Parameter identification of biphasic hyperelastic continuum artery model featuring the pull-back algorithm

Mathematical modeling of the large deformations with continuum mechanics allows the investigation of mechanical response of arteries. Numerous theories have introduced to examine the arterial mechanics throughout the years. Among them, hyperelasticity is an effective tool to model such biological tissues. It allows realistic modeling of biphasic microstructure of an arterial wall. The characterization of material parameters of a hyperelastic model is a challenging task because of multi-convex nature of them. Mostly, pressure myography is utilized to obtain the physical response of an artery. This \textit{in-vitro} experiment yields one dependent output as a result of applied axial tension and radial pressure. When combined with the multi-parameter models, this causes an overfitting problem. The main hypothesis of this thesis is that the potential difficulty can be averted by incorporating the pull-back operation a priori the deformation cycle in the optimization routine. As a second hypothesis, we assert that morphological changes effect the stiffness of both the matrix and fiber phases of the artery and can be assessed by utilizing a series of fitting on pressure myography data for different combinations of fiber angles and fiber volume ratios. The augmented optimization scheme including the pull-back algorithm introduced here assists to overcome these issues by accurately guessing the excised radii while an optimization runs globally to fit the given pressure-radius data to a proper parameter set. The proposed optimization scheme fits the data with $R^2>0.99$. When this procedure is applied to the same dataset with varying fiber angles it has seen that the axially leaned fibers increase the infinitesimal shear modulus of the ground substance while lower fiber angles result in storing much less energy. In the case of a morphological change, the most sensitive material parameter appears to be the exponential stiffening parameter of fibers.