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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
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URI: https://cronfa.swan.ac.uk/Record/cronfa71735
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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. 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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. 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spelling 2026-05-08T11:10:51.9033987 v2 71735 2026-04-13 A systematic comparison of membrane, shell, and 3D solid formulations for nonlinear vascular biomechanics 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false 2026-04-13 ACEM 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. Journal Article Journal of the Mechanical Behavior of Biomedical Materials 179 107423 Elsevier BV 1751-6161 1878-0180 Nonlinear membrane; Rotation free shell; Arterial wall mechanics 1 7 2026 2026-07-01 10.1016/j.jmbbm.2026.107423 COLLEGE NANME Aerospace Civil Electrical and Mechanical Engineering COLLEGE CODE ACEM Swansea University Another institution paid the OA fee 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. 2026-05-08T11:10:51.9033987 2026-04-13T12:29:37.5438638 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Taeouk Kim 0000-0003-2690-123x 1 Rogelio Ortigosa 0000-0002-4542-2237 2 Nitesh Nama 0000-0002-5249-4992 3 Miquel Aguirre 4 Antonio Gil 0000-0001-7753-1414 5 Jay D. Humphrey 0000-0003-1011-2025 6 C. Alberto Figueroa 7 71735__36681__56bf904718314e91bcd09ab5dd224d9f.pdf 71735.VOR.pdf 2026-05-08T11:08:50.4510093 Output 4270501 application/pdf Version of Record true © 2026 The Authors. This is an open access article under the CC BY-NC license. true eng http://creativecommons.org/licenses/by-nc/4.0/
title A systematic comparison of membrane, shell, and 3D solid formulations for nonlinear vascular biomechanics
spellingShingle A systematic comparison of membrane, shell, and 3D solid formulations for nonlinear vascular biomechanics
Antonio Gil
title_short A systematic comparison of membrane, shell, and 3D solid formulations for nonlinear vascular biomechanics
title_full A systematic comparison of membrane, shell, and 3D solid formulations for nonlinear vascular biomechanics
title_fullStr A systematic comparison of membrane, shell, and 3D solid formulations for nonlinear vascular biomechanics
title_full_unstemmed A systematic comparison of membrane, shell, and 3D solid formulations for nonlinear vascular biomechanics
title_sort A systematic comparison of membrane, shell, and 3D solid formulations for nonlinear vascular biomechanics
author_id_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2
author_id_fullname_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2_***_Antonio Gil
author Antonio Gil
author2 Taeouk Kim
Rogelio Ortigosa
Nitesh Nama
Miquel Aguirre
Antonio Gil
Jay D. Humphrey
C. Alberto Figueroa
format Journal article
container_title Journal of the Mechanical Behavior of Biomedical Materials
container_volume 179
container_start_page 107423
publishDate 2026
institution Swansea University
issn 1751-6161
1878-0180
doi_str_mv 10.1016/j.jmbbm.2026.107423
publisher Elsevier BV
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering
document_store_str 1
active_str 0
description 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.
published_date 2026-07-01T06:05:14Z
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