Regularization techniques and inverse approaches in 3D Traction Force Microscopy

The conception of inverse methods in the context of Traction Force Microscopy (TFM) is influenced by multiple factors, such as nonlinear effects, dimensionality (2D/3D), and regularization/constraints, amongst others. Solving the inverse problem often requires the inversion of a matrix, and the pres...

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Autores: Apolinar-Fernández, Alejandro, Blázquez-Carmona, Pablo, Ruiz-Mateos, Raquel, Barrasa-Fano, Jorge, Van Oosterwyck, Hans, Reina-Romo, Esther, Sanz-Herrera, José A.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2024
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/386659
Acceso en línea:http://hdl.handle.net/10261/386659
https://api.elsevier.com/content/abstract/scopus_id/85200477826
Access Level:acceso abierto
Palabra clave:Finite element method
Inverse methods
Mechanobiology
Nonlinear continuum mechanics
Tikhonov regularization
Traction force microscopy
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spelling Regularization techniques and inverse approaches in 3D Traction Force MicroscopyApolinar-Fernández, AlejandroBlázquez-Carmona, PabloRuiz-Mateos, RaquelBarrasa-Fano, JorgeVan Oosterwyck, HansReina-Romo, EstherSanz-Herrera, José A.Finite element methodInverse methodsMechanobiologyNonlinear continuum mechanicsTikhonov regularizationTraction force microscopyThe conception of inverse methods in the context of Traction Force Microscopy (TFM) is influenced by multiple factors, such as nonlinear effects, dimensionality (2D/3D), and regularization/constraints, amongst others. Solving the inverse problem often requires the inversion of a matrix, and the presence of noise in the measured displacements can lead to unrealistic reconstructed tractions. To address this issue, Tikhonov regularization is commonly used, penalizing high norm values of computed tractions. The aim of this study is to compare the performance of different inverse methodologies (including some original variations) in 3D TFM, considering constraint imposition and regularization along the formulation. The different methodologies are numerically elaborated within a novel combined Newton–Raphson/Finite Element Method scheme that provides converged solutions in few iterations. The impact of constraint imposition and regularization in traction reconstruction is evaluated in terms of accuracy, efficiency (CPU time), and inherent characteristics of the methodology. Results show that, applying regularization and constraints (based on the fulfillment of fundamental principles) provides the best traction reconstruction, while simultaneously ensuring an optimum estimate of the maximum traction, at the cost of high CPU time and low efficiency. Moreover, regularization-based methods introduce the challenge of calibrating the regularization parameter, usually done under subjective criteria. On the other hand, non-regularized but constrained methods may represent a nice compromise between accuracy and efficiency, while avoiding pre-processing and calibration of such regularization parameter. It is emphasized the importance of considering not only traction reconstruction quality but also the efficiency and complexity of implementation (intrusiveness) when selecting an appropriate inverse method for TFM analysis.A.A.-F. and J.A.S.-H. gratefully acknowledge the Financial support from MCIN/AEI/10.13039/501100011033 [PID2021-126051OB-C42]. J.B.-F. was supported by Research Foundation Flanders (FWO) junior postdoctoral fellowship 1259223N. The authors gratefully acknowledge the resources and guidance provided by Prof. Gijsje Koenderink and Dr. Iain Muntz from TU Delft to perform the shear rheology measurements.Peer reviewedElsevier BVAgencia Estatal de Investigación (España)Ministerio de Ciencia e Innovación (España)Research Foundation - FlandersBlázquez-Carmona, Pablo [0000-0002-7605-5812]Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]202520252024info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Publisher's versioninfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/10261/386659https://api.elsevier.com/content/abstract/scopus_id/85200477826reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Inglés#PLACEHOLDER_PARENT_METADATA_VALUE#info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2021-126051OB-C42https://doi.org/10.1016/j.ijmecsci.2024.109592Síinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/3866592026-05-22T06:33:51Z
dc.title.none.fl_str_mv Regularization techniques and inverse approaches in 3D Traction Force Microscopy
title Regularization techniques and inverse approaches in 3D Traction Force Microscopy
spellingShingle Regularization techniques and inverse approaches in 3D Traction Force Microscopy
Apolinar-Fernández, Alejandro
Finite element method
Inverse methods
Mechanobiology
Nonlinear continuum mechanics
Tikhonov regularization
Traction force microscopy
title_short Regularization techniques and inverse approaches in 3D Traction Force Microscopy
title_full Regularization techniques and inverse approaches in 3D Traction Force Microscopy
title_fullStr Regularization techniques and inverse approaches in 3D Traction Force Microscopy
title_full_unstemmed Regularization techniques and inverse approaches in 3D Traction Force Microscopy
title_sort Regularization techniques and inverse approaches in 3D Traction Force Microscopy
dc.creator.none.fl_str_mv Apolinar-Fernández, Alejandro
Blázquez-Carmona, Pablo
Ruiz-Mateos, Raquel
Barrasa-Fano, Jorge
Van Oosterwyck, Hans
Reina-Romo, Esther
Sanz-Herrera, José A.
