Mechanical Properties of Arteries : Identification and Application
Abstract: In this Licentiate of Engineering thesis, a method is proposed that identiﬁes the mechanical properties of arteries in vivo. The mechanical properties of an artery are linked to the development of cardiovascular diseases. The possibility to identify the mechanical properties of an artery inside the human body could, thus, facilitate disease diagnostization, treatment and monitoring.Supplied with information obtainable in the clinic, typically limited to time- resolved pressure-radius measurement pairs, the proposed in vivo parameter identi- ﬁcation method calculates six representative parameters by solving a minimization problem. The artery is treated as a homogeneous, incompressible, residual stress- free, thin-walled tube consisting of an elastin dominated matrix with embedded collagen ﬁbers referred to as the constitutive membrane model. To validate the in vivo parameter identiﬁcation method, in silico arteries in the form of ﬁnite element models are created using published data for the human abdominal aorta. With these in silico arteries which serve as mock experiments with pre-deﬁned material parameters and boundary conditions, in vivo-like pressure-radius data sets are generated. The mechanical properties of the in silico arteries are then determined using the proposed parameter identiﬁcation method. By comparing the identiﬁed and the pre-deﬁned parameters, the identiﬁcation method is quantitatively validated. The parameters for the radius of the stress-free state and the material constant associated with elastin show high agreement in case of healthy arteries. Larger diﬀerences are obtained for the material constants associated with collagen, and the largest discrepancy occurs for the in situ axial prestretch. For arteries with a pathologically small elastin content, incorrect parameters are identiﬁed but the presence of a diseased artery is revealed by the parameter identiﬁcation method.Furthermore, the identiﬁed parameters are used in the constitutive membrane model to predict the stress state of the artery in question. The stress state is thereby decomposed into an isotropic and an anisotropic component which are primarily associated with the elastin dominated matrix and the collagen ﬁbers, respectively. In order to assess the accuracy of the predicted stress, it is compared to the known stress state of the in silico arteries. The comparison of the predicted and the in silico decomposed stress states show a close agreement for arteries exhibiting a low transmural stress gradient. With increasing transmural stress gradient the agreement deteriorates.The proposed in vivo parameter identiﬁcation method is capable of identifying adequate parameters and predicting the decomposed stress state reasonably well for healthy human abdominal aortas from in vivo-like data.
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