{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,24]],"date-time":"2026-10-24T05:54:28Z","timestamp":1792821268639,"version":"4.5.0"},"reference-count":53,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T00:00:00Z","timestamp":1649116800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["R01 HL142042"],"award-info":[{"award-number":["R01 HL142042"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["aapm.onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Medical Physics"],"published-print":{"date-parts":[[2022,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:sec><jats:title>Purpose<\/jats:title><jats:p>Osteoporosis is a bone disease associated with enhanced bone loss, microstructural degeneration, and fracture\u2010risk. Finite element (FE) modeling is used to estimate trabecular bone (Tb) modulus from high\u2010resolution three\u2010dimensional (3\u2010D) imaging modalities including micro\u2010computed tomography (CT), magnetic resonance imaging (MRI), and high\u2010resolution peripheral quantitative CT (HR\u2010pQCT). This paper validates an application of voxel\u2010based continuum finite element analysis (FEA) to predict Tb modulus from clinical CT imaging under a condition similar to in vivo imaging by comparing with measures derived by micro\u2010CT and experimental approaches.<\/jats:p><\/jats:sec><jats:sec><jats:title>Method<\/jats:title><jats:p>Voxel\u2010based continuum FEA methods for CT imaging were implemented using linear and nonlinear models and applied on distal tibial scans under a condition similar to in vivo imaging. First, tibial axis in a CT scan was aligned with the coordinate <jats:italic>z<\/jats:italic>\u2010axis at 150\u00a0\u03bcm isotropic voxels. FEA was applied on an upright cylindrical volume of interests (VOI) with its axis coinciding with the tibial bone axis. Voxel volume, edge, and vertex elements and their connectivity were defined as per the isotropic image grid. A calibration phantom was used to calibrate CT numbers in Hounsfield unit to bone mineral density (BMD) values, which was then converted into calcium hydroxyapatite (CHA) density. Mechanical properties at each voxel volume element was defined using its ash\u2010density defined on CT\u2010derived CHA density. For FEA, the bottom surface of the cylindrical VOI was fixed and a constant displacement was applied along the <jats:italic>z<\/jats:italic>\u2010direction at each vertex element on the top surface to simulate a physical axial compressive loading condition. Finally, a Poisson's ratio of 0.3 was applied, and Tb modulus (MPa) was computed as the ratio of average von Mises stress (MPa) of volume elements on the top surface and the applied displacement. FEA parameters including mesh element size, substep number, and different tolerance values were optimized.<\/jats:p><\/jats:sec><jats:sec><jats:title>Results<\/jats:title><jats:p>CT\u2010derived Tb modulus values using continuum FEA showed high linear correlation with the micro\u2010CT\u2010derived reference values (<jats:italic>r<\/jats:italic>\u00a0\u2208\u00a0[0.87 0.90]) as well as experimentally measured values (<jats:italic>r<\/jats:italic>\u00a0\u2208\u00a0[0.80 0.87]). Linear correlation of computed modulus with their reference values using continuum FEA with linear modeling was comparable with that obtained by nonlinear modeling. Nonlinear continuum FEA\u2010based modulus values (mean of 1087.2\u00a0MPa) showed greater difference from their reference values (mean of 1498.9\u00a0MPa using micro\u2010CT\u2010based FEA) as compared with linear continuum methods. High repeat CT scan reproducibility (intra\u2010class correlation [ICC]\u00a0=\u00a00.98) was observed for computed modulus values using both linear and nonlinear continuum FEA. It was observed that high stress regions coincide with Tb microstructure as fuzzily characterized by BMD values. Distributions of von Mises stress over Tb microstructure and marrow regions were significantly different (<jats:italic>p<\/jats:italic>\u00a0&lt;\u00a010<jats:sup>\u20138<\/jats:sup>).