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REVIEW 4 major objections 5 minor 25 references

A combined Machine Learning and Finite Element Modelling tool for the surgical planning of craniosynostosis correction

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A multi-output support vector regressor trained on finite-element simulations predicts post-operative skull shape from 3D photographs, with $R^2 = 0.95$ on synthetic test data.

desk verdict A genuinely tested surrogate model whose abstract oversells it: the synthetic R2=0.95 is real, the real-patient validation (R2=-3.58) is honestly reported but fatal to the clinical claim. read the letter →

arxiv 2506.03202 v1 pith:V5JRFMWY submitted 2025-06-02 eess.IV cs.CVcs.LGphysics.med-ph

Itxasne Antúnez Sáenz , Ane Alberdi Aramendi , David Dunaway , Juling Ong , Lara Deliège , Amparo Sáenz , Anita Ahmadi Birjandi , Noor UI Owase Jeelani
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Silvia Schievano Alessandro Borghi
This is my paper
classification eess.IVcs.CVcs.LGphysics.med-ph
keywords SpringassistedcranioplastySurrogatemodelStatisticalshapemodellingSagittalcraniosynostosisFiniteelementSupportvectorregression3DphotographySurgicalplanning
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

The authors aim to turn surgical planning for spring-assisted cranioplasty, the main treatment for sagittal craniosynostosis (a condition in which the skull's midline suture fuses early, producing a long narrow head), into a radiation-free, real-time prediction. They build synthetic skulls from 30 preoperative CT scans by applying population-average soft-tissue thickness, skull thickness, and suture locations, run 2,356 finite-element simulations spanning different osteotomy placements and spring properties, then train machine-learning regressors to reproduce the simulated post-operative skull shapes. Their multi-output support vector regressor reaches $R^2 = 0.95$ on held-out synthetic cases, with mean squared error 0.042 and mean absolute error 0.122. On 13 real patients with pre- and post-operative 3D photographs, the same model gives $R^2 = -3.58$ and an average surface error of $2.70 \pm 0.58$ mm, which the authors attribute to growth and to the simplifying assumptions of the synthetic model. If that gap closes, clinicians could compare surgical scenarios in seconds from a 3D photograph alone, without CT scans.

What carries the argument

The engine is a statistical shape model (SSM) paired with a multi-output support vector regressor. SSM applies principal component analysis to skull meshes, representing each skull as the population mean plus a weighted combination of eigenmodes; the same compression is applied to the 2,356 finite-element output meshes. The regressor learns the mapping from input mode weights plus age, osteotomy parameters, and spring stiffness and free length to output mode weights, so a prediction is a full skull surface. This is what reduces hours of finite-element computation to a function evaluation.

What would settle it

Take a prospective cohort of at least 30 sagittal craniosynostosis patients, feed each preoperative 3D photograph and the actual surgical parameters into the trained model, and compare predicted surfaces with 3-week follow-up scans using the same $R^2$ and per-vertex error metrics as the paper's validation; if $R^2$ stays near or below zero rather than approaching the synthetic 0.95, the synthetic FEM training data do not transfer to real surgery.

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Extended reading notes

Core claim

The paper's central claim is that post-operative skull shape after spring-assisted cranioplasty can be predicted as a function of patient age, surgical parameters (osteotomy position and width), spring characteristics, and a compressed description of the pre-operative head shape, using a machine-learning surrogate of finite-element simulations. The surrogate is a multi-output support vector regressor trained on 2,356 synthetic outcomes generated by finite-element models built from population-averaged skull and skin thickness and average suture positions; on the synthetic test set it achieves $R^2 = 0.95$, MSE = 0.042, and MAE = 0.122. The authors further claim this enables outcome prediction from 3D photographs in real time, eliminating CT and the engineering expertise otherwise needed for finite-element planning. They report an average surface error of $2.70 \pm 0.58$ mm on 13 real patients, alongside a validation $R^2$ of -3.58, and identify growth and population-averaged modelling assumptions as the main sources of the discrepancy.

Load-bearing premise

The load-bearing premise is that finite-element simulations built from population-average skull and skin thickness, average suture positions, and uniform material properties faithfully reproduce what actually happens when a real baby's skull is operated on.

