Graph Convolutional Networks for Coronary Artery Segmentation in Cardiac CT Angiography

Ivana I\v{s}gum; Jelmer M. Wolterink; Tim Leiner

REVIEW 3 major objections 4 minor 13 references

Graph Convolutional Networks for Coronary Artery Segmentation in Cardiac CT Angiography

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Coronary lumen segmentation improves when the network also sees the mesh graph.

desk verdict A clean, fairly evaluated GCN application to coronary lumen meshing whose central claim over the MLP baseline needs per-segment statistics before I'd trust the gap. read the letter →

arxiv 1908.05343 v1 pith:4RBTVH5Y submitted 2019-08-14 eess.IV cs.CV

Jelmer M. Wolterink , Tim Leiner , Ivana Išgum This is my paper · ORCID

classification eess.IVcs.CV

keywords graphconvolutionalnetworkscoronaryCTangiographylumensegmentationtubularsurfacemeshcenterlineextractionmedicalimagecardiacimagingdeeplearning

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 tries to show that a graph convolutional network operating directly on a tubular surface mesh can segment the coronary artery lumen from cardiac CT angiography with sub-voxel accuracy and without post-processing smoothing. The authors model the vessel wall as a fixed tube around an automatically extracted centerline, and the network regresses one radial distance per mesh vertex from image intensity rays combined with features of neighboring vertices. On 78 coronary segments from a public evaluation framework, the method reaches a Dice similarity coefficient of 0.75 in healthy and 0.73 in diseased segments, with mean surface distances around 0.25 to 0.28 mm. The key empirical claim is that adding GCN layers improves overlap and accuracy over an equally sized multi-layer perceptron that sees the same rays but no mesh neighbors, producing smoother and more accurate surfaces.

What carries the argument

The load-bearing object is a tubular surface mesh $G(V,E)$ built around an automatically extracted coronary centerline: each vertex is anchored to a centerline point and a fixed angle $\varphi_v$ in a cross-sectional plane, so the only free parameter per vertex is the radial distance $r_v$. A five-layer graph convolutional network, using the element-wise mean aggregator of GraphSAGE, propagates hidden features across the mesh edges and regresses $r_v$ from 32 image-intensity samples along a ray. The network is trained with the cubed-distance loss $(1/|V|)\sum_{v\in V} |r_v^3 - f(x_v)^3|$. This machinery carries the argument because neighborhood propagation across the fixed mesh graph is what produces smooth, contiguous surfaces without explicit regularization or post-processing; removing it, as in the MLP baseline, lowers overlap and accuracy.

What would settle it

Take a CCTA image and displace the extracted centerline by 0.5 mm in random directions, then rerun the trained GCN; if the Dice similarity coefficient or mean surface distance degrades materially, the reported accuracy is largely an artifact of centerline placement rather than a robust lumen-surface estimate.

Watch

Extended reading notes

Core claim

The central discovery, on the paper's own terms, is that the inclusion of mesh information through GCN layers improves coronary lumen segmentation over a baseline without mesh interaction. Instead of classifying voxels, the network solves a regression problem for each vertex of a tubular surface mesh: given a fixed centerline, each vertex is pinned to a fixed angle in a cross-sectional plane, and the network predicts the single radial distance $r_v$ to the lumen wall. Input features are image intensities sampled along rays, and five GCN layers propagate hidden representations across the mesh graph so that each vertex prediction is informed by vertices up to five steps away. This yields Dice similarity coefficients of 0.75/0.73 and mean surface distances of 0.25/0.28 mm on healthy and diseased segments, and a controlled comparison with a multi-layer perceptron using the same parameters shows substantially higher overlap and accuracy for the GCN.

Load-bearing premise

The whole method assumes the coronary artery centerline is accurate enough that constraining each mesh vertex to a fixed angle and a single radial distance around that centerline can capture the true lumen surface; the paper itself notes that the exact centerline location can cause noticeable differences in accuracy.

