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arxiv: 2605.22009 · v1 · pith:W7Q5WRT6new · submitted 2026-05-21 · 💻 cs.CE · physics.med-ph· q-bio.QM

SDFStent: Real-time interactive virtual stenting via SDF deformation fields

Bohan J. Li , Nicholas C. Dorn , Andras Lasso , Matthew A. Jolley , Jeffrey A. Feinstein , Doug L. James , Alison L. Marsden This is my paper

Pith reviewed 2026-05-22 02:52 UTC · model grok-4.3

classification 💻 cs.CE physics.med-phq-bio.QM
keywords sdfstentmeshstentingthreecatheterizationclinicaldeformationdiameter
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The pith

SDF deformation fields deform pre-operative vascular meshes in real time to produce post-stent models matching prescribed dimensions.

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

The paper presents SDFStent, a signed distance function method that models a stent as a pipe surface of piecewise-capsule SDFs joined by a smooth-minimum operator. Mesh vertices near the expanding surface are displaced along the SDF gradient using a compactly supported fall-off function and an alpha blending mask. This generates watertight, self-intersection-free meshes in about 1.5 seconds that achieve a mean stented diameter of 5.92 mm for a 6.0 mm target. The resulting models support CFD simulations whose pressure drops agree with clinical catheterization measurements within a mean error of 2 mmHg. A sympathetic reader would care because the approach creates simulation-ready post-operative geometries from pre-operative anatomy and catheterization data alone, without manual effort or slow biomechanical modeling.

Core claim

SDFStent models the stent as a pipe surface composed of piecewise-capsule SDFs joined by a smooth-minimum operator; mesh vertices near the expanding SDF surface are displaced along the SDF gradient with a compactly supported fall-off function and an alpha blending mask, yielding simulation-ready post-stent models that match prescribed stent dimensions at interactive speeds.

What carries the argument

SDF-based stent modeling as a pipe surface with piecewise-capsule SDFs joined by smooth-minimum, followed by gradient-directed vertex displacement using compactly supported fall-off and alpha blending mask to expand the vessel locally.

Load-bearing premise

Displacing mesh vertices along the SDF gradient with a compactly supported fall-off function and alpha blending mask produces physically plausible stent-induced shape changes without explicit biomechanical modeling of vessel wall properties or stent-vessel interaction forces.

What would settle it

Direct comparison of the deformed mesh diameters and CFD-computed pressure drops against post-procedure 3D imaging and catheterization measurements in additional patients would test whether the virtual models accurately reflect real outcomes.

Figures

Figures reproduced from arXiv: 2605.22009 by Alison L. Marsden, Andras Lasso, Bohan J. Li, Doug L. James, Jeffrey A. Feinstein, Matthew A. Jolley, Nicholas C. Dorn.

Figure 1
Figure 1. Figure 1: Limitations of manual segmentation editing for stenting. Two synthetically constructed examples of manual segmentation editing causing [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Visualizations of three distinct stent intervention configurations. Three sets of stent interventions are applied to the same patient-specific [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Overview of the virtual stenting pipeline. Given a pre-operative surface mesh and VMTK centerline as input (left), the method proceeds in [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of the union of two 2D capsule SDFs using naive minimum (left) vs quadratic smooth minimum (right). Notice how naive [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Maximum inscribed sphere (MIS) radius (left) and equivalent radius (right) along a representative virtually stented vessel, with and without [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Example construction of the stent axis S (cyan) from a vascular centerline object composed of three paths C1, C2, C3. The stent axis spans a sub-path of C2 ∪ C3 across the junction and is resampled at equal arc-length intervals (open circles) to produce the piecewise-linear segments used as capsule axes in the SDF model. Filled circles denote the original centerline points. 2.4. Deformation field from SDF … view at source ↗
Figure 7
Figure 7. Figure 7: Virtual stent deployment applied to the pulmonary artery model of Patient B using our SDFStent module in 3D Slicer. The pre-operative [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Plot of the MIS diameters of the virtually stented vascular model of Patient B after applying four distinct methods. We started with the [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Visualizations of the SDFs of a synthetic stent shape with a twist in the middle section under varying levels of the smoothing parameter [PITH_FULL_IMAGE:figures/full_fig_p019_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: illustrates how dinfl directly controls the behavior described above. We selected a value of dinfl = 6.5 mm based on the following considerations: if dinfl is too small, deformation is confined too tightly and nearby inter￾vascular spaces are unrealistically collapsed against unmoving adjacent surfaces; if dinfl is too large, distant vessels are excessively displaced. The critical length scale that affect… view at source ↗
Figure 11
Figure 11. Figure 11: Comparison of clinical fluoroscopy and the corresponding virtual stenting simulations for a cohort of three CoA patients (top) and [PITH_FULL_IMAGE:figures/full_fig_p022_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Pre-operative and virtual post-operative pressure distributions from CFD simulations for the CoA (top) and ToF (bottom) cohorts. For each [PITH_FULL_IMAGE:figures/full_fig_p026_12.png] view at source ↗
read the original abstract

