Using uniaxial pseudorandom stress stimuli to develop soft tissue constitutive equations
A nonlinear systems identification method was used to develop constitutive equations for soft tissue specimens under uniaxial tension. The constitutive equations are developed from a single test by applying a pseudorandom Gaussian (PGN) stress input to the specimen, measuring the resulting strain, a...
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| Veröffentlicht in: | Annals of biomedical engineering 2002-01, Vol.30 (1), p.44-53 |
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| creator | Hoffman, Allen H Grigg, Peter |
| description | A nonlinear systems identification method was used to develop constitutive equations for soft tissue specimens under uniaxial tension. The constitutive equations are developed from a single test by applying a pseudorandom Gaussian (PGN) stress input to the specimen, measuring the resulting strain, and calculating the Volterra-Wiener kernels. First and second order kernels were developed for two tissues with widely different properties, rat medial collateral knee ligaments, and rat skin. These kernels were used to predict the strain response to a variety of sinusoidal stress inputs. These predicted strains were compared with the measured strain response using the normalized mean squared error (NMSE). Results showed NMSEs in the range of 0.01-0.08 provided that the magnitudes of the applied stresses were present in the original PGN stress input. Overall, the method provides a means to develop soft tissue constitutive equations that can predict both nonlinear and viscoelastic behavior over a wide range of stress inputs. |
| doi_str_mv | 10.1114/1.1432689 |
| format | Article |
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The constitutive equations are developed from a single test by applying a pseudorandom Gaussian (PGN) stress input to the specimen, measuring the resulting strain, and calculating the Volterra-Wiener kernels. First and second order kernels were developed for two tissues with widely different properties, rat medial collateral knee ligaments, and rat skin. These kernels were used to predict the strain response to a variety of sinusoidal stress inputs. These predicted strains were compared with the measured strain response using the normalized mean squared error (NMSE). Results showed NMSEs in the range of 0.01-0.08 provided that the magnitudes of the applied stresses were present in the original PGN stress input. Overall, the method provides a means to develop soft tissue constitutive equations that can predict both nonlinear and viscoelastic behavior over a wide range of stress inputs.</description><identifier>ISSN: 0090-6964</identifier><identifier>EISSN: 1573-9686</identifier><identifier>DOI: 10.1114/1.1432689</identifier><identifier>PMID: 11874141</identifier><language>eng</language><publisher>United States: Springer Nature B.V</publisher><subject>Animals ; Connective Tissue - physiology ; Elasticity ; Error analysis ; Gaussian noise (electronic) ; Medial Collateral Ligament, Knee - physiology ; Models, Statistical ; Nonlinear Dynamics ; Nonlinear equations ; Normal Distribution ; Numerical methods ; Rats ; Rats, Sprague-Dawley ; Skin Physiological Phenomena ; Stochastic Processes ; Stress, Mechanical ; Systems analysis ; Tissue ; Viscosity</subject><ispartof>Annals of biomedical engineering, 2002-01, Vol.30 (1), p.44-53</ispartof><rights>Biomedical Engineering Society 2002</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c372t-1524da4a825a1c86090b98fb51d5adc0d77ac96e4c3d49837838ba3153df7d893</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/11874141$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Hoffman, Allen H</creatorcontrib><creatorcontrib>Grigg, Peter</creatorcontrib><title>Using uniaxial pseudorandom stress stimuli to develop soft tissue constitutive equations</title><title>Annals of biomedical engineering</title><addtitle>Ann Biomed Eng</addtitle><description>A nonlinear systems identification method was used to develop constitutive equations for soft tissue specimens under uniaxial tension. The constitutive equations are developed from a single test by applying a pseudorandom Gaussian (PGN) stress input to the specimen, measuring the resulting strain, and calculating the Volterra-Wiener kernels. First and second order kernels were developed for two tissues with widely different properties, rat medial collateral knee ligaments, and rat skin. These kernels were used to predict the strain response to a variety of sinusoidal stress inputs. These predicted strains were compared with the measured strain response using the normalized mean squared error (NMSE). Results showed NMSEs in the range of 0.01-0.08 provided that the magnitudes of the applied stresses were present in the original PGN stress input. Overall, the method provides a means to develop soft tissue constitutive equations that can predict both nonlinear and viscoelastic behavior over a wide range of stress inputs.