Editorial extensions

If this is right

If the central claim holds, coronary lumen segmentation for stenosis detection and blood-flow simulation can be produced directly as contiguous sub-voxel surface meshes, without graph-cut smoothing or explicit calcium removal.
The controlled MLP comparison shows that neighborhood propagation on the mesh, not just the ray features, is responsible for the improvement in overlap and mean surface distance.
Because the method directly outputs a surface rather than voxel labels, the architecture itself supplies the smoothness that earlier tubular-mesh methods needed additional penalties or post-processing to enforce.
The authors identify centerline dependence as a shared limitation, so accuracy on a new scan is bounded by the quality of the automatically extracted centerline.

Reading between the lines

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

Inference: Because the graph is fixed by the centerline and angular sampling, the same trained network could in principle generate meshes at different resolutions by re-sampling the graph without retraining; the paper does not test this.
Inference: The mean aggregator ignores spatial relations between neighbors; adding edge features that encode angular or geodesic offsets, a direction the authors flag, could make the network sensitive to local curvature and stenosis shape.
Inference: The explicit admission that centerline location causes noticeable accuracy differences suggests a testable design: jointly optimize centerline extraction and radial-distance regression rather than treating them as separate stages.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Two things you should know. First, this is a legitimate and cleanly executed application of GCNs to coronary lumen surface mesh prediction, with a fair MLP baseline that keeps parameter count and training procedure identical. Second, the central claim—that adding mesh information via GCN layers improves accuracy—rests on pooled mean metrics from 78 segments in 18 patients, with no error bars or paired significance tests. The evidence is suggestive, not conclusive.

What's actually new: tubular mesh vertex regression has been around (Lugauer, Freiman), and GCNs have been used for airways and cortex, but the combination—regressing radial vertex positions on a coronary lumen mesh with a GCN—is new. The controlled comparison is a real strength: same data, same 14,567 parameters, same training procedure, so the difference isolates the graph neighborhood aggregation. The method is also practically attractive: no post-processing smoothing, and it produces contiguous sub-voxel meshes that compare well with prior work and human experts on the public challenge.

Where it's soft. The GCN-over-MLP advantage is reported as means over segments, but segments from the same patient are correlated, and no per-segment values, confidence intervals, or paired tests are given. The MSD differences (0.25 vs 0.32, 0.28 vs 0.31 mm) are small relative to in-plane resolution (0.29–0.43 mm), so measurement noise could matter. The Hausdorff distance is actually slightly worse for GCN in diseased segments (1.86 vs 1.84), so the "more accurate" claim is really carried by DSC and MSD. The acknowledged centerline sensitivity is real, but it affects both arms equally, so it doesn't undermine the comparative claim. The dataset is small (18 volumes), which is normal for this challenge, but it means the reproducibility of the GCN-vs-MLP gap across patients and seeds is untested. No code is released, which makes it hard to check the statistical robustness yourself.

Net: a solid conference-level contribution for the MICCAI-type audience. It deserves a serious referee: the method is clearly described, the evaluation is fair as far as it goes, and the missing statistics are a tractable revision, not a fundamental flaw. I'd ask for per-segment numbers, patient-clustered error bars, and ideally code or external validation. I wouldn't desk-reject it.

Referee Report

3 major / 4 minor

Summary. The paper proposes a graph convolutional network (GCN) for coronary artery lumen segmentation in cardiac CT angiography. A tubular surface mesh is constructed around an automatically extracted centerline, with each vertex described by a fixed angle and a predicted radial distance. Image features are extracted along rays at each vertex, and a five-layer GCN with a mean aggregator predicts the radial distance, propagating information between neighboring mesh vertices. The method is evaluated on 78 coronary artery segments from 18 CCTA volumes of the public Coronary Artery Stenoses Detection and Quantification Evaluation Framework using leave-one-patient-out cross-validation. The authors report DSC of 0.75/0.73, MSD of 0.25/0.28 mm, and HD of 1.53/1.86 mm for healthy/diseased segments, and compare against an MLP baseline with the same number of parameters and training procedure to support the claim that mesh information improves segmentation overlap and accuracy.

