{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T08:01:21Z","timestamp":1791446481717,"version":"4.3.3"},"reference-count":33,"publisher":"Wiley","issue":"7","license":[{"start":{"date-parts":[[2026,6,25]],"date-time":"2026-06-25T00:00:00Z","timestamp":1782345600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2026,6,25]],"date-time":"2026-06-25T00:00:00Z","timestamp":1782345600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52275015"],"award-info":[{"award-number":["52275015"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Numer Methods Biomed Eng"],"published-print":{"date-parts":[[2026,7]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>\n                    In recent years, flexible needles have garnered significant research attention due to their outstanding steerable flexibility. Path planning of flexible needles is key to achieving intelligent navigation. However, existing path\u2010planning methods for flexible needles are often trapped in local optima, failing to identify the globally optimal insertion trajectory. In order to solve this problem, this paper proposes a novel hybrid path planning algorithm by combining particle swarm optimization (PSO) and simulated annealing (SA) mechanism to enhance the global search capabilities. By integrating the probabilistic judgment and the annealing mechanism of SA, the particle diffusion mechanism can be changed and the inertia weight of PSO can be dynamically adjusted, which effectively reduces the risk of premature convergence of the algorithm. Simulations were conducted in a prostate\u2010anatomy\u2010mimicking environment, and the results demonstrated that the proposed algorithm can achieve superior planning outcomes compared to the traditional PSO. To verify the effectiveness of the proposed algorithm, five trials of insertion experiments were performed for each of two targets. For target\n                    <jats:sub>1<\/jats:sub>\n                    , the experimental results showed a mean error of 1.25\u2009mm, a root mean square error of 1.43\u2009mm, and a maximum error of 2.22\u2009mm. For target\n                    <jats:sub>2<\/jats:sub>\n                    , the corresponding errors were 1.21\u2009mm, 1.40\u2009mm, and 2.19\u2009mm, respectively. This level of accuracy met the requirements of general clinical procedures and supports the feasibility and accuracy of the proposed algorithm. This work advanced the clinical applications of the flexible needle and enhanced the development of intelligent navigation systems.\n                  <\/jats:p>","DOI":"10.1002\/cnm.70194","type":"journal-article","created":{"date-parts":[[2026,6,26]],"date-time":"2026-06-26T05:55:23Z","timestamp":1782453323000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Path Planning of Flexible Needle Based on Improved Particle Swarm Optimization Algorithm"],"prefix":"10.1002","volume":"42","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2984-3795","authenticated-orcid":false,"given":"Yan\u2010Jiang","family":"Zhao","sequence":"first","affiliation":[{"name":"Key Laboratory of Advanced Manufacturing and Intelligent Technology, Ministry of Education Harbin University of Science and Technology  Harbin Heilongjiang China"},{"name":"Weihai Research Institute Harbin University of Science and Technology  Weihai Shandong 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