Editorial extensions

If this is right

  • Preoperative planning can be done from a 3D photograph and planned surgical parameters, with no CT scan and no radiation exposure.
  • Surgeons could simulate many spring placements and choices in seconds, rather than committing to one configuration based on experience and age.
  • Because the surrogate inherits the finite-element model's behaviour, the machine-learning step introduces little additional error on synthetic data; the practical limit of the tool is how faithfully the FEM represents real surgery.
  • The same model could be inverted to search for surgical parameters that maximise the cranial index, a direction the paper explicitly identifies for future work.

Reading between the lines

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

  • My reading: the negative real-patient $R^2$ is evidence that the bottleneck is the finite-element model's fidelity, not the regressor, since the regressor fits the synthetic dataset almost perfectly; improvements should target growth modelling and personalised thickness and suture inputs before model architecture.
  • A testable extension would be to retrain the surrogate on FEM cases that include per-patient skull thickness and suture geometry inferred from photographs, and check whether real-patient $R^2$ rises above the current -3.58; the paper cites skull-inference from photos as future work.
  • If validated, the same photo-to-surrogate pipeline could transfer to other cranial vault procedures or to longitudinal follow-up, where the surrogate is trained once on a population and evaluated on surface scans.
  • The clinically meaningful quantity is the $2.70 \pm 0.58$ mm surface error on real patients, not the synthetic $R^2$; whether that error is acceptable depends on a clinical threshold the paper has not defined.
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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 / 5 minor

Summary. The paper proposes a pipeline for real-time prediction of postoperative skull shape after spring-assisted cranioplasty (SAC) for sagittal craniosynostosis. The method uses population-average skull and soft-tissue thickness to convert 3D photographs into synthetic skull models, simulates surgical outcomes with finite element modelling (FEM) across a design of experiments (2356 simulations), and trains a multi-output support vector regressor to predict FEM output shape modes from patient age, surgical parameters, spring properties, and preoperative shape modes. The abstract reports a test-set R² of 0.95 with MSE and MAE below 0.13. The paper also reports an independent validation on 13 real patients in Section 3.4, where the model achieves R² = -3.58, MSE = 1.41, and MAE = 0.88.

Significance. If the reported accuracy held on real patients, the tool would be a valuable non-ionising alternative to CT-based FEM planning for SAC. The pipeline is methodologically coherent, uses an independent external cohort for validation, and the authors are transparent about the poor validation performance in Section 3.4. However, the central claim of the paper—that the surrogate model predicts real surgical outcomes from 3D photographs—is contradicted by that validation. The negative R² means the model is worse than predicting the mean postoperative shape, so the proposed tool currently has no demonstrated clinical predictive value. The abstract and discussion substantially overstate the findings by foregrounding the synthetic test metrics and the mean surface error without a null-model baseline.