Significance. If the central claim is established, the work is a useful contribution to coronary lumen segmentation: it addresses the need for contiguous, sub-voxel, mesh-based segmentations for downstream stenosis assessment and CFD, and it demonstrates that graph convolutions on a tubular mesh can serve as an intrinsic smoothness mechanism, avoiding post-processing such as graph cuts or CRFs. The experimental design has notable strengths: evaluation on a public challenge framework, leave-one-patient-out cross-validation, automatic centerline extraction, and a controlled ablation where the GCN and MLP have identical trainable parameter counts and training setup. However, the reported quantitative support for the central GCN-over-MLP claim is limited to pooled mean metrics without measures of variability or statistical testing, and the patient-level correlation of segments is not accounted for. The dataset is also small (18 volumes), so reproducibility across patients and training seeds remains unquantified.

major comments (3)

[§4, Table 1] The central comparative claim that the GCN improves segmentation over the MLP baseline is not supported by inferential statistics. The reported DSC, MSD, and HD values are pooled means over 78 segments from only 18 patients, with no standard deviations, confidence intervals, or paired significance tests. Because leave-one-patient-out cross-validation is used, segments from the same patient are correlated, so treating all 78 segments as independent is inappropriate. Moreover, the MSD differences (0.07 mm for healthy and 0.03 mm for diseased segments) are smaller than the in-plane voxel size (0.29–0.43 mm), so measurement noise could plausibly account for them. Please provide per-segment or per-patient paired results, a paired test such as Wilcoxon signed-rank or a patient-clustered bootstrap, and state whether multiple training seeds were used.
[§4, Table 1] The abstract and Section 5 state that mesh information improves segmentation 'accuracy', but the Hausdorff distance results do not consistently support this: in diseased segments the GCN has HD 1.86 mm versus 1.84 mm for the MLP, i.e. slightly worse. The claim should be qualified to overlap (DSC) and mean surface distance, or the HD comparison should be tested and reported separately. As written, the blanket statement overstates the evidence in Table 1.
[§5, Discussion] The Discussion acknowledges that 'the exact location of this coronary artery centerline can lead to noticeable differences in segmentation accuracy.' This sensitivity is not quantified in the paper. Although the centerline is a shared input to both the GCN and MLP arms, so it does not by itself undermine the relative comparison, it does affect the absolute accuracy claims and the practical utility of the method. Please report the magnitude of this sensitivity or provide evidence that the reported results are stable with respect to small centerline perturbations.

minor comments (4)

[§4, Table 1] The text says the inclusion of GCN layers leads to 'substantially higher overlap (DSC) and better accuracy (MSD)'; this wording is appropriate only for DSC and MSD, not for HD, and could be adjusted to avoid the inconsistency noted in the major comments.
[§2-§4] The abstract and Section 2 say that surface meshes enclosing the full coronary artery tree were automatically extracted, but the evaluation and training are described per segment. Please clarify whether the method is applied to the full tree and then scored per segment, or trained per segment, so that the unit of analysis is unambiguous.
[§4] The description of training says each network was trained for 50,000 iterations, but no information is given about random seed(s) or the number of repetitions. A brief statement about seed sensitivity would help assess reproducibility, especially given that the reported differences are small.
[Throughout] Minor typographical slips include 'Table 1 lists results the three expert observers' (missing 'of') and the rendering of one author's surname as 'Iˇsgum'; these should be corrected.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central GCN-versus-MLP comparison is a controlled ablation evaluated on external reference annotations.

