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A systematic comparison of membrane, shell, and 3D solid formulations for nonlinear vascular biomechanics

Taeouk Kim Orcid Logo, Rogelio Ortigosa Orcid Logo, Nitesh Nama Orcid Logo, Miquel Aguirre, Antonio Gil Orcid Logo, Jay D. Humphrey Orcid Logo, C. Alberto Figueroa

Journal of the Mechanical Behavior of Biomedical Materials, Volume: 179, Start page: 107423

Swansea University Author: Antonio Gil Orcid Logo

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DOI (Published version): 10.1016/j.jmbbm.2026.107423

Abstract

Typical computational methods for vascular biosolid mechanics represent the blood vessel wall as a membrane, shell, or 3D solid. Each of these formulations has advantages and disadvantages concerning accuracy, ease of implementation, and computational costs. Despite the widespread use of these formu...

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Published in: Journal of the Mechanical Behavior of Biomedical Materials
ISSN: 1751-6161 1878-0180
Published: Elsevier BV 2026
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa71735
Abstract: Typical computational methods for vascular biosolid mechanics represent the blood vessel wall as a membrane, shell, or 3D solid. Each of these formulations has advantages and disadvantages concerning accuracy, ease of implementation, and computational costs. Despite the widespread use of these formulations, a systematic comparison of the performance and accuracy of these formulations for nonlinear vascular biomechanics has remained wanting. Therefore, the decision regarding the optimal choice often relies on intuition or previous experience, with unclear consequences of choosing one approach over the other. Here, we present a systematic comparison among three different formulations to represent the vessel wall as: (i) a nonlinear membrane, (ii) a nonlinear, rotation-free shell, and (iii) a nonlinear 3D solid. For the 3D solid model, we consider two different implementations employing linear and quadratic interpolation. Convergence analysis for displacement and stress are presented for all formulations. We compare results in both idealized and subject-specific mouse aortic geometries. For the idealized cylindrical geometry, we compare our results against the axisymmetric solution for five different wall thickness-to-radius ratios. Subsequently, a comparison of these approaches is presented for an idealized arterial bifurcation having regionally varying wall thickness. Lastly, we compare results for a subject-specific mouse geometry with regionally varying material properties and wall thickness. External tissue support boundary conditions model the effect of perivascular tissue. Based on our results, the rotation-free shell formulation represents the most advantageous compromise between computational cost and accuracy for large scale vascular biomechanics applications that include complex geometries.
Keywords: Nonlinear membrane; Rotation free shell; Arterial wall mechanics
College: Faculty of Science and Engineering
Funders: C.A. Figueroa acknowledges the support from National Institutes of Health, United States (R01-HL158723 and U01HL135842) and by the Edward B. Diethrich M.D. Professorship. Furthermore, Dr. Figueroa acknowledges (R01 HL105297) with J.D. Humphrey. N. Nama acknowledges the support from the American Heart Association, United States (23CDA1048343). R. Ortigosa acknowledges support of grant PID2022-141957OA-C22 funded by MICIU/AEI/10.13039/501100011033 and by ERDF A way of making Europe, and also the support of grant 21996/PI/22 funded by Fundacion Seneca - Agencia de Ciencia y Tecnologia de la Region de Murcia. M. Aguirre acknowledges the support of Grant PID2022-136668OA-I00 funded by MCIN/AEI/10.13039/501100011033 and by ERDF A way of making Europe, and by grant RYC2023-042592-I funded by MICIU/AEI/10.13039/501100011033 and by ESF+. A.J. Gil acknowledges the support of The UK Leverhulme Trust through a Leverhulme Fellowship.
Start Page: 107423

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