{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T00:52:28Z","timestamp":1791247948793,"version":"4.1.0"},"reference-count":75,"publisher":"Springer Science and Business Media LLC","license":[{"start":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T00:00:00Z","timestamp":1791158400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T00:00:00Z","timestamp":1791158400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Med Biol Eng Comput"],"DOI":"10.1007\/s11517-026-03692-z","type":"journal-article","created":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T07:20:58Z","timestamp":1791184858000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Path-dependent viscoelastic\u2013hyperelastic response of brain tissue under multistage shear loading"],"prefix":"10.1007","author":[{"given":"Hadi","family":"Nosrati","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mehdi","family":"Shafieian","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kurosh","family":"Darvish","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,10,5]]},"reference":[{"issue":"4","key":"3692_CR1","doi-asserted-by":"publisher","first-page":"216","DOI":"10.1016\/j.cjtee.2020.06.001","volume":"23","author":"F-R Chang","year":"2020","unstructured":"Chang F-R, Huang H-L, Schwebel DC, Chan AH, Hu G-Q (2020) Global road traffic injury statistics: challenges, mechanisms and solutions. Chin J Traumatol 23(4):216\u2013218. https:\/\/doi.org\/10.1016\/j.cjtee.2020.06.001","journal-title":"Chin J Traumatol"},{"issue":"19","key":"3692_CR2","doi-asserted-by":"publisher","DOI":"10.3390\/ijerph191912112","volume":"19","author":"PK Leszczy\u0144ski","year":"2022","unstructured":"Leszczy\u0144ski PK, Kalinowska J, Mitura K, Sholokhova D (2022) Injuries to users of single-track vehicles. Int J Environ Res Public Health 19(19):12112. https:\/\/doi.org\/10.3390\/ijerph191912112","journal-title":"Int J Environ Res Public Health"},{"key":"3692_CR3","doi-asserted-by":"publisher","DOI":"10.1016\/j.cobme.2022.100422","volume":"24","author":"X Zhan","year":"2022","unstructured":"Zhan X, Oeur A, Liu Y, Zeineh MM, Grant GA, Margulies SS, Camarillo DB (2022) Translational models of mild traumatic brain injury tissue biomechanics. Curr Opin Biomed Eng 24:100422. https:\/\/doi.org\/10.1016\/j.cobme.2022.100422","journal-title":"Curr Opin Biomed Eng"},{"issue":"2\u20133","key":"3692_CR4","doi-asserted-by":"publisher","first-page":"144","DOI":"10.1179\/016164101101198488","volume":"23","author":"L Zhang","year":"2001","unstructured":"Zhang L, Yang KH, King AI (2001) Biomechanics of neurotrauma. Neurol Res 23(2\u20133):144\u2013156. https:\/\/doi.org\/10.1179\/016164101101198488","journal-title":"Neurol Res"},{"key":"3692_CR5","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1007\/978-1-4939-3816-2_17","volume":"1462","author":"DK Cullen","year":"2016","unstructured":"Cullen DK, Harris JP, Browne KD, Wolf JA, Duda JE, Meaney DF, Margulies SS, Smith DH (2016) A porcine model of traumatic brain injury via head rotational acceleration. Methods Mol Biol 1462:289\u2013324. https:\/\/doi.org\/10.1007\/978-1-4939-3816-2_17","journal-title":"Methods Mol Biol"},{"issue":"3","key":"3692_CR6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1097\/00002727-200011000-00002","volume":"23","author":"AE Davis","year":"2000","unstructured":"Davis AE (2000) Mechanisms of traumatic brain injury: biomechanical, structural and cellular considerations. Crit Care Nurs Q 23(3):1\u201313. https:\/\/doi.org\/10.1097\/00002727-200011000-00002","journal-title":"Crit Care Nurs Q"},{"key":"3692_CR7","unstructured":"Peerless S, Rewcastle N (1967) Shear injuries of the