An Unfitted Method with Elastic Bed Boundary Conditions for the Analysis of Heterogeneous Arterial Sections

Stephan Gahima, Pedro Díez, Marco Stefanati, José Félix Rodríguez Matas and Alberto García-González ()
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Stephan Gahima: Laboratori de Càlcul Numèric, E.T.S. de Ingeniería de Caminos, Universitat Politècnica de Catalunya, 08034 Barcelona, Spain
Pedro Díez: Laboratori de Càlcul Numèric, E.T.S. de Ingeniería de Caminos, Universitat Politècnica de Catalunya, 08034 Barcelona, Spain
Marco Stefanati: Laboratory of Biological Structure Mechanics (LaBS), Department of Chemistry, Materials and Chemical Engineering “Giulio Natta”, Politecnico di Milano, 20133 Milan, Italy
José Félix Rodríguez Matas: Laboratory of Biological Structure Mechanics (LaBS), Department of Chemistry, Materials and Chemical Engineering “Giulio Natta”, Politecnico di Milano, 20133 Milan, Italy
Alberto García-González: Laboratori de Càlcul Numèric, E.T.S. de Ingeniería de Caminos, Universitat Politècnica de Catalunya, 08034 Barcelona, Spain

Mathematics, 2023, vol. 11, issue 7, 1-17

Abstract: This manuscript presents a novel formulation for a linear elastic model of a heterogeneous arterial section undergoing uniform pressure in a quasi-static regime. The novelties are twofold. First, an elastic bed support on the external boundary (elastic bed boundary condition) replaces the classical Dirichlet boundary condition (i.e., blocking displacements at arbitrarily selected nodes) for elastic solids to ensure a solvable problem. In addition, this modeling approach can be used to effectively account for the effect of the surrounding material on the vessel. Secondly, to study many geometrical configurations corresponding to different patients, we devise an unfitted strategy based on the Immersed Boundary (IB) framework. It allows using the same (background) mesh for all possible configurations both to describe the geometrical features of the cross-section (using level sets) and to compute the solution of the mechanical problem. Results on coronary arterial sections from realistic segmented images demonstrate that the proposed unfitted IB-based approach provides results equivalent to the standard finite elements (FE) for the same number of active degrees of freedom with an average difference in the displacement field of less than 0.5%. However, the proposed methodology does not require the use of a different mesh for every configuration. Thus, it is paving the way for dimensionality reduction.

Keywords: elastic bed boundary condition; robin boundary condition; immersed boundary method; level set; arterial biomechanics; unfitted method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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