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A constitutive model for the time-dependent, nonlinear stress response of fibrin networks.

van Kempen TH, Peters GW, van de Vosse FN - Biomech Model Mechanobiol (2015)

Bottom Line: The results show three dominating nonlinear features: softening over multiple deformation cycles, strain stiffening and increasing viscous dissipation during a deformation cycle.A sensitivity analysis provides insights into the influence of the eight fit parameters.The model developed is able to describe the rich, time-dependent, nonlinear behavior of the fibrin network.

View Article: PubMed Central - PubMed

Affiliation: Department of Biomedical Engineering, Eindhoven University of Technology, PO Box 513, 5600MB, Eindhoven, The Netherlands, t.h.s.v.kempen@tue.nl.

ABSTRACT
Blood clot formation is important to prevent blood loss in case of a vascular injury but disastrous when it occludes the vessel. As the mechanical properties of the clot are reported to be related to many diseases, it is important to have a good understanding of their characteristics. In this study, a constitutive model is presented that describes the nonlinear viscoelastic properties of the fibrin network, the main structural component of blood clots. The model is developed using results of experiments in which the fibrin network is subjected to a large amplitude oscillatory shear (LAOS) deformation. The results show three dominating nonlinear features: softening over multiple deformation cycles, strain stiffening and increasing viscous dissipation during a deformation cycle. These features are incorporated in a constitutive model based on the Kelvin-Voigt model. A network state parameter is introduced that takes into account the influence of the deformation history of the network. Furthermore, in the period following the LAOS deformation, the stiffness of the networks increases which is also incorporated in the model. The influence of cross-links created by factor XIII is investigated by comparing fibrin networks that have polymerized for 1 and 2 h. A sensitivity analysis provides insights into the influence of the eight fit parameters. The model developed is able to describe the rich, time-dependent, nonlinear behavior of the fibrin network. The model is relatively simple which makes it suitable for computational simulations of blood clot formation and is general enough to be used for other materials showing similar behavior.

No MeSH data available.


Related in: MedlinePlus

The NSP, , in time during LAOS (a). The colors correspond to the strains shown in Fig. 1b. After a change in strain, the NSP levels off to a new value denoted by  that decreases with the strain (b). The dashed lines are obtained with the model [see Eqs. (5) and (6)]
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Fig3: The NSP, , in time during LAOS (a). The colors correspond to the strains shown in Fig. 1b. After a change in strain, the NSP levels off to a new value denoted by that decreases with the strain (b). The dashed lines are obtained with the model [see Eqs. (5) and (6)]

Mentions: The values of can be interpreted as a local derivative of the stress with respect to strain, at the strain ,3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} G_0\left( t,\gamma \right) = \left. \frac{\partial \tau }{\partial \gamma }\right/ _{\gamma = 0}, \end{aligned}$$\end{document}G0t,γ=∂τ∂γγ=0,and are estimated by a linearization of the positive stresses at the strains of . For the cycles with a strain amplitude of , the stresses at maximal strain are used for the linearization. The accuracy of this method increases with increasing strain amplitude, because the corresponding stresses are higher and the signals contain less noise, as visible in Fig. 2c. Values for the NSP are subsequently found using the relation between the shear modulus and the NSP (Eq. (2)),4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} x\left( t, \gamma \right) = \frac{G_{0}}{G_{00}}. \end{aligned}$$\end{document}xt,γ=G0G00.Results for the NSP during a LAOS experiment are shown in Fig. 3 with the colors corresponding to the LAOS protocol in Fig. 1b.Fig. 3


A constitutive model for the time-dependent, nonlinear stress response of fibrin networks.

van Kempen TH, Peters GW, van de Vosse FN - Biomech Model Mechanobiol (2015)

The NSP, , in time during LAOS (a). The colors correspond to the strains shown in Fig. 1b. After a change in strain, the NSP levels off to a new value denoted by  that decreases with the strain (b). The dashed lines are obtained with the model [see Eqs. (5) and (6)]
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

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Fig3: The NSP, , in time during LAOS (a). The colors correspond to the strains shown in Fig. 1b. After a change in strain, the NSP levels off to a new value denoted by that decreases with the strain (b). The dashed lines are obtained with the model [see Eqs. (5) and (6)]
Mentions: The values of can be interpreted as a local derivative of the stress with respect to strain, at the strain ,3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} G_0\left( t,\gamma \right) = \left. \frac{\partial \tau }{\partial \gamma }\right/ _{\gamma = 0}, \end{aligned}$$\end{document}G0t,γ=∂τ∂γγ=0,and are estimated by a linearization of the positive stresses at the strains of . For the cycles with a strain amplitude of , the stresses at maximal strain are used for the linearization. The accuracy of this method increases with increasing strain amplitude, because the corresponding stresses are higher and the signals contain less noise, as visible in Fig. 2c. Values for the NSP are subsequently found using the relation between the shear modulus and the NSP (Eq. (2)),4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} x\left( t, \gamma \right) = \frac{G_{0}}{G_{00}}. \end{aligned}$$\end{document}xt,γ=G0G00.Results for the NSP during a LAOS experiment are shown in Fig. 3 with the colors corresponding to the LAOS protocol in Fig. 1b.Fig. 3

Bottom Line: The results show three dominating nonlinear features: softening over multiple deformation cycles, strain stiffening and increasing viscous dissipation during a deformation cycle.A sensitivity analysis provides insights into the influence of the eight fit parameters.The model developed is able to describe the rich, time-dependent, nonlinear behavior of the fibrin network.

View Article: PubMed Central - PubMed

Affiliation: Department of Biomedical Engineering, Eindhoven University of Technology, PO Box 513, 5600MB, Eindhoven, The Netherlands, t.h.s.v.kempen@tue.nl.

ABSTRACT
Blood clot formation is important to prevent blood loss in case of a vascular injury but disastrous when it occludes the vessel. As the mechanical properties of the clot are reported to be related to many diseases, it is important to have a good understanding of their characteristics. In this study, a constitutive model is presented that describes the nonlinear viscoelastic properties of the fibrin network, the main structural component of blood clots. The model is developed using results of experiments in which the fibrin network is subjected to a large amplitude oscillatory shear (LAOS) deformation. The results show three dominating nonlinear features: softening over multiple deformation cycles, strain stiffening and increasing viscous dissipation during a deformation cycle. These features are incorporated in a constitutive model based on the Kelvin-Voigt model. A network state parameter is introduced that takes into account the influence of the deformation history of the network. Furthermore, in the period following the LAOS deformation, the stiffness of the networks increases which is also incorporated in the model. The influence of cross-links created by factor XIII is investigated by comparing fibrin networks that have polymerized for 1 and 2 h. A sensitivity analysis provides insights into the influence of the eight fit parameters. The model developed is able to describe the rich, time-dependent, nonlinear behavior of the fibrin network. The model is relatively simple which makes it suitable for computational simulations of blood clot formation and is general enough to be used for other materials showing similar behavior.

No MeSH data available.


Related in: MedlinePlus