brain. Canadian Med Assoc J 96(10):577\u2013582. https:\/\/pmc.ncbi.nlm.nih.gov\/articles\/PMC1936040\/"},{"issue":"4","key":"3692_CR8","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1001\/jama.1968.03140170001001","volume":"204","author":"AK Ommaya","year":"1968","unstructured":"Ommaya AK, Faas F, Yarnell P (1968) Whiplash injury and brain damage: an experimental study. JAMA 204(4):285\u2013289. https:\/\/doi.org\/10.1001\/jama.1968.03140170001001","journal-title":"JAMA"},{"issue":"9","key":"3692_CR9","doi-asserted-by":"publisher","first-page":"1941","DOI":"10.1007\/s10439-018-02148-2","volume":"47","author":"TC Harris","year":"2019","unstructured":"Harris TC, De Rooij R, Kuhl E (2019) The shrinking brain: cerebral atrophy following traumatic brain injury. Ann Biomed Eng 47(9):1941\u20131959. https:\/\/doi.org\/10.1007\/s10439-018-02148-2","journal-title":"Ann Biomed Eng"},{"issue":"13","key":"3692_CR10","doi-asserted-by":"publisher","first-page":"1879","DOI":"10.1089\/neu.2020.7445","volume":"38","author":"T Wu","year":"2021","unstructured":"Wu T, Hajiaghamemar M, Giudice JS, Alshareef A, Margulies SS, Panzer MB (2021) Evaluation of tissue-level brain injury metrics using species-specific simulations. J Neurotrauma 38(13):1879\u20131888. https:\/\/doi.org\/10.1089\/neu.2020.7445","journal-title":"J Neurotrauma"},{"issue":"3","key":"3692_CR11","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1089\/089771504322972095","volume":"21","author":"R Raghupathi","year":"2004","unstructured":"Raghupathi R, Mehr MF, Helfaer MA, Margulies SS (2004) Traumatic axonal injury is exacerbated following repetitive closed head injury in the neonatal pig. J Neurotrauma 21(3):307\u2013316. https:\/\/doi.org\/10.1089\/089771504322972095","journal-title":"J Neurotrauma"},{"issue":"1","key":"3692_CR12","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1016\/j.jneumeth.2011.09.003","volume":"203","author":"MJ Kane","year":"2012","unstructured":"Kane MJ, Angoa-P\u00e9rez M, Briggs DI, Viano DC, Kreipke CW, Kuhn DM (2012) A mouse model of human repetitive mild traumatic brain injury. J Neurosci Methods 203(1):41\u201349. https:\/\/doi.org\/10.1016\/j.jneumeth.2011.09.003","journal-title":"J Neurosci Methods"},{"issue":"11","key":"3692_CR13","doi-asserted-by":"publisher","first-page":"2578","DOI":"10.1016\/j.jbiomech.2014.06.002","volume":"47","author":"R Anderson","year":"2014","unstructured":"Anderson R, Sandoz B, Dutschke J, Finnie J, Turner R, Blumbergs P, Manavis J, Vink R (2014) Biomechanical studies in an ovine model of non-accidental head injury. J Biomech 47(11):2578\u20132583. https:\/\/doi.org\/10.1016\/j.jbiomech.2014.06.002","journal-title":"J Biomech"},{"issue":"9","key":"3692_CR14","doi-asserted-by":"publisher","first-page":"912","DOI":"10.1212\/wnl.30.9.912","volume":"30","author":"JF Annegers","year":"1980","unstructured":"Annegers JF, Grabow JD, Kurland LT, Laws ER Jr (1980) The incidence, causes, and secular trends of head trauma in Olmsted County, Minnesota, 1935\u20131974. Neurology 30(9):912\u2013919. https:\/\/doi.org\/10.1212\/wnl.30.9.912","journal-title":"Neurology"},{"issue":"2","key":"3692_CR15","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1136\/jnnp-2012-303938","volume":"84","author":"K Dams-O'Connor","year":"2013","unstructured":"Dams-O\u2019Connor K, Gibbons LE, Bowen JD, McCurry SM, Larson EB, Crane PK (2013) Risk for late-life re-injury, dementia and death among individuals with traumatic brain injury: a population-based study. J Neurol Neurosurg Psychiatry 84(2):177\u2013182. https:\/\/doi.org\/10.1136\/jnnp-2012-303938","journal-title":"J Neurol Neurosurg