Inverse modelling of image-based patient-specific blood vessels: zero-pressure geometry and in vivo stress incorporation

Joris Bols; Joris Degroote; Bram Trachet; Benedict Verhegghe; Patrick Segers; Jan Vierendeels

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2013)

  • Volume: 47, Issue: 4, page 1059-1075
  • ISSN: 0764-583X

Abstract

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In vivo visualization of cardiovascular structures is possible using medical images. However, one has to realize that the resulting 3D geometries correspond to in vivo conditions. This entails an internal stress state to be present in the in vivo measured geometry of e.g. a blood vessel due to the presence of the blood pressure. In order to correct for this in vivo stress, this paper presents an inverse method to restore the original zero-pressure geometry of a structure, and to recover the in vivo stress field of the final, loaded structure. The proposed backward displacement method is able to solve the inverse problem iteratively using fixed point iterations, but can be significantly accelerated by a quasi-Newton technique in which a least-squares model is used to approximate the inverse of the Jacobian. The here proposed backward displacement method allows for a straightforward implementation of the algorithm in combination with existing structural solvers, even if the structural solver is a black box, as only an update of the coordinates of the mesh needs to be performed.

How to cite

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Bols, Joris, et al. "Inverse modelling of image-based patient-specific blood vessels: zero-pressure geometry and in vivo stress incorporation." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 47.4 (2013): 1059-1075. <http://eudml.org/doc/273090>.

@article{Bols2013,
abstract = {In vivo visualization of cardiovascular structures is possible using medical images. However, one has to realize that the resulting 3D geometries correspond to in vivo conditions. This entails an internal stress state to be present in the in vivo measured geometry of e.g. a blood vessel due to the presence of the blood pressure. In order to correct for this in vivo stress, this paper presents an inverse method to restore the original zero-pressure geometry of a structure, and to recover the in vivo stress field of the final, loaded structure. The proposed backward displacement method is able to solve the inverse problem iteratively using fixed point iterations, but can be significantly accelerated by a quasi-Newton technique in which a least-squares model is used to approximate the inverse of the Jacobian. The here proposed backward displacement method allows for a straightforward implementation of the algorithm in combination with existing structural solvers, even if the structural solver is a black box, as only an update of the coordinates of the mesh needs to be performed.},
author = {Bols, Joris, Degroote, Joris, Trachet, Bram, Verhegghe, Benedict, Segers, Patrick, Vierendeels, Jan},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {backward displacement method; inverse modelling; image-based modelling; patient-specific blood vessels; in vivo stress; prestress; zero-pressure geometry; in vivo stress},
language = {eng},
number = {4},
pages = {1059-1075},
publisher = {EDP-Sciences},
title = {Inverse modelling of image-based patient-specific blood vessels: zero-pressure geometry and in vivo stress incorporation},
url = {http://eudml.org/doc/273090},
volume = {47},
year = {2013},
}

TY - JOUR
AU - Bols, Joris
AU - Degroote, Joris
AU - Trachet, Bram
AU - Verhegghe, Benedict
AU - Segers, Patrick
AU - Vierendeels, Jan
TI - Inverse modelling of image-based patient-specific blood vessels: zero-pressure geometry and in vivo stress incorporation
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2013
PB - EDP-Sciences
VL - 47
IS - 4
SP - 1059
EP - 1075
AB - In vivo visualization of cardiovascular structures is possible using medical images. However, one has to realize that the resulting 3D geometries correspond to in vivo conditions. This entails an internal stress state to be present in the in vivo measured geometry of e.g. a blood vessel due to the presence of the blood pressure. In order to correct for this in vivo stress, this paper presents an inverse method to restore the original zero-pressure geometry of a structure, and to recover the in vivo stress field of the final, loaded structure. The proposed backward displacement method is able to solve the inverse problem iteratively using fixed point iterations, but can be significantly accelerated by a quasi-Newton technique in which a least-squares model is used to approximate the inverse of the Jacobian. The here proposed backward displacement method allows for a straightforward implementation of the algorithm in combination with existing structural solvers, even if the structural solver is a black box, as only an update of the coordinates of the mesh needs to be performed.
LA - eng
KW - backward displacement method; inverse modelling; image-based modelling; patient-specific blood vessels; in vivo stress; prestress; zero-pressure geometry; in vivo stress
UR - http://eudml.org/doc/273090
ER -

References

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