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An efficient end-to-end computational framework for the generation of ECG calibrated volumetric models of human atrial electrophysiology

T0 review · 5 major / 5 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read The paper claims an automated workflow can generate ECG-calibrated volumetric atrial models from CT scans in under ten minutes, with fast-model P-waves matching full biophysical simulation to about 3.7% RMSE.

desk verdict A genuinely useful automation pipeline for biatrial modeling, but the ECG-calibration claim outruns the evidence and one mesh-quality statement in the paper contradicts another. read the letter →

arxiv 2502.03322 v1 pith:JBOBRGLL submitted 2025-02-05 math.NA cs.CEcs.NAq-bio.TO

Elena Zappon , Luca Azzolin , Matthias A.F. Gsell , Franz Thaler , Anton J. Prassl , Robert Arnold , Karli Gillette , Mohammadreza Kariman
show 7 more authors
Martin Manninger-Wünscher Daniel Scherr Aurel Neic Martin Urschler Christoph M. Augustin Edward J. Vigmond Gernot Plank
This is my paper · ORCID
classification math.NAcs.CEcs.NAq-bio.TO MSC 65M6092C3065N5092C50
keywords atrialelectrophysiologydigitaltwinsvolumetricbiatrialmodelsreaction-eikonalmodelreaction-diffusionelectrocardiogramcalibrationuniversalcoordinatesinter-atrialconduction
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 is trying to establish that high-fidelity, patient-specific computational models of the human atria, calibrated to the surface ECG, can be produced automatically and fast enough to build virtual patient cohorts and digital-twin snapshots at scale. The authors report a single workflow that takes a clinical CT scan through segmentation, volumetric wall construction, fiber and anatomical labeling, universal coordinate computation, torso registration, and inter-atrial pathway definition, producing a simulation-ready model in under ten minutes at reaction-eikonal resolution. They also report that the fast reaction-eikonal forward ECG reproduces the P-waves of a full reaction-diffusion simulation with an average root-mean-square error of 3.71%. If these claims hold, the practical payoff is that hundreds of patient-specific atrial models can be generated and parameter-swept for in silico studies, therapy planning, and regulatory-style testing.

What carries the argument

The load-bearing object is the end-to-end processing chain built on a volumetric image-stack representation. Instead of extruding a surface manifold, atrial walls are grown by rule-based erosion and dilation directly on the segmented image stack, which avoids topological errors and yields mesh quality above the 0.99 threshold used for bidomain solvers. Multiple Laplace-Dirichlet problems with Dirichlet boundary conditions on automatically detected orifices generate both the anatomical labels (sino-atrial node, crista terminalis, pectinate muscles, Bachmann's bundle, fossa ovalis) and the universal atrial coordinates that make parameter fields addressable. Inter-atrial conduction is parameterized by auto-generated conducting cables anchored at coordinate-defined sites, so insertion points can be swept without remeshing. The forward ECG uses a simplified reaction-eikonal model, which tracks activation times rather than full wavefront dynamics, combined with lead fields; reaction-diffusion conductivities are calibrated so both models propagate at matching velocities, reducing a full P-wave computation from roughly nineteen minutes to about one second.

What would settle it

Run the calibrated reaction-diffusion model on a cohort of patients and compare its simulated activation times and P-waves against clinically recorded electro-anatomical maps; if the model systematically misses measured local activation times by more than a small threshold, then the 3.71% agreement between the fast and full models does not establish clinical accuracy.

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Extended reading notes

Core claim

The central discovery is that the bottleneck to scalable atrial modelling is not any single component but the integration: a volumetric, image-stack-based wall extrusion that avoids topological errors, a set of Laplace-Dirichlet solutions that turn automatically detected orifices into anatomical labels and universal atrial coordinates, and a cable-based parameterization of inter-atrial conduction that allows insertion sites and velocities to be swept without remeshing. On 50 atrial fibrillation patients, the workflow produced meshes with element quality above 0.99, required no manual correction in 38 of 50 cases at the main processing stage, and generated ready-to-simulate models in an average of about 9 minutes at 0.90 mm resolution. The fast reaction-eikonal model, calibrated to the reaction-diffusion model's conduction velocities, produced activation maps and P-waves closely matching the gold standard, with an average P-wave RMSE of 3.71% across the 12 leads.

