{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,11,6]],"date-time":"2026-11-06T03:28:19Z","timestamp":1793935699071,"version":"4.8.0"},"reference-count":40,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,9,11]],"date-time":"2026-09-11T00:00:00Z","timestamp":1789084800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001659","name":"German Research Foundation","doi-asserted-by":"publisher","award":["FOR5628"],"award-info":[{"award-number":["FOR5628"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"German Research Foundation","doi-asserted-by":"publisher","award":["CRC1340 Matrix in Vision"],"award-info":[{"award-number":["CRC1340 Matrix in Vision"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"German Research Foundation","doi-asserted-by":"publisher","award":["GRK2260 BIOQIC"],"award-info":[{"award-number":["GRK2260 BIOQIC"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Medical Image Analysis"],"published-print":{"date-parts":[[2027,1]]},"DOI":"10.1016\/j.media.2026.104317","type":"journal-article","created":{"date-parts":[[2026,9,11]],"date-time":"2026-09-11T15:56:40Z","timestamp":1789142200000},"page":"104317","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Multifrequency neural network-based wave inversion in MR elastography with uncertainty quantification"],"prefix":"10.1016","volume":"115","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-7315-3673","authenticated-orcid":false,"given":"H\u00e9lo\u00efse","family":"Bustin","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tom","family":"Meyer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6081-7595","authenticated-orcid":false,"given":"Jakob","family":"Jordan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lars","family":"Walczak","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9458-2221","authenticated-orcid":false,"given":"Heiko","family":"Tzsch\u00e4tzsch","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ingolf","family":"Sack","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0737-7375","authenticated-orcid":false,"given":"Anja","family":"Hennemuth","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.media.2026.104317_bib1","series-title":"Advances in Neural Information Processing Systems","first-page":"14927","article-title":"Deep Evidential Regression","author":"Amini","year":"2020"},{"key":"10.1016\/j.media.2026.104317_bib2","doi-asserted-by":"crossref","DOI":"10.1126\/sciadv.adp3363","article-title":"Making sense of scattering: seeing microstructure through shear waves","volume":"10","author":"Annio","year":"2024","journal-title":"Sci. Adv."},{"key":"10.1016\/j.media.2026.104317_bib3","article-title":"SNR Weighting for shear wave speed reconstruction in Tomoelastography","volume":"34","author":"Ariyurek","year":"2020","journal-title":"NMR Biomed."},{"key":"10.1016\/j.media.2026.104317_bib4","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1148\/radiol.10092489","article-title":"Viscoelasticity-based staging of hepatic fibrosis with multifrequency MR elastography","volume":"257","author":"Asbach","year":"2010","journal-title":"Radiology"},{"key":"10.1016\/j.media.2026.104317_bib5","doi-asserted-by":"crossref","first-page":"2321","DOI":"10.1002\/mrm.25332","article-title":"Real-time 4D phase unwrapping applied to magnetic resonance elastography","volume":"73","author":"Barnhill","year":"2014","journal-title":"Magn. Reson. Med."},{"key":"10.1016\/j.media.2026.104317_bib6","series-title":"Lect. Notes Comput. Sci.","isbn-type":"print","first-page":"418","article-title":"Multifrequency neural network-based wave inversion in MR Elastography","author":"Bustin","year":"2025","ISBN":"https:\/\/id.crossref.org\/isbn\/9783032049469"},{"key":"10.1016\/j.media.2026.104317_bib7","doi-asserted-by":"crossref","first-page":"103642","DOI":"10.1016\/j.media.2025.103642","article-title":"ElastoNet: neural network-based multicomponent MR elastography wave inversion with uncertainty quantification","volume":"105","author":"Bustin","year":"2025","journal-title":"Med. Image Anal."},{"key":"10.1016\/j.media.2026.104317_bib8","series-title":"Theory of Viscoelasticity","author":"Christensen","year":"1982"},{"key":"10.1016\/j.media.2026.104317_bib9","doi-asserted-by":"crossref","first-page":"1680","DOI":"10.1038\/s41597-025-05968-9","article-title":"MR elastography datasets including phantom, liver, and brain","volume":"12","author":"Feng","year":"2025","journal-title":"Sci. Data"},{"key":"10.1016\/j.media.2026.104317_bib10","doi-asserted-by":"crossref","first-page":"1513","DOI":"10.1007\/s10462-023-10562-9","article-title":"A survey of uncertainty in deep neural networks","volume":"56","author":"Gawlikowski","year":"2023","journal-title":"Artif. Intell. Rev."