulas for self-connectivity (fraction of intra-color edges in the Mapper graph), scattering (normalized variance of node colors across connected components), and homogeneity (entropy of the color distribution within each component). These definitions are now stated in sufficient detail that the reported index values can be recomputed from the underlying point clouds. revision: yes
Referee: [Results] Results: No sample size (number of animals or total hemodynamic measurements per pacing condition) is stated, the statistical test underlying the p < 0.01 values is unspecified, and no correction for multiple comparisons is mentioned despite the use of three indices and multiple regional contrasts.

Authors: We acknowledge the reporting omissions. The hemodynamic recordings were obtained from the prior swine study (N = 8 animals, with 12–18 measurements per pacing site and mode). We have now stated these numbers in Methods, identified the statistical procedure (Kruskal–Wallis test followed by post-hoc Dunn tests), and applied Bonferroni correction across the three indices and regional contrasts. The corrected p-values and sample-size information appear in the revised Results. revision: yes
Referee: [Methods] Methods: No sensitivity or robustness analyses are presented for Mapper hyperparameters (filter functions, number of intervals, clustering resolution) or for the preprocessing steps applied to the four hemodynamic variables. The reported regional differences and endocardial-versus-epicardial contrast therefore cannot be distinguished from possible artifacts of the chosen configuration.

Authors: We recognize that the absence of sensitivity checks limits confidence in the findings. In the revision we have added a dedicated robustness subsection that repeats the Mapper pipeline across a grid of interval counts (8–20), clustering resolutions, and two alternative filter functions, as well as with and without z-score normalization of the hemodynamic variables. The basal-versus-mid/apical self-connectivity contrast remains statistically significant in all tested configurations; these results and the corresponding supplementary figures have been incorporated into the revised manuscript. revision: yes

Circularity Check

0 steps flagged

No significant circularity; analysis is data-driven

full rationale

The paper applies the Mapper algorithm to distributions of four hemodynamic variables and computes novel indices (self-connectivity, scattering, homogeneity) directly from the resulting graphs. Statistical comparisons (e.g., basal vs. mid/apical self-connectivity values and p-values) are performed on these computed quantities without any model fitting, parameter prediction, or derivation that reduces the reported differences to the inputs by construction. No self-citations, uniqueness theorems, or ansatzes are invoked in a load-bearing way. The central claims remain independent observational results from the data.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 3 invented entities

The central claim depends on the Mapper algorithm producing interpretable graphs from the four hemodynamic variables and on the three new indices faithfully quantifying connectivity, scattering, and homogeneity without additional validation against independent biological benchmarks.

axioms (1)

domain assumption The Mapper algorithm, when applied to point clouds of hemodynamic variables, yields graphs whose topological features correspond to biologically relevant differences in cardiac response.
Invoked implicitly in the methods description of applying Mapper to the distributions of hemodynamic variables.

invented entities (3)

self-connectivity index no independent evidence
purpose: Quantify the degree of connectivity within the colored Mapper graphs
Newly introduced quantitative measure whose exact formula is not provided in the abstract.
scattering index no independent evidence
purpose: Quantify the degree of scattering within the colored Mapper graphs
Newly introduced quantitative measure whose exact formula is not provided in the abstract.
homogeneity index no independent evidence
purpose: Quantify the degree of homogeneity within the colored Mapper graphs
Newly introduced quantitative measure whose exact formula is not provided in the abstract.

pith-pipeline@v0.9.0 · 5556 in / 1549 out tokens · 49163 ms · 2026-05-10T05:57:50.079383+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

21 extracted references

[1]

Amor ´os-Figueras, E

G. Amor ´os-Figueras, E. Jorge, S. Raga, et al. (2018), Comparison between endocardial and epicardial cardiac resynchronization in an experimental model of non-ischaemic car- diomyopathy, EP Europace 20(7):1209–1216

2018
[2]

Bordachar, N

P. Bordachar, N. Grenz, P. Jais, et al. (2012), Left ventricular endocardial or triventricu- lar pacing to optimize cardiac reshynchronization therapy in a chronic canine model of ischemic heart failure, Am. J. Physiol. Heart Circ. Physiol. 303(2):207–215

2012
[3]

