Numerical modelling of a peripheral arterial stenosis using dimensionally reduced models and kernel methods.

Area of Science:

• Computational fluid dynamics
• Biomedical engineering
• Medical imaging analysis

Background:

• Peripheral artery stenosis significantly impacts blood flow dynamics.
• Accurate simulation of blood flow in arteries is crucial for diagnosis and treatment planning.
• Existing full models can be computationally expensive for real-time analysis.

Purpose of the Study:

• To develop and evaluate model reduction techniques for simulating blood flow in peripheral arterial stenosis.
• To create efficient surrogate models for rapid analysis of stenosis impact.
• To demonstrate the utility of these models for parameter optimization and state estimation.

Main Methods:

• Utilized mixed-dimension models (1-D and 0-D) to generate training data.
• Developed kernel-based surrogate models parameterized by stenosis degree.
• Combined mixed-dimension and surrogate models for efficient simulation.

Main Results:

• Surrogate models accurately reproduced simulation data for blood flow with peripheral stenosis.
• Achieved significant speedups (orders of magnitude) compared to full models.
• Demonstrated efficient parameter optimization and state estimation capabilities.

Conclusions:

• Model reduction techniques, particularly surrogate models, offer a highly efficient approach to simulating blood flow in stenosed tibial arteries.
• These methods enable rapid assessment of stenosis severity on blood flow dynamics.
• The developed surrogate models are valuable tools for clinical applications requiring fast computational fluid dynamics analysis.