Load-bearing premise

The claim that the fast reaction-eikonal ECG matches the clinical gold standard rests on the assumption that the reaction-diffusion model with its calibrated conductivities is itself a faithful representation of human atrial electrophysiology; if that gold standard is wrong, the 3.71% error only measures agreement between two models.

Editorial extensions

If this is right

  • Each patient CT can yield a simulation-ready biatrial-torso model in under ten minutes at reaction-eikonal resolution, making large virtual cohorts feasible.
  • The fast reaction-eikonal forward ECG can replace reaction-diffusion simulations for calibration sweeps, since the average P-wave RMSE between the two is 3.71%.
  • Inter-atrial conduction pathways can be parameterized as automatically generated cables with tunable anchoring sites and conduction velocities, enabling sweeps over Bachmann's bundle insertion geometry without remeshing.
  • Parameters governing the P-wave, such as the sino-atrial node exit location and right-atrial conduction velocity, can be sampled to produce envelopes that cover clinical P-waves in most leads.
  • Generated meshes have element quality above the threshold considered critical for bidomain simulations, so the same anatomy supports both fast calibration and high-fidelity mechanistic studies.

Reading between the lines

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

  • The 3.71% RMSE is a model-to-model consistency check, not validation against measured human atrial electrophysiology; clinical validity would require comparing against invasive activation maps or ECG data in a cohort.
  • The cable-based inter-atrial parameterization could be reused to model reentrant circuits such as atrial flutter once a forward model capable of reentry is used, since the framework exposes inter-atrial anatomy as a tunable parameter.
  • The assumption of uniform atrial wall thickness likely limits patient specificity in regions where wall thickness varies, and a testable extension is to integrate patient-specific thickness maps once imaging resolution permits.
  • Because the P-wave is a global observation, the workflow does not by itself resolve the identifiability problem: many parameter sets may reproduce the same P-wave, so a dedicated optimization with uniqueness analysis is needed.
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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

5 major / 5 minor

Summary. The manuscript describes an end-to-end computational workflow for generating volumetric biatrial models from patient CT images, annotating anatomical structures and fiber architecture, computing volumetric universal atrial coordinates, modeling inter-atrial conduction with auto-generated cables, and computing 12-lead atrial P-waves using a reaction-eikonal lead-field forward model. The workflow was evaluated on 50 atrial fibrillation patients, with reported processing times for coarse (0.90 mm, reaction-eikonal) and fine (0.25 mm, reaction-diffusion) meshes, an R-E versus R-D comparison of activation and P-waves, parametric studies of Bachmann bundle insertion and SAN location, and a one-patient pseudo-calibration of the simulated P-wave to clinical ECG data.

Significance. The paper's concrete strengths are the large cohort of 50 real CT datasets, the reported per-stage processing times, the automated anatomical labeling pipeline, the flexible cable-based representation of inter-atrial connections, and the very fast R-E forward model for P-wave computation. If the mesh-quality and automation claims are made internally consistent, and if the ECG-calibration claim is appropriately scoped, the framework would be a useful contribution to scalable atrial digital twin generation. The R-E/R-D comparison, while currently only a model-to-model consistency check, is valuable as a numerical verification, but it is not a clinical validation of the relationship between simulated and measured P-waves.