full rationale

The paper's derivation chain is self-contained: an automatically extracted centerline defines a tubular mesh, ray features x_v are sampled from the CCTA image, and a GCN with the GraphSAGE mean aggregator (Eq. 1) regresses the radial distances r_v. Reference values for training come from the public Coronary Artery Stenoses Detection and Quantification Evaluation Framework (Ref. [5]), not from the network's own outputs. Evaluation uses Dice similarity coefficient, mean surface distance, and Hausdorff distance computed by the same external challenge platform. The only self-citation is the authors' prior CNN-based centerline extractor [13], which is a preprocessing input rather than the claimed result; both the GCN and the MLP baseline share the same centerline, so any centerline sensitivity, including the limitation acknowledged in the Discussion, affects both arms equally and does not make the comparison circular. The central claim that 'inclusion of mesh information in a GCN improves segmentation overlap and accuracy over a baseline model without interaction on the mesh' is supported by a matched ablation: both networks contain 14,567 trainable parameters, are trained identically for 50,000 iterations, and differ only in whether the layer aggregates neighbor features (Eq. 1) or acts as a standard fully-connected layer. No fitted parameter is renamed as a prediction, no result is forced by self-citation, and no equation reduces by construction to its own inputs. The absence of per-segment paired statistics is a statistical rigor concern, not a circularity concern.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The method relies on standard machine learning choices (graph architecture, ray geometry) and domain assumptions about vessel shape and centerline reliability. No new physical entities or unexplained constants are introduced.

free parameters (4)

number of ray angles per cross-section = 24
Chosen by hand; fixes the graph structure and resolution of the surface mesh.
ray length and number of input features = 3.2 mm, 32 features
Chosen by hand; determines how much image context each vertex sees and limits the maximum radius.
GCN depth and width = 5 layers, 64 hidden units
Chosen by hand; depth sets the neighborhood aggregation range.
loss exponent = 3
Cubing r in Eq. 2 is a hand-chosen weighting to emphasize large errors.

assumptions (5)

domain assumption The vessel wall is a star-shaped tube around a known centerline, with each vertex position determined by a single radial distance at fixed angles.
Section 3.1 constrains the mesh to this geometric form; it may fail at bifurcations or with highly irregular lumens.
domain assumption The automatically extracted centerline is accurate enough for mesh construction.
The method relies on the centerline from [13]; the authors note in the Discussion that centerline location noticeably affects accuracy.
domain assumption Image values along the ray at 0.1 mm resolution contain sufficient information to predict the lumen boundary.
The input vector is raw HU values along the ray, clipped to 0-1000 HU, with no explicit feature engineering.
domain assumption Reference annotations in the challenge are valid ground truth.
Evaluation uses the challenge framework's expert annotations; inter-observer variability is reported in Table 1.
domain assumption The mean aggregator (GraphSAGE) provides an appropriate inductive bias.
The authors acknowledge that the aggregator ignores spatial relations between neighbors, which is a stated limitation.

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Cite this review

Pith. "Pith review of Graph Convolutional Networks for Coronary Artery Segmentation in Cardiac CT Angiography." pith.science (2026). https://pith.science/paper/4RBTVH5Y

@misc{pith2026190805343,
  author       = {Pith},
  title        = {Pith review of: Graph Convolutional Networks for Coronary Artery Segmentation in Cardiac CT Angiography},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4RBTVH5Y}},
  note         = {Machine review of arXiv:1908.05343}
}

read the original abstract

Detection of coronary artery stenosis in coronary CT angiography (CCTA) requires highly personalized surface meshes enclosing the coronary lumen. In this work, we propose to use graph convolutional networks (GCNs) to predict the spatial location of vertices in a tubular surface mesh that segments the coronary artery lumen. Predictions for individual vertex locations are based on local image features as well as on features of neighboring vertices in the mesh graph. The method was trained and evaluated using the publicly available Coronary Artery Stenoses Detection and Quantification Evaluation Framework. Surface meshes enclosing the full coronary artery tree were automatically extracted. A quantitative evaluation on 78 coronary artery segments showed that these meshes corresponded closely to reference annotations, with a Dice similarity coefficient of 0.75/0.73, a mean surface distance of 0.25/0.28 mm, and a Hausdorff distance of 1.53/1.86 mm in healthy/diseased vessel segments. The results showed that inclusion of mesh information in a GCN improves segmentation overlap and accuracy over a baseline model without interaction on the mesh. The results indicate that GCNs allow efficient extraction of coronary artery surface meshes and that the use of GCNs leads to regular and more accurate meshes.