<\/jats:p><\/jats:sec><jats:sec><jats:title>Conclusion<\/jats:title><jats:p>Voxel\u2010based continuum FEA offers surrogate measures of Tb modulus from CT imaging under a condition similar to in vivo imaging that alleviates the need for segmentation of Tb and marrow regions, while accounting for bone distribution at the microstructural level. This relaxation of binary segmentation will extend the scope of FEA application to assess mechanical properties of bone microstructure at relatively low\u2010resolution imaging.<\/jats:p><\/jats:sec>","DOI":"10.1002\/mp.15629","type":"journal-article","created":{"date-parts":[[2022,3,23]],"date-time":"2022-03-23T14:15:00Z","timestamp":1648044900000},"page":"3886-3899","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":36,"title":["Finite element analysis of trabecular bone microstructure using CT imaging and continuum mechanical modeling"],"prefix":"10.1002","volume":"49","author":[{"given":"Indranil","family":"Guha","sequence":"first","affiliation":[{"name":"Department of Electrical and Computer Engineering College of Engineering University of Iowa  Iowa City Iowa USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaoliu","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering College of Engineering University of Iowa  Iowa City Iowa USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chamith S.","family":"Rajapakse","sequence":"additional","affiliation":[{"name":"Departments of Radiology and Orthopaedic Surgery University of Pennsylvania  Philadelphia Pennsylvania USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gregory","family":"Chang","sequence":"additional","affiliation":[{"name":"Department of Radiology New York University Grossman School of Medicine  New York New York USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Punam K.","family":"Saha","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering College of Engineering University of Iowa  Iowa City Iowa USA"},{"name":"Department of Radiology Carver College of Medicine University of Iowa  Iowa City Iowa USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2022,4,5]]},"reference":[{"key":"e_1_2_7_2_1","doi-asserted-by":"publisher","DOI":"10.1172\/JCI66746"},{"key":"e_1_2_7_3_1","doi-asserted-by":"publisher","DOI":"10.5152\/eurjrheum.2016.048"},{"key":"e_1_2_7_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/0895-4356(88)90036-4"},{"key":"e_1_2_7_5_1","doi-asserted-by":"publisher","DOI":"10.1002\/jemt.20501"},{"key":"e_1_2_7_6_1","doi-asserted-by":"publisher","DOI":"10.1172\/JCI111096"},{"key":"e_1_2_7_7_1","doi-asserted-by":"publisher","DOI":"10.1002\/jbmr.3105"},{"key":"e_1_2_7_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00223-020-00680-9"},{"key":"e_1_2_7_9_1","doi-asserted-by":"publisher","DOI":"10.1148\/radiol.11111044"},{"key":"e_1_2_7_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.bone.2010.05.039"},{"key":"e_1_2_7_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9290(98)00118-3"},{"key":"e_1_2_7_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jbiomech.2006.06.004"},{"key":"e_1_2_7_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.bone.2013.07.028"},{"key":"e_1_2_7_14_1","doi-asserted-by":"publisher","DOI":"10.1097\/01.blo.0000164400.37905.22"},{"key":"e_1_2_7_15_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jbiomech.2007.05.004"},{"key":"e_1_2_7_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0268-0033(01)00110-3"},{"key":"e_1_2_7_17_1","doi-asserted-by":"publisher","DOI":"10.1359\/jbmr.070603"},{"key":"e_1_2_7_18_1","doi-asserted-by":"publisher","DOI":"10.1359\/jbmr.080108"},{"key":"e_1_2_7_19_1","doi-asserted-by":"publisher","DOI":"10.1016\/S8756-3282(02)00736-6"},{"key":"e_1_2_7_20_1","doi-asserted-by":"publisher","DOI":"10.1002\/jbmr.33"},{"key":"e_1_2_7_21_1","doi-asserted-by":"publisher","DOI":"10.1002\/mp.12632"},{"key":"e_1_2_7_22_1","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0116907"},{"key":"e_1_2_7_23_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11657-020-0708-9"},{"key":"e_1_2_7_24_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejrad.2013.10.024"},{"key":"e_1_2_7_25_1","doi-asserted-by":"publisher","DOI":"10.1302\/2046-3758.78.BJR-2018-0025.R1"},{"key":"e_1_2_7_26_1","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9290(88)90186-8"},{"key":"e_1_2_7_27_1","doi-asserted-by":"publisher","DOI":"10.1016\/S8756-3282(99)00246-X"},{"key":"e_1_2_7_28_1","doi-asserted-by":"publisher","DOI":"10.1002\/jbm4.10484"},{"key":"e_1_2_7_29_1","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9290(93)90059-N"},{"key":"e_1_2_7_30_1","doi-asserted-by":"publisher","DOI":"10.1118\/1.4923753"},{"key":"e_1_2_7_31_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0734-189X(86)80047-0"},{"key":"e_1_2_7_32_1","doi-asserted-by":"publisher","DOI":"10.1109\/TMI.2015.2417112"},{"key":"e_1_2_7_33_1","doi-asserted-by":"crossref","unstructured":"MeijeringEH