Psychiatry"},{"issue":"7","key":"3692_CR16","doi-asserted-by":"publisher","first-page":"1075","DOI":"10.1177\/0363546507299239","volume":"35","author":"BP Boden","year":"2007","unstructured":"Boden BP, Tacchetti RL, Cantu RC, Knowles SB, Mueller FO (2007) Catastrophic head injuries in high school and college football players. Am J Sports Med 35(7):1075\u20131081. https:\/\/doi.org\/10.1177\/0363546507299239","journal-title":"Am J Sports Med"},{"issue":"1","key":"3692_CR17","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1146\/annurev-pathol-012615-044116","volume":"11","author":"J Hay","year":"2016","unstructured":"Hay J, Johnson VE, Smith DH, Stewart W (2016) Chronic traumatic encephalopathy: the neuropathological legacy of traumatic brain injury. Annu Rev Pathol Mech Dis 11(1):21\u201345. https:\/\/doi.org\/10.1146\/annurev-pathol-012615-044116","journal-title":"Annu Rev Pathol Mech Dis"},{"issue":"1","key":"3692_CR18","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1007\/s00401-015-1515-z","volume":"131","author":"AC McKee","year":"2016","unstructured":"McKee AC, Cairns NJ, Dickson DW, Folkerth RD, Keene CD, Litvan I, Perl DP, Stein TD, Vonsattel J-P, Stewart W, Tripodis Y, Crary JF, Bieniek KF, Dams-O\u2019Connor K, Alvarez VE, Gordon WA (2016) The first NINDS\/NIBIB consensus meeting to define neuropathological criteria for the diagnosis of chronic traumatic encephalopathy. Acta Neuropathol 131(1):75\u201386. https:\/\/doi.org\/10.1007\/s00401-015-1515-z","journal-title":"Acta Neuropathol"},{"issue":"1","key":"3692_CR19","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1093\/brain\/aws307","volume":"136","author":"AC McKee","year":"2013","unstructured":"McKee AC, Stein TD, Nowinski CJ, Stern RA, Daneshvar DH, Alvarez VE, Lee H-S, Hall G, Wojtowicz SM, Baugh CM (2013) The spectrum of disease in chronic traumatic encephalopathy. Brain 136(1):43\u201364. https:\/\/doi.org\/10.1093\/brain\/aws307","journal-title":"Brain"},{"issue":"1","key":"3692_CR20","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1152\/jn.00898.2017","volume":"120","author":"ME Huibregtse","year":"2018","unstructured":"Huibregtse ME (2018) Improving the translational potential of rodent models to study the behavioral and pathophysiological effects of repetitive mild traumatic brain injury. J Neurophysiol 120(1):1\u20133. https:\/\/doi.org\/10.1152\/jn.00898.2017","journal-title":"J Neurophysiol"},{"key":"3692_CR21","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1016\/j.pharmthera.2019.02.016","volume":"198","author":"WS Hoogenboom","year":"2019","unstructured":"Hoogenboom WS, Branch CA, Lipton ML (2019) Animal models of closed-skull, repetitive mild traumatic brain injury. Pharmacol Ther 198:109\u2013122. https:\/\/doi.org\/10.1016\/j.pharmthera.2019.02.016","journal-title":"Pharmacol Ther"},{"issue":"8","key":"3692_CR22","doi-asserted-by":"publisher","first-page":"1777","DOI":"10.1007\/s10439-025-03765-4","volume":"53","author":"H Nosrati","year":"2025","unstructured":"Nosrati H, Shafieian M, Abolfathi N (2025) A comprehensive analysis of inconsistencies in the brain\u2019s conventional ex vivo mechanical experiments. Ann Biomed Eng 53(8):1777\u20131796. https:\/\/doi.org\/10.1007\/s10439-025-03765-4","journal-title":"Ann Biomed Eng"},{"issue":"12","key":"3692_CR23","doi-asserted-by":"publisher","first-page":"2592","DOI":"10.1016\/j.jmps.2006.05.004","volume":"54","author":"G Franceschini","year":"2006","unstructured":"Franceschini G, Bigoni D, Regitnig P, Holzapfel GA (2006) Brain tissue deforms similarly to filled elastomers and follows consolidation theory. J Mech Phys Solids 