{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:06:43Z","timestamp":1760144803037,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2024,5,20]],"date-time":"2024-05-20T00:00:00Z","timestamp":1716163200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Bioengineering"],"abstract":"<jats:p>Background: The mechanical characteristics of bone are crucial for comprehending its functionality and response to different load conditions, which are essential for advancing medical treatments, implants, and prosthetics. By employing mathematical modeling to analyze the mechanical properties of bone, we can assess stress and deformation under both normal and abnormal conditions. This analysis offers valuable perspectives on potential fracture risks, the effects of diseases, and the effectiveness of various treatments. Therefore, researchers are attempting to find an adequate mathematical description of the mechanical properties of bone. Methods: Experimental stress\u2013stretch external loading curves were obtained through investigations of canine vertebrae. The obtained experimental curves were fitted using the SciPy Python library with a slightly modified logistic function (logistic function plus additional const). Results: The resulting coefficient of determination\u00a0R2\u00a0(R squared) for most curves was near 0.999, indicating that an appropriate fitting function was selected for the description of the experimental stress\u2013stretch curves. Conclusions: The stress\u2013stretch behavior of canine vertebrae can be described using a logistic function modified by adding additional parameters for the most accurate fitting results.<\/jats:p>","DOI":"10.3390\/bioengineering11050516","type":"journal-article","created":{"date-parts":[[2024,5,20]],"date-time":"2024-05-20T08:20:31Z","timestamp":1716193231000},"page":"516","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Quantitative Analysis of Stress\u2013Stretch Curves in Canine Lumbar Vertebrae Using Modified Logistic Functions"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3258-6985","authenticated-orcid":false,"given":"Ernest","family":"Kostenko","sequence":"first","affiliation":[{"name":"Department of Veterinary, Faculty of Agrotechnologies, Vilniaus Kolegija\/Higher Education Institution, 08105 Vilnius, Lithuania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1228-9433","authenticated-orcid":false,"given":"Rimantas","family":"Stonkus","sequence":"additional","affiliation":[{"name":"Department of Mechatronics, Robotics and Digital Manufacturing, Vilnius Gediminas Technical University, 10105 Vilnius, Lithuania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5471-0046","authenticated-orcid":false,"given":"Jakov","family":"\u0160engaut","sequence":"additional","affiliation":[{"name":"Jakov\u2019s Veterinary Centre, 03147 Vilnius, Lithuania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2003-9159","authenticated-orcid":false,"given":"Nikolaj","family":"Vi\u0161niakov","sequence":"additional","affiliation":[{"name":"Institute of Mechanical Science, Vilnius Gediminas Technical University, 10105 Vilnius, Lithuania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8431-2292","authenticated-orcid":false,"given":"Algirdas","family":"Maknickas","sequence":"additional","affiliation":[{"name":"Institute of Mechanical Science, Vilnius Gediminas Technical University, 10105 Vilnius, Lithuania"},{"name":"Department of Biomechanical Engineering, Vilnius Gediminas Technical University, 10105 Vilnius, Lithuania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,5,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"e15805","DOI":"10.7717\/peerj.15805","article-title":"Development and validation of lumbar spine finite element model","volume":"11","author":"Wiczenbach","year":"2023","journal-title":"PeerJ."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1789","DOI":"10.1097\/01.brs.0000225993.57349.df","article-title":"Nonlinear finite element model predicts vertebral bone strength and fracture site","volume":"31","author":"Imai","year":"2006","journal-title":"Spine"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"E1291","DOI":"10.1097\/BRS.0000000000000540","article-title":"Specimen-specific nonlinear finite element modeling to predict vertebrae fracture loads after vertebroplasty","volume":"39","author":"Matsuura","year":"2014","journal-title":"Spine"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1016\/S1350-4533(01)00076-5","article-title":"Stress analysis of the disc adjacent to interbody fusion in lumbar spine","volume":"23","author":"Chen","year":"2001","journal-title":"Med. 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