major comments (5)
  1. [§3.1 and §4.3] The mesh-quality claims are contradictory. Section 3.1 states "Worst element quality was always below 0.99, according to the quality metric [55], which is considered a critical threshold in simulations using R-D solvers such as openCARP", while Section 4.3 states "achieving element quality exceeding a threshold of 0.99, which has been empirically identified as critical for cardiac bidomain simulations." These statements cannot both describe the same 50-model cohort. If the worst element quality is below 0.99, then the R-D meshes do not meet the stated critical threshold, which undermines both the "suitable for R-D" claim and the reliability of the R-D "gold standard" simulations used in Table 7. Please report the actual element-quality distribution, the minimum value, and the fraction of elements below the threshold, and correct the contradictory wording.
  2. [§3.7 and Table 11] The ECG-calibration demonstration is limited to a single patient and is essentially a fit to the data used for evaluation. Section 3.7 states "One anatomical model of a patient was selected", and the parameters (SAN location, RA conduction velocities, BB insertion sites) are chosen by minimizing RMSE against the measured P-wave, with no independent test set, cross-validation, or uncertainty quantification. Moreover, the simulated P-wave envelope does not cover the clinical signal in leads aVL, -aVR, and V1, and the Discussion attributes the V1 discrepancy to fibrotic tissue that is not modeled. The title's "ECG calibrated" claim is therefore stronger than what is demonstrated; the paper should reframe this as a feasibility demonstration of a pseudo-calibration workflow and explicitly state the identifiability and generalization limitations.
  3. [§3.3, Table 7, §2.2.2 and Table 4] The R-E/R-D comparison is presented as the validation of the fast forward model, but Section 3.3 says the results are "illustrated for a representative test case", and Table 7 reports a single row of RMSE values without indicating whether the 3.71% average is over the 50-patient cohort or one geometry. Please state the sample size and report per-case variability. In addition, because the R-D conductivities in Table 4 are calibrated with the ForCEPSS framework to reproduce the R-E conduction velocities, the RMSE in Table 7 measures model-to-model consistency under matched parameters, not accuracy against independent human electrophysiology; the "gold standard" wording in Section 3.3 should be qualified accordingly.
  4. [§3.1, Table 5 and §3.1.1] The automation statistics are internally inconsistent. Section 3.1 states that "all 50 cases in both resolutions were processed automatically in the majority of cases (38), with only minimal user intervention required in 22 cases", which does not add to 50. Table 5 lists 19 and 22 cases requiring manual correction at the first two stages, while Section 3.1.1 reports 21 cases for the CS/IVC landmark switch and 22 cases for IVC discard-tissue adjustment. Since "highly automated" is a headline claim, please provide a coherent per-stage and per-case accounting (for example, a table of correction types and a clear statement of how many of the 50 cases required any manual intervention).
  5. [§3.2, Table 6 and §4.6] The reported computational performance of the R-E model is inconsistent. Section 3.2 states that computation of a full biatrial activation sequence with a high-fidelity ECG takes about 1.00 s, while Table 6 reports "EP simulation ≈ 27 s" for the 0.90 mm/R-E case, and Section 4.6 states "A full single forward simulation lasted ≈ 27.00 s only where the actual evaluation of the EP model amounted only to ≈ 3.00 s." These numbers need to be reconciled with a precise definition of what is included in each timing (setup, lead-field computation, eikonal solve, ECG time-series generation) and on which hardware and mesh size they were measured.
minor comments (5)
  1. [§2.2.2] The global ECG scaling factor of 0.2 is introduced without justification; since the RMSE metric is amplitude-sensitive, the scaling should be reported as part of the model definition or the calibration procedure, not as an ad hoc post-processing step.
  2. [§3.7] There is a typo in "electrophysiologicalglsep excitability"; it should presumably be "electrophysiological excitability".
  3. [Table 4] The table heading contains a typo: "surface-to-volume ration" should be "surface-to-volume ratio".
  4. [§2.2.1] The sentence "The origin of the cable in the RA was chosen superior to the CS, at a distance between 3 and 8 .00 mm [21] from the CS ostium" could be clarified, since a range without a prescription for how it was chosen in the implemented models makes the parameter not fully reproducible.
  5. [§5] The Limitations section is candid about the uniform wall-thickness assumption and the cable approximation for inter-atrial connections, but the Discussion in Section 4.6 still uses the P-wave fit results as evidence of clinical compatibility; the wording should be adjusted to match the caveats stated in Section 5.

