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Updated: Apr 5, 2026
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Lumped-Parameter and Finite Element Modeling of Heart Failure with Preserved Ejection Fraction
Published on: February 13, 2021
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Numerical modeling of heart valves using resistive Eulerian surfaces
Aymen Laadhari1, Alfio Quarteroni2
1Computer Vision Laboratory, Institut für Bildverarbeitung, Department of Information Technology and Electrical Engineering, Swiss Federal Institute of Technology-ETHZ, CH-8092, Zürich, Switzerland.
Summary
This study presents a new mathematical model for heart valve function, coupling blood flow with leaflet dynamics. The validated model accurately simulates healthy and pathological heart valves with computational efficiency.
Area of Science:
- Computational fluid dynamics
- Biomedical engineering
- Mathematical modeling
Background:
- Accurate simulation of heart valve function is crucial for understanding cardiovascular diseases.
- Existing models often face challenges in coupling fluid dynamics with thin, deformable structures like valve leaflets.
- A need exists for computationally efficient models that can capture both healthy and pathological valve behaviors.
Purpose of the Study:
- To develop and numerically implement a novel mathematical model for heart valve functioning.
- To couple pulsatile blood flow with the dynamics of highly deformable valve leaflets.
- To create a model capable of simulating both healthy and pathological heart valve conditions efficiently.
Main Methods:
- Adoption of a resistive Eulerian surfaces framework to couple blood flow and leaflet mechanics.
- Integration of a lumped-parameter model for leaflet movement and blood dynamics.
- Utilization of a reduced circulation model for systemic hemodynamics and boundary condition simulation.
- Implementation of efficient time and spatial discretization techniques.
Main Results:
- Successful development and numerical implementation of the proposed mathematical model.
- Demonstration of the model's capability to couple pulsatile blood flow with deformable valve leaflets.
- Validation through numerical experiments in both 2D and 3D cases, illustrating accuracy.
- The model proves relatively simple for describing healthy and pathological valve function.
Conclusions:
- The developed mathematical model provides an accurate and computationally affordable approach to simulating heart valve function.
- The resistive Eulerian surfaces framework effectively couples fluid-structure interaction for thin, deformable leaflets.
- The model's ability to handle both healthy and pathological cases offers significant potential for clinical and research applications.
- Efficient numerical implementation ensures practical applicability for complex biomechanical simulations.
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