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REVIEW 4 major objections 7 minor 1 cited by

Geometric deep learning for local growth prediction on abdominal aortic aneurysm surfaces

T0 review · 4 major / 7 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper shows that an SE(3)-symmetric transformer can predict local aneurysm growth as vertex-wise deformation vectors on the 3D artery wall, with a median diameter error of 1.18 mm and 0.93 accuracy for predicting 55 mm threshold…

desk verdict A well-engineered surface-based AAA growth predictor with a real evaluation leak: the per-patient neural fields used for historic-growth inputs are fitted to future scans, so the headline 1.18 mm and 0.93 numbers likely overstate causal predictive skill. read the letter →

arxiv 2506.08729 v2 pith:FSQPKC65 submitted 2025-06-10 cs.CV cs.AI

Dieuwertje Alblas , Patryk Rygiel , Julian Suk , Kaj O. Kappe , Marieke Hofman , Christoph Brune , Kak Khee Yeung , Jelmer M. Wolterink This is my paper
classification cs.CVcs.AI
keywords abdominalaorticaneurysmgeometricdeeplearninggrowthpredictionSE(3)equivariancetransformertemporalaugmentationneuralfieldsvascularsurface
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 establish that the local growth of an abdominal aortic aneurysm can be predicted directly on the 3D surface of the patient's aorta, rather than from summary measurements such as maximum diameter. The authors train an SE(3)-symmetric transformer that takes a vascular mesh with local morphological, hemodynamic, and historical-growth features embedded at each vertex, and outputs a 3D deformation vector per vertex prescribing how the surface moves by a chosen time step. On a cross-validated cohort of 24 patients they report a median diameter error of 1.18 mm, and the model correctly identifies 13 of 14 patients whose aneurysm will or will not exceed the 55 mm surgical threshold within two years. If these numbers hold, personalized surveillance intervals and earlier anticipation of surgery would become feasible from standard CTA scans.

What carries the argument

The mechanism that carries the argument is LaB-GATr, a geometric algebra transformer that is equivariant under rotations and translations (SE(3)). It represents each vertex's local geometry and features as 16-dimensional multivectors in the projective geometric algebra G(3,0,1), processes them in a coarsened tokenization with self-attention, and interpolates back to the full mesh; this is what lets the network predict deformation vectors directly on the non-Euclidean vascular surface without flattening it. The second mechanism is temporal augmentation via per-patient neural fields f_{p,theta}: a neural field approximates the velocity field of each patient's growth, is solved as a neural ODE to produce the vascular surface at any queried time, and during training provides target surfaces for randomly sampled time steps between six months and two years, conditioning the model on arbitrary intervals and smoothing its predicted trajectories.

What would settle it

Retrain the model with the per-patient continuous growth models fitted only on scans up to (and excluding) the target scan, and compare the median diameter error and two-year threshold accuracy against the reported 1.18 mm and 0.93; a substantial degradation would show the current evaluation benefits from future information.

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Extended reading notes

Core claim

The central claim is that a neural network, LaB-GATr, can predict pointwise aneurysm growth as a vertex-wise 3D deformation field on the vascular surface, conditioned on an arbitrary time step, and that this local prediction is more accurate than two baselines: predicting no growth and linearly extrapolating the past six months of growth. The model embeds multi-physical features—thrombus thickness, local radius, geodesic distances to inlets and outlets, time-averaged wall shear stress, oscillatory shear index, and historical growth—into the projective geometric algebra G(3,0,1), where the transformer operates on downsampled tokens and interpolates back to the full mesh. To handle irregularly spaced scans, the authors fit a per-patient continuous deformation model (a neural field solved as a neural ODE) and use it for temporal augmentation during training. On successive-scan predictions in the cross-validation cohort, the model achieves a median diameter error of 1.18 mm and a median relative growth volume difference of 0.10, and it classifies two-year threshold crossing with 0.93 accuracy. On an external validation set from a different hospital, errors in the time-step range seen during training lie in the same range, though the model tends to overestimate growth.

Load-bearing premise

The load-bearing premise is that each patient's continuous growth model, fitted on all of that patient's scans including ones after the prediction moment, faithfully describes growth that was already known at prediction time; if it encodes the future, then the reported errors are optimistic.

Editorial extensions

If this is right

  • If the model's accuracy transfers to routine clinical data, surveillance intervals could be personalized: patients with slow predicted local growth could be monitored less frequently, and those approaching the threshold could be scheduled earlier.
  • The time-conditioned model lets clinicians sample the predicted diameter trajectory at monthly resolution, which can flag when the 55 mm threshold is likely to be crossed between actual scan visits.
  • The external validation results suggest the method generalizes across hospitals and patient populations for time steps up to two years, although growth tends to be overestimated on the external cohort.
  • The SE(3)-equivariant surface representation avoids distortions from flattening the vessel, making it straightforward to extend the same pipeline to other arteries or to other progressively deforming anatomies such as tumor growth.

