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

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.

References in corpus (1)

• Numerical method of characteristics for one-dimensional blood flow

Cited by in corpus (6)

• Analysis of target data-dependent greedy kernel algorithms: Convergence rates for $f$-, $f\cdot P$- and $f/P$-greedy
• A 1D-0D-3D coupled model for simulating blood flow and transport processes in breast tissue
• Kernel Methods for Surrogate Modeling
• On the optimality of target-data-dependent kernel greedy interpolation in Sobolev Reproducing Kernel Hilbert Spaces
• Greedy regularized kernel interpolation
• A 3D-1D coupled blood flow and oxygen transport model to generate microvascular networks