On the physical consistency between three-dimensional and one-dimensional models in haemodynamics
In this work we discuss the reliability of the coupling among three-dimensional (3D) and one-dimensional (1D) models that describe blood flowing into the circulatory tree. In particular, we study the physical consistency of the 1D model with respect to the 3D one. To this aim, we introduce a general...
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| Published in | Journal of computational physics Vol. 244; pp. 97 - 112 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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01.07.2013
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| Abstract | In this work we discuss the reliability of the coupling among three-dimensional (3D) and one-dimensional (1D) models that describe blood flowing into the circulatory tree. In particular, we study the physical consistency of the 1D model with respect to the 3D one. To this aim, we introduce a general criterion based on energy balance for the proper choice of coupling conditions between models. We also propose a way to include in the 1D model the effect of the external tissue surrounding the vessel and we discuss its importance whenever this effect is considered in the 3D model. Finally, we propose several numerical results in real human carotids, studying different configurations for the 1D model and highlighting the best one in view of the physical consistency. |
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| AbstractList | In this work we discuss the reliability of the coupling among three-dimensional (3D) and one-dimensional (1D) models that describe blood flowing into the circulatory tree. In particular, we study the physical consistency of the 1D model with respect to the 3D one. To this aim, we introduce a general criterion based on energy balance for the proper choice of coupling conditions between models. We also propose a way to include in the 1D model the effect of the external tissue surrounding the vessel and we discuss its importance whenever this effect is considered in the 3D model. Finally, we propose several numerical results in real human carotids, studying different configurations for the 1D model and highlighting the best one in view of the physical consistency. In this work we discuss the reliability of the coupling among three-dimensional (3D) and one-dimensional (ID) models that describe blood flowing into the circulatory tree. In particular, we study the physical consistency of the 1D model with respect to the 3D one. To this aim, we introduce a general criterion based on energy balance for the proper choice of coupling conditions between models. We also propose a way to include in the ID model the effect of the external tissue surrounding the vessel and we discuss its importance whenever this effect is considered in the 3D model. Finally, we propose several numerical results in real human carotids, studying different configurations for the ID model and highlighting the best one in view of the physical consistency. |
| Author | Vergara, Christian Quarteroni, Alfio Formaggia, Luca |
| Author_xml | – sequence: 1 givenname: Luca surname: Formaggia fullname: Formaggia, Luca email: luca.formaggia@polimi.it organization: MOX, Dipartimento di Matematica, Politecnico di Milano, Italy – sequence: 2 givenname: Alfio surname: Quarteroni fullname: Quarteroni, Alfio email: alfio.quarteroni@epfl.ch organization: MOX, Dipartimento di Matematica, Politecnico di Milano, Italy – sequence: 3 givenname: Christian surname: Vergara fullname: Vergara, Christian email: christian.vergara@unibg.it organization: Dipartimento di Ingegneria dell’Informazione e Metodi Matematici, Università degli Studi Bergamo, Dalmine (BG), Italy |
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| Cites_doi | 10.1016/j.cma.2005.04.014 10.1137/S1540345902408482 10.1007/s007910050030 10.1016/j.jbiomech.2005.02.021 10.1137/090772836 10.1016/j.jbiomech.2009.01.034 10.1007/s007910050039 10.1007/978-88-470-1152-6 10.1201/b14172-49 10.1016/j.cma.2007.05.008 10.1152/ajpheart.00666.2007 10.1016/0045-7825(81)90049-9 10.1016/j.compfluid.2010.11.032 10.1023/A:1010835316564 10.1007/s10237-011-0289-z 10.1016/S0021-9290(99)00201-8 10.1137/S003614290038296X 10.1051/m2an:2007039 10.1016/j.cma.2012.05.017 10.1016/0045-7825(82)90128-1 10.1023/B:ENGI.0000007980.01347.29 10.1016/j.cma.2005.05.009 10.1016/S0045-7825(01)00302-4 10.1002/cnm.1457 10.1007/s10665-009-9281-3 10.1007/s10439-010-0132-1 |
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| Snippet | In this work we discuss the reliability of the coupling among three-dimensional (3D) and one-dimensional (1D) models that describe blood flowing into the... In this work we discuss the reliability of the coupling among three-dimensional (3D) and one-dimensional (ID) models that describe blood flowing into the... |
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| SubjectTerms | Blood Cardiovascular simulation Circulation Consistency Geometrical multiscale Human Human carotid Joining Mathematical models Surrounding tissue Three dimensional Three dimensional models Total pressure |
| Title | On the physical consistency between three-dimensional and one-dimensional models in haemodynamics |
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