Figures

Figures reproduced from arXiv: 1908.05343 by the authors.

**Figure 2.** A GCN layer in the proposed method. The graph convolutional network [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Example segmentation, showing how the GCN has learned to exclude [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: Left coronary artery tree segmented using (a) multi-layer perceptron [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

13 extracted references · 13 canonical work pages

[1]

In: Medical Imaging with Deep Learning (MIDL) (2018)

Cucurull, G., Wagstyl, K., Casanova, A., Veliˇ ckovi´ c, P., Jakobsen, E., Drozdzal, M., Romero, A., Evans, A., Bengio, Y.: Convolutional neural networks for mesh- based parcellation of the cerebral cortex. In: Medical Imaging with Deep Learning (MIDL) (2018)

work page 2018
[2]

Freiman, M., Nickisch, H., Prevrhal, S., Schmitt, H., Vembar, M., Maurovich- Horvat, P., Donnelly, P., Goshen, L.: Improving CCTA-based lesions’ hemodynamic signiﬁcance assessment by accounting for partial volume modeling in automatic coronary lumen segmentation. Med. Phys. 44(3), 1040–1049 (2017)

work page 2017
[3]

In: Adv Neural Inf Process Syst (NIPS)

Hamilton, W., Ying, Z., Leskovec, J.: Inductive representation learning on large graphs. In: Adv Neural Inf Process Syst (NIPS). pp. 1024–1034 (2017)

work page 2017
[4]

In: Int Conf Learn Represent (ICLR) (2017)

Kipf, T.N., Welling, M.: Semi-supervised classiﬁcation with graph convolutional networks. In: Int Conf Learn Represent (ICLR) (2017)

work page 2017
[5]

Med Image Anal 17(8), 859–876 (2013)

Kiri¸ sli, H., Schaap, M., Metz, C., Dharampal, A., Meijboom, W., Papadopoulou, S., Dedic, A., Nieman, K., De Graaf, M., Meijs, M., et al.: Standardized evaluation framework for evaluating coronary artery stenosis detection, stenosis quantiﬁcation and lumen segmentation algorithms in computed tomography angiography. Med Image Anal 17(8), 859–876 (2013)

work page 2013
[6]

IEEE Trans Med Imag (2019)

Lee, M.C.H., Petersen, K., Pawlowski, N., Glocker, B., Schaap, M.: Tetris: Tem- plate transformer networks for image segmentation with shape priors. IEEE Trans Med Imag (2019)

work page 2019
[7]

J Cardiovasc Comput Tomogr 8(5), 342–358 (2014)

Leipsic, J., Abbara, S., Achenbach, S., Cury, R., Earls, J.P., Mancini, G.J., Nieman, K., Pontone, G., Raﬀ, G.L.: SCCT guidelines for the interpretation and reporting of coronary CT angiography: a report of the society of cardiovascular computed tomography guidelines committee. J Cardiovasc Comput Tomogr 8(5), 342–358 (2014)

work page 2014
[8]

Med Image Anal 13(6), 819–845 (2009)

Lesage, D., Angelini, E.D., Bloch, I., Funka-Lea, G.: A review of 3D vessel lu- men segmentation techniques: models, features and extraction schemes. Med Image Anal 13(6), 819–845 (2009)

work page 2009

Show all 13 references

[9]

Med Image Anal 42, 60–88 (2017)

Litjens, G., Kooi, T., Bejnordi, B.E., Setio, A.A.A., Ciompi, F., Ghafoorian, M., Van Der Laak, J.A., Van Ginneken, B., S´ anchez, C.I.: A survey on deep learning in medical image analysis. Med Image Anal 42, 60–88 (2017)

2017
[10]

In: International MICCAI Workshop on Medical Computer Vision

Lugauer, F., Zheng, Y., Hornegger, J., Kelm, B.M.: Precise lumen segmentation in coronary computed tomography angiography. In: International MICCAI Workshop on Medical Computer Vision. pp. 137–147. Springer (2014)

2014
[11]

