The uncertainty associated with an individual abdominal aortic aneurysm (AAA) rupture carries a considerable amount of health risks as well as social and economic burden. There is a need for advanced technologies to mitigate this burden by early detection, patient-specific risk assessment and clinical management. Computational vascular mechanics has been of great interest along with the recent advances in medical imaging, experimental techniqueand computational simulations. In particular, computational modeling of vascular growth and remodeling (G&R) has provided further understanding of the G&R process that occurs in vascular diseases. Despite rapid expansion of our knowledge of vascular G&R, developing patient-specific models of AAA evolution is still an open problem and subject to numerous challenges.In this study, a framework is presented where, first the identification of the intrinsic material and geometric parameters for patient-specific modeling is addressed and then a finite element model of AAA G&R that accounts for medical image-based geometrical models is introduced. With regard to the material parameters, estimation of parameters of a multifiber family model for passive arteries in the presence of the measurement noise is considered.First, the uncertainty propagation due to the errors in variables is carefully characterized using the constitutive model. Then, the parameter estimation of the artery model is formulated into nonlinear least squares optimization with an appropriately chosen weight from the uncertainty model. The proposed technique is evaluated using multiple sets of synthesized data with fictitious measurement noises. The results of the estimation are comparedwith those of the conventional nonlinear least squares optimization without a proper weight factor. The proposed method significantly improves the quality of parameter estimation as the amplitude of the errors in variables becomes larger. We also investigate model selection criteria to decide the optimal number of fiber families in the multi-fiber family model with respect to the experimental data. The effect of multiple models for mechanical behavior ofarteries is also investigated. Distribution of the geometric parameters, being wall thickness and fiber orientations, are estimated using a 2-D parameterization of the vessel wall surface and a global approximationscheme integrated within an inverse optimization routine. Two conditions determine the objective of the optimization. First, the fundamental assumption in adaptation models, namely the existence of vascular homeostasis in normal vessels, should be maintained in a vessel model built from medical images. Second, the deviation of vessel wall from the original/image geometry subject to the normal pressure should be minimized. The same inverse technique is used to investigate the consequence of different homeostasis assumptions on the optimized distribution of parameters. The numerical optimization method results in a considerable improvement in both satisfying homeostatic condition and minimizing the deviation of geometry from the original shape based on in-vivo images.Then, a finite element model of stress-mediated G&R of arteries based on medical image-based geometries is presented for simulation of AAAs. Degradation of elastin initiates a local dilatation of the aorta while stress-mediated turnover of collagen and smooth muscle compensates the loss of elastin. Stress distributions and expansion rates during the aneurysm growthare studied for multiple spatial distributions of elastin degradation and kinetic parameters of the growth. Temporal variations of the elastin degradation and kinetic parameters are also investigated with either direct time-dependent degradation or stretch-induced degradation as possible biochemical and biomechanical mechanisms for elastin degradation. The results show that this computational model has the capability to capture the complexities ofaneurysm progression due to variations of geometry, extent of damage, and stress-mediated turnover as an important step towards patient-specific modeling.
Read