major comments (4)
  1. [Abstract and Section 3.3-3.4] The abstract's central claim ('the resulting multi-output support vector regressor model achieves a R2 metric of 0.95 and MSE and MAE below 0.13') is based solely on the held-out split of FEM simulations in Section 3.3. The independent validation on 13 real patients in Section 3.4 reports R² = -3.58, MSE = 1.41, and MAE = 0.88. A negative R² means the model performs worse than a trivial predictor returning the mean postoperative shape. Presenting the synthetic R² without the validation result is misleading and does not support the stated goal of predicting surgical outcomes for new patients.
  2. [Section 4 (Discussion)] The Discussion claims clinical usefulness from a mean surface error of 2.70 ± 0.58 mm and compares this to Borghi et al. (2020). This comparison is not benchmarked against a null model. A constant prediction equal to the average follow-up shape could plausibly achieve a mean surface error at or below 2.70 mm on these 13 patients, in which case the model adds no predictive value. The paper does not report the baseline surface error for such a null predictor, so the error-rate claim does not establish that the model generalises to real outcomes.
  3. [Sections 2.2-2.4 and 3.4] The load-bearing assumption that a surrogate trained on FEM outputs can generalise to real surgical outcomes is empirically rejected by the validation in Section 3.4. The FEM models are built from population-averaged skull/skin thickness, uniform material properties, and artificial suture locations (Sections 2.2-2.3), and the trained model reproduces those simulations well. However, the validation shows no predictive signal on real postoperative 3D photographs (R² = -3.58). The Discussion lists possible causes such as growth and population-averaged parameters, but the magnitude of the negative R² indicates that the model is not merely noisy; it fails to capture the actual surgical response. This invalidates the clinical prediction claim unless the model is retrained or fundamentally revised.
  4. [Section 2.5.1] The validation preprocessing is under-specified: the postoperative 3D photographs are 'scaled down to omit the growth factor' that was not in the FEM, but the scaling method (e.g., global uniform scaling, landmark-based alignment, or volume normalisation) is not described. Because the validation metric is a surface-distance error, the scaling choice directly affects the reported 2.70 mm error and the R² value. Without details and a sensitivity analysis, the validation result cannot be fully interpreted or reproduced.
minor comments (5)
  1. [Section 2.4.1] Equations (2) and (3) use inconsistent notation: the preoperative vector is indexed to N_preop while the postoperative vector is indexed to N_postop, but the text later states the mean shapes are both in ℝ^{N×3}; the relationship between N_preop and N_postop and the template's node count should be clarified.
  2. [Section 2.1] The text states the CT population has 30 patients and the validation population has 13 patients, but the age ranges are given as '5.8 ± 1.15 months' and '5.1 ± 1.0' respectively; the second entry is missing the unit 'months'.
  3. [Section 3.2] The SSM retains 11 modes for both input and output shapes, but the output modes account for only 90% of variance while the input modes account for 94%. The potential impact of discarding 10% of output variance on the prediction metrics is not discussed.
  4. [Figure 12] The predicted-versus-actual plots for the first four modes would benefit from showing the R² and error metrics for each individual mode, since the aggregate R² of 0.95 may conceal modes with poor prediction that nonetheless contribute to the final shape error.
  5. [Section 2.3] The paper states that bone and suture are assigned viscoelastic material properties via a Prony series, but the actual parameter values are only cited to earlier work; for reproducibility, the key material constants (or a reference table) should be included.

Circularity Check

3 steps flagged · score 4.0 of 10

The clinical prediction claim rests on a self-citation chain: the reported R2=0.95 is accuracy on FEM-generated outputs, and the FEM-to-clinical bridge is asserted via the same group's prior papers, while the paper's own real-patient validation contradicts that bridge.

  1. self citation load bearing [Section 4 (Discussion and Conclusions)]
    "The feasibility of FEM for predicting surgical outcomes in SAC has been established, validated, and optimized by the research group (Borghi et al., 2017, 2020, 2018; Garate Andikoetxea et al., 2023)."

    The ML surrogate's training labels are FEM outputs (Sections 2.3-2.5). The only support offered for equating those FEM outputs with actual post-SAC skull shapes is this sentence, which cites exclusively papers with overlapping authorship. No external validation of that FEM is provided in this paper; instead, Section 3.4 reports R2=-3.58 on 13 real patients, directly contradicting the asserted feasibility. The clinical prediction claim therefore depends on a load-bearing self-citation rather than on an independently verified result.

  2. fitted input called prediction [Abstract; Section 3.3 vs Section 3.4]
    "The resulting multi-output support vector regressor model achieves a R2 metric of 0.95 and MSE and MAE below 0.13."

    The R2=0.95 is Section 3.3's test-set performance on a held-out split of 2356 FEM-generated outputs; it is not measured on any real patient outcome. Section 3.4 states that 'performance declined when compared to the actual surgical output' and reports R2=-3.58. Presenting the synthetic FEM-reproduction accuracy as 'the resulting model' performance for surgical planning substitutes the surrogate's internal fit for clinical prediction: the quantity actually predicted in the headline metric is the FEM simulator's output, not the surgical outcome.

1 more flagged steps
  1. ansatz smuggled in via citation [Section 2.2.2 and Section 2.3 (Image Processing and Finite Element Modelling)]
    "Sutures were artificially created on the model following the method by (Garate Andikoetxea et al., 2023), assuming a width of 2 mm ... The material properties assigned to each part were defined based on (Borghi et al., 2020)."

