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Conventional elastography quantifies stiffness in soft (e.g. brain, liver) tissue, but robust quantification in stiff (e.g. musculoskeletal) tissues is challenging due to dissipation of high frequency shear waves. We describe new development of <jats:italic>finite deformation elastography<\/jats:italic> that utilizes magnetic resonance imaging of low frequency, physiological-level (large magnitude) displacements, coupled to an iterative topology optimization routine to investigate stiffness heterogeneity, including spatial gradients and inclusions. We reconstruct 2D and 3D stiffness distributions in bilayer agarose hydrogels and silicon materials that exhibit heterogeneous displacement\/strain responses. We map stiffness in porcine and sheep articular cartilage deep within the bony articular joint space <jats:italic>in situ<\/jats:italic> for the first time. Elevated cartilage stiffness localized to the superficial zone is further related to collagen fiber compaction and loss of water content during cyclic loading, as assessed by independent <jats:italic>T<\/jats:italic><jats:sub>2<\/jats:sub> measurements. We additionally describe technical challenges needed to achieve <jats:italic>in vivo<\/jats:italic> elastography measurements. Our results introduce new functional imaging biomarkers, which can be assessed nondestructively, with clinical potential to diagnose and track progression of disease in early stages, including osteoarthritis or tissue degeneration.<\/jats:p>","DOI":"10.1038\/s41598-020-64723-9","type":"journal-article","created":{"date-parts":[[2020,5,14]],"date-time":"2020-05-14T10:03:18Z","timestamp":1589450598000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Finite deformation elastography of articular cartilage and biomaterials based on imaging and topology optimization"],"prefix":"10.1038","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2927-6890","authenticated-orcid":false,"given":"Luyao","family":"Cai","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Eric A.","family":"Nauman","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Claus B. 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