A method for identifying mechanical properties of arterial tissue in vivo is proposed in this paper and it is numerically validated for the human abdominal aorta. Supplied with pressureradius data, the method determines six parameters representing relevant mechanical properties of an artery. In order to validate the method, 22 finite element arteries are created using published data for the human abdominal aorta. With these in silico abdominal aortas, which serve as mock experiments with exactly known material properties and boundary conditions, pressure-radius data sets are generated and the mechanical properties are identified using the proposed parameter identification method. By comparing the identified and pre-defined parameters, the method is quantitatively validated. For healthy abdominal aortas, the parameters show good agreement for the material constant associated with elastin and the radius of the stress-free state over a large range of values. Slightly larger discrepancies occur for the material constants associated with collagen, and the largest relative difference is obtained for the in situ axial prestretch. For pathological abdominal aortas incorrect parameters are identified, but the identification method reveals the presence of diseased aortas. The numerical validation indicates that the proposed parameter identification method is able to identify adequate parameters for healthy abdominal aortas and reveals pathological aortas from in vivo-like data.

In this paper an existing in vivo parameter identification method for arteries is extended to account for smooth muscle activity. Within this method a continuum-mechanical model, whose parameters relate to the mechanical properties of the artery, is fit to clinical data by solving a minimization problem. Including smooth muscle activity in the model increases the number of parameters. This may lead to overparameterization, implying that several parameter combinations solve the minimization problem equally well and it is therefore not possible to determine which set of parameters represents the mechanical properties of the artery best. To prevent overparameterization the model is fit to clinical data measured at different levels of smooth muscle activity. Three conditions are considered for the human abdominal aorta: basal during rest; constricted, induced by lower-body negative pressure; and dilated, induced by physical exercise. By fitting the model to these three arterial conditions simultaneously a unique set of model parameters is identified and the model prediction agrees well with the clinical data.

No part of this publication may be reproduced, stored in a retrieval system, or be transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without prior permission of the author. Note The appended papers have been reformatted to fit the layout of the thesis. The figures of Paper I have been reproduced in black and white and the associated text has been adjusted accordingly. The author's contribution The research expressed in the appended papers as well as the writing has been performed primarily by the author.

The author's contribution All authors contributed to the design and analysis in the papers above. Jan-Lucas Gade is responsible for all finite element and MATLAB implementations, and performed the numerical and statistical analyses in all studies. In addition, the manuscripts were prepared and submitted by him after they were critically reviewed by all authors.

In this study, we consider identification of parameters in a non-linear continuum-mechanical model of arteries by fitting the models response to clinical data. The fitting of the model is formulated as a constrained non-linear, non-convex least-squares minimization problem. The model parameters are directly related to the underlying physiology of arteries, and correctly identified they can be of great clinical value. The non-convexity of the minimization problem implies that incorrect parameter values, corresponding to local minima or stationary points may be found, however. Therefore, we investigate the feasibility of using a branch-and-bound algorithm to identify the parameters to global optimality. The algorithm is tested on three clinical data sets, in each case using four increasingly larger regions around a candidate global solution in the parameter space. In all cases, the candidate global solution is found already in the initialization phase when solving the original non-convex minimization problem from multiple starting points, and the remaining time is spent on increasing the lower bound on the optimal value. Although the branch-and-bound algorithm is parallelized, the overall procedure is in general very time-consuming.