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Selected Publication:

Eriksson, T.
Cardiovascular Mechanics: The Biomechanics of Arteries and the Human Heart.
[ Dissertation ] Technische Universität Graz; 2011. pp.139.


Authors Med Uni Graz:
Eriksson Thomas
Plank Gernot

Modeling in biomechanics plays an important role in simulating biological functions and has great potential to aid medical clinicians in determining the cause of a disease, the type of treatment or by aiding in the training of a surgical procedure. Cardiovascular diseases (CVDs) are the leading cause of mortality today. This thesis therefore aims at developing a framework for the modeling CVDs, such as cerebral aneurysms or heart diseases with increased myofiber dispersion as seen in, e.g., hypertrophic cardiomyopathy. To this end, a three-dimensional growth model of a human saccular cerebral aneurysm is presented that includes the anisotropy of the medial layer. It is shown that including fibers in the media reduces the maximum principal stress, thickness increase and shear stress in the aneurysm wall. It is also shown that the axial pre-stretch has a large impact on the stress levels and thickness increase in the aneurysm wall. In addition, the constituents needed for the numerical implementation of a structurally based constitutive law describing the behavior of passive myocardium is shown. A comparison is made between this invariant based model and a commonly used Green-Lagrange strain based model and it is shown that using material parameters retrieved when both models is fitted against a simple shear mode experiment, the invariant based model is better suited to predict the stress in the myocardium for other modes of deformation. The passive cardiac model is coupled together with an evolution equation responsible for generating the active stress. A model of the left ventricle (LV) is presented where pressure is calculated as a response to the change in the ventricular volume in order to ensure physiologically realistic pressure-volume loops. The influence of myocardial fiber and sheet distribution is investigated by using two different setups, a generic setup and one based on experiments. The results implies that spacial heterogeneity may play a critical role in mechanical contraction of the LV and that geometrical descriptions of deformation are needed when evaluating the accuracy of a ventricular model. Further, a novel approach to model the disarray of both the fiber and sheet orientations evident in, especially diseased, myocardium is presented. Analytical and numerical simulations show that the dispersion parameter has great effect on myocardial deformation and stress development. The results also show that the dispersion has a significant impact on pressure-volume loops of an LV, and in future simulations the presented dispersion model for myocardium may advantageously be used together with models of, e.g., growth and remodeling of various cardiac diseases. In cases where fiber-reinforced models are extended to include the effect of distributed fiber orientations, neither the mathematical nor physical motivation for tension-compression fiber switching is clear, and in fact several choices exist for the material modeler. Therefore, methods to study such switching mechanisms is explored by analyzing six potential switching cases. Two different permeations of the dispersed fiber-reinforced model is proposed, depending on whether one can assume that the fibers are (nearly) uncoupled or strongly coupled to the isotropic ground matrix.

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