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Modeling initial strain distribution in soft tissues with application to arteries
Linköping University, Department of Management and Engineering, Mechanics. Linköping University, The Institute of Technology.
Linköping University, Department of Management and Engineering, Mechanics. Linköping University, The Institute of Technology.
Linköping University, Department of Management and Engineering, Mechanics. Linköping University, The Institute of Technology.ORCID iD: 0000-0001-8460-0131
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.

Place, publisher, year, edition, pages
2006. Vol. 5, no 1, 27-38 p.
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-14331DOI: 10.1007/s10237-005-0008-8OAI: oai:DiVA.org:liu-14331DiVA: diva2:23258
Available from: 2007-03-16 Created: 2007-03-16 Last updated: 2017-05-15
In thesis
1. Soft Tissue Mechanics with Emphasis on Residual Stress Modeling
Open this publication in new window or tab >>Soft Tissue Mechanics with Emphasis on Residual Stress Modeling
2007 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis concerns residual stress modeling in soft living tissues. The word living means that the tissue interacts with surrounding organs and that it can change its internal properties to optimize its function. From the first day all tissues are under pressure, due, for example, to gravity, other surrounding organs that utilize pressure on the specific tissue, and the pressure from the blood that circulates within the body. This means that all organs grow and change properties under load, and an unloaded configuration is never present within the body. When a tissue is removed from the body, the obtained unloaded state is not naturally stress free. This stress within an unloaded body is called residual stress. It is believed that the residual stress helps the tissue to optimize its function by homogenizing the transmural stress distribution.

The thesis is composed of two parts: in the first part an introduction to soft tissues and basic modeling is given and the second part consist of a collection of five manuscripts. The first four papers show how residual stress can be modeled. We also derive evolution equation for growth and remodeling and show how residual stress develops under constant pressure. The fifth paper deals with damage and viscosity in soft tissues.

Place, publisher, year, edition, pages
Institutionen för konstruktions- och produktionsteknik, 2007. 27 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1081
Keyword
Mechanics, Residual Stress, Growth, Remodeling
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:liu:diva-8490 (URN)978-91-85715-50-3 (ISBN)
Public defence
2007-04-13, Sal C3, Hus C, Linköpings universitet, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2007-03-16 Created: 2007-03-16 Last updated: 2017-05-15
2. Arterial mechanics: noninvasive identification of constitutive parameters and residual stress
Open this publication in new window or tab >>Arterial mechanics: noninvasive identification of constitutive parameters and residual stress
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:nbn:se:liu:diva-29062 (URN)14316 (Local ID)91-85297-85-2 (ISBN)14316 (Archive number)14316 (OAI)
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
3. Modeling Residual Stress Fields in Soft Tissues with Application to Human Arteries
Open this publication in new window or tab >>Modeling Residual Stress Fields in Soft Tissues with Application to Human Arteries
2004 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Biomechanics or Mechanics of Biology comprises many different fields. This thesis deals with soft tissues or living tissues and the fact that these materials live in a pressurized environment. This means that an unloaded tissue may not be stress free. The stress in an unloaded body is usually called residual stress. This thesis consist of an introduction to continuum mechanics and to soft tissues, and three research papers.

The first paper deals with a zero stress configuration and the question of compatibility. It is shown that the zero stress configuration not necessarily constitutes a compatible body. The condition for compatibility is analyzed and exemplified on a cylinder and a sphere.

In the second paper a model for residually stressed arteries based on local deformations is developed. The material properties for a human aorta is identified by the solution to an optimization problem. The resulting initial strains show a non constant behavior and this behavior cannot be described by the commonly used opening- angle model.

The last paper is about formulating boundary value problems for initially stressed bodies in three different reference configurations. Firstly, the equilibrium equation and constitutive relation are stated on the unloaded residually stressed body. Secondly, all material points are relieved from stress by a tangent map and the new stress free configuration, which may be incompatible, is used to state the boundary value problem. Thirdly; we use the relieving tangent map to induce a new metric on the body. This induced metric is in general non Euclidean. Finally, we formulate the boundary value problem on this manifold.

Place, publisher, year, edition, pages
Linköping: Linköpings universitet, 2004. 40 p.
Series
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1118
Series
LiU-TEK-LIC, 47
Keyword
Continuum Mechanics, Modeling, Residual Stress, Soft Tissues
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-22418 (URN)1633 (Local ID)91-85295-48-5 (ISBN)1633 (Archive number)1633 (OAI)
Available from: 2009-10-07 Created: 2009-10-07 Last updated: 2013-11-12

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Olsson, TobiasStålhand, JonasKlarbring, Anders

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