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Arterial mechanics: noninvasive identification of constitutive parameters and residual stress
Linköping University, Department of Mechanical Engineering. Linköping University, The Institute of Technology.
2005 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis concerns the mechanical modelling of arteries, and particularly a method to identify parameters describing the mechanical properties using only clinically obtainable in vivo measurements. The artery is modelled as a fibre reinforced, incompressible, thick-walled cylinder subjected to large deformations and a residual stress field. The residual stress field is parameterized using two methods: the classical opening angle method and the virtual configuration method. In the former method, the parameterization is obtained from the geometry of the cylindrical sector that an artery springs open into after a radial cut through the wall, while the latter method is based on a more general approach where the artery is relieved of stress by a local tangent map.

The model parameters are identified in a minimization problem. This is a well known technique for parameter identification; however, a simultaneous identification of the material and the residual stretch parameters has not been done for soft tissues before. Two particular diffculties are encountered in the minimization: first, the non convexity of the objective function, and second, the amount of information available in the measured pressure radius response is limited and the solution must be checked for over parameterization. The thesis studies these aspects and tries to relieve some of the problems by introducing physical or physiologically motivated constraints on the minimization.

The results presented in the four papers show that the method is feasible. It is also shown that the opening angle method can fail to give a true parameterization of the residual stress and that the virtual configuration method is preferable.

Place, publisher, year, edition, pages
Linköping: Linköpings universitet , 2005. , 59 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 941
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-29062Local ID: 14316ISBN: 91-85297-85-2 (print)OAI: oai:DiVA.org:liu-29062DiVA: diva2:249874
Public defence
2005-06-09, Sal C3, Hus C, Linköpings universitet, Linköping, 10:15 (Swedish)
Opponent
Available from: 2009-10-09 Created: 2009-10-09 Last updated: 2012-12-03
List of papers
1. Towards in vivo aorta material identification and stress estimation
Open this publication in new window or tab >>Towards in vivo aorta material identification and stress estimation
2004 (English)In: Biomechanics and Modeling in Mechanobiology, ISSN 1617-7959, E-ISSN 1617-7940, Vol. 2, no 3, 169-186 p.Article in journal (Refereed) Published
Abstract [en]

This paper addresses the problem of constructing a mechanical model for the abdominal aorta and calibrating its parameters to in vivo measurable data. The aorta is modeled as a pseudoelastic, thick-walled, orthotropic, residually stressed cylindrical tube, subjected to an internal pressure. The model parameters are determined by stating a minimization problem for the model pressure and computing the optimal solution by a minimization algorithm. The data used in this study is in vivo pressure–diameter data for the abdominal aorta of a 24-year-old man. The results show that the axial, circumferential and radial stresses have magnitudes in the span 0 to 180 kPa. Furthermore, the results show that it is possible to determine model parameters directly from in vivo measurable data. In particular, the parameters describing the residual stress distribution can be obtained without interventional procedures.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-22567 (URN)10.1007/s10237-003-0038-z (DOI)1837 (Local ID)1837 (Archive number)1837 (OAI)
Available from: 2009-10-07 Created: 2009-10-07 Last updated: 2017-12-13
2. Aorta in vivo parameter identification using an axial force constraint
Open this publication in new window or tab >>Aorta in vivo parameter identification using an axial force constraint
2005 (English)In: Biomechanics and Modeling in Mechanobiology, ISSN 1617-7959, E-ISSN 1617-7940, Vol. 3, no 4, 191-199 p.Article in journal (Refereed) Published
Abstract [en]

It was shown in a previous study by Stålhand et al. (2004) that both material and residual strain parameters for an artery can be identified noninvasively from an in vivo clinical pressure–diameter measurement. The only constraints placed on the model parameters in this previous study was a set of simple box constraints. More advanced constraints can also be utilized, however. These constraints restrict the model parameters implicitly by demanding the state of the artery to behave in a specified way. It has been observed in vitro that the axial force is nearly invariant to the pressure at the physiological operation point. In this paper, we study the possibility to include this behaviour as a constraint in the parameter optimization. The method is tested on an in vivo obtained pressure–diameter cycle for a 24-year-old human. Presented results show that the constrained parameter identification procedure proposed here can be used to obtain good results, and we believe that it may be applied to account for other observed behaviours as well.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-30656 (URN)10.1007/s10237-004-0057-4 (DOI)16253 (Local ID)16253 (Archive number)16253 (OAI)
Available from: 2009-10-09 Created: 2009-10-09 Last updated: 2017-12-13
3. Modeling initial strain distribution in soft tissues with application to arteries
Open this publication in new window or tab >>Modeling initial strain distribution in soft tissues with application to arteries
2006 (English)In: Biomechanics and Modeling in Mechanobiology, ISSN 1617-7959, E-ISSN 1617-7940, Vol. 5, no 1, 27-38 p.Article in journal (Refereed) Published
Abstract [en]

A general theory for computing and identifying the stress field in a residually stressed tissue is presented in this paper. The theory is based on the assumption that a stress free state is obtained by letting each point deform independently of its adjacent points. This local unloading represents an initial strain, and can be described by a tangent map. When experimental data is at hand in a specific situation, the initial strain field may be identified by stating a nonlinear minimization problem where this data is fitted to its corresponding model response. To illustrate the potential of such a method for identifying initial strain fields, the application to an in vivo pressure–radius measurement for a human aorta is presented. The result shows that the initial strain is inconsistent with the strain obtained with the opening-angle-method. This indicates that the opening-angle-method has a too restrictive residual strain parameterization, in this case.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-14331 (URN)10.1007/s10237-005-0008-8 (DOI)
Available from: 2007-03-16 Created: 2007-03-16 Last updated: 2017-12-13
4. In vivo parameter identification in arteries including smooth muscle contraction
Open this publication in new window or tab >>In vivo parameter identification in arteries including smooth muscle contraction
(English)Manuscript (preprint) (Other academic)
Abstract [en]

This paper presents an approach for including the active properties and a general residual stress distribution in the mechanical modelling of arteries by using a constrained mixture theory and local tangent maps. The model is used to identify passive and active properties, and a general residual stress distribution from in vivo measurements on a human femoral artery by solving a minimization problem. The results show that the active stress developed in the vascular smooth muscles tends to make the transmural stretch and stress distribution more uniform then for the passive response. We believe this indicates that it is important to account for active properties when modelling muscular arteries.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-85898 (URN)
Available from: 2012-12-03 Created: 2012-12-03 Last updated: 2017-05-15

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