To address the issue of computational efficiency related to the modelling of blood flow in complex networks, we derive a family of nonlinear lumped-parameter models for blood flow in compliant vessels departing from a well-established one-dimensional model. These 0D models must preserve important nonlinear properties of the original 1D model: the nonlinearity of the pressure-area relation and the pressure-dependent parameters characterizing the 0D models, the resistance R and the inductance L, defined in terms of a time-dependent cross-sectional area subject to pressure changes. We introduce suitable coupling conditions to join 0D vessels through 0D junctions and construct 0D networks preserving the original 1D network topology. The newly derived nonlinear 0D models are then applied to several arterial networks and the predicted results are compared against (i) the reference 1D results, to validate the models and assess their ability to reproduce good approximations of pressure and flow waveforms in all vessels at a much lower computational cost, measured in terms of CPU time, and (ii) the linear 0D results, to evaluate the improvement gained by including certain nonlinearities in the 0D models, in terms of agreement with the 1D results.
Accepté le :
Publié le :
DOI : 10.1051/m2an/2022052
Keywords: Blood flow, lumped-parameter models, nonlinearity, coupling, arterial networks
@article{M2AN_2022__56_5_1579_0,
author = {Ghitti, Beatrice and Toro, Eleuterio Francisco and M\"uller, Lucas Omar},
title = {Nonlinear lumped-parameter models for blood flow simulations in networks of vessels},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1579--1627},
year = {2022},
publisher = {EDP-Sciences},
volume = {56},
number = {5},
doi = {10.1051/m2an/2022052},
mrnumber = {4454157},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2022052/}
}
TY - JOUR AU - Ghitti, Beatrice AU - Toro, Eleuterio Francisco AU - Müller, Lucas Omar TI - Nonlinear lumped-parameter models for blood flow simulations in networks of vessels JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2022 SP - 1579 EP - 1627 VL - 56 IS - 5 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2022052/ DO - 10.1051/m2an/2022052 LA - en ID - M2AN_2022__56_5_1579_0 ER -
%0 Journal Article %A Ghitti, Beatrice %A Toro, Eleuterio Francisco %A Müller, Lucas Omar %T Nonlinear lumped-parameter models for blood flow simulations in networks of vessels %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2022 %P 1579-1627 %V 56 %N 5 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2022052/ %R 10.1051/m2an/2022052 %G en %F M2AN_2022__56_5_1579_0
Ghitti, Beatrice; Toro, Eleuterio Francisco; Müller, Lucas Omar. Nonlinear lumped-parameter models for blood flow simulations in networks of vessels. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 56 (2022) no. 5, pp. 1579-1627. doi: 10.1051/m2an/2022052
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