# 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

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

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topBols, 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 -

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