Reading between the lines

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

  • Because the per-patient continuous growth models are fitted on each patient's entire scan sequence, including scans after the prediction time, the 'historic growth' input and the temporal-augmentation targets may carry future information; a clinical deployment would need to confirm that performance holds when only past scans are available.
  • The ablation finding that hemodynamic features do not significantly help suggests geometry may already encode much of the hemodynamic signal; a testable extension would be to train without CFD features and compare prediction accuracy on a larger cohort.
  • The method could be applied to other pathologies with progressive shape change, e.g., tumor growth, using the same time-conditioned surface deformation framework; this would require per-patient continuous models from longitudinal imaging, just as here.
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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

4 major / 7 minor

Summary. This paper presents LaB-GATr, an SE(3)-equivariant transformer that predicts AAA growth as per-vertex 3D deformation vectors on surface meshes of the abdominal aorta, conditioned on local morphological, hemodynamic, and historic growth features and a time step. To handle irregular follow-up intervals, per-patient neural fields f_{p,theta} are fit to each patient's full CTA scan sequence, providing a continuous deformation model used for temporal augmentation during training, for computing the 'historic growth' input feature, and for generating interpolated evaluation targets. On 5-fold cross-validation over 24 patients (113 CTAs), the model reports median diameter error 1.18 mm and HD95 2.75 mm, outperforming zero-growth and historical-extrapolation baselines, and an accuracy of 0.93 (N=14) for predicting whether the AAA exceeds 55 mm within two years. An external validation on 7 patients (25 CTAs) is also reported.

Significance. Strengths: (i) the surface-based representation avoids distortion of flattening methods and preserves local anatomy; (ii) the SE(3)-equivariant architecture is methodologically appropriate for rotation/translation-invariant growth prediction; (iii) the temporal augmentation via neural ODEs is a creative use of implicit neural representations to learn from sparse irregular longitudinal data; (iv) the authors evaluate on a real multi-site dataset and report both local (HD95) and clinically relevant (diameter, threshold-crossing) metrics. If the information-leakage concern is resolved, the approach would constitute a solid contribution to geometric deep learning for personalized AAA surveillance. However, the current evaluation protocol does not yet support the stated performance claims.

major comments (4)
  1. [2.4.3 and 2.3] The historic growth feature F_hist is computed from the per-patient continuous model f_{p,theta}, which is optimized on the complete scan sequence T_p of each patient (Section 2.3, Eq. (2)-(3)), including scans after the prediction time t. Therefore F_hist(t) = dist(M_{p,t-6mo}, M_{p,t}) is not a purely past quantity; future observations influence the inferred deformation at t-6 months. Because Section 3.4 (Table 3) shows that removing F_hist significantly worsens diameter error (p=0.016), the leaked feature is a plausible driver of the reported 1.18 mm median error. The paper needs a causal refit evaluation: for each prediction target at time t_i, fit a new f using only scans at times <= t_i, compute F_hist from that model, and report all metrics. Without this, the main table does not reflect a deployment setting where only past scans exist.
  2. [2.6 and Table 2] The baseline B_hist is defined as linear extrapolation of the deformation from the same future-fitted f_{p,theta} (Section 2.6). Thus both B_hist and g_theta have access to future information in the input feature, and the comparison in Table 2 does not isolate g_theta's forecasting ability. The reported improvement over B_hist may partly arise from g_theta learning to approximate f rather than from genuinely predictive surface features. A clean comparison would use a causally refit f for B_hist and for the F_hist input of g_theta.
  3. [3.2 and 3.5] The time-conditioning experiment (Figure 8) and the fixed-time-step comparisons on the external cohort (Figure 13) evaluate g_theta against target models generated by f_{p,theta}, which is the same function used to create the temporal-augmentation training targets (Section 2.5) and the historic-growth input (Section 2.4.3). Consequently, these experiments measure agreement with f and are circular with respect to the training procedure. The statement in Section 3.2 that the diameter error 'stays below 2.5 mm for Delta t=24 months' is therefore not evidence about accuracy against observed ground truth. These experiments should either be re-run against observed scans or clearly labeled as consistency checks rather than performance evaluations.
  4. [3.2 (Figure 9)] The 0.93 accuracy for the two-year threshold-crossing prediction is computed on N=14 patients (6 crossing, 8 not crossing). With this sample size the 95% confidence interval for accuracy is roughly 66%-99.8%, so the result is not strong evidence of clinical utility. The paper should report a confidence interval or credible interval and should temper the corresponding abstract claim.
minor comments (7)
  1. [Section 2.3] The sentence 'Without loss of generality, we the discretize vascular manifold' contains a typo; it should read 'Without loss of generality, we discretize the vascular manifold'.
  2. [Sections 2.1 and 2.3] The neural field weights are denoted theta, the same symbol used for the growth-prediction network g_theta in Section 2.1; using different symbols (e.g., phi for f) would avoid confusion.
  3. [Section 2.5] The hyperparameters t_min and t_max are only defined in Section 3; state them in the method section as well.
  4. [Table 3] The feature-subset indicators in the first three columns are not visible in the preprint text; please render the table so each row clearly shows which of F_morph, F_hemo, F_hist are included.
  5. [Figure 8 caption] Explicitly state that the target models are generated by f_{p,theta}, as is done in the text, so readers do not mistake the comparison for observed scans.
  6. [Discussion] Add a limitation paragraph addressing the causal validity of the per-patient neural fields, namely that in the current protocol f is fitted on the full scan sequence including future time points; this is the main obstacle to clinical translation of the reported metrics.
  7. [Reference [17]] Reference [17] has an incomplete journal/arXiv identifier ('arXive-prints, arXiv-2407'); please provide the full citation.

