Summary In this work, we consider two kinds of model reduction techniquesto
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-Dand
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 parametrisedby
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.
%0 Journal Article
%1 koppl2018numerical
%A Köppl, Tobias
%A Santin, Gabriele
%A Haasdonk, Bernard
%A Helmig, Rainer
%D 2018
%J International Journal for Numerical Methods in Biomedical Engineering
%K blood dimensionally flow from:mhartmann ians kernel methods, mixed-dimension models, peripheral real-time reduced simulations simulations, stenosis, surrogate vorlaeufig
%N ja
%P e3095
%R 10.1002/cnm.3095
%T Numerical modelling of a peripheral arterial stenosis using dimensionally
reduced models and kernel methods
%U https://onlinelibrary.wiley.com/doi/abs/10.1002/cnm.3095
%V 0
%X Summary In this work, we consider two kinds of model reduction techniquesto
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-Dand
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 parametrisedby
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.
@article{koppl2018numerical,
abstract = {Summary In this work, we consider two kinds of model reduction techniquesto
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-Dand
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 parametrisedby
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.},
added-at = {2018-07-20T10:54:55.000+0200},
author = {K{\"o}ppl, Tobias and Santin, Gabriele and Haasdonk, Bernard and Helmig, Rainer},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2832dacbae634d8ae21c67ac44f94850c/mathematik},
doi = {10.1002/cnm.3095},
file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/KSHH2017_www_preprint.pdf:PDF},
interhash = {979f2097ba9c22d67096e59e5c6d7a3e},
intrahash = {832dacbae634d8ae21c67ac44f94850c},
journal = {International Journal for Numerical Methods in Biomedical Engineering},
keywords = {blood dimensionally flow from:mhartmann ians kernel methods, mixed-dimension models, peripheral real-time reduced simulations simulations, stenosis, surrogate vorlaeufig},
note = {e3095 cnm.3095},
number = {ja},
owner = {santinge},
pages = {e3095},
timestamp = {2019-12-18T14:37:55.000+0100},
title = {Numerical modelling of a peripheral arterial stenosis using dimensionally
reduced models and kernel methods},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/cnm.3095},
volume = 0,
year = 2018
}