{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T20:58:10Z","timestamp":1774558690908,"version":"3.50.1"},"reference-count":57,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2021,12,13]],"date-time":"2021-12-13T00:00:00Z","timestamp":1639353600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002261","name":"Russian Foundation for Basic Research","doi-asserted-by":"publisher","award":["20-08-00818"],"award-info":[{"award-number":["20-08-00818"]}],"id":[{"id":"10.13039\/501100002261","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Institute of Strength Physics and Materials Science","award":["FWRW-2021-009"],"award-info":[{"award-number":["FWRW-2021-009"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>Arthritis is a degenerative disease that primarily affects the cartilage and meniscus of the knee joint. External acoustic stimulation is used to treat this disease. This article presents a numerical model of the knee joint aimed at the computer-aided study of the regenerative effects of shockwave treatment. The presented model was verified and validated. A numerical analysis of the conditions for the regeneration of the tissues of the knee joint under shockwave action was conducted. The results allow us to conclude that to obtain the conditions required for the regeneration of cartilage tissues and meniscus (compressive stresses above the threshold value of 0.15 MPa to start the process of chondrogenesis; distortional strains above the threshold value of 0.05% characterized by the beginning of the differentiation of the tissues in large volumes; fluid pressure corresponding to the optimal level of 68 kPa to transfer tissue cells in large volumes), the energy flux density of therapeutic shockwave loading should exceed 0.3 mJ\/mm2.<\/jats:p>","DOI":"10.3390\/ma14247678","type":"journal-article","created":{"date-parts":[[2021,12,14]],"date-time":"2021-12-14T01:20:41Z","timestamp":1639444841000},"page":"7678","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Numerical Modeling of Shockwave Treatment of Knee Joint"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3346-367X","authenticated-orcid":false,"given":"Galina","family":"Eremina","sequence":"first","affiliation":[{"name":"Institute of Strength Physics and Materials Science of Siberian Branch Russian Academy of Sciences, 2\/4, Pr. Akademicheskii, 634055 Tomsk, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0213-1701","authenticated-orcid":false,"given":"Alexey","family":"Smolin","sequence":"additional","affiliation":[{"name":"Institute of Strength Physics and Materials Science of Siberian Branch Russian Academy of Sciences, 2\/4, Pr. 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