In: Medical Imaging with Deep Learning (MIDL) (2018)

Selvan, R., Kipf, T., Welling, M., Pedersen, J.H., Petersen, J., de Bruijne, M.: Extraction of airways using graph neural networks. In: Medical Imaging with Deep Learning (MIDL) (2018)

2018
[12]

J Am Coll Cardiol 61(22), 2233–2241 (2013)

Taylor, C.A., Fonte, T.A., Min, J.K.: Computational ﬂuid dynamics applied to car- diac computed tomography for noninvasive quantiﬁcation of fractional ﬂow reserve: scientiﬁc basis. J Am Coll Cardiol 61(22), 2233–2241 (2013)

2013
[13]

Med Image Anal 51, 46–60 (2019)

Wolterink, J.M., van Hamersvelt, R.W., Viergever, M.A., Leiner, T., Iˇ sgum, I.: Coronary artery centerline extraction in cardiac CT angiography using a cnn-based orientation classiﬁer. Med Image Anal 51, 46–60 (2019)

2019

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

In: Medical Imaging with Deep Learning (MIDL) (2018)

Cucurull, G., Wagstyl, K., Casanova, A., Veliˇ ckovi´ c, P., Jakobsen, E., Drozdzal, M., Romero, A., Evans, A., Bengio, Y.: Convolutional neural networks for mesh- based parcellation of the cerebral cortex. In: Medical Imaging with Deep Learning (MIDL) (2018)

work page 2018

[2] [2]

Freiman, M., Nickisch, H., Prevrhal, S., Schmitt, H., Vembar, M., Maurovich- Horvat, P., Donnelly, P., Goshen, L.: Improving CCTA-based lesions’ hemodynamic signiﬁcance assessment by accounting for partial volume modeling in automatic coronary lumen segmentation. Med. Phys. 44(3), 1040–1049 (2017)

work page 2017

[3] [3]

In: Adv Neural Inf Process Syst (NIPS)

Hamilton, W., Ying, Z., Leskovec, J.: Inductive representation learning on large graphs. In: Adv Neural Inf Process Syst (NIPS). pp. 1024–1034 (2017)

work page 2017

[4] [4]

In: Int Conf Learn Represent (ICLR) (2017)

Kipf, T.N., Welling, M.: Semi-supervised classiﬁcation with graph convolutional networks. In: Int Conf Learn Represent (ICLR) (2017)

work page 2017

[5] [5]

Med Image Anal 17(8), 859–876 (2013)

Kiri¸ sli, H., Schaap, M., Metz, C., Dharampal, A., Meijboom, W., Papadopoulou, S., Dedic, A., Nieman, K., De Graaf, M., Meijs, M., et al.: Standardized evaluation framework for evaluating coronary artery stenosis detection, stenosis quantiﬁcation and lumen segmentation algorithms in computed tomography angiography. Med Image Anal 17(8), 859–876 (2013)

work page 2013

[6] [6]

IEEE Trans Med Imag (2019)

Lee, M.C.H., Petersen, K., Pawlowski, N., Glocker, B., Schaap, M.: Tetris: Tem- plate transformer networks for image segmentation with shape priors. IEEE Trans Med Imag (2019)

work page 2019

[7] [7]

J Cardiovasc Comput Tomogr 8(5), 342–358 (2014)

Leipsic, J., Abbara, S., Achenbach, S., Cury, R., Earls, J.P., Mancini, G.J., Nieman, K., Pontone, G., Raﬀ, G.L.: SCCT guidelines for the interpretation and reporting of coronary CT angiography: a report of the society of cardiovascular computed tomography guidelines committee. J Cardiovasc Comput Tomogr 8(5), 342–358 (2014)

work page 2014

[8] [8]

Med Image Anal 13(6), 819–845 (2009)

Lesage, D., Angelini, E.D., Bloch, I., Funka-Lea, G.: A review of 3D vessel lu- men segmentation techniques: models, features and extraction schemes. Med Image Anal 13(6), 819–845 (2009)

work page 2009