Circularity Check

2 steps flagged · score 4.0 of 10

Partial circularity: the R-D 'gold standard' is calibrated to match R-E conduction velocities, and the P-wave calibration is fit to the same clinical signal; a separate mesh-quality contradiction is a correctness risk, not circularity.

  1. fitted input called prediction [Section 2.2.2, Table 4; Section 3.3, Table 7]
    "To identify the electrical conductivities for the R-D model at the targeted mesh resolution that match the R-E conduction velocities, the ForCEPSS framework [47] was employed, using reported values [92] for initialization."

    The R-D model is designated the 'gold standard' in Section 3.3, but its conductivities are fitted by the authors' ForCEPSS framework to reproduce the R-E model's prescribed conduction velocities (Table 4). The subsequent comparison reports an average RMSE of 3.71% between R-E and R-D P-waves (Table 7). This is not an independent test of R-E accuracy: the target quantity, conduction velocity, is an input to the R-D fit, so the agreement largely reflects the success of that fit. It measures model-to-model consistency under matched parameters, not validation against an external, clinically calibrated gold standard.

  2. fitted input called prediction [Section 3.7, Table 11 and Figure 13]
    "In a first pseudo-calibration step for a fixed SAN exit site and baseline velocities in the RA, the location of BB was varied in interactive simulation runs to obtain a close approximation of the terminal half of the P-wave."

    The clinical P-wave used as the evaluation target is the same signal used to steer the interactive BB placement and to sample the SAN exit site and RA conduction velocities. The reported RMSE range [1.72%, 2.79%] (Table 11) is therefore a fit residual to the calibration data, not a prediction on held-out data. Since the paper frames this as a demonstration of calibration feasibility rather than a blinded validation, this is a partial circularity; the conclusion that 'the P-wave can be closely captured' is the success criterion of the fitting procedure itself.

full rationale

The anatomical model generation (Section 2.1), UAC computation (Section 2.1.5), inter-atrial cable formulation (Section 2.2.1), and rule-based fiber/label annotation are self-contained engineering contributions benchmarked on 50 CT datasets; these are not circular. The main circularity is in the R-E/R-D 'gold standard' comparison: Table 4's R-D conductivities are explicitly fitted with ForCEPSS to match the R-E conduction velocities, so the 3.71% average RMSE in Table 7 is a consistency measure between two models sharing the same prescribed CVs rather than an independent accuracy assessment of R-E against a clinically validated gold standard. This is partial, not total, because matching local CVs does not by itself force identical wavefront dynamics or ECGs. The Section 3.7 calibration demonstrates fitting rather than prediction: the BB anchor was chosen interactively to approximate the same clinical P-wave, and the SAN/velocity sample RMSE is evaluated on the same signal, so the reported [1.72%, 2.79%] RMSE is a fit residual. The paper is candid about the latter ('pseudo-calibration') and about identifiability limitations in Section 5, which lowers the severity. Self-citations to [42, 74, 77] support the RELF fidelity claim, but the paper also provides its own R-E/R-D comparison, so the claim does not reduce solely to a self-citation chain. Separately flagged as a correctness risk, not circularity: Section 3.1 states 'Worst element quality was always below 0.99' while Section 4.3 claims 'element quality exceeding a threshold of 0.99'; this internal contradiction should be resolved but does not by itself constitute a circular derivation.

Assumptions & free parameters 8 free parameters · 6 assumptions · 2 invented entities

The central workflow depends on many hand-chosen geometric and electrophysiological parameters, and the forward-model validation relies on a model-to-model consistency check rather than an external gold standard. The most load-bearing free parameters are the per-region conduction velocities and the conductivities calibrated to match them, since they determine the P-wave morphology that the paper claims to compute.