NiessenWJ PluimJP ViergeverMA \u201cQuantitative comparison of sinc\u2010approximating kernels for medical image interpolation \u201dProceedings ofInternational Conference on Medical Image Computing and Computer\u2010Assisted Intervention 210\u2010217 1999.","DOI":"10.1007\/10704282_23"},{"key":"e_1_2_7_34_1","doi-asserted-by":"publisher","DOI":"10.1016\/S8756-3282(99)00281-1"},{"key":"e_1_2_7_35_1","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9290(92)90255-Y"},{"key":"e_1_2_7_36_1","volume-title":"A First Course in the Finite Element Method","author":"Logan DL","year":"2011"},{"key":"e_1_2_7_37_1","doi-asserted-by":"publisher","DOI":"10.1016\/S1350-4533(01)00094-7"},{"key":"e_1_2_7_38_1","doi-asserted-by":"publisher","DOI":"10.1016\/S8756-3282(03)00210-2"},{"key":"e_1_2_7_39_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-7550-8"},{"key":"e_1_2_7_40_1","doi-asserted-by":"publisher","DOI":"10.1201\/b16295"},{"key":"e_1_2_7_41_1","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-4636(199607)31:3<373::AID-JBM11>3.0.CO;2-K"},{"key":"e_1_2_7_42_1","first-page":"219","article-title":"A practical strain hardening function","volume":"51","author":"Voce E","year":"1955","journal-title":"Metallurgia"},{"key":"e_1_2_7_43_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9290(03)00071-X"},{"key":"e_1_2_7_44_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jbiomech.2007.02.010"},{"key":"e_1_2_7_45_1","doi-asserted-by":"crossref","unstructured":"ChenC JinD ZhangX LevySM SahaPK Segmentation of trabecular bone for in vivo CT imaging using a novel approach of computing spatial variation in bone and marrow intensities.Proceedings of Asian Conference on Computer Vision 3\u201015 2016.","DOI":"10.1007\/978-3-319-54526-4_1"},{"key":"e_1_2_7_46_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.amepre.2005.06.001"},{"key":"e_1_2_7_47_1","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6560\/abc367"},{"key":"e_1_2_7_48_1","doi-asserted-by":"publisher","DOI":"10.1148\/radiol.12110462"},{"key":"e_1_2_7_49_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.medengphy.2006.11.002"},{"key":"e_1_2_7_50_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.bone.2021.115882"},{"key":"e_1_2_7_51_1","doi-asserted-by":"publisher","DOI":"10.1118\/1.4928481"},{"key":"e_1_2_7_52_1","doi-asserted-by":"publisher","DOI":"10.1002\/jor.1100150115"},{"key":"e_1_2_7_53_1","doi-asserted-by":"publisher","DOI":"10.1002\/jbmr.141"},{"key":"e_1_2_7_54_1","doi-asserted-by":"publisher","DOI":"10.1109\/TBME.2014.2313564"}],"container-title":["Medical Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/mp.15629","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/mp.15629","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/aapm.onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/mp.15629","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,24]],"date-time":"2023-08-24T07:49:19Z","timestamp":1692863359000},"score":1,"resource":{"primary":{"URL":"https:\/\/aapm.onlinelibrary.wiley.com\/doi\/10.1002\/mp.15629"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,5]]},"references-count":53,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2022,6]]}},"alternative-id":["10.1002\/mp.15629"],"URL":"https:\/\/doi.org\/10.1002\/mp.15629","archive":["Portico"],"relation":{},"ISSN":["0094-2405","2473-4209"],"issn-type":[{"value":"0094-2405","type":"print"},{"value":"2473-4209","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,4,5]]},"assertion":[{"value":"2022-02-14","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2022-03-11","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2022-04-05","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}