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Cross-Anatomy Transfer Versus Sparse Interpolation in Digital-Twin-Oriented Aortic Fluid-Structure Interaction Surrogates

Ali Nourbakhsh, Mohammad Reza Niroomand, Erfan Nourbakhsh

arXiv:2609.16322v1cs.AIcs.LG

TL;DR

Mesh-node interpolation can be mistaken for transfer to an unseen anatomy, and sparse labels can make improvements appear to come from a multi-anatomy prior. This study evaluates a geometry-only prior and same-anchor interpolation controls across four aortic anatomies; zero-shot transfer is poor, while direct interpolation matches or exceeds prior-based adaptation on several outcomes.

  • Problem

    Random node splits can estimate interpolation within a solved surface while overstating transfer to unseen anatomy, and sparse-label gains may reflect interpolation rather than a multi-anatomy prior.

    Source: §I · p. 1

  • Method

    The study evaluates a geometry-only multi-anatomy prior with zero-shot testing and sparse FSI-label field completion, comparing adaptation with same-anchor interpolation controls.

    Source: §I · p. 2, C. Research Question 2: Sparse Labels… · p. 5, G. Anchor-Selection Robustness · p. 6

  • Results

    Zero-shot transfer was uniformly poor, and direct same-anchor IDW/RBF interpolation matched or exceeded prior-based adaptation on several outcomes.

    Source: B. Research Question 1: Zero-Shot… · p. 4, §VII · p. 8

  • Takeaways & Limitations

    Sparse FSI-derived labels support within-anatomy field completion, but this four-anatomy study establishes no cross-anatomy transfer advantage beyond direct interpolation.

    Source: §VII · p. 8

    The effective sample size is four anatomies, sparse anchors are oracle simulation values rather than clinical observables, and the FSI reference lacks convergence testing.

    Source: §V · p. 7

Abstract

from arXiv · show

Surrogate credibility for fluid-structure interac- tion (FSI) requires distinguishing transfer across independent anatomies from interpolation within an already sampled surface. Four de-identified human aortic models from the Vascular Model Repository were reconstructed into separate lumen and nominal 1.5-mm wall domains and analyzed under matched first-cycle two-way FSI. A geometry-only LightGBM prior, selected by leave-one-anatomy-out development on three anatomies, was zero-shot evaluated on a fourth, then probed with a post-zero- shot sparse field-completion case study over six targets. Zero-shot transfer was poor across all targets. At a five-percent anchor level (203 anchors, 3,852 evaluation nodes), prior-plus-adaptation reached an oscillatory shear index (OSI) R2 of 0.603. However, same-anchor controls tuned only on the three development anatomies were stronger for several outcomes: inverse-distance weighting reached R2 = 0.829 (OSI), 0.617 (peak von Mises stress), 0.676 (mean stress); radial basis function interpolation reached 0.917, 0.714, 0.778. Sparse within-anatomy labels thus support field completion, but this four-anatomy cohort gives no evidence the cross-anatomy prior adds value beyond direct interpolation. We frame this as a first computational stage toward a measurement-linked digital twin: the surrogate/update layer is evaluated here, while larger cohorts, converged FSI, measurable patient-side inputs, and physics-informed learning remain future work, not a claim of a complete clinical twin. Our code, data and computation files are available at https://github. com/ali-nourbakhsh2005/Aortic-FSI-Sparse-Field-Completion

I. INTRODUCTION

The paper separates within-anatomy interpolation from transfer to unseen anatomy and evaluates a geometry-only prior against same-anchor controls. It frames the work as a surrogate evaluation stage toward a future digital twin, not a new learning algorithm or a complete synchronized twin.

I. INTRODUCTION

  • Patient-specific FSI is informative but costly to prepare and solve repeatedly, motivating surrogate modeling for full-field prediction.The paper notes that prior cardiovascular surrogate work uses varied validation units, making the distinction between independent anatomies and other test settings central to interpretation.Source: §I · p. 1
  • Mesh nodes from one anatomy are not independent patients, so random node splits can measure surface interpolation while overstating transfer to an unseen anatomy.Sparse labels from a new anatomy can also improve reconstruction through simple interpolation, motivating controls that use the same labels without a multi-anatomy prior.Source: §I · p. 1
  • The paper uses digital-twin-oriented narrowly for a surrogate/update layer that could feed a future cardiovascular twin, not a complete synchronized twin.The cited roadmap distinguishes static models from twins updated through real-world data assimilation.Source: §I · p. 1
  • The evaluation asks whether a geometry-only prior transfers without target labels, how sparse anchors affect reconstruction, and whether adaptation beats same-anchor interpolation.It also tests whether development-derived residual bands or geometry-shift scores associate with error on the separate anatomy.Source: §I · p. 1
  • The contribution is an evaluation framework and falsifiable baseline comparison, not a new learning algorithm.Source: §I · p. 2