54(12):2592\u20132620. https:\/\/doi.org\/10.1016\/j.jmps.2006.05.004","journal-title":"J Mech Phys Solids"},{"key":"3692_CR24","doi-asserted-by":"publisher","DOI":"10.3389\/fmech.2021.708350","volume":"7","author":"A Greiner","year":"2021","unstructured":"Greiner A, Reiter N, Paulsen F, Holzapfel GA, Steinmann P, Comellas E, Budday S (2021) Poro-viscoelastic effects during biomechanical testing of human brain tissue. Front Mech Eng 7:708350. https:\/\/doi.org\/10.3389\/fmech.2021.708350","journal-title":"Front Mech Eng"},{"issue":"6","key":"3692_CR25","doi-asserted-by":"publisher","DOI":"10.1115\/1.4056480","volume":"145","author":"GM Boiczyk","year":"2023","unstructured":"Boiczyk GM, Pearson N, Kote VB, Sundaramurthy A, Subramaniam DR, Rubio JE, Unnikrishnan G, Reifman J, Monson KL (2023) Rate- and region-dependent mechanical properties of G\u00f6ttingen minipig brain tissue in simple shear and unconfined compression. J Biomech Eng 145(6):061004. https:\/\/doi.org\/10.1115\/1.4056480","journal-title":"J Biomech Eng"},{"issue":"3","key":"3692_CR26","doi-asserted-by":"publisher","first-page":"907","DOI":"10.1007\/s10237-016-0860-8","volume":"16","author":"AE Forte","year":"2017","unstructured":"Forte AE, Gentleman SM, Dini D (2017) On the characterization of the heterogeneous mechanical response of human brain tissue. Biomech Model Mechanobiol 16(3):907\u2013920. https:\/\/doi.org\/10.1007\/s10237-016-0860-8","journal-title":"Biomech Model Mechanobiol"},{"issue":"5","key":"3692_CR27","doi-asserted-by":"publisher","first-page":"1729","DOI":"10.1007\/s10237-023-01739-w","volume":"22","author":"J Hinrichsen","year":"2023","unstructured":"Hinrichsen J, Reiter N, Br\u00e4uer L, Paulsen F, Kaessmair S, Budday S (2023) Inverse identification of region-specific hyperelastic material parameters for human brain tissue. Biomech Model Mechanobiol 22(5):1729\u20131749. https:\/\/doi.org\/10.1007\/s10237-023-01739-w","journal-title":"Biomech Model Mechanobiol"},{"key":"3692_CR28","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1016\/j.actbio.2016.10.036","volume":"48","author":"S Budday","year":"2017","unstructured":"Budday S, Sommer G, Birkl C, Langkammer C, Haybaeck J, Kohnert J, Bauer M, Paulsen F, Steinmann P, Kuhl E, Holzapfel GA (2017) Mechanical characterization of human brain tissue. Acta Biomater 48:319\u2013340. https:\/\/doi.org\/10.1016\/j.actbio.2016.10.036","journal-title":"Acta Biomater"},{"key":"3692_CR29","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1016\/j.actbio.2025.07.046","volume":"203","author":"J Hou","year":"2025","unstructured":"Hou J, Jiang K, Ramanathan A, Kumar AS, Zhang W, Zhao L, Wu T, Pidaparti R, Zhu D, Li G, Song K, Liu T, Razavi MJ, Kuhl E, Wang X (2025) Mechanical characterization of brain tissue: experimental techniques, human testing considerations, and perspectives. Acta Biomater 203:181\u2013213. https:\/\/doi.org\/10.1016\/j.actbio.2025.07.046","journal-title":"Acta Biomater"},{"key":"3692_CR30","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtherbio.2025.104292","volume":"133","author":"H Nosrati","year":"2025","unstructured":"Nosrati H, Shafieian M, Abolfathi N (2025) The importance of brain thermomechanics in clinical neurosurgery and simulations. J Therm Biol 133:104292. https:\/\/doi.org\/10.1016\/j.jtherbio.2025.104292","journal-title":"J Therm Biol"},{"key":"3692_CR31","doi-asserted-by":"publisher","first-page":"205","DOI":"10.4271\/2000-01-SC15","volume":"44","author":"MT Prange","year":"2000","unstructured":"Prange MT, Meaney DF, Margulies SS (2000) Defining brain mechanical properties: effects of region, direction, and species. Stapp Car Crash J 44:205\u2013213. https:\/\/doi.org\/10.4271\/2000-01-SC15","journal-title":"Stapp