free parameters (8)
  • UAC boundary constants R and r = R=0.1, r=0.04
    Chosen in Tables 2 and 3 to define the parametrization of interfaces and orifice positions in the UAC space; no data fitting shown.
  • UAC orifice target positions alpha_cs, beta_cs, alpha_ipv, beta_ipv = 0.2, 0.8, 0.25, 0.25
    Specified in Table 3 to fix CS, LIPV, RIPV locations in UAC space; arbitrary choices without a fitting procedure.
  • Regional wall thickness values = Prescribed per region (Section 2.1.2), not patient-specific
    Atrial walls are grown with uniform literature-based thickness rather than measured patient-specific thickness; Section 5 explicitly lists this as a limitation.
  • Per-region conduction velocities (vl, vt) = RA 0.97/0.74, LA 0.98/0.76, CT 1.21/0.92, PM 1.30/0.99, BB 1.40/1.08, FO 0.33/0.24 m/s
    Table 4; based on literature ranges and scaled to obtain physiological total activation times; the R-D conductivities are then calibrated to match these velocities.
  • R-D tissue conductivities (gi,l, ge,l, gi,t, ge,t) = Table 4 values
    Computed with ForCEPSS to reproduce the R-E conduction velocities at 0.25 mm resolution; they are fit to the R-E target, making the R-E/R-D comparison consistency-driven.
  • SAN radius and length = 2.5 mm radius (Section 2.1.4), 2.2 cm band (Section 3.7)
    Chosen based on literature but used as fixed geometry parameters for the focal SAN model.
  • IC cable conduction velocities = Tuned to physiological inter-atrial delays (Section 2.2.2)
    Explicitly described as parameters to be calibrated, affecting the timing of LA activation and P-wave morphology.
  • ECG scaling factor = 0.2
    Applied to all simulated ECGs to match observed magnitudes (Section 2.2.2); a global gain fitted to data.
assumptions (6)
  • standard math Laplace-Dirichlet solutions provide valid distance-like coordinates for atrial parametrization.
    Used throughout Sections 2.1.4 and 2.1.5; assumes the atrial wall domain is a bounded domain where LD solves yield monotone fields between boundary conditions.
  • domain assumption The Courtemanche et al. cell model with region-specific parameterization adequately represents human atrial cellular dynamics.
    Section 2.2.2; inherited from prior literature, not re-validated here.
  • domain assumption The five inter-atrial pathways (BB, CS, FO rim, superior-posterior, middle-posterior) are the only electrical connections between the atria.
    Section 2.2.1; based on histology citations but adopted as a modeling constraint.
  • domain assumption The template torso from a different subject is a valid volume conductor for each patient.
    Section 2.1.6; the patient's own torso is not imaged, and electrode positions are transferred with GO-ICP registration.
  • ad hoc to paper Uniform regional wall thickness is an acceptable anatomical approximation.
    Sections 2.1.2 and 5; the paper acknowledges this is a simplification that may alter source-sink relations.
  • domain assumption Rule-based fiber orientations approximate patient-specific fiber architecture.
    Section 2.1.4; used to set conduction anisotropy, with no patient-specific verification.
invented entities (2)
  • Auto-generated inter-atrial conduction cables
    purpose: To model the five inter-atrial pathways as discrete 1D conducting strands connecting RA and LA, replacing explicit volumetric meshing.
    The cables are a modeling construct anchored at histology-informed locations, but no direct experimental measurement of their trajectories or properties is provided; the paper itself notes this is an approximation (Section 5).
  • Cigarette-shaped SAN focal activation site with insulating boundary
    purpose: To represent the sino-atrial node as a parametric source for P-wave calibration.
    Simplified from the physiological SAN to a geometric band; the paper states it avoids biophysical detail (Section 3.7).

