{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T09:53:37Z","timestamp":1769162017129,"version":"3.49.0"},"reference-count":28,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2009,7,9]],"date-time":"2009-07-09T00:00:00Z","timestamp":1247097600000},"content-version":"vor","delay-in-days":189,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"US Army\u2019s Breast Cancer Research Program","award":["W81XWH-05-1-0461"],"award-info":[{"award-number":["W81XWH-05-1-0461"]}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Biomedical Imaging"],"published-print":{"date-parts":[[2009,1]]},"abstract":"<jats:p>Elastography is developed as a quantitative approach to imaging linear elastic properties of tissues to detect suspicious tumors. In this paper a nonlinear elastography method is introduced for reconstruction of complex breast tissue properties. The elastic parameters are estimated by optimally minimizing the difference between the computed forces and experimental measures. A nonlinear adjoint method is derived to calculate the gradient of the objective function, which significantly enhances the numerical efficiency and stability. Simulations are conducted on a three\u2010dimensional heterogeneous breast phantom extracting from real imaging including fatty tissue, glandular tissue, and tumors. An\nexponential\u2010form of nonlinear material model is applied. The effect of noise is taken into account. \nResults demonstrate that the proposed nonlinear method opens the door toward nonlinear elastography\nand provides guidelines for future development and clinical application in breast cancer study.<\/jats:p>","DOI":"10.1155\/2009\/406854","type":"journal-article","created":{"date-parts":[[2009,7,9]],"date-time":"2009-07-09T17:20:18Z","timestamp":1247160018000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["Elastography Method for Reconstruction of Nonlinear Breast Tissue Properties"],"prefix":"10.1155","volume":"2009","author":[{"given":"Z. G.","family":"Wang","sequence":"first","affiliation":[]},{"given":"Y.","family":"Liu","sequence":"additional","affiliation":[]},{"given":"G.","family":"Wang","sequence":"additional","affiliation":[]},{"given":"L. 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Inverse finite element characterization of soft tissue with aspiration experiments Ph.D. dissertation 2004 Swiss Federal Institute of Technology Switzerland."},{"key":"e_1_2_8_25_2","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/47\/12\/310"},{"key":"e_1_2_8_26_2","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/20\/1\/017"},{"key":"e_1_2_8_27_2","doi-asserted-by":"publisher","DOI":"10.1117\/1.1352753"},{"key":"e_1_2_8_28_2","volume-title":"Numerical Recipes: The Art of Scientific Computing","author":"Press W. 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