},{"key":"10.1016\/j.media.2026.104317_bib11","doi-asserted-by":"crossref","first-page":"909","DOI":"10.1016\/j.wavemoti.2013.03.002","article-title":"Wave propagation in linear viscoelastic media with completely monotonic relaxation moduli","volume":"50","author":"Hanyga","year":"2013","journal-title":"Wave Motion"},{"key":"10.1016\/j.media.2026.104317_bib12","series-title":"Magnetic resonance elastography: Physical background and medical applications","author":"Hirsch","year":"2017"},{"key":"10.1016\/j.media.2026.104317_bib13","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1002\/mrm.24674","article-title":"MR elastography of the liver and the spleen using a piezoelectric driver, single-shot wave-field acquisition, and multifrequency dual parameter reconstruction","volume":"71","author":"Hirsch","year":"2013","journal-title":"Magn. Reson. Med."},{"key":"10.1016\/j.media.2026.104317_bib14","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.jmr.2014.11.009","article-title":"Tabletop magnetic resonance elastography for the measurement of viscoelastic parameters of small tissue samples","volume":"251","author":"Ipek-Ugay","year":"2015","journal-title":"J. Magn. Reson."},{"key":"10.1016\/j.media.2026.104317_bib15","article-title":"Rapid stiffness mapping in soft biologic tissues with micrometer resolution using optical multifrequency time-harmonic elastography","volume":"12","author":"Jordan","year":"2024","journal-title":"Adv. Sci."},{"key":"10.1016\/j.media.2026.104317_bib16","doi-asserted-by":"crossref","first-page":"1435","DOI":"10.1002\/mrm.29066","article-title":"Microscopic multifrequency mr elastography for mapping viscoelasticity in zebrafish","volume":"87","author":"Jordan","year":"2021","journal-title":"Magn. Reson. Med."},{"key":"10.1016\/j.media.2026.104317_bib17","doi-asserted-by":"crossref","DOI":"10.7717\/peerj-cs.951","article-title":"Deep learning methods for inverse problems","volume":"8","author":"Kamyab","year":"2022","journal-title":"PeerJ Comput. Sci."},{"key":"10.1016\/j.media.2026.104317_bib18","series-title":"Medical Image Computing and Computer Assisted Intervention \u2013 MICCAI 2025","first-page":"381","article-title":"Physics-informed neural operators for tissue elasticity reconstruction","author":"Kim","year":"2025"},{"key":"10.1016\/j.media.2026.104317_bib19","doi-asserted-by":"crossref","DOI":"10.1038\/s41598-024-79991-y","article-title":"Multimodal assessment of brain stiffness variation in healthy subjects using magnetic resonance elastography and ultrasound time-harmonic elastography","volume":"14","author":"Klemmer Chand\u00eda","year":"2024","journal-title":"Sci. Rep."},{"key":"10.1016\/j.media.2026.104317_bib20","series-title":"Proceedings of 1st International Conference on Image Processing","first-page":"36","article-title":"Local multiscale frequency and bandwidth estimation","author":"Knutsson","year":"1994"},{"key":"10.1016\/j.media.2026.104317_bib21","doi-asserted-by":"crossref","DOI":"10.1016\/j.media.2025.103457","article-title":"Measurement of biomechanical properties of transversely isotropic biological tissue using traveling wave expansion","volume":"101","author":"Ma","year":"2025","journal-title":"Med. Image Anal."},{"issue":"9","key":"10.1016\/j.media.2026.104317_bib22","doi-asserted-by":"crossref","first-page":"2631","DOI":"10.1109\/TMI.2023.3261346","article-title":"MR Elastography with optimization-based phase unwrapping and traveling wave expansion-based neural network (TWENN)","volume":"42","author":"Ma","year":"2023","journal-title":"IEEE Trans. Med. Imaging"},{"key":"10.1016\/j.media.2026.104317_bib23","doi-asserted-by":"crossref","first-page":"2377","DOI":"10.1002\/mrm.28627","article-title":"MR elastography: principles, guidelines, and terminology","volume":"85","author":"Manduca","year":"2020","journal-title":"Magn. Reson. Med."},{"key":"10.1016\/j.media.2026.104317_bib24","unstructured":"Meinert, N., Lavin, A., 2021. Multivariate deep evidential regression. arXiv doi: 10.48550\/ARXIV.2104.06135."},{"key":"10.1016\/j.media.2026.104317_bib25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.pnmrs.2024.05.002","article-title":"Magnetic resonance elastography in a nutshell: tomographic imaging of soft tissue viscoelasticity for detecting and staging disease with a focus on inflammation","volume":"144\u2013145","author":"Meyer","year":"2024","journal-title":"Prog. Nucl. Magn. Reson. Spectrosc."},{"key":"10.1016\/j.media.2026.104317_bib26","doi-asserted-by":"crossref","first-page":"1840","DOI":"10.1002\/mrm.29320","article-title":"Comparison of inversion methods in MR elastography: an open-access pipeline for processing multifrequency shear-wave data and demonstration in a phantom, human kidneys, and brain","volume":"88","author":"Meyer","year":"2022","journal-title":"Magn. Reson. Med."},{"key":"10.1016\/j.media.2026.104317_bib27","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1016\/j.echo.2024.11.009","article-title":"Cardiac elastography with external vibration for quantification of diastolic myocardial stiffness","volume":"38","author":"Meyer","year":"2025","journal-title":"J. Am. Soc. Echocardiogr."