Circularity Check

3 steps flagged · score 7.0 of 10

The 'historic growth' input feature and the temporal-augmentation targets are both derived from per-patient neural fields fitted to the full scan sequence including future scans, so the headline metrics are partly driven by future information; a causal refit test is needed.

  1. fitted input called prediction [Section 2.3 and Section 2.4.3]
    "To optimize the neural field f_{p_i,theta}, we solve the initial value problem in Equation (2) as a neural ODE [10], using all vascular models of patient p_i at time points t in T_{p_i}. ... We compute the historic growth feature F^hist_{p_i,t} ... from the personalized, continuous AAA growth models f_{p_i,theta}. ... For each t >= 0 in T_{p_i}, we approximate the vascular model six months earlier using f_{p_i,theta}."

    The neural field f_{p_i,theta} that defines 'historic growth' is fitted to every scan of the patient, including scans after the prediction time t. Therefore the six-month-back position M_{p_i,t-6months}, and hence the scalar F^hist input, is a function of the future trajectory that g_theta is asked to predict. The feature is named 'historic' but is not causally past; it encodes post-t observations through the global ODE fit. Because Section 3.4 shows F^hist significantly improves diameter error (p=0.016), the Table 2 median diameter error of 1.18 mm and the 0.93 threshold accuracy in Section 3.2 are at least partly attributable to this future-fitted input rather than to a causal surface-growth model.

  2. other [Section 3.2 (Figure 8), repeated in Section 3.5 (Figure 13)]
    "Starting from the second vascular model, i.e. M_{p_i,t_1}, we let g_theta predict the vascular model for Delta t in {6,7,8,...,24} months. We computed the maximum diameter for the predicted vascular model and compare this with the target vascular model obtained from f_{p_i,theta}. Note that in this experiment we evaluate performance based on interpolated shapes, as the vascular models are not available from the ground-truth data at these exact time points."

    The 'target' in this time-conditioning experiment is generated by the same per-patient neural field f_{p_i,theta} used to create temporal-augmentation training targets (Section 2.5) and to compute the historic-growth input feature. Comparing g_theta with f-generated shapes is therefore a self-consistency check with the training-data generator, not an unbiased test on observed scans; it cannot support the claim that the model predicts real AAA growth at arbitrary Delta t. The paper acknowledges that these are interpolated shapes, which is the point: the benchmark is circular with respect to the neural-field interpolation.

1 more flagged steps
  1. fitted input called prediction [Section 2.6 and Table 2]
    "Second, we use the historical growth from continuous model f_{p_i,theta} to extrapolate local growth patterns. We use the deformation from the past six months proportional to Delta t as the vertex-wise deformation vectors. This method, which we denote by B_hist, can be considered as a linear extrapolation of the growth."

