A data-driven framework to identify restenosis-prone regions in femoral arteries from geometric and inflow waveform parameters

TL;DR

The paper addresses restenosis risk mapping in peripheral arterial disease by leveraging CFD-derived haemodynamic indices while overcoming CFD's computational burden through a data-driven ML–ROM approach. It jointly samples vessel geometry (six parameters) and inlet waveform variability (PCA of real waveforms) to predict restenosis-prone regions defined by four threshold schemes, using POD to obtain reduced-order representations and ML to predict corresponding POD coefficients for region reconstruction. The Fourier-based ML models deliver the best predictive performance (median BA > 0.92 across definitions) and enable online inference with speed-ups around $10^9$, substantially accelerating risk assessment. The framework supports fast, personalized vascular risk mapping and points toward future physics-informed enhancements and richer geometric representations to further improve generalization and interpretability.

Abstract

Haemodynamic indices derived from Computational Fluid Dynamics (CFD), such as Time-averaged Wall Shear Stress (TAWSS) and Oscillatory Shear Index (OSI), are closely associated with restenosis risk in Peripheral Arterial Disease (PAD). However, translating these insights into clinical practice may require computationally efficient approaches such as Reduced Order Model (ROM) or Machine Learning (ML). In this work, we developed an ML-ROM framework to predict critical, restenosis-prone, haemodynamic regions accounting for both vessel geometries and inlet flow waveforms. We generated 500 synthetic femoral-artery geometries parameterised by six geometric parameters, and created physiologically realistic inflow waveforms via Principal Component Analysis (PCA) of patient data. CFD was used to obtain the Wall Shear Stress (WSS) distribution, from which TAWSS and OSI were computed. Critical regions were then defined by applying threshold-based criteria to the TAWSS and OSI. Four critical-region definitions were considered: two with vessel-specific relative thresholds (TAWSS< 33rd percentile and OSI> 66nd percentile) and two with absolute thresholds (TAWSS< 0.5 Pa and OSI> 0.2). Proper orthogonal decomposition (POD) was then applied to these high-dimensional critical-region data to obtain ROMs; These were then used to train ML models from which the critical region regions could be reconstructed. Three ML architectures were explored: a Fourier-based architecture, a Long Short-term Memory (LSTM) architecture, and a Convolutional Neural Network (CNN) architecture. The Fourier models achieved the highest performance, with the median values of Balanced Accuracy (BA) exceeding 0.92 across all critical-region definitions. The ML-ROM framework also offered a substantial speed-up ratio, about nine orders of magnitude faster than traditional CFD.

Figures (8)

• Figure 1: Diagrammatic overview of the study methodology. (a) Synthetic stenosed geometries and inflow waveforms were generated and used in CFD simulations to obtain haemodynamic indices, and thresholds were applied to identify critical regions which served as FOMs. (b) POD was applied to FOMs to identify POD modes. (c) ML models were trained on geometric and inlet flowrate waveform parameters to predict POD coefficients, which were then used to reconstruct the predicted critical regions.
• Figure 2: Dataset generation. (a) Synthetic geometries are created by deforming a baseline model in three steps, using six geometric parameters. Examples of generated geometries are shown. (b) Synthetic flowrate waveforms obtained by applying PCA to 12 real flowrate waveforms and randomising coefficients. Examples of original and synthetic waveforms are shown.
• Figure 3: ML models. The models explored in our study are named after their treatment of the inlet flowrate waveform input: (a) Fourier model, (b) LSTM model, and (c) CNN model.
• Figure 4: POD reconstruction performance. BA of reconstructed critical regions as a function of mode number $i$ for (a) TAWSS33, (b) OSI66, (c) TAWSS0.5, and (d) OSI0.2. Results are shown for training (grey), validation (red), and test (purple) datasets.
• Figure 5: Comparison of test dataset BA across the three ML models for four critical-region definitions: (a) TAWSS33, (b) OSI66, (c) TAWSS0.5, and (d) OSI0.2. Each raincloud plot shows case-wise distribution, combining a half-violin (distribution), a boxplot (median and interquartile range), and a dot plot (each test case). Results of pairwise Wilcoxon signed-rank tests are shown with * for $p < 0.05$, and ** for $p \geq 0.05$ .