Car Crash J"},{"issue":"1","key":"3692_CR32","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1016\/j.jbiomech.2005.11.004","volume":"40","author":"S Cheng","year":"2007","unstructured":"Cheng S, Bilston LE (2007) Unconfined compression of white matter. J Biomech 40(1):117\u2013124. https:\/\/doi.org\/10.1016\/j.jbiomech.2005.11.004","journal-title":"J Biomech"},{"issue":"3","key":"3692_CR33","doi-asserted-by":"publisher","first-page":"991","DOI":"10.1007\/s10439-020-02643-5","volume":"49","author":"F Eskandari","year":"2021","unstructured":"Eskandari F, Shafieian M, Aghdam MM, Laksari K (2021) Structural anisotropy vs. mechanical anisotropy: the contribution of axonal fibers to the material properties of brain white matter. Ann Biomed Eng 49(3):991\u2013999. https:\/\/doi.org\/10.1007\/s10439-020-02643-5","journal-title":"Ann Biomed Eng"},{"issue":"1","key":"3692_CR34","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1007\/s10237-012-0387-6","volume":"12","author":"RJH Cloots","year":"2013","unstructured":"Cloots RJH, van Dommelen JAW, Kleiven S, Geers MGD (2013) Multi-scale mechanics of traumatic brain injury: predicting axonal strains from head loads. Biomech Model Mechanobiol 12(1):137\u2013150. https:\/\/doi.org\/10.1007\/s10237-012-0387-6","journal-title":"Biomech Model Mechanobiol"},{"issue":"8","key":"3692_CR35","doi-asserted-by":"publisher","first-page":"1905","DOI":"10.1016\/j.jmbbm.2011.06.007","volume":"4","author":"S Chatelin","year":"2011","unstructured":"Chatelin S, Deck C, Renard F, Kremer S, Heinrich C, Armspach J-P, Willinger R (2011) Computation of axonal elongation in head trauma finite element simulation. J Mech Behav Biomed Mater 4(8):1905\u20131919. https:\/\/doi.org\/10.1016\/j.jmbbm.2011.06.007","journal-title":"J Mech Behav Biomed Mater"},{"key":"3692_CR36","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1016\/j.jmbbm.2017.07.014","volume":"74","author":"S Budday","year":"2017","unstructured":"Budday S, Sommer G, Holzapfel GA, Steinmann P, Kuhl E (2017) Viscoelastic parameter identification of human brain tissue. J Mech Behav Biomed Mater 74:463\u2013476. https:\/\/doi.org\/10.1016\/j.jmbbm.2017.07.014","journal-title":"J Mech Behav Biomed Mater"},{"key":"3692_CR37","doi-asserted-by":"publisher","first-page":"1187","DOI":"10.1007\/s11831-019-09352-w","volume":"27","author":"S Budday","year":"2020","unstructured":"Budday S, Ovaert TC, Holzapfel GA, Steinmann P, Kuhl E (2020) Fifty shades of brain: a review on the mechanical testing and modeling of brain tissue. Arch Comput Methods Eng 27:1187\u20131230. https:\/\/doi.org\/10.1007\/s11831-019-09352-w","journal-title":"Arch Comput Methods Eng"},{"issue":"5\u20136","key":"3692_CR38","doi-asserted-by":"publisher","first-page":"255","DOI":"10.3233\/BIR-2010-0576","volume":"47","author":"S Chatelin","year":"2010","unstructured":"Chatelin S, Constantinesco A, Willinger R (2010) Fifty years of brain tissue mechanical testing: from in vitro to in vivo investigations. Biorheology 47(5\u20136):255\u2013276. https:\/\/doi.org\/10.3233\/BIR-2010-0576","journal-title":"Biorheology"},{"issue":"3","key":"3692_CR39","doi-asserted-by":"publisher","DOI":"10.1115\/1.2907746","volume":"130","author":"M Hrapko","year":"2008","unstructured":"Hrapko M, van Dommelen JAW, Peters GWM, Wismans JSHM (2008) The influence of test conditions on characterization of the mechanical properties of brain tissue. J Biomech Eng 130(3):031003. https:\/\/doi.org\/10.1115\/1.2907746","journal-title":"J Biomech Eng"},{"key":"3692_CR40","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1016\/j.jmbbm.2013.07.017","volume":"28","author":"B