# A Statistical Shape Modeling Approach for the Derivation of a Data‐Driven Geometry‐Aware Lumped Arterial Stenosis Model

## TL;DR

This paper introduces a new model for predicting blood flow through heart artery blockages by combining shape data and fluid dynamics simulations.

## Contribution

A novel data-driven, geometry-aware lumped stenosis model is introduced using statistical shape modeling and CFD simulations.

## Key findings

- Only five shape modes were sufficient to describe geometric variability in stenosis.
- The new model improved pressure drop prediction accuracy by 18% compared to conventional models.
- Integration into a 1D pulse wave framework improved alignment with high-fidelity CFD results.

## Abstract

Existing lumped arterial stenosis models struggle to accurately capture the pressure and flow relationship of complex lesion morphologies, thereby limiting their ability to accurately evaluate lesions. To overcome these limitations, we introduce a geometry‐informed, data‐driven lumped stenosis model that incorporates realistic lesion shapes using statistical shape modeling (SSM). By generating a large dataset of synthetic coronary stenoses, hence focusing on epicardial lesions, and evaluating them through high‐fidelity 3D computational fluid dynamics (CFD), we derived reference pressure drops across a diverse range of lesion geometries and flow regimes. These CFD‐derived pressures and flows, along with their corresponding shape coefficients, were used to train a lumped parameter model capable of rapidly estimating trans‐lesional pressure drops. Remarkably, only five shape modes were necessary to effectively describe the geometric variability, underscoring the efficiency of the approach. Compared to a conventional lumped model, our approach significantly improved pressure drop prediction accuracy, especially in the case of irregular stenosis morphologies. Integration of the new data‐driven lumped stenosis model within a 1D pulse wave propagation framework was also successful, aligning simulated pressure and flow waveforms much closer with high‐fidelity CFD‐coupled results. In turn, the estimation of the fractional flow reserve, a clinically validated index of lesion‐specific ischemia, also improved by 18% compared to a conventional lumped model. Although only validated using synthetic lesion data, the model's architecture allows easy integration of additional shape features and lesion‐specific parameters, paving the way for future validation on patient‐derived geometries.

A data‐driven workflow for constructing a geometry‐aware lumped arterial stenosis model: Statistical shape modeling extracts geometry‐specific shape modes from synthetically generated coronary lesion geometries. Large‐scale 3D CFD simulations over varying Reynolds numbers yield the geometries their viscous (Kv) and inertial (Kt) loss coefficients. Then, non‐linear regression models map the extracted shape modes to their corresponding Kv and Kt to produce the final geometry‐specific lumped stenosis model.