    The synthetic training population is constructed from population-average skull and skin thickness, average suture positions, and material/spring parameters imported from the same group's earlier works. The ML model then learns this synthetic input-output mapping. Because the real surgical outcome is never directly observed in training, every ansatz in those prior papers is inherited by construction. The paper does not re-derive or independently validate these assumptions; the Discussion instead calls the numerical models 'already validated' by self-citations. This is how the earlier FEM ansatz is carried into the ML prediction without new evidence.

full rationale

The surrogate itself is a legitimate technical object: R2=0.95 on held-out FEM outputs shows that the SVM learned the FEM mapping from inputs to output shape modes. That part is not circular. The circularity enters at the level of the clinical claim. The abstract and Discussion present this surrogate accuracy as predictive of surgical outcomes, but the only bridge from FEM outputs to real post-SAC shapes is a set of same-group citations (Borghi et al. 2017, 2018, 2020; Garate Andikoetxea et al. 2023). Moreover, the paper's own independent validation on 13 real patients gives R2=-3.58, MSE=1.41 and MAE=0.88, meaning the bridge is not merely unverified but empirically contradicted. The 2.70 +/- 0.58 mm mean error cited in the Discussion is not benchmarked against a mean-shape null model, so it does not restore the link. These observations fit patterns 3 and 2: a load-bearing self-citation chain, and a synthetic reproduction accuracy being called a prediction. The score is 4 rather than higher because the ML surrogate does have independent internal content, and the paper at least reports the negative real-patient validation openly. The central clinical claim, however, is not supported by an independent derivation; it reduces to the same group's prior FEM assertions.

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

The central predictive claim rests on population-averaged geometry and material properties, a self-cited FEM framework, and truncated shape modes. Only the 13-patient validation is independent, and it fails, so these assumptions are load-bearing and currently unvalidated.

free parameters (4)
  • Population mean skull thickness (t_skull) = 2.02 ± 0.33 mm (population average)
    Applied uniformly to all synthetic skull models instead of measuring each patient's skull thickness; affects all FEM geometry.
  • Population mean soft tissue thickness (t_skin) = 3.42 ± 0.51 mm (population average)
    Used as uniform offset to convert each 3D photograph into a synthetic skull; affects every output shape.
  • Number of retained SSM modes = 11 (94% input variance, 90% output variance)
    Truncation threshold chosen by the authors; determines the regression target dimensionality and discards shape variation.
  • Design of experiments ranges (A, AP, LAT) = A: 18-30%, AP: 47-63%, LAT: 10-25%
    Surgical parameter ranges used to generate training configurations; specified by the authors, not derived from outcome data.
assumptions (5)
  • domain assumption Population-average skull thickness, soft tissue thickness, and suture width/location are representative of each individual patient.
    Section 2.2 replaces per-patient CT-derived values with cohort means; if this fails, the synthetic skulls misrepresent individuals.
  • ad hoc to paper Uniform inward offset of a 3D photograph by t_skin reconstructs an accurate skull geometry.
    Section 2.2.2; no validation that the offset surface matches true skull shape, only the population average.
  • domain assumption The FEM setup (isotropic viscoelastic bone, linear springs, no suture tearing) reproduces spring-assisted cranioplasty biomechanics.
    Section 2.3; material models and spring data are imported from prior studies by the same group, and Section 3.4 shows the simulated outputs do not match real outcomes.
  • domain assumption PCA modes capturing 94% input and 90% output variance preserve enough information for clinically relevant outcome prediction.
    Section 2.4.1; truncated modes discard variance that may include shape changes relevant to outcome.
  • ad hoc to paper A surrogate model trained on FEM outputs can generalize to real surgical outcomes.
    Implied by the abstract's R2=0.95 claim; Section 3.4 contradicts this with R2=-3.58 on real patients.