</description><subject>Animals</subject><subject>Connective Tissue - physiology</subject><subject>Elasticity</subject><subject>Error analysis</subject><subject>Gaussian noise (electronic)</subject><subject>Medial Collateral Ligament, Knee - physiology</subject><subject>Models, Statistical</subject><subject>Nonlinear Dynamics</subject><subject>Nonlinear equations</subject><subject>Normal Distribution</subject><subject>Numerical methods</subject><subject>Rats</subject><subject>Rats, Sprague-Dawley</subject><subject>Skin Physiological Phenomena</subject><subject>Stochastic Processes</subject><subject>Stress, Mechanical</subject><subject>Systems analysis</subject><subject>Tissue</subject><subject>Viscosity</subject><issn>0090-6964</issn><issn>1573-9686</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2002</creationdate><recordtype>article</recordtype><sourceid>EIF</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNqFkUtLxDAUhYMozji68A9IcCG6qOY2aR5LEV8guFFwVzJNKhnaZqZJBv33RmZAcKGrA5ePwzn3IHQM5BIA2BVcAqMll2oHTaEStFBc8l00JUSRgivOJugghAUhAJJW-2iSVTBgMEVvr8EN7zgNTn843eFlsMn4UQ_G9zjE0YaQxfWpczh6bOzadn6Jg28jji6EZHHjh0zEFN3aYrtKOrp8OUR7re6CPdrqDL3e3b7cPBRPz_ePN9dPRUNFGQuoSmY007KsNDSS58RzJdt5BabSpiFGCN0obllDDVOSCknlXFOoqGmFkYrO0NnGdzn6VbIh1r0Lje06PVifQi2ASZq7_guWwAQlnGbw_E8QSP4cUTynmaHTX-jCp3HIfWulytyGM8jQxQZqRh_CaNt6Obpej5_Zqf7er4Z6u19mT7aGad5b80NuB6NfGSiUxw</recordid><startdate>200201</startdate><enddate>200201</enddate><creator>Hoffman, Allen H</creator><creator>Grigg, Peter</creator><general>Springer Nature B.V</general><scope>CGR</scope><scope>CUY</scope><scope>CVF</scope><scope>ECM</scope><scope>EIF</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7QF</scope><scope>7QO</scope><scope>7QQ</scope><scope>7SC</scope><scope>7SE</scope><scope>7SP</scope><scope>7SR</scope><scope>7TA</scope><scope>7TB</scope><scope>7U5</scope><scope>7X7</scope><scope>7XB</scope><scope>88E</scope><scope>8AO</scope><scope>8BQ</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FH</scope><scope>8FI</scope><scope>8FJ</scope><scope>8FK</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AEUYN</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BBNVY</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>BHPHI</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>F28</scope><scope>FR3</scope><scope>FYUFA</scope><scope>GHDGH</scope><scope>GNUQQ</scope><scope>H8D</scope><scope>H8G</scope><scope>HCIFZ</scope><scope>JG9</scope><scope>JQ2</scope><scope>K9.</scope><scope>KR7</scope><scope>L6V</scope><scope>L7M</scope><scope>LK8</scope><scope>L~C</scope><scope>L~D</scope><scope>M0S</scope><scope>M1P</scope><scope>M7P</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>P64</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>7X8</scope></search><sort><creationdate>200201</creationdate><title>Using uniaxial pseudorandom stress stimuli to develop soft tissue constitutive equations</title><author>Hoffman, Allen H ; Grigg, Peter</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c372t-1524da4a825a1c86090b98fb51d5adc0d77ac96e4c3d49837838ba3153df7d893</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2002</creationdate><topic>Animals</topic><topic>Connective Tissue - physiology</topic><topic>Elasticity</topic><topic>Error analysis</topic><topic>Gaussian noise (electronic)</topic><topic>Medial Collateral Ligament, Knee - physiology</topic><topic>Models, Statistical</topic><topic>Nonlinear Dynamics</topic><topic>Nonlinear equations</topic><topic>Normal Distribution</topic><topic>Numerical methods</topic><topic>Rats</topic><topic>Rats, Sprague-Dawley</topic><topic>Skin Physiological Phenomena</topic><topic>Stochastic Processes</topic><topic>Stress, Mechanical</topic><topic>Systems analysis</topic><topic>Tissue</topic><topic>Viscosity</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hoffman, Allen H</creatorcontrib><creatorcontrib>Grigg, Peter</creatorcontrib><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Aluminium