Abstract
Summary 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 (1âD
and 0âD models, the soâcalled mixedâdimension model) and on
the other hand surrogate models produced by kernel methods. Both
methods are combined in such a way that the mixedâdimension 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 wellâtrained 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.
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