A. Study Design and Evaluation Hierarchy

  • The study uses three anatomies for development and a fourth for zero-shot evaluation, with A4 files available during preprocessing but excluded from model selection.A4 sparse-calibration results are post-zero-shot case studies rather than a locked external test.Source: A. Study Design and Evaluation Hierarchy · p. 2

B. Repository Source, Geometry Reconstruction, and Data Governance

Four public, de-identified vascular models were reconstructed into separate lumen and wall domains and analyzed with individualized anatomy under standardized FSI conditions. The setup includes explicit modeling assumptions and lacks formal mesh- and time-step-convergence testing.

B. Repository Source, Geometry Reconstruction, and Data Governance

  • Public Vascular Model Repository files were used without direct identifiers, participant contact, intervention, or new clinical data collection.The original VMR-to-study label mapping was not preserved, so anatomy labels are not assigned to specific VMR identifiers without documentation.Source: B. Repository Source, Geometry… · p. 2
  • A deterministic ParaView-to-CATIA workflow created separate lumen and wall solids, imposing a nominal 1.5-mm wall thickness as a modeling assumption rather than an image-measured value.Source: B. Repository Source, Geometry… · p. 2

C. Anatomy-Specific FSI Under Standardized Assumptions

  • Anatomy was individualized, but inflow, outlet pressure, and material parameters were standardized, so the simulations represent anatomy-specific FSI under standardized conditions.The wall used benchmark Mooney–Rivlin settings without calibration to tissue tests; no prestress, zero-pressure correction, or external pressure load was applied.Source: C. Anatomy-Specific FSI Under… · p. 2

B. Repository Source, Geometry Reconstruction, and Data Governance

  • The reconstructed models show opaque blood-lumen domains and translucent CATIA-generated wall domains at matched display scale; these are renderings, not patient photographs.Source: Figure 1 · p. 2

C. Anatomy-Specific FSI Under Standardized Assumptions

  • All cases used the same one-second inlet waveform and 0-Pa-gauge outlet, and exported 21 fields at 0.05-s spacing; the interval includes startup from rest.The A2 solution stored a complete state through exactly 1.0 s before a later step failed.Source: C. Anatomy-Specific FSI Under… · p. 2
  • Formal mesh-refinement and time-step convergence series were unavailable, so the fields are not claimed to be mesh- or time-step-independent.Output-sampling checks supported the finer grid but did not replace formal convergence testing.Source: C. Anatomy-Specific FSI Under… · pp. 2–3

D. Vector Wall Shear Stress and Mechanical Targets

The paper reconstructs wall shear quantities from velocity gradients and apparent viscosity, then defines time-based flow metrics and mechanical stress targets on exported states. Checks against native COMSOL traction assess post-processing consistency, not physiological correctness.

D. Vector Wall Shear Stress and Mechanical Targets

  • The viscous tensor and tangential wall traction are reconstructed from apparent viscosity, velocity gradients, and the unit normal.Source: D. Vector Wall Shear Stress and… · p. 3
  • TAWSS uses trapezoidal quadrature over 21 exported states, while peak WSS and structural targets use saved-state maxima and temporal-mean von Mises stress.RRT is defined from OSI and TAWSS and is not capped; its large anatomy-4 values motivated a log(1 + y) transform and rank-based reporting.Source: D. Vector Wall Shear Stress and… · p. 3
  • Stress amplitude was dropped because minimum von Mises stress was near zero and amplitude nearly duplicated cycle maximum, so treating both as independent would double-count one field.The reported correlation was r = 1.000000, with amplitude equal to 0.5 σmax within relative deviation below 10^-7.Source: D. Vector Wall Shear Stress and… · p. 3
  • Against native COMSOL traction on two anatomies, reconstructed TAWSS had low errors, while the validation supports post-processing consistency rather than FSI physiological correctness.Anatomy 3 and 4 TAWSS IQR-normalized RMSE values were 0.0119 and 0.0094, respectively; anatomy-4 RRT remained unstable in raw scale because near-singular values dominate squared error.Source: D. Vector Wall Shear Stress and… · p. 3

E. Geometry-Only Multi-Anatomy Prior

The geometry-only prior represents each inner-wall node with descriptors derived from the point cloud and uses target-specific LightGBM models selected through anatomy-held-out development.