    B_hist is derived from the same future-fitted f_{p_i,theta}; its 'past six months' deformation is not purely past. Since Table 2 reports B_hist as the main comparison for g_theta, the comparison does not control for the future-information leak: both the baseline and the proposed model's input are computed from a field that has seen the target future scan. This makes the reported relative improvement over B_hist partially a comparison between two different uses of the same leaked function rather than a clean causal benchmark.

full rationale

The central derivation is not equivalent to its inputs by definition: g_theta is an SE(3)-symmetric transformer with independent architectural content, and the headline 1.18 mm is computed on observed successive scans, not on f-generated shapes. However, the claimed causal prediction is contaminated by a future-fitted input. Section 2.3 fits each patient's neural field f_{p_i,theta} to the full set of scans T_{p_i}, including scans after the prediction time t; Section 2.4.3 then uses this same f to form the 'historic growth' feature by querying the surface six months before t. Because f is a global spatio-temporal fit, that feature can encode post-t information. Section 3.4 shows that removing this feature significantly worsens diameter error (p=0.016), so the leak is a plausible driver of Table 2's 1.18 mm and Section 3.2's 0.93 accuracy (N=14, no CI). The B_hist baseline in Table 2 uses the same f and therefore does not isolate the leak. In addition, Section 3.2 and Figure 13 evaluate the model against f-generated targets, a circular self-consistency check with the temporal-augmentation generator. The external validation (Section 3.5) inherits the same input construction, so it does not remove the problem. No load-bearing self-citation chain was found; the issue is data-construction circularity, not citation circularity.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The paper rests on a set of modeling assumptions about smooth growth, per-patient neural fields as pseudo-ground-truth, and Chamfer distance as a proxy for growth. No new physical entities are introduced. The main hidden dependency is the future-fitted neural field that generates both training targets and input features.

free parameters (3)
  • temporal augmentation time step range = [0.5, 2] years
    Hyperparameters t_min=6 months and t_max=2 years bound the randomly sampled time steps during training (Section 2.5). Chosen by hand, not optimized per data.
  • mesh downsampling ratio = 0.05
    eta=0.05 controls the coarse mesh size in LaB-GATr tokenization (Section 2.1.3).
  • past growth window = 6 months
    The historic growth feature measures growth over the past six months (Section 2.4.3). This window is a modeling choice.
assumptions (5)
  • domain assumption AAA growth can be modeled as a diffeomorphic deformation of the vessel surface, driven by a time-dependent velocity field.
    Section 2.3 assumes every patient's surface evolution is a continuous, smooth flow, enabling neural field interpolation.
  • ad hoc to paper Per-patient neural fields f_{p,theta}, trained with Chamfer distance, accurately represent growth over the full observation interval.
    The entire training and feature extraction pipeline relies on f as ground truth for arbitrary time steps; this is not validated against an external reference.
  • domain assumption Chamfer distance between deformed and reference meshes is a valid measure of growth for training and evaluation.
    Chamfer distance does not enforce point correspondences; it only measures proximity, which could misjudge local growth direction. Used as the loss (Eq. 3) and in metrics.
  • domain assumption Rigid alignment of meshes by centerlines using ICP establishes sufficient correspondence for local growth estimation.
    Section 2.2 assumes alignment quality is adequate for vertex-wise deformation prediction.
  • domain assumption Hemodynamic features computed with standardized boundary conditions are informative about growth.
    The authors note in Section 4 that personalized boundary conditions may reveal more information, so the standardized CFD results are an unvalidated proxy.

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Cite this review

Pith. "Pith review of Geometric deep learning for local growth prediction on abdominal aortic aneurysm surfaces." pith.science (2026). https://pith.science/paper/FSQPKC65

@misc{pith2026250608729,
  author       = {Pith},
  title        = {Pith review of: Geometric deep learning for local growth prediction on abdominal aortic aneurysm surfaces},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FSQPKC65}},
  note         = {Machine review of arXiv:2506.08729}
}
read the original abstract

Abdominal aortic aneurysms (AAAs) are progressive focal dilatations of the abdominal aorta. AAAs may rupture, with a survival rate of only 20\%. Current clinical guidelines recommend elective surgical repair when the maximum AAA diameter exceeds 55 mm in men or 50 mm in women. Patients that do not meet these criteria are periodically monitored, with surveillance intervals based on the maximum AAA diameter. However, this diameter does not take into account the complex relation between the 3D AAA shape and its growth, making standardized intervals potentially unfit. Personalized AAA growth predictions could improve monitoring strategies. We propose to use an SE(3)-symmetric transformer model to predict AAA growth directly on the vascular model surface enriched with local, multi-physical features. In contrast to other works which have parameterized the AAA shape, this representation preserves the vascular surface's anatomical structure and geometric fidelity. We train our model using a longitudinal dataset of 113 computed tomography angiography (CTA) scans of 24 AAA patients at irregularly sampled intervals. After training, our model predicts AAA growth to the next scan moment with a median diameter error of 1.18 mm. We further demonstrate our model's utility to identify whether a patient will become eligible for elective repair within two years (acc = 0.93). Finally, we evaluate our model's generalization on an external validation set consisting of 25 CTAs from 7 AAA patients from a different hospital. Our results show that local directional AAA growth prediction from the vascular surface is feasible and may contribute to personalized surveillance strategies.