Carlsson (2009), Topology and data, Bull

G. Carlsson (2009), Topology and data, Bull. Amer. Math. Soc. 46(2):255–308

2009
[4]

Dłotko, W

P. Dłotko, W. Qiu, and S. T. Rudkin (2024), Financial ratios and stock returns reappraised through a topological data analysis lens, Eur. J. Finance 30(1), 53–77

2024
[5]

Dzemali, F

O. Dzemali, F. Bakhtiary, S. Dogan, et al. (2006), Perioperative biventricular pacing leads to improvement of hemodynamics in patients with reduced left-ventricular function – in- terim results, Clinical Trial Pacing Clin. Electrophysiol. 9(12):1341–1345

2006
[6]

A. A. Hagberg, D. A. Schult, and P. J. Swart (2008), Exploring network structure, dynam- ics, and function using NetworkX, Proceedings of the 7th Python in Science Conference (SciPy2008), pp. 11–15

2008
[7]

T. S. C. Hinks, X. Zhou, K. J. Staples, et al. (2015), Innate and adaptive T cells in asth- matic patients: Relationship to severity and disease mechanisms, J. Allergy Clin. Im- munol. 136(2):323–333

2015
[8]

Kalyanaraman, M

A. Kalyanaraman, M. Kamruzzaman, and B. Krishnamoorthy (2019), Interesting paths in the Mapper complex, J. Comput. Geom. 10(1):500–531

2019
[9]

Kepler Mapper, https://kepler-mapper.scikit-tda.org/en/latest/
[10]

Kim and J

K. Kim and J. Altmann (2017), Effect of homophily on network formation, Commun. Nonlinear Sci. Numer. Simulat. 44:482–494. 11

2017
[11]

Li, W.-Y

L. Li, W.-Y . Cheng, B. S. Glicksberg, et al. (2015), Identification of type 2 dia- betes subgroups through topological analysis of patient similarity, Sci. Transl. Med. 7(311):311ra174

2015
[12]

T. Liao, Y . Wei, M. Luo, et al. (2019),tmap:an integrative framework based on topolog- ical data analysis for population-scale microbiome stratification and association studies, Genome Biol. 20(1):293

2019
[13]

P. Y . Lum, G. Singh, A. Lehman, et al. (2013), Extracting insights from the shape of complex data using topology, Sci. Rep. 3(1236)

2013
[14]

Y . Ma, X. Liu, N. Shah, and J. Tang (2022), Is homophily a necessity for graph neural networks? Proceedings of ICLR 2022

2022
[15]

Nicolau, A

M. Nicolau, A. J. Levine, and G. Carlsson (2011), Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival, Proc. Natl. Acad. Sci. USA 108(17):7265–7270

2011
[16]

Purvine, D

E. Purvine, D. Brown, B. Jefferson, et al. (2023), Experimental observations of the topol- ogy of convolutional neural network activations, Proceedings of AAAI’23, 1065:9470– 9479

2023
[17]

Rucco, E

M. Rucco, E. Merelli, D. Herman, et al. (2015), Using topological data analysis for diag- nosis pulmonary embolism, J. Theor. Appl. Comput. Sci. 9:41–55, 10

2015
[18]

Singh, F

G. Singh, F. M ´emoli, and G. Carlsson (2007), Topological methods for the analysis of high dimensional data sets and 3D object recognition, Eurographics Symposium on Point- Based Graphics

2007
[19]

Soriano-Amores, Z

M. Soriano-Amores, Z. Moreno-Weidmann, E. Jorge, et al. (2025), Premature ventricular contractions on healthy and diseased hearts: Differential acute effect of coupling interval and location, Heart Rhythm., in press

2025
[20]

Tao and S

Y . Tao and S. Ge (2025), A distribution-guided Mapper algorithm, BMC Bioinformatics 26:73

2025
[21]

Y . Yao, J. Sun, X. Huang, et al. (2009), Topological methods for exploring low-density states in biomolecular folding pathways, J. Chem. Phys.130(14):144115. 12 Supplementary Tables and Figures The following four variables have been used in the present study: left-ventricular peak pressure (LVP), maximum rising rate of LVP (DPDT+), minimum rising rate of...

2009