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 Brea, Raquel, Barrasa Fano, Jorge, Van Oosterwyck, Hans, Reina Romo, Esther, Sanz Herrera, José Antonio
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2024
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/163707
Acceso en línea:https://hdl.handle.net/11441/163707
https://doi.org/10.1016/j.ijmecsci.2024.109592
Access Level:acceso abierto
Palabra clave:Nonlinear continuum mechanics
Finite element method
Mechanobiology
Traction force microscopy
Inverse methods
Tikhonov regularization
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spelling Regularization techniques and inverse approaches in 3D Traction Force MicroscopyApolinar Fernández, AlejandroBlázquez Carmona, PabloRuiz-Mateos Brea, RaquelBarrasa Fano, JorgeVan Oosterwyck, HansReina Romo, EstherSanz Herrera, José AntonioNonlinear continuum mechanicsFinite element methodMechanobiologyTraction force microscopyInverse methodsTikhonov regularizationThe 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.ElsevierIngeniería Mecánica y FabricaciónMecánica de Medios Continuos y Teoría de EstructurasTEP111: Ingeniería MecánicaTEP245: Ingeniería de las Estructuras2024info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/163707https://doi.org/10.1016/j.ijmecsci.2024.109592reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésInternational Journal of Mechanical Sciences, 283 (109592).MCIN/AEI/10.13039/501100011033PID2021-126051OB-C42https://www.sciencedirect.com/science/article/pii/S0020740324006337?via%3Dihubinfo:eu-repo/semantics/openAccessoai:idus.us.es:11441/1637072026-06-17T12:51:07Z
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
Nonlinear continuum mechanics
Finite element method
Mechanobiology
Traction force microscopy
Inverse methods
Tikhonov regularization
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 Brea, Raquel
Barrasa Fano, Jorge
Van Oosterwyck, Hans
Reina Romo, Esther
Sanz Herrera, José Antonio
author Apolinar Fernández, Alejandro
author_facet Apolinar Fernández, Alejandro
Blázquez Carmona, Pablo
Ruiz-Mateos Brea, Raquel
Barrasa Fano, Jorge
Van Oosterwyck, Hans
Reina Romo, Esther
Sanz Herrera, José Antonio
author_role author
author2 Blázquez Carmona, Pablo
Ruiz-Mateos Brea, Raquel
Barrasa Fano, Jorge
Van Oosterwyck, Hans
Reina Romo, Esther
Sanz Herrera, José Antonio
author2_role author
author
author
author
author
author
dc.contributor.none.fl_str_mv Ingeniería Mecánica y Fabricación
Mecánica de Medios Continuos y Teoría de Estructuras
TEP111: Ingeniería Mecánica
TEP245: Ingeniería de las Estructuras
dc.subject.none.fl_str_mv Nonlinear continuum mechanics
Finite element method
Mechanobiology
Traction force microscopy
Inverse methods
Tikhonov regularization
topic Nonlinear continuum mechanics
Finite element method
Mechanobiology
Traction force microscopy
Inverse methods
Tikhonov regularization
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
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/163707
https://doi.org/10.1016/j.ijmecsci.2024.109592
url https://hdl.handle.net/11441/163707
https://doi.org/10.1016/j.ijmecsci.2024.109592
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv International Journal of Mechanical Sciences, 283 (109592).
MCIN/AEI/10.13039/501100011033
PID2021-126051OB-C42
https://www.sciencedirect.com/science/article/pii/S0020740324006337?via%3Dihub
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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