E. Geometry-Only Multi-Anatomy Prior

  • Each node is represented by 21 geometry descriptors, including normalized pseudo-centerline position, radial measures, curvature, tangent alignment, and shape ratios.The pseudo-centerline is built by principal-axis projection, 24 axial quantile bins, bin-centroid smoothing, and nearest-centerline assignment.Source: E. Geometry-Only Multi-Anatomy Prior · p. 3
  • Target transforms were fixed by outcome, and three target-specific LightGBM complexity levels were compared with three-fold leave-one-anatomy-out selection.Anatomy-balanced node weights prevented the densest mesh from dominating fitting; candidate selection minimized mean normalized MAE, with Spearman correlation secondary.Source: E. Geometry-Only Multi-Anatomy Prior · p. 3

F. Sparse Field Completion and Same-Anchor Controls

Sparse FSI-derived anchors are used to complete the remaining field, with same-anchor interpolation controls separating within-anatomy completion from any added value of a multi-anatomy prior. The section also defines evaluation metrics and checks anchor-selection and uncertainty diagnostics.

F. Sparse Field Completion and Same-Anchor Controls

  • Sparse calibration uses FSI-derived anchor labels, not clinical measurements, and does not demonstrate end-to-end clinical updating or speedup when labels require full FSI.Wall-stress anchors have no direct measurement analogue.Source: F. Sparse Field Completion and… · p. 3
  • At 5% anchors, prior adaptation fits a ridge affine correction and then a distance-weighted k = 10 nearest-neighbor model to anchor residuals; anchors are excluded from evaluation.Anchor sets at 1%, 2%, 5%, or 10% are selected using geometry only, making the experiment transductive.Source: F. Sparse Field Completion and… · p. 3
  • Same-anchor controls use distance-weighted KNN, IDW, and thin-plate-spline RBF interpolation, with hyperparameters selected on A1–A3 5% LOAO development data.The controls use no A1–A3 target fields and are fixed for secondary A4 comparisons.Source: F. Sparse Field Completion and… · p. 3

G. Metrics, Dependence Sensitivities, and Empirical Bands

  • Primary metrics are R2, MAE, RMSE, Spearman ρ, and top-decile overlap; RRT is additionally evaluated in log(1 + RRT) space.Six-target means are unweighted macro-averages, and wall nodes are not treated as independent subjects for inferential p-values.Source: G. Metrics, Dependence Sensitivities,… · p. 3
  • At 5% anchors, robustness is checked with 10 alternative KMeans seeds and 10 uniform random anchor sets using development-selected IDW across six tasks.The node-weighted primary metrics are supplemented by local-spacing weighting and five equal-count centerline blocks on A4.Source: G. Metrics, Dependence Sensitivities,… · pp. 3–4
  • The empirical residual band uses the largest of three held-out-anatomy 90th-percentile residuals and is not a distribution-free 90% predictive interval.Local geometry shift is measured using pair-calibrated 10-nearest-neighbor distances in the same eight features; the unconstrained RBF baseline yields 21 out-of-range OSI predictions among 3,852 A4 non-anchor nodes at 5%.Source: G. Metrics, Dependence Sensitivities,… · p. 4

III. RESULTS

The computational-reference audits show that flow and mechanical rankings differ across anatomies, while WSS agreement checks support the reconstruction implementation. The stress-amplitude audit found the metric redundant under the first-cycle unloaded initialization.

A. Computational-Reference Audits

  • Anatomy 2 had the highest global saved-state peak WSS (134.27 Pa) and 95th-percentile TAWSS (4.56 Pa), while anatomy 1 had the largest 95th-percentile saved-state maximum von Mises stress (10.55 kPa).The table summarizes computational anatomy and FSI, and the differing rankings support separate interpretation of flow and mechanical fields rather than one fixed-weight risk score.Source: A. Computational-Reference Audits · p. 4, Table I · p. 4
  • WSS agreement audits on anatomies 3 and 4 showed near-unity slopes and millipascal-scale TAWSS bias and MAE, supporting the reconstruction implementation.The table’s scope is computational anatomy and FSI summary.Source: A. Computational-Reference Audits · p. 4, Table I · p. 4
  • Stress amplitude was effectively half of cycle maximum because minimum stress was near zero under first-cycle unloaded initialization, so amplitude was dropped from primary averages and tables.Source: A. Computational-Reference Audits · p. 4

B. Research Question 1: Zero-Shot Cross-Anatomy Transfer Is Weak

The geometry-only prior transferred poorly to the held-out anatomy, while sparse-label reconstruction improved but did not consistently outperform direct interpolation. Development-only controls and held-out comparisons likewise found no consistent incremental value from the cross-anatomy prior.

