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Non-linear viscoelastic behavior of abdominal aortic aneurysm thrombus.

van Dam EA, Dams SD, Peters GW, Rutten MC, Schurink GW, Buth J, van de Vosse FN - Biomech Model Mechanobiol (2007)

Bottom Line: To describe the phenomena observed experimentally, a non-linear multimode model is presented.The parameters for this model are obtained by fitting this model successfully to the experiments.To determine the influence on the wall stress of the behavior observed the model proposed needs to implemented in the finite element wall stress analysis.

View Article: PubMed Central - PubMed

Affiliation: Department of Biomedical Engineering, Technische Universiteit Eindhoven, PO box 513, WH4.120, 5600 MB, Eindhoven, The Netherlands.

ABSTRACT
The objective of this work was to determine the linear and non-linear viscoelastic behavior of abdominal aortic aneurysm thrombus and to study the changes in mechanical properties throughout the thickness of the thrombus. Samples are gathered from thrombi of seven patients. Linear viscoelastic data from oscillatory shear experiments show that the change of properties throughout the thrombus is different for each thrombus. Furthermore the variations found within one thrombus are of the same order of magnitude as the variation between patients. To study the non-linear regime, stress relaxation experiments are performed. To describe the phenomena observed experimentally, a non-linear multimode model is presented. The parameters for this model are obtained by fitting this model successfully to the experiments. The model cannot only describe the average stress response for all thrombus samples but also the highest and lowest stress responses. To determine the influence on the wall stress of the behavior observed the model proposed needs to implemented in the finite element wall stress analysis.

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Related in: MedlinePlus

The inelastic part of F, Fp transforms the undeformed state C0 to a relaxed stress-free configuration, Cp and is modeled by a dashpot. Cp is a fictitious state that would be recovered instantaneously when all loads were removed from the material element. The elastic part, Fe, of F transforms the stress-free state Cp elastically into the deformed state Ct. This part is modeled by a spring
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Fig2: The inelastic part of F, Fp transforms the undeformed state C0 to a relaxed stress-free configuration, Cp and is modeled by a dashpot. Cp is a fictitious state that would be recovered instantaneously when all loads were removed from the material element. The elastic part, Fe, of F transforms the stress-free state Cp elastically into the deformed state Ct. This part is modeled by a spring

Mentions: The changes of volume and shape of an arbitrary solid material are described by the deformation gradient tensor F. F is split (Fig. 2) into an elastic part, Fe, and an inelastic part Fp: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rm{dx}} = {\rm{F}} \cdot {\rm{d}}{{\rm{x}}_0};{\rm{F}} = {{\rm{F}}_e} \cdot {{\rm{F}}_p},$$\end{document}, where dx0 represents a material line element in the undeformed state, C0, and dx represents it in the deformed state, Ct. The inelastic part of F, Fp, transforms the undeformed state, C0, to a relaxed stress-free configuration, Cp. This is a fictitious state that would be recovered instantaneously when all loads were removed from the material line-element. The elastic part, Fe, of F transforms the stress-free state, Cp, elastically into the deformed state, Ct. Next, the elastic Finger tensor, Be, can be introduced: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm{B}}_e} = {{\rm{F}}_e} \cdot {\rm{F}}_e^{\rm{T}}$$\end{document}


Non-linear viscoelastic behavior of abdominal aortic aneurysm thrombus.

van Dam EA, Dams SD, Peters GW, Rutten MC, Schurink GW, Buth J, van de Vosse FN - Biomech Model Mechanobiol (2007)

The inelastic part of F, Fp transforms the undeformed state C0 to a relaxed stress-free configuration, Cp and is modeled by a dashpot. Cp is a fictitious state that would be recovered instantaneously when all loads were removed from the material element. The elastic part, Fe, of F transforms the stress-free state Cp elastically into the deformed state Ct. This part is modeled by a spring
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2813187&req=5

Fig2: The inelastic part of F, Fp transforms the undeformed state C0 to a relaxed stress-free configuration, Cp and is modeled by a dashpot. Cp is a fictitious state that would be recovered instantaneously when all loads were removed from the material element. The elastic part, Fe, of F transforms the stress-free state Cp elastically into the deformed state Ct. This part is modeled by a spring
Mentions: The changes of volume and shape of an arbitrary solid material are described by the deformation gradient tensor F. F is split (Fig. 2) into an elastic part, Fe, and an inelastic part Fp: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rm{dx}} = {\rm{F}} \cdot {\rm{d}}{{\rm{x}}_0};{\rm{F}} = {{\rm{F}}_e} \cdot {{\rm{F}}_p},$$\end{document}, where dx0 represents a material line element in the undeformed state, C0, and dx represents it in the deformed state, Ct. The inelastic part of F, Fp, transforms the undeformed state, C0, to a relaxed stress-free configuration, Cp. This is a fictitious state that would be recovered instantaneously when all loads were removed from the material line-element. The elastic part, Fe, of F transforms the stress-free state, Cp, elastically into the deformed state, Ct. Next, the elastic Finger tensor, Be, can be introduced: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm{B}}_e} = {{\rm{F}}_e} \cdot {\rm{F}}_e^{\rm{T}}$$\end{document}

Bottom Line: To describe the phenomena observed experimentally, a non-linear multimode model is presented.The parameters for this model are obtained by fitting this model successfully to the experiments.To determine the influence on the wall stress of the behavior observed the model proposed needs to implemented in the finite element wall stress analysis.

View Article: PubMed Central - PubMed

Affiliation: Department of Biomedical Engineering, Technische Universiteit Eindhoven, PO box 513, WH4.120, 5600 MB, Eindhoven, The Netherlands.

ABSTRACT
The objective of this work was to determine the linear and non-linear viscoelastic behavior of abdominal aortic aneurysm thrombus and to study the changes in mechanical properties throughout the thickness of the thrombus. Samples are gathered from thrombi of seven patients. Linear viscoelastic data from oscillatory shear experiments show that the change of properties throughout the thrombus is different for each thrombus. Furthermore the variations found within one thrombus are of the same order of magnitude as the variation between patients. To study the non-linear regime, stress relaxation experiments are performed. To describe the phenomena observed experimentally, a non-linear multimode model is presented. The parameters for this model are obtained by fitting this model successfully to the experiments. The model cannot only describe the average stress response for all thrombus samples but also the highest and lowest stress responses. To determine the influence on the wall stress of the behavior observed the model proposed needs to implemented in the finite element wall stress analysis.

Show MeSH
Related in: MedlinePlus