Industry Abstracts</collection><collection>Biotechnology Research Abstracts</collection><collection>Ceramic Abstracts</collection><collection>Computer and Information Systems Abstracts</collection><collection>Corrosion Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Engineered Materials Abstracts</collection><collection>Materials Business File</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Health & Medical Collection</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Medical Database (Alumni Edition)</collection><collection>ProQuest Pharma Collection</collection><collection>METADEX</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Natural Science Collection</collection><collection>Hospital Premium Collection</collection><collection>Hospital Premium Collection (Alumni Edition)</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest One Sustainability</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>Biological Science Collection</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>Natural Science Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><collection>Health Research Premium Collection</collection><collection>Health Research Premium Collection (Alumni)</collection><collection>ProQuest Central Student</collection><collection>Aerospace Database</collection><collection>Copper Technical Reference Library</collection><collection>SciTech Premium Collection</collection><collection>Materials Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Health & Medical Complete (Alumni)</collection><collection>Civil Engineering Abstracts</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>ProQuest Biological Science Collection</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Health & Medical Collection (Alumni Edition)</collection><collection>Medical Database</collection><collection>Biological Science Database</collection><collection>Engineering Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Biotechnology and BioEngineering Abstracts</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><collection>MEDLINE - Academic</collection><jtitle>Annals of biomedical engineering</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hoffman, Allen H</au><au>Grigg, Peter</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Using uniaxial pseudorandom stress stimuli to develop soft tissue constitutive equations</atitle><jtitle>Annals of biomedical engineering</jtitle><addtitle>Ann Biomed Eng</addtitle><date>2002-01</date><risdate>2002</risdate><volume>30</volume><issue>1</issue><spage>44</spage><epage>53</epage><pages>44-53</pages><issn>0090-6964</issn><eissn>1573-9686</eissn><abstract>A nonlinear systems identification method was used to develop constitutive equations for soft tissue specimens under uniaxial tension. The constitutive equations are developed from a single test by applying a pseudorandom Gaussian (PGN) stress input to the specimen, measuring the resulting strain, and calculating the Volterra-Wiener kernels. First and second order kernels were developed for two tissues with widely different properties, rat medial collateral knee ligaments, and rat skin. These kernels were used to predict the strain response to a variety of sinusoidal stress inputs. These predicted strains were compared with the measured strain response using the normalized mean squared error (NMSE). Results showed NMSEs in the range of 0.01-0.08 provided that the magnitudes of the applied stresses were present in the original PGN stress input. Overall, the method provides a means to develop soft tissue constitutive equations that can predict both nonlinear and viscoelastic behavior over a wide range of stress inputs.</abstract><cop>United States</cop><pub>Springer Nature B.V</pub><pmid>11874141</pmid><doi>10.1114/1.1432689</doi><tpages>10</tpages></addata></record> |
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| subjects | Animals Connective Tissue - physiology Elasticity Error analysis Gaussian noise (electronic) Medial Collateral Ligament, Knee - physiology Models, Statistical Nonlinear Dynamics Nonlinear equations Normal Distribution Numerical methods Rats Rats, Sprague-Dawley Skin Physiological Phenomena Stochastic Processes Stress, Mechanical Systems analysis Tissue Viscosity |
| title | Using uniaxial pseudorandom stress stimuli to develop soft tissue constitutive equations |
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