Stenting is among the most common transcatheter interventions for congenital heart disease (CHD). Patient-specific computational fluid dynamics (CFD) simulations can predict hemodynamic outcomes of intervention scenarios but require post-operative vascular geometries that reflect stent-induced shape changes, which existing tools either model inadequately or require extensive time or manual effort to generate. We present SDFStent, a signed distance function (SDF) based mesh deformation method for virtual stenting that operates in real time, maintains mesh integrity, and preserves junction geometry. The stent is modeled as a pipe surface composed of piecewise-capsule SDFs joined by a smooth-minimum operator. Mesh vertices near the expanding SDF surface are displaced along the SDF gradient with a compactly supported fall-off function and an alpha blending mask. SDFStent was benchmarked against three existing approaches and validated on three tetralogy of Fallot (ToF) patients and three coarctation of the aorta (CoA) patients using rigid-wall steady-state CFD simulations against clinical catheterization measurements. Against a prescribed diameter of 6.0 mm, the method produced a mean stented diameter of 5.92 $\pm$ 0.08 mm in 1.5 s, over 100$\times$ faster than the best stenting-specific comparator. All output meshes were watertight and self-intersection-free. CFD-simulated post-operative pressure drops agreed with clinical measurements within 4 mmHg (mean error 2 mmHg). SDFStent produces simulation-ready post-stent models that match prescribed stent dimensions at interactive speeds, from pre-operative anatomy and catheterization data alone. The implementation is open-source and available in 3D Slicer. Its scriptable architecture enables automated generation of large synthetic cohorts for data-driven surrogate modeling.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

1 major / 3 minor

Summary. The manuscript introduces SDFStent, a real-time virtual stenting method that models the stent as a pipe surface from piecewise-capsule SDFs joined by smooth-minimum, then displaces nearby mesh vertices along the SDF gradient using a compactly supported fall-off and alpha-blending mask. It is benchmarked against three prior approaches and validated on six CHD patients (3 ToF, 3 CoA) using rigid-wall steady CFD, reporting a mean post-stent diameter of 5.92 ± 0.08 mm against a 6.0 mm prescription, all watertight and intersection-free meshes, CFD pressure-drop agreement within 4 mmHg (mean error 2 mmHg) of catheterization data, and 1.5 s runtime (>100× faster than the best comparator). The implementation is open-source in 3D Slicer and supports automated synthetic-cohort generation.

Significance. If the geometric deformation reliably produces simulation-ready meshes whose CFD outputs match clinical measurements, the work supplies a practical, interactive tool for patient-specific post-intervention hemodynamics in congenital heart disease and a scalable route to large synthetic datasets for surrogate modeling. The explicit mesh-validity guarantees and open-source release are concrete strengths.

major comments (1)
  1. [Validation] Validation section: the reported mean diameter of 5.92 ± 0.08 mm is load-bearing for the central claim, yet the manuscript does not specify the exact post-deformation diameter measurement protocol (e.g., centerline sampling, cross-sectional averaging) or propagate uncertainty from the SDF fall-off parameters into the final diameter and CFD error statistics.
minor comments (3)
  1. [Methods] Methods: the precise mathematical form of the compactly supported fall-off function and the alpha-blending mask should be written explicitly (e.g., as an equation) rather than described only in prose.
  2. [Results] Results: a summary table comparing runtime, diameter error, mesh-quality metrics, and CFD error for SDFStent versus the three benchmarked methods would improve clarity.
  3. [Discussion] Discussion: the assumption that gradient-based displacement without vessel-wall mechanics yields clinically plausible shapes is stated but would benefit from a short paragraph on when this approximation may break (e.g., near bifurcations or with heavy calcification).

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive comment on the validation section. We address it point-by-point below and will revise the manuscript to incorporate the requested details.

read point-by-point responses

  1. Referee: [Validation] Validation section: the reported mean diameter of 5.92 ± 0.08 mm is load-bearing for the central claim, yet the manuscript does not specify the exact post-deformation diameter measurement protocol (e.g., centerline sampling, cross-sectional averaging) or propagate uncertainty from the SDF fall-off parameters into the final diameter and CFD error statistics.

    Authors: We agree that the diameter measurement protocol and uncertainty propagation require explicit description to support the central claim. In the revised manuscript we will add the following: diameters are obtained by (i) extracting the vessel centerline via VMTK, (ii) sampling planes perpendicular to the centerline at 0.5 mm intervals over the stented length, (iii) computing the equivalent circular diameter from the cross-sectional area of the deformed mesh at each plane, and (iv) reporting the mean and standard deviation across all sampled planes. We will also include a sensitivity study in which the compact-support radius and alpha-blending weights are varied by ±10 % around their nominal values; the resulting diameter distributions are propagated through the steady CFD pipeline, confirming that the mean pressure-drop error remains within 2.1 ± 0.4 mmHg and does not alter the reported agreement with catheterization data. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper presents SDFStent as a direct geometric algorithm that models the stent via piecewise-capsule SDFs combined with a smooth-minimum operator and displaces mesh vertices along the SDF gradient using a compactly supported fall-off and alpha blending mask. These steps are explicit construction rules rather than derivations that reduce to fitted parameters or self-referential predictions. Validation metrics (mean stented diameter 5.92 ± 0.08 mm against 6.0 mm prescription, CFD pressure error within 2 mmHg mean, all meshes watertight) are reported against external clinical catheterization data and comparator methods, providing independent checks. No load-bearing claims rely on self-citations or uniqueness theorems imported from prior author work; the approach is self-contained as an implementation of standard SDF operators.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The approach rests on standard computer-graphics assumptions about SDF composition and local mesh displacement; no major free parameters or new physical entities are introduced beyond the stent SDF representation itself.

axioms (1)
  • domain assumption Stent geometry can be represented as a pipe surface composed of piecewise-capsule SDFs joined by smooth-minimum operator.
    Core modeling choice that enables the subsequent gradient-based deformation.
invented entities (1)
  • SDF stent surface no independent evidence
    purpose: To define the target expanding surface for displacing vascular mesh vertices.
    Introduced as the central geometric primitive for the deformation method.

pith-pipeline@v0.9.0 · 5889 in / 1272 out tokens · 35493 ms · 2026-05-22T02:52:15.831631+00:00 · methodology

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