Forward and inverse problems in elasticity imaging of soft tissues
In elasticity imaging, a surface deformation is applied to an object using small pistons, and the resulting induced strains in the interior of the object are measured using ultrasonic imaging. Two important problems are considered: (1) the forward problem of determining the strains induced by a know...
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| Veröffentlicht in: | IEEE transactions on nuclear science 1994-08, Vol.41 (4), p.1639-1648 |
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| container_title | IEEE transactions on nuclear science |
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| creator | Raghavan, K.R. Yagle, A.E. |
| description | In elasticity imaging, a surface deformation is applied to an object using small pistons, and the resulting induced strains in the interior of the object are measured using ultrasonic imaging. Two important problems are considered: (1) the forward problem of determining the strains induced by a known deformation of an object with known elasticity; and (2) the inverse problem of reconstructing elasticity from measured strains and the equations of equilibrium. The method of finite differences is used to solve the forward problem for a given piston configuration; some nontrivial issues arise in determining boundary conditions. The finite difference equations are then rearranged into a linear system of equations which formulates the inverse problem; this system can be solved for the unknown elasticities. This formulation of the inverse problem is completely consistent with the forward problem; this is useful for iterative methods in which the deformation is adaptively changed. A comparison between simulated and actual measured results demonstrate the feasibility of the proposed procedure.< > |
| doi_str_mv | 10.1109/23.322961 |
| format | Article |
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Two important problems are considered: (1) the forward problem of determining the strains induced by a known deformation of an object with known elasticity; and (2) the inverse problem of reconstructing elasticity from measured strains and the equations of equilibrium. The method of finite differences is used to solve the forward problem for a given piston configuration; some nontrivial issues arise in determining boundary conditions. The finite difference equations are then rearranged into a linear system of equations which formulates the inverse problem; this system can be solved for the unknown elasticities. This formulation of the inverse problem is completely consistent with the forward problem; this is useful for iterative methods in which the deformation is adaptively changed. A comparison between simulated and actual measured results demonstrate the feasibility of the proposed procedure.< ></description><identifier>ISSN: 0018-9499</identifier><identifier>EISSN: 1558-1578</identifier><identifier>DOI: 10.1109/23.322961</identifier><identifier>CODEN: IETNAE</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Biological and medical sciences ; Biological tissues ; Computerized, statistical medical data processing and models in biomedicine ; Difference equations ; Elasticity ; Finite difference methods ; Image reconstruction ; Inverse problems ; Medical sciences ; Models and simulation ; Pistons ; Strain measurement ; Ultrasonic imaging ; Ultrasonic variables measurement</subject><ispartof>IEEE transactions on nuclear science, 1994-08, Vol.41 (4), p.1639-1648</ispartof><rights>1995 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c337t-59cdb1205eb8313be527e3b2550e32a969a6913b479a861a117564d3e64fe9203</citedby><cites>FETCH-LOGICAL-c337t-59cdb1205eb8313be527e3b2550e32a969a6913b479a861a117564d3e64fe9203</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/322961$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>309,310,314,776,780,785,786,792,23909,23910,25118,27901,27902,54733</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/322961$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=3397472$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Raghavan, K.R.</creatorcontrib><creatorcontrib>Yagle, A.E.</creatorcontrib><title>Forward and inverse problems in elasticity imaging of soft tissues</title><title>IEEE transactions on nuclear science</title><addtitle>TNS</addtitle><description>In elasticity imaging, a surface deformation is applied to an object using small pistons, and the resulting induced strains in the interior of the object are measured using ultrasonic imaging. Two important problems are considered: (1) the forward problem of determining the strains induced by a known deformation of an object with known elasticity; and (2) the inverse problem of reconstructing elasticity from measured strains and the equations of equilibrium. The method of finite differences is used to solve the forward problem for a given piston configuration; some nontrivial issues arise in determining boundary conditions. The finite difference equations are then rearranged into a linear system of equations which formulates the inverse problem; this system can be solved for the unknown elasticities. This formulation of the inverse problem is completely consistent with the forward problem; this is useful for iterative methods in which the deformation is adaptively changed. A comparison between simulated and actual measured results demonstrate the feasibility of the proposed procedure.