author Apolinar-Fernández, Alejandro
author_facet Apolinar-Fernández, Alejandro
Blázquez-Carmona, Pablo
Ruiz-Mateos, Raquel
Barrasa-Fano, Jorge
Van Oosterwyck, Hans
Reina-Romo, Esther
Sanz-Herrera, José A.
author_role author
author2 Blázquez-Carmona, Pablo
Ruiz-Mateos, Raquel
Barrasa-Fano, Jorge
Van Oosterwyck, Hans
Reina-Romo, Esther
Sanz-Herrera, José A.
author2_role author
author
author
author
author
author
dc.contributor.none.fl_str_mv Agencia Estatal de Investigación (España)
Ministerio de Ciencia e Innovación (España)
Research Foundation - Flanders
Blázquez-Carmona, Pablo [0000-0002-7605-5812]
Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
dc.subject.none.fl_str_mv Finite element method
Inverse methods
Mechanobiology
Nonlinear continuum mechanics
Tikhonov regularization
Traction force microscopy
topic Finite element method
Inverse methods
Mechanobiology
Nonlinear continuum mechanics
Tikhonov regularization
Traction force microscopy
description The conception of inverse methods in the context of Traction Force Microscopy (TFM) is influenced by multiple factors, such as nonlinear effects, dimensionality (2D/3D), and regularization/constraints, amongst others. Solving the inverse problem often requires the inversion of a matrix, and the presence of noise in the measured displacements can lead to unrealistic reconstructed tractions. To address this issue, Tikhonov regularization is commonly used, penalizing high norm values of computed tractions. The aim of this study is to compare the performance of different inverse methodologies (including some original variations) in 3D TFM, considering constraint imposition and regularization along the formulation. The different methodologies are numerically elaborated within a novel combined Newton–Raphson/Finite Element Method scheme that provides converged solutions in few iterations. The impact of constraint imposition and regularization in traction reconstruction is evaluated in terms of accuracy, efficiency (CPU time), and inherent characteristics of the methodology. Results show that, applying regularization and constraints (based on the fulfillment of fundamental principles) provides the best traction reconstruction, while simultaneously ensuring an optimum estimate of the maximum traction, at the cost of high CPU time and low efficiency. Moreover, regularization-based methods introduce the challenge of calibrating the regularization parameter, usually done under subjective criteria. On the other hand, non-regularized but constrained methods may represent a nice compromise between accuracy and efficiency, while avoiding pre-processing and calibration of such regularization parameter. It is emphasized the importance of considering not only traction reconstruction quality but also the efficiency and complexity of implementation (intrusiveness) when selecting an appropriate inverse method for TFM analysis.
publishDate 2024
dc.date.none.fl_str_mv 2024
2025
2025
dc.type.none.fl_str_mv info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
Publisher's version
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/386659
https://api.elsevier.com/content/abstract/scopus_id/85200477826
url http://hdl.handle.net/10261/386659
https://api.elsevier.com/content/abstract/scopus_id/85200477826
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv #PLACEHOLDER_PARENT_METADATA_VALUE#
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2021-126051OB-C42
https://doi.org/10.1016/j.ijmecsci.2024.109592
Sí
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier BV
publisher.none.fl_str_mv Elsevier BV
dc.source.none.fl_str_mv reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC
instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
reponame_str DIGITAL.CSIC. Repositorio Institucional del CSIC
collection DIGITAL.CSIC. Repositorio Institucional del CSIC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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