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

Published online by Cambridge University Press:  13 June 2013

Joris Bols ,
Joris Degroote ,
Bram Trachet ,
Benedict Verhegghe ,
Patrick Segers  and
Jan Vierendeels
Joris Bols
Affiliation:
Department of Flow, Heat and Combustion Mechanics, Sint-Pietersnieuwstraat 41, 9000 Ghent, Belgium.. Joris.Bols@UGent.be IBiTech-bioMMeda, De Pintelaan 185, 9000 Ghent, Belgium.
Joris Degroote
Affiliation:
Department of Flow, Heat and Combustion Mechanics, Sint-Pietersnieuwstraat 41, 9000 Ghent, Belgium.. Joris.Bols@UGent.be
Bram Trachet
Affiliation:
IBiTech-bioMMeda, De Pintelaan 185, 9000 Ghent, Belgium.
Benedict Verhegghe
Affiliation:
IBiTech-bioMMeda, De Pintelaan 185, 9000 Ghent, Belgium.
Patrick Segers
Affiliation:
IBiTech-bioMMeda, De Pintelaan 185, 9000 Ghent, Belgium.
Jan Vierendeels
Affiliation:
Department of Flow, Heat and Combustion Mechanics, Sint-Pietersnieuwstraat 41, 9000 Ghent, Belgium.. Joris.Bols@UGent.be
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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.

Keywords

Backward displacement methodinverse modellingimage-based modellingpatient-specific blood vesselsin vivo stressprestresszero-pressure geometry
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 4: Direct and inverse modeling of the cardiovascular and respiratory systems , July 2013 , pp. 1059 - 1075
Copyright
© EDP Sciences, SMAI, 2013

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