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

TL;DR

This paper combines dimensionally reduced blood flow models with kernel-based surrogate models to efficiently simulate and analyze the impact of peripheral arterial stenosis, enabling rapid parameter studies and optimizations.

Contribution

It introduces a novel hybrid approach that integrates mixed-dimension models with kernel methods for fast and accurate blood flow simulation in stenosed arteries.

Findings

Surrogate models reproduce simulation data with high accuracy.

Speedup of several orders over full models for parameter variation analysis.

Efficient solution of parameter optimization and state estimation problems.

Abstract

In this work, we consider two kinds of model reduction techniques to simulate blood flow through the largest systemic arteries, where a stenosis is located in a peripheral artery i.e. in an artery that is located far away from the heart. For our simulations we place the stenosis in one of the tibial arteries belonging to the right lower leg (right post tibial artery). The model reduction techniques that are used are on the one hand dimensionally reduced models (1-D and 0-D models, the so-called mixed-dimension model) and on the other hand surrogate models produced by kernel methods. Both methods are combined in such a way that the mixed-dimension models yield training data for the surrogate model, where the surrogate model is parametrised by the degree of narrowing of the peripheral stenosis. By means of a well-trained surrogate model, we show that simulation data can be reproduced with a satisfactory accuracy and that parameter optimisation or state estimation problems can be solved in a very efficient way. Furthermore it is demonstrated that a surrogate model enables us to present after a very short simulation time the impact of a varying degree of stenosis on blood flow, obtaining a speedup of several orders over the full model.