Identification of mechanical properties of arteries with certification of global optimality

Jan-Lucas Gade (), Carl-Johan Thore and Jonas Stålhand
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Jan-Lucas Gade: Linköping University
Carl-Johan Thore: Linköping University
Jonas Stålhand: Linköping University

Journal of Global Optimization, 2022, vol. 82, issue 1, No 10, 195-217

Abstract: Abstract 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.

Keywords: Global optimization; Branch-and-bound; Artery; In vivo (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10898-021-01037-8

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