},{"key":"10.1016\/j.media.2026.104317_bib28","doi-asserted-by":"crossref","first-page":"1268","DOI":"10.1002\/jmri.25868","article-title":"Magnetic resonance elastography is as accurate as liver biopsy for liver fibrosis staging","volume":"47","author":"Morisaka","year":"2017","journal-title":"J. Magn. Reson. Imaging"},{"key":"10.1016\/j.media.2026.104317_bib29","doi-asserted-by":"crossref","first-page":"502","DOI":"10.1097\/RLI.0000000000000862","article-title":"Liquid-liver phantom: mimicking the viscoelastic dispersion of human liver for ultrasound- and MRI-based elastography","volume":"57","author":"Morr","year":"2022","journal-title":"Invest. Radiol."},{"key":"10.1016\/j.media.2026.104317_bib30","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1002\/mrm.28247","article-title":"An analytical solution to the dispersion-by-inversion problem in magnetic resonance elastography","volume":"84","author":"Mura","year":"2020","journal-title":"Magn. Reson. Med."},{"key":"10.1016\/j.media.2026.104317_bib31","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1002\/mrm.27019","article-title":"Artificial neural networks for stiffness estimation in magnetic resonance elastography","volume":"80","author":"Murphy","year":"2017","journal-title":"Magn. Reson. Med."},{"key":"10.1016\/j.media.2026.104317_bib32","doi-asserted-by":"crossref","first-page":"1854","DOI":"10.1126\/science.7569924","article-title":"Magnetic resonance elastography by direct visualization of propagating acoustic strain waves","volume":"269","author":"Muthupillai","year":"1995","journal-title":"Science"},{"key":"10.1016\/j.media.2026.104317_bib33","series-title":"Medical Image Computing and Computer Assisted Intervention \u2013 MICCAI 2023","first-page":"333","article-title":"Physics-informed neural networks for tissue elasticity reconstruction in magnetic resonance elastography","author":"Ragoza","year":"2023"},{"key":"10.1016\/j.media.2026.104317_bib34","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1038\/s42254-022-00543-2","article-title":"Magnetic resonance elastography from fundamental Softtissue mechanics to diagnostic imaging","volume":"5","author":"Sack","year":"2022","journal-title":"Nat. Rev. Phys."},{"key":"10.1016\/j.media.2026.104317_bib35","doi-asserted-by":"crossref","first-page":"5672","DOI":"10.1039\/c3sm50552a","article-title":"Structure-sensitive elastography: on the viscoelastic powerlaw behavior of in vivo human tissue in health and disease","volume":"9","author":"Sack","year":"2013","journal-title":"Soft Matter"},{"key":"10.1016\/j.media.2026.104317_bib36","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1097\/RLI.0000000000001231","article-title":"Technical recommendation on multi-driver multifrequency MR Elastography for tomographic mapping of abdominal stiffness with a focus on the pancreas and pancreatic ductal adenocarcinoma","volume":"61","author":"Schattenfroh","year":"2025","journal-title":"Invest. Radiol."},{"key":"10.1016\/j.media.2026.104317_bib37","doi-asserted-by":"crossref","DOI":"10.1016\/j.media.2020.101710","article-title":"Artificial neural networks for magnetic resonance elastography stiffness estimation in inhomogeneous materials","volume":"63","author":"Scott","year":"2020","journal-title":"Med. Image Anal."},{"key":"10.1016\/j.media.2026.104317_bib38","doi-asserted-by":"crossref","first-page":"916","DOI":"10.1002\/mrm.29226","article-title":"Impact of material homogeneity assumption on cortical stiffness estimates by MR elastography","volume":"88","author":"Scott","year":"2022","journal-title":"Magn. Reson. Med."},{"key":"10.1016\/j.media.2026.104317_bib39","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.media.2016.01.001","article-title":"Tomoelastography by multifrequency wave number recovery from time-harmonic propagating shear waves","volume":"30","author":"Tzsch\u00e4tzsch","year":"2016","journal-title":"Med. Image Anal."},{"key":"10.1016\/j.media.2026.104317_bib40","doi-asserted-by":"crossref","DOI":"10.1038\/s41524-024-01473-6","article-title":"Outlier-detection for reactive machine learned potential energy surfaces","volume":"11","author":"Vazquez-Salazar","year":"2025","journal-title":"NPJ Comput. Mater."}],"container-title":["Medical Image Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1361841526003865?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1361841526003865?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,11,6]],"date-time":"2026-11-06T03:08:01Z","timestamp":1793934481000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S1361841526003865"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2027,1]]},"references-count":40,"alternative-id":["S1361841526003865"],"URL":"https:\/\/doi.org\/10.1016\/j.media.2026.104317","relation":{},"ISSN":["1361-8415"],"issn-type":[{"value":"1361-8415","type":"print"}],"subject":[],"published":{"date-parts":[[2027,1]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Multifrequency neural network-based wave inversion in MR elastography with uncertainty quantification","name":"articletitle","label":"Article Title"},{"value":"Medical Image Analysis","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.media.2026.104317","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 The Authors. Published by Elsevier B.V.","name":"copyright","label":"Copyright"}],"article-number":"104317"}}