B. Research Question 1: Zero-Shot Cross-Anatomy Transfer Is Weak

  • Zero-shot R2 on anatomy 4 was −0.159 for TAWSS, −0.374 for OSI, approximately 0 for RRT, −0.027 for peak WSS, −0.095 for maximum VM, and −0.056 for mean VM.The native-tree-count refit remained poor, and with only three development anatomies the geometry representation did not support reliable zero-shot transfer.Source: B. Research Question 1: Zero-Shot… · pp. 4–5

C. Research Question 2: Sparse Labels Improve Reconstruction of Non-Anchor Nodes

  • At 5% calibration, prior-plus-adaptation on anatomy 4 reached OSI R2 = 0.603 across 203 anchors and 3,852 evaluation nodes; development LOAO curves improved monotonically as within-anatomy labels increased.Target-specific behavior was heterogeneous, and 5% was retained as the primary setting for a clear development-fold gain without doubling the anchor burden to 10%.Source: C. Research Question 2: Sparse Labels… · p. 5, Figure 3 · p. 5

D. Research Question 3: Same-Anchor Interpolation Matches or Outperforms Prior-Based Adaptation

  • In A1–A3 5% LOAO, selected IDW/RBF exceeded prior-plus-adaptation macro R2 in every held-out anatomy, and the gap held across A4 calibration fractions from 1% to 10%.For A1, A2, and A3, the respective IDW/RBF versus prior macro R2 values were 0.555/0.576 vs. 0.553, 0.587/0.665 vs. 0.529, and 0.446/0.475 vs. 0.327.Source: D. Research Question 3: Same-Anchor… · p. 5
  • RBF reconstructed OSI and maximum VM particularly well but was less stable for peak WSS and produced a few out-of-range OSI values; IDW was more uniform across targets.The results support target-specific baseline selection rather than one universal algorithm.Source: D. Research Question 3: Same-Anchor… · p. 5
  • At 5% calibration, IDW/RBF reached six-task macro R2 of 0.431/0.425 versus 0.311 for prior-plus-adaptation; RBF excelled on OSI and stress, while the prior was more competitive for TAWSS/peak WSS.No single rule dominated, but the cross-anatomy prior gave no consistent incremental value.Source: Table III · p. 5, D. Research Question 3: Same-Anchor… · p. 5

E. Research Question 4: Empirical Residual Bands and Geometry Shift Are Diagnostic, Not Guarantees

Empirical residual bands covered most anatomy-4 non-anchor values but were wide and descriptive rather than formal guarantees. Geometry-shift associations with error varied by target and were negligible for maximum wall stress.

E. Research Question 4: Empirical Residual Bands and Geometry Shift Are Diagnostic, Not Guarantees

  • Anatomy-4 empirical bands covered 88.4–91.4% across the six targets, but median widths ranged from 1.53 to 2.05 development IQRs and were not formal predictive guarantees.Coverage was 88.4% for TAWSS, 91.4% for OSI, 90.0% for RRT, 89.4% for peak WSS, 90.3% for maximum VM, and 90.1% for mean VM.Source: E. Research Question 4: Empirical… · p. 5
  • On anatomy 4 at 5% calibration, direct IDW/RBF interpolation frequently equaled or exceeded prior-plus-adaptation.Source: Figure 4 · p. 5
  • Geometry-shift association with normalized absolute error was target-dependent and negligible for maximum wall stress, making the OOD score a geometry-support marker rather than an error oracle.Reported correlations included ρ = 0.292 for OSI, 0.224 for RRT, and 0.151 for TAWSS.Source: E. Research Question 4: Empirical… · pp. 5–6

F. Dependence and Mesh-Density Sensitivities

Same-anchor interpolation controls constrain claims that a multi-anatomy prior improves sparse field completion. Robustness and timing checks qualify the comparison, while mesh nodes remain dependent observations.