Rashid","year":"2013","unstructured":"Rashid B, Destrade M, Gilchrist MD (2013) Mechanical characterization of brain tissue in simple shear at dynamic strain rates. J Mech Behav Biomed Mater 28:71\u201385. https:\/\/doi.org\/10.1016\/j.jmbbm.2013.07.017","journal-title":"J Mech Behav Biomed Mater"},{"issue":"4","key":"3692_CR41","doi-asserted-by":"publisher","first-page":"423","DOI":"10.1115\/1.2798289","volume":"119","author":"BR Donnelly","year":"1997","unstructured":"Donnelly BR, Medige J (1997) Shear properties of human brain tissue. J Biomech Eng 119(4):423\u2013432. https:\/\/doi.org\/10.1115\/1.2798289","journal-title":"J Biomech Eng"},{"key":"3692_CR42","doi-asserted-by":"publisher","first-page":"54","DOI":"10.1016\/j.ijnonlinmec.2015.02.014","volume":"75","author":"M Destrade","year":"2015","unstructured":"Destrade M, Gilchrist MD, Murphy JG, Rashid B, Saccomandi G (2015) Extreme softness of brain matter in simple shear. Int J Non-Linear Mech 75:54\u201358. https:\/\/doi.org\/10.1016\/j.ijnonlinmec.2015.02.014","journal-title":"Int J Non-Linear Mech"},{"issue":"2","key":"3692_CR43","doi-asserted-by":"publisher","first-page":"244","DOI":"10.1115\/1.1449907","volume":"124","author":"MT Prange","year":"2002","unstructured":"Prange MT, Margulies SS (2002) Regional, directional, and age-dependent properties of the brain undergoing large deformation. J Biomech Eng 124(2):244\u2013252. https:\/\/doi.org\/10.1115\/1.1449907","journal-title":"J Biomech Eng"},{"issue":"6","key":"3692_CR44","doi-asserted-by":"publisher","first-page":"925","DOI":"10.1115\/1.2354208","volume":"128","author":"X Ning","year":"2006","unstructured":"Ning X, Zhu Q, Lanir Y, Margulies SS (2006) A transversely isotropic viscoelastic constitutive equation for brainstem undergoing finite deformation. J Biomech Eng 128(6):925\u2013933. https:\/\/doi.org\/10.1115\/1.2354208","journal-title":"J Biomech Eng"},{"issue":"3","key":"3692_CR45","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1177\/0006355X2005042003003","volume":"42","author":"S Nicolle","year":"2005","unstructured":"Nicolle S, Lounis M, Willinger R, Palierne JF (2005) Shear linear behavior of brain tissue over a large frequency range. Biorheology 42(3):209\u2013223. https:\/\/doi.org\/10.1177\/0006355X2005042003003","journal-title":"Biorheology"},{"issue":"4","key":"3692_CR46","doi-asserted-by":"publisher","DOI":"10.1115\/1.2939290","volume":"130","author":"TS Cohen","year":"2008","unstructured":"Cohen TS, Smith AW, Massouros PG, Bayly PV, Shen AQ, Genin GM (2008) Inelastic behavior in repeated shearing of bovine white matter. J Biomech Eng 130(4):044504. https:\/\/doi.org\/10.1115\/1.2939290","journal-title":"J Biomech Eng"},{"key":"3692_CR47","doi-asserted-by":"publisher","DOI":"10.3389\/fbioe.2024.1462148","volume":"12","author":"A Mazhari","year":"2024","unstructured":"Mazhari A, Shafieian M (2024) Toward understanding the brain tissue behavior due to preconditioning: an experimental study and RVE approach. Front Bioeng Biotechnol 12:1462148. https:\/\/doi.org\/10.3389\/fbioe.2024.1462148","journal-title":"Front Bioeng Biotechnol"},{"issue":"9","key":"3692_CR48","doi-asserted-by":"publisher","first-page":"1339","DOI":"10.1016\/j.jbiomech.2003.12.032","volume":"37","author":"A Gefen","year":"2004","unstructured":"Gefen A, Margulies SS (2004) Are in vivo and in situ brain tissues mechanically similar? J Biomech 37(9):1339\u20131352. https:\/\/doi.org\/10.1016\/j.jbiomech.2003.12.032","journal-title":"J Biomech"},{"key":"3692_CR49","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmbbm.2024.106489","volume":"153","author":"A