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Cite this review

Pith. "Pith review of A combined Machine Learning and Finite Element Modelling tool for the surgical planning of craniosynostosis correction." pith.science (2026). https://pith.science/paper/V5JRFMWY

@misc{pith2026250603202,
  author       = {Pith},
  title        = {Pith review of: A combined Machine Learning and Finite Element Modelling tool for the surgical planning of craniosynostosis correction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/V5JRFMWY}},
  note         = {Machine review of arXiv:2506.03202}
}
read the original abstract

Craniosynostosis is a medical condition that affects the growth of babies' heads, caused by an early fusion of cranial sutures. In recent decades, surgical treatments for craniosynostosis have significantly improved, leading to reduced invasiveness, faster recovery, and less blood loss. At Great Ormond Street Hospital (GOSH), the main surgical treatment for patients diagnosed with sagittal craniosynostosis (SC) is spring assisted cranioplasty (SAC). This procedure involves a 15x15 mm2 osteotomy, where two springs are inserted to induce distraction. Despite the numerous advantages of this surgical technique for patients, the outcome remains unpredictable due to the lack of efficient preoperative planning tools. The surgeon's experience and the baby's age are currently relied upon to determine the osteotomy location and spring selection. Previous tools for predicting the surgical outcome of SC relied on finite element modeling (FEM), which involved computed tomography (CT) imaging and required engineering expertise and lengthy calculations. The main goal of this research is to develop a real-time prediction tool for the surgical outcome of patients, eliminating the need for CT scans to minimise radiation exposure during preoperative planning. The proposed methodology involves creating personalised synthetic skulls based on three-dimensional (3D) photographs, incorporating population average values of suture location, skull thickness, and soft tissue properties. A machine learning (ML) surrogate model is employed to achieve the desired surgical outcome. The resulting multi-output support vector regressor model achieves a R2 metric of 0.95 and MSE and MAE below 0.13. Furthermore, in the future, this model could not only simulate various surgical scenarios but also provide optimal parameters for achieving a maximum cranial index (CI).

Figures

Figures reproduced from arXiv: 2506.03202 by the authors.

Figure 5
Figure 5. Upper view of the 3D scans of the validation population [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 2
Figure 2. Force vs Opening curve followed by the springs in the uncrimping phase [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Upper view of the CT scans of the population [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (10 more)
Figure 7
Figure 7. Figure 7: CDF of input modes I. Antúnez Sáenz et al.: Preprint submitted to Elsevier Page 7 of 13 [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 8
Figure 8. Figure 8: CDF of output modes [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]
Figure 10
Figure 10. Figure 10: Influence of the output modes. I. Antúnez Sáenz et al.: Preprint submitted to Elsevier Page 8 of 13 [PITH_FULL_IMAGE:figures/full_fig_p008_10.png]
Figure 9
Figure 9. Figure 9: Influence of the input modes [PITH_FULL_IMAGE:figures/full_fig_p008_9.png]
Figure 11
Figure 11. Figure 11: R 2 values scored by the different regression algorithms. Linear Regression (LR), Random Forest (RF), Decision Tree (DT), X Gradient Boosting(XGB), Support Vector Machine (SVM), Gradient Boosting (GB) and AdaBoost (AB) [PITH_FULL_IMAGE:figures/full_fig_p009_11.png]
Figure 12
Figure 12. Figure 12: Predicted vs actual values of the first 4 modes. I. Antúnez Sáenz et al.: Preprint submitted to Elsevier Page 9 of 13 [PITH_FULL_IMAGE:figures/full_fig_p009_12.png]
Figure 13
Figure 13. Figure 13: Preoperative 3D Photograph (left), follow-up vs prediction (middle) and distribution of the surface error (right) of a patient with an average error of 1.88 mm [PITH_FULL_IMAGE:figures/full_fig_p010_13.png]
Figure 14
Figure 14. Figure 14: Preoperative 3D Photograph (left), follow-up vs prediction (middle) and distribution of the surface error (right) of a patient with an average error of 2.07 mm [PITH_FULL_IMAGE:figures/full_fig_p010_14.png]
Figure 15
Figure 15. Figure 15: Preoperative 3D Photograph (left), follow-up vs prediction (middle) and distribution of the surface error (right) of a patient with an average error of 3.62 mm [PITH_FULL_IMAGE:figures/full_fig_p010_15.png]
Figure 16
Figure 16. Figure 16: Preoperative 3D Photograph (left), follow-up vs prediction (middle) and distribution of the surface error (right) of a patient with an average error of 3.39 mm. I. Antúnez Sáenz et al.: Preprint submitted to Elsevier Page 10 of 13 [PITH_FULL_IMAGE:figures/full_fig_p0…

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    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

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