Fast generation of 3D flow obstacles from parametric surface models: application to cardiac valves

TL;DR

This work tackles the costly setup of CFD simulations for valvular flow by transforming parametric heart valve models into fast-to-use 3D resistive obstacles (RIIS). It introduces an adaptive surface representation built from Bézier curves and polylines, and provides three distance-to-surface algorithms (minimization, sampling, triangulation) plus two mesh-traversal strategies (exhaustive and recursive) to extract obstacle nodes efficiently. Triangulation offers the best speed-accuracy balance, while recursive neighbor search dramatically reduces computations for large meshes. Demonstrations on an aortic valve model and a newly proposed mitral valve model show the pipeline’s generality and potential for rapid valve-shape updates in inverse-estimation and simulation workflows.

Abstract

Due to the computationally demanding nature of fluid-structure interaction simulations, heart valve simulation is a complex task. A simpler alternative is to model the valve as a resistive flow obstacle that can be updated dynamically without altering the mesh, but this approach can also become computationally expensive for large meshes. In this work, we present a fast method for computing the resistive flow obstacle of a heart valve. The method is based on a parametric surface model of the valve, which is defined by a set of curves. The curves are adaptively sampled to create a polyline representation, which is then used to generate the surface. The surface is represented as a set of points, allowing for efficient distance calculations to determine whether mesh nodes belong to the valve surface. We introduce three algorithms for computing these distances: minimization, sampling, and triangulation. Additionally, we implement two mesh traversal strategies: exhaustive node iteration and recursive neighbor search. The latter significantly reduces the number of distance calculations by only considering neighboring nodes. Our pipeline is demonstrated on both a previously reported aortic valve model and a newly proposed mitral valve model, highlighting its flexibility and efficiency for rapid valve shape updates in computational simulations.

Figures (17)

• Figure 1: Overview of the cusps in the aortic valve.
• Figure 2: Curves used for defining the aortic valve cusp.
• Figure 3: Example of mitral valve in open state.
• Figure 4: Pipeline of generating valve surface from parameters.
• Figure 5: Example of one step of recursive subdivision using de Casteljau algorithm.