< ></description><subject>Biological and medical sciences</subject><subject>Biological tissues</subject><subject>Computerized, statistical medical data processing and models in biomedicine</subject><subject>Difference equations</subject><subject>Elasticity</subject><subject>Finite difference methods</subject><subject>Image reconstruction</subject><subject>Inverse problems</subject><subject>Medical sciences</subject><subject>Models and simulation</subject><subject>Pistons</subject><subject>Strain measurement</subject><subject>Ultrasonic imaging</subject><subject>Ultrasonic variables measurement</subject><issn>0018-9499</issn><issn>1558-1578</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1994</creationdate><recordtype>article</recordtype><recordid>eNqFkD1PwzAQhi0EEqUwsDJ5QEgMKT47juMRKgpIlVhgjpzkUhmlSfGloP77GqWCkel07z333gdjlyBmAMLeSTVTUtoMjtgEtM4T0CY_ZhMhIE9sau0pOyP6iGmqhZ6wh0Ufvl2ouetq7rsvDIR8E_qyxTVFgWPraPCVH3bcr93KdyveN5z6ZuCDJ9oinbOTxrWEF4c4Ze-Lx7f5c7J8fXqZ3y-TSikzJNpWdQlSaCxzBapELQ2qUmotUElnM-syG_XUWJdn4ACMztJaYZY2aKVQU3Yz-sb1PuPcoVh7qrBtXYf9lgqZy1wIYf8FIbOp1qAjeDuCVeiJAjbFJsQjw64AUfy8s5CqGN8Z2euDqaPKtU1wXeXpt0Epa1IjI3Y1Yh4R_6qjxx5ZI3q9</recordid><startdate>19940801</startdate><enddate>19940801</enddate><creator>Raghavan, K.R.</creator><creator>Yagle, A.E.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7QO</scope><scope>8FD</scope><scope>FR3</scope><scope>P64</scope><scope>7U5</scope><scope>L7M</scope></search><sort><creationdate>19940801</creationdate><title>Forward and inverse problems in elasticity imaging of soft tissues</title><author>Raghavan, K.R. ; Yagle, A.E.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c337t-59cdb1205eb8313be527e3b2550e32a969a6913b479a861a117564d3e64fe9203</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1994</creationdate><topic>Biological and medical sciences</topic><topic>Biological tissues</topic><topic>Computerized, statistical medical data processing and models in biomedicine</topic><topic>Difference equations</topic><topic>Elasticity</topic><topic>Finite difference methods</topic><topic>Image reconstruction</topic><topic>Inverse problems</topic><topic>Medical sciences</topic><topic>Models and simulation</topic><topic>Pistons</topic><topic>Strain measurement</topic><topic>Ultrasonic imaging</topic><topic>Ultrasonic variables measurement</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Raghavan, K.R.</creatorcontrib><creatorcontrib>Yagle, A.E.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Biotechnology Research Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Biotechnology and BioEngineering Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>IEEE transactions on nuclear science</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Raghavan, K.R.</au><au>Yagle, A.E.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Forward and inverse problems in elasticity imaging of soft tissues</atitle><jtitle>IEEE transactions on nuclear science</jtitle><stitle>TNS</stitle><date>1994-08-01</date><risdate>1994</risdate><volume>41</volume><issue>4</issue><spage>1639</spage><epage>1648</epage><pages>1639-1648</pages><issn>0018-9499</issn><eissn>1558-1578</eissn><coden>IETNAE</coden><abstract>In elasticity imaging, a surface deformation is applied to an object using small pistons, and the resulting induced strains in the interior of the object are measured using ultrasonic imaging. Two important problems are considered: (1) the forward problem of determining the strains induced by a known deformation of an object with known elasticity; and (2) the inverse problem of reconstructing elasticity from measured strains and the equations of equilibrium. The method of finite differences is used to solve the forward problem for a given piston configuration; some nontrivial issues arise in determining boundary conditions. The finite difference equations are then rearranged into a linear system of equations which formulates the inverse problem; this system can be solved for the unknown elasticities. This formulation of the inverse problem is completely consistent with the forward problem; this is useful for iterative methods in which the deformation is adaptively changed. 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| ispartof | IEEE transactions on nuclear science, 1994-08, Vol.41 (4), p.1639-1648 |
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| source | IEEE Xplore |
| subjects | Biological and medical sciences Biological tissues Computerized, statistical medical data processing and models in biomedicine Difference equations Elasticity Finite difference methods Image reconstruction Inverse problems Medical sciences Models and simulation Pistons Strain measurement Ultrasonic imaging Ultrasonic variables measurement |
| title | Forward and inverse problems in elasticity imaging of soft tissues |
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