Mechanical Properties of Arteries: An <em>In Vivo</em> Parameter Identification Method

Supplied with information obtainable in the clinic, typically limited to time-resolved pressure-radius measurement pairs, the proposed in vivo parameter identification method solves a non-convex minimization problem to determine parameters related to the mechanical properties of the blood vessel. The artery is treated as a homogeneous, incompressible, residual stress-free, thin-walled tube consisting of an elastin dominated matrix with embedded collagen fibers. 

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 and it is shown that the parameters agree well for healthy arteries. Furthermore, the identified parameters are used to compare the stress state in the arterial model and in the in silico arteries. 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. The comparison of the decomposed stress states shows a close agreement for arteries exhibiting a physiological stress gradient.

Another important aspect is the identification of parameters by solving a non-convex minimization problem. The non-convexity of the problem implies that incorrect parameter values, corresponding to local minima, may be found when common gradient-based solution techniques are employed. A problem-specific global algorithm based on the branch-and-bound method is, therefore, created which ensures that the global minimum and accordingly the correct parameters are obtained. It turns out that the gradient-based solution technique identifies the correct parameters if certain requirements are met, among others the use of the heuristic multi-start method.

In a last step, the in vivo parameter identification method is extended to also identify parameters related to smooth muscle contraction. To prevent an overparameterization caused by the increased number of model parameters, the model is simultaneously fit to clinical data measured during three different arterial conditions: basal; constricted; and dilated. Despite the simple contraction model the extended method fits the clinical data well. 

Finally, in this dissertation it is shown that the proposed in vivo parameter identification method identifies the mechanical properties of arteries well. An open question for future research is how this method can be applied in a clinical setting to facilitate cardiovascular disease diagnostization, treatment and monitoring.