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

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.