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Cite this review

Pith. "Pith review of An efficient end-to-end computational framework for the generation of ECG calibrated volumetric models of human atrial electrophysiology." pith.science (2026). https://pith.science/paper/JBOBRGLL

@misc{pith2026250203322,
  author       = {Pith},
  title        = {Pith review of: An efficient end-to-end computational framework for the generation of ECG calibrated volumetric models of human atrial electrophysiology},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JBOBRGLL}},
  note         = {Machine review of arXiv:2502.03322}
}
read the original abstract

Computational models of atrial electrophysiology (EP) are increasingly utilized for applications such as the development of advanced mapping systems, personalized clinical therapy planning, and the generation of virtual cohorts and digital twins. These models have the potential to establish robust causal links between simulated in silico behaviors and observed human atrial EP, enabling safer, cost-effective, and comprehensive exploration of atrial dynamics. However, current state-of-the-art approaches lack the fidelity and scalability required for regulatory-grade applications, particularly in creating high-quality virtual cohorts or patient-specific digital twins. Challenges include anatomically accurate model generation, calibration to sparse and uncertain clinical data, and computational efficiency within a streamlined workflow. This study addresses these limitations by introducing novel methodologies integrated into an automated end-to-end workflow for generating high-fidelity digital twin snapshots and virtual cohorts of atrial EP. These innovations include: (i) automated multi-scale generation of volumetric biatrial models with detailed anatomical structures and fiber architecture; (ii) a robust method for defining space-varying atrial parameter fields; (iii) a parametric approach for modeling inter-atrial conduction pathways; and (iv) an efficient forward EP model for high-fidelity electrocardiogram computation. We evaluated this workflow on a cohort of 50 atrial fibrillation patients, producing high-quality meshes suitable for reaction-eikonal and reaction-diffusion models and demonstrating the ability to simulate atrial ECGs under parametrically controlled conditions. These advancements represent a critical step toward scalable, precise, and clinically applicable digital twin models and virtual cohorts, enabling enhanced patient-specific predictions and therapeutic planning.

Figures

Figures reproduced from arXiv: 2502.03322 by the authors.

Figure 1
Figure 1. Schematic outline of the end-to-end framework for the generation of ECG-calibrated volumetric models of patient [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. (a) Point-wise curvature on the blood pool surface mesh. The figure also highlights the correlation between the surface [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Left: Mesh quality computed on the biatrial model. Right: Boundaries on the RA and LA 15 LD problems employed [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: (a) Identification and labeling of the atrial orifices. Different labels are used for endocardial and epicardial tissue [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: (a) Distribution of the coordinate α, representing the SV C-to-IVC coordinate for the RA, and the lateral-to-septal coordinate for the LA. (b) Distribution of the coordinate β, representing the lateral-to-septal coordinate for the RA, and the posterior-to-anterior coor…
Figure 6
Figure 6. Figure 6: (a) Interfaces and boundary surfaces in the RA and LA and their parametrization. (b) Dirichlet values at the [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]
Figure 7
Figure 7. Figure 7: (a) Combined conformal atria-torso mesh generated by registering a patient atrial model, generated with our workflow, [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]
Figure 8
Figure 8. Figure 8: (a) Representation of 35 out of 50 generated biatrial models. Only a subset of the generated geometries is repre [PITH_FULL_IMAGE:figures/full_fig_p019_8.png]
Figure 9
Figure 9. Figure 9: First/Second row: Transmembrane potential [PITH_FULL_IMAGE:figures/full_fig_p021_9.png]
Figure 10
Figure 10. Figure 10: Influence of BB LA insertion site. First row: Biatrial activation map obtained for BB reference insertion site along [PITH_FULL_IMAGE:figures/full_fig_p022_10.png]
Figure 11
Figure 11. Figure 11: First row-left: Investigated LA entry site areas of the three cables representing the BB. The different colors identify [PITH_FULL_IMAGE:figures/full_fig_p023_11.png]
Figure 12
Figure 12. Figure 12: First row: P-wave obtained when including (blue) and excluding (black) the RA endocardial tissue outside of the [PITH_FULL_IMAGE:figures/full_fig_p024_12.png]
Figure 13
Figure 13. Figure 13: P-wave based calibration of the atrial activation sequence. Top row, left: Constant ICs configuration obtained by [PITH_FULL_IMAGE:figures/full_fig_p026_13.png]

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Forward citations

Cited by 1 Pith paper

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Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.