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An improved parameter estimation and comparison for soft tissue constitutive models containing an exponential function

Ankush Aggarwal Orcid Logo

Biomechanics and Modeling in Mechanobiology, Volume: 16

Swansea University Author: Ankush Aggarwal Orcid Logo

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DOI (Published version): 10.1007/s10237-017-0889-3

Abstract

Motivated by the well-known result that stiffness of soft tissue is proportional to the stress, many of the constitutive laws for soft tissues contain an exponential function. In this work, we analyze properties of the exponential function and how it affects the estimation and comparison of elastic...

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Published in: Biomechanics and Modeling in Mechanobiology
ISSN: 1617-7959
Published: 2017
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URI: https://cronfa.swan.ac.uk/Record/cronfa32140
first_indexed 2017-03-02T13:44:54Z
last_indexed 2020-07-15T18:48:57Z
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spelling 2020-07-15T15:13:57.9165026 v2 32140 2017-02-27 An improved parameter estimation and comparison for soft tissue constitutive models containing an exponential function 33985d0c2586398180c197dc170d7d19 0000-0002-1755-8807 Ankush Aggarwal Ankush Aggarwal true false 2017-02-27 Motivated by the well-known result that stiffness of soft tissue is proportional to the stress, many of the constitutive laws for soft tissues contain an exponential function. In this work, we analyze properties of the exponential function and how it affects the estimation and comparison of elastic parameters for soft tissues. In particular, we find that as a consequence of the exponential function there are lines of high covariance in the elastic parameter space. As a result, one can have widely varying mechanical parameters defining the tissue stiffness but similar effective stress–strain responses. Drawing from elementary algebra, we propose simple changes in the norm and the parameter space, which significantly improve the convergence of parameter estimation and robustness in the presence of noise. More importantly, we demonstrate that these changes improve the conditioning of the problem and provide a more robust solution in the case of heterogeneous material by reducing the chances of getting trapped in a local minima. Based upon the new insight, we also propose a transformed parameter space which will allow for rational parameter comparison and avoid misleading conclusions regarding soft tissue mechanics. Journal Article Biomechanics and Modeling in Mechanobiology 16 1617-7959 Soft tissues, Biomechanics, Constitutive laws, Nonlinear elasticity, Parameter estimation, Inverse modeling 31 12 2017 2017-12-31 10.1007/s10237-017-0889-3 COLLEGE NANME COLLEGE CODE Swansea University 2020-07-15T15:13:57.9165026 2017-02-27T17:51:31.0920141 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Ankush Aggarwal 0000-0002-1755-8807 1 0032140-02032017112108.pdf aggarwal2017.pdf 2017-03-02T11:21:08.8570000 Output 5823164 application/pdf Version of Record true 2017-03-02T00:00:00.0000000 This article is distributed under the terms of the Creative Commons Attribution 4.0 International License true eng http://creativecommons.org/licenses/by/4.0
title An improved parameter estimation and comparison for soft tissue constitutive models containing an exponential function
spellingShingle An improved parameter estimation and comparison for soft tissue constitutive models containing an exponential function
Ankush Aggarwal
title_short An improved parameter estimation and comparison for soft tissue constitutive models containing an exponential function
title_full An improved parameter estimation and comparison for soft tissue constitutive models containing an exponential function
title_fullStr An improved parameter estimation and comparison for soft tissue constitutive models containing an exponential function
title_full_unstemmed An improved parameter estimation and comparison for soft tissue constitutive models containing an exponential function
title_sort An improved parameter estimation and comparison for soft tissue constitutive models containing an exponential function
author_id_str_mv 33985d0c2586398180c197dc170d7d19
author_id_fullname_str_mv 33985d0c2586398180c197dc170d7d19_***_Ankush Aggarwal
author Ankush Aggarwal
author2 Ankush Aggarwal
format Journal article
container_title Biomechanics and Modeling in Mechanobiology
container_volume 16
publishDate 2017
institution Swansea University
issn 1617-7959
doi_str_mv 10.1007/s10237-017-0889-3
college_str Faculty of Science and Engineering
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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 Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised
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description Motivated by the well-known result that stiffness of soft tissue is proportional to the stress, many of the constitutive laws for soft tissues contain an exponential function. In this work, we analyze properties of the exponential function and how it affects the estimation and comparison of elastic parameters for soft tissues. In particular, we find that as a consequence of the exponential function there are lines of high covariance in the elastic parameter space. As a result, one can have widely varying mechanical parameters defining the tissue stiffness but similar effective stress–strain responses. Drawing from elementary algebra, we propose simple changes in the norm and the parameter space, which significantly improve the convergence of parameter estimation and robustness in the presence of noise. More importantly, we demonstrate that these changes improve the conditioning of the problem and provide a more robust solution in the case of heterogeneous material by reducing the chances of getting trapped in a local minima. Based upon the new insight, we also propose a transformed parameter space which will allow for rational parameter comparison and avoid misleading conclusions regarding soft tissue mechanics.
published_date 2017-12-31T13:07:53Z
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score 11.048042

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