{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,19]],"date-time":"2026-09-19T10:41:42Z","timestamp":1789814502704,"version":"4.0.1"},"reference-count":56,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2025,12,26]],"date-time":"2025-12-26T00:00:00Z","timestamp":1766707200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,12,26]],"date-time":"2025-12-26T00:00:00Z","timestamp":1766707200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/501100001711","name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","doi-asserted-by":"publisher","award":["212855"],"award-info":[{"award-number":["212855"]}],"id":[{"id":"10.13039\/501100001711","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":[[2026,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:sec>\n                    <jats:title>Background<\/jats:title>\n                    <jats:p>Deformable image registration (DIR) is a crucial tool in radiotherapy for analyzing anatomical changes and motion patterns. Current DIR implementations rely on discrete volumetric motion representation, which often leads to compromised accuracy and uncertainty when handling significant anatomical changes and sliding boundaries. This limitation affects the reliability of subsequent contour propagation and dose accumulation procedures, particularly in regions with complex anatomical interfaces such as the lung\u2010chest wall\u00a0boundary.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Purpose<\/jats:title>\n                    <jats:p>Given that organ motion is inherently a continuous process in both space and time, we aimed to develop a model that preserves these fundamental properties. Drawing inspiration from fluid mechanics, we propose a novel approach using implicit neural representation (INR) for continuous modeling of patient anatomical motion. This approach ensures spatial and temporal continuity while effectively unifying Eulerian and Lagrangian specifications to enable natural continuous motion modeling and frame interpolation. The integration of these specifications provides a more comprehensive understanding of anatomical deformation\u00a0patterns.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Methods<\/jats:title>\n                    <jats:p>We propose an INR\u2010based approach modeling motion continuously in both space and time, named continues\u2010sPatial\u2010temporal deformable image registration (CPT\u2010DIR). This method fits a multilayer perception network to map the 3D coordinate , to its corresponding velocity vector . Displacement vectors  are then calculated by integrating velocity vectors over time using an Euler method numerical scheme. The above spatial and temporal continuous motion design also enables continuous frame interpolation (CPT\u2010Interp). The DIR's and interpolation's performance were tested on the DIR\u2010Lab dataset and the Abdominal\u2010DIR\u2010QA dataset, using metrics of landmark accuracy (target registration error), contour conformity (Dice), and image similarity (mean absolute error).<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>CPT\u2010DIR clearly reduced landmark TRE from  to  mm over DIRLab and from  to  mm over the challenging Abdominal\u2010DIR\u2010QA dataset, surpassing B\u2010spline results across all cases. The whole\u2010body region MAE improved from  to  HU for DIRLab, and from  to  HU for Abdominal\u2010DIR\u2010QA. In the challenging sliding boundary region, CPT\u2010DIR demonstrated superior performance compared to B\u2010spline, reducing ribcage MAE from  HU (unregistered) to  HU and improving Dice coefficients from  to . The training\u2010free CPT\u2010Interp method enhanced previous deep learning\u2010based approaches, improving upon UVI\u2010Net with reduced MAE ( vs. ) and increased peak signal\u2010to\u2010noise ratio (PSNR) ( vs. ), while eliminating training dataset dependencies. Both CPT\u2010DIR and CPT\u2010Interp achieved substantial computational efficiency, completing operations in under 3 s compared to several minutes required by conventional B\u2010spline\u00a0methods.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Conclusion<\/jats:title>\n                    <jats:p>By leveraging the continuous representations, the CPT\u2010DIR method enhances registration and interpolation accuracy, automation, and speed. The method achieves high accuracy on intra\u2010fractional thoracic datasets and demonstrates improved performance over conventional methods in more challenging inter\u2010fractional abdominal registration scenarios, highlighting its potential for robust applications in radiotherapy. The improved efficiency and accuracy of CPT\u2010DIR make it particularly suitable for real\u2010time adaptive radiotherapy\u00a0applications.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1002\/mp.70248","type":"journal-article","created":{"date-parts":[[2025,12,26]],"date-time":"2025-12-26T15:50:16Z","timestamp":1766764216000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Continuous sPatial\u2010temporal deformable image registration and 4D frame interpolation"],"prefix":"10.1002","volume":"53","author":[{"given":"Xia","family":"Li","sequence":"first","affiliation":[{"name":"Center for Proton Therapy Paul Scherrer Institut Villigen Switzerland"},{"name":"Department of Computer Science ETH Z\u00fcrich Z\u00fcrich Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Runzhao","family":"Yang","sequence":"additional","affiliation":[{"name":"Department of Computer Science ETH Z\u00fcrich Z\u00fcrich Switzerland"},{"name":"Department of Automation Tsinghua Univeristy Beijing China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Muheng","family":"Li","sequence":"additional","affiliation":[{"name":"Center for Proton Therapy Paul Scherrer Institut Villigen Switzerland"},{"name":"Department of Physics ETH Z\u00fcrich Z\u00fcrich Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiangtai","family":"Li","sequence":"additional","affiliation":[{"name":"S\u2010Lab Nanyang Technological University Singapore Singapore"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Antony J.","family":"Lomax","sequence":"additional","affiliation":[{"name":"Center for Proton Therapy Paul Scherrer Institut Villigen Switzerland"},{"name":"Department of Physics ETH Z\u00fcrich Z\u00fcrich Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Joachim M.","family":"Buhmann","sequence":"additional","affiliation":[{"name":"Department of Computer Science ETH Z\u00fcrich Z\u00fcrich Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ye","family":"Zhang","sequence":"additional","affiliation":[{"name":"Center for Proton Therapy Paul Scherrer Institut Villigen Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2025,12,26]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/S1053-4296(95)80004-2"},{"key":"e_1_2_8_3_1","doi-asserted-by":"publisher","DOI":"10.3857\/roj.2017.00325"},{"key":"e_1_2_8_4_1","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6560\/ad0d8a"},{"key":"e_1_2_8_5_1","doi-asserted-by":"publisher","DOI":"10.1080\/0284186X.2019.1620331"},{"key":"e_1_2_8_6_1","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/57\/7\/1779"},{"key":"e_1_2_8_7_1","doi-asserted-by":"crossref","unstructured":"MokTC ChungAC.Large deformation diffeomorphic image registration with laplacian pyramid networks. 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