Bakhtiarydavijani","year":"2024","unstructured":"Bakhtiarydavijani A, Stone TW (2024) Impact of prior axonal injury on subsequent injury during brain tissue stretching\u2013a mesoscale computational approach. J Mech Behav Biomed Mater 153:106489. https:\/\/doi.org\/10.1016\/j.jmbbm.2024.106489","journal-title":"J Mech Behav Biomed Mater"},{"key":"3692_CR50","doi-asserted-by":"publisher","DOI":"10.1007\/s10439-026-04169-8","author":"C Zhang","year":"2026","unstructured":"Zhang C, Wu L, Ji S (2026) A model of axonal damage accumulation from real-world head impact exposure. Ann Biomed Eng. https:\/\/doi.org\/10.1007\/s10439-026-04169-8","journal-title":"Ann Biomed Eng"},{"issue":"4","key":"3692_CR51","doi-asserted-by":"publisher","first-page":"527","DOI":"10.1002\/jnr.24079","volume":"96","author":"R Vink","year":"2018","unstructured":"Vink R (2018) Large animal models of traumatic brain injury. J Neurosci Res 96(4):527\u2013535. https:\/\/doi.org\/10.1002\/jnr.24079","journal-title":"J Neurosci Res"},{"key":"3692_CR52","doi-asserted-by":"publisher","first-page":"79","DOI":"10.4271\/2003-22-0005","volume":"47","author":"EG Takhounts","year":"2003","unstructured":"Takhounts EG, Crandall JR, Darvish K (2003) On the importance of nonlinearity of brain tissue under large deformations. Stapp Car Crash J 47:79\u201392. https:\/\/doi.org\/10.4271\/2003-22-0005","journal-title":"Stapp Car Crash J"},{"issue":"9","key":"3692_CR53","doi-asserted-by":"publisher","first-page":"633","DOI":"10.1016\/S1350-4533(01)00101-1","volume":"23","author":"KK Darvish","year":"2001","unstructured":"Darvish KK, Crandall JR (2001) Nonlinear viscoelastic effects in oscillatory shear deformation of brain tissue. Med Eng Phys 23(9):633\u2013645. https:\/\/doi.org\/10.1016\/S1350-4533(01)00101-1","journal-title":"Med Eng Phys"},{"issue":"6","key":"3692_CR54","doi-asserted-by":"publisher","first-page":"731","DOI":"10.1016\/j.jbiomech.2009.01.023","volume":"42","author":"F Pervin","year":"2009","unstructured":"Pervin F, Chen WW (2009) Dynamic mechanical response of bovine gray matter and white matter brain tissues under compression. J Biomech 42(6):731\u2013735. https:\/\/doi.org\/10.1016\/j.jbiomech.2009.01.023","journal-title":"J Biomech"},{"issue":"5","key":"3692_CR55","doi-asserted-by":"publisher","first-page":"623","DOI":"10.1177\/0006355X2006043005004","volume":"43","author":"M Hrapko","year":"2006","unstructured":"Hrapko M, van Dommelen JAW, Peters GWM, Wismans JSHM (2006) The mechanical behaviour of brain tissue: large strain response and constitutive modelling. Biorheology 43(5):623\u2013636. https:\/\/doi.org\/10.1177\/0006355X2006043005004","journal-title":"Biorheology"},{"issue":"14","key":"3692_CR56","doi-asserted-by":"publisher","first-page":"2839","DOI":"10.1016\/j.jbiomech.2010.06.014","volume":"43","author":"B Galle","year":"2010","unstructured":"Galle B, Ouyang H, Shi R, Nauman EA (2010) A transversely isotropic constitutive model of excised guinea pig spinal cord white matter. J Biomech 43(14):2839\u20132843. https:\/\/doi.org\/10.1016\/j.jbiomech.2010.06.014","journal-title":"J Biomech"},{"key":"3692_CR57","volume-title":"Non-linear elastic deformations","author":"RW Ogden","year":"1997","unstructured":"Ogden RW (1997) Non-linear elastic deformations. Courier Corporation, Mineola, NY"},{"issue":"7","key":"3692_CR58","doi-asserted-by":"publisher","first-page":"1276","DOI":"10.1016\/j.jbiomech.2013.02.014","volume":"46","author":"B Rashid","year":"2013","unstructured":"Rashid B, Destrade M, Gilchrist MD (2013) Influence of preservation temperature on the measured mechanical properties of brain tissue. J Biomech 46(7):1276\u20131281. https:\/\/doi