Figures

Figures reproduced from arXiv: 2506.08729 by the authors.

Figure 1
Figure 1. Our local AAA growth prediction method. We use a transformer 𝑔𝜃 that predicts local AAA growth over a time step Δ𝑡 given 𝑝𝑖 ,𝑡, a mesh model of the AAA vasculature with multi-physical features 𝑝𝑖 ,𝑡 embedded on the vertices. For each vertex, 𝑔𝜃 estimates a 3D deformation vector. Together, these vectors prescribe the deformation of 𝑝𝑖 ,𝑡 into 𝑝𝑖 ,𝑡+Δ𝑡 . vascular surface and local features to a 2D plane, parame￾te… view at source ↗
Figure 2
Figure 2. Overview of the LaB-GATr architecture 𝑔𝜃 , adapted from [46]. Patient-specific features, local geometry and time step are embedded per vertex as multi-vectors in 𝐆(3, 0, 1) ( 1 ). Next, 𝑝𝑖 ,𝑡 is tokenized into coarse 𝑝𝑖 ,𝑡 ( 2 ). Tokens are fed into the geometric algebra transformer (GATr) ( 3 ), whose output is interpolated to the resolution of 𝑝𝑖 ,𝑡 ( 4 ). Lastly, the network outputs are projected back to ℝ3 ( … view at source ↗
Figure 3
Figure 3. Surveillance intervals, number of scans and maximum diameters of the AAAs for patients in our training dataset (Seoul National University hospital, South Korea) [24] and our external validation set (Amsterdam UMC, The Netherlands), shown in the top and bottom plots, respectively. ODE Solve ... Neural field [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: Continuous representation of AAA growth for an individual patient. We approximate the velocity field 𝑣𝑝𝑖 (𝑥, 𝑡) by a neural field 𝑓𝑝𝑖 ,𝜃 conditioned on spatio-temporal coordinates (bottom). We solve a neural ODE (top) involving 𝑓𝑝𝑖 ,𝜃 to deform 𝑝𝑖 ,0 into the vascular…
Figure 5
Figure 5. Figure 5: Training procedure for 𝑔𝜃 using temporal augmenta￾tion. First, we randomly sample a time point 𝑡 from 𝑇̃ 𝑝𝑖 ( 1 ) and a time step Δ𝑡 ∈ [𝑡min,𝑡max] ( 2 ). Next, we acquire the target vascular model 𝑝𝑖 ,𝑡+Δ𝑡 using 𝑓𝑝𝑖 ,𝜃 ( 3 ). Then, we let 𝑔𝜃 predict the growth from …
Figure 6
Figure 6. Figure 6: Vascular models of five patients in our training dataset, with the infrarenal aorta, the section of the vascular model used to evaluate the performance of our growth predic￾tion model, marked in red. : Preprint submitted to Elsevier Page 12 of 11 [PITH_FULL_IMAGE:figu…
Figure 7
Figure 7. Figure 7: Diameter profiles of three different patients from the cross-validation cohort ( [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]
Figure 8
Figure 8. Figure 8: Median and IQR diameter error of the growth prediction as a function of the time step Δ𝑡. 7 1 60 TN FP FN TP Predicted Reference [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]
Figure 9
Figure 9. Figure 9: Prediction of whether and when the AAA diameter exceeds 55 mm within a two-year period. Left: Confusion matrix showing the performance of 𝑔𝜃 in classifying whether the diameter threshold is exceeded within two years. Right: Comparison of predicted and observed time int…
Figure 11
Figure 11. Figure 11: Boxplots containing the HD95 and diameter error for the growth predictions with Δ𝑡 = 24 months using 𝑔𝜃 trained with and without temporal augmentation (Section 2.5), respectively. (a) Growth prediction performance for time steps smaller than two years. (b) Growth pred…
Figure 12
Figure 12. Figure 12: Growth prediction performance of the ensemble on the external validation set (A1-A7, [PITH_FULL_IMAGE:figures/full_fig_p014_12.png]
Figure 13
Figure 13. Figure 13: Visualization of growth predictions for two patients in the Amsterdam cohort using standardized time steps (Δ𝑡 ∈ {6, 12, 18, 24} months, with local surface indicated on the vascular models. Performance metrics are shown for each growth prediction, as well as 2D cross …

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Cited by 1 Pith paper

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.