F. Dependence and Mesh-Density Sensitivities

  • Five longitudinal pseudo-centerline blocks showed substantial TAWSS block-to-block variability, while node-density weighting preserved the qualitative OSI and mechanical-field ordering.Prior-plus-adaptation TAWSS block R2 ranged 0.086–0.633, IDW −0.032–0.762, and RBF −1.979–0.895.Source: F. Dependence and Mesh-Density… · p. 6

G. Anchor-Selection Robustness

  • Across 10 alternative 5% seeds, IDW’s same-anchor conclusion persisted; representative KMeans selection improved stability modestly over random anchors.Nearest-anchor distance was not strictly monotonic with error, so it is a support diagnostic rather than an error model.Source: G. Anchor-Selection Robustness · p. 6

H. Computational Cost Context

  • The post-hoc audit found completion and adaptation runtimes far below archived FSI solve times, but it establishes no end-to-end clinical speedup.A1 runtime was unrecoverable, and oracle FSI anchors plus CAD/meshing and measurement acquisition were outside the audit.Source: H. Computational Cost Context · p. 6

A. What the Baseline Changes

  • Sparse within-anatomy field completion is feasible, but the four-anatomy prior adds little demonstrable value beyond sparse labels and direct interpolation.The same-anchor comparison is stronger when interpolation settings are selected only on A1–A3 and fixed.Source: A. What the Baseline Changes · p. 6
  • Large geometry cohorts and training support matched to test distributions motivate cross-shape surrogacy, but complexity needs direct-baseline evidence in this few-anatomy, smooth-field regime.The reported negative zero-shot result and stronger same-anchor controls do not support crediting a sophisticated prior in this setting.Source: A. What the Baseline Changes · p. 6

B. Meaning of the Sparse Anchors

Sparse anchors are oracle FSI values used to test field completion, not a demonstrated clinical update mechanism. The study’s standardized, first-cycle scope and weak geometry-only transfer motivate a staged path toward a measurement-linked twin.

B. Meaning of the Sparse Anchors

  • The 5% anchors are oracle labels from the full FSI reference, making this an upper-bound field-completion experiment rather than a practical clinical operating point.If anchor values require a full FSI run, the experiment saves no computation; wall stress has no direct measurement analogue here.Source: B. Meaning of the Sparse Anchors · p. 6

C. Numerical and Physiological Scope

  • The controlled first-cycle fields use common inflow, outlet pressure, and material constants, so wall stresses are computational response fields rather than physiological or rupture stresses.Saved-state maximum VM shifted 16.5–33.4% with temporal spacing, while temporal-mean VM was more stable at 7.5–12.8%; formal convergence and physiological sensitivity remain necessary.Source: C. Numerical and Physiological Scope · pp. 6–7, Figure 6 · p. 7

D. Why the Current Cross-Anatomy Prior Underperforms

  • Weak zero-shot transfer is consistent with only three development anatomies, pseudo-centerline-based correspondence, pointwise features without surface connectivity or FSI physics, and locally smooth targets favoring interpolation.The fixed physiology also limits the model to geometry-conditioned variation.Source: D. Why the Current Cross-Anatomy Prior… · p. 7

E. Roadmap Toward an Advanced Digital Twin

  • The demonstrated scope is the computational surrogate/update layer, not a complete clinical twin with dynamic linkage and real-world data assimilation.The roadmap calls for expanded and validated FSI, physics-informed architectures, measurable signals, uncertainty handling, longitudinal updating, and prospective external validation.Source: E. Roadmap Toward an Advanced Digital… · p. 7

V. LIMITATIONS

This study supports comparative computational-surrogate conclusions, not rupture-risk or clinical claims. Its conclusion is limited by four anatomies, oracle labels, and unconverged standardized FSI, while identifying measurement-linked and physics-informed work as future stages.

V. LIMITATIONS

  • Effective sample size is four anatomies, and the first-cycle standardized FSI, oracle anchors, transductive completion, and unconverged fields restrict conclusions to computational comparisons.Direct interpolation outperformed prior-based adaptation on several targets; RBF can violate the OSI range, and empirical bands and repeated-seed checks have no formal statistical guarantee.Source: §V · p. 7

VI. DATA, CODE, AND DECLARATIONS

  • The analysis uses publicly released VMR model files, and its reproducibility package includes code, processed tables, outputs, and sensitivity analyses.The exact VMR identifier-to-A1–A4 mapping is incomplete in derived filenames.Source: §VI · pp. 7–8

VII. CONCLUSION

  • The conclusion finds no demonstrated cross-anatomy transfer advantage beyond same-anchor interpolation and frames the work as an initial surrogate evaluation, not a completed clinical twin.Further stages require more anatomies, converged and pressure-loaded FSI, measurement-linked inputs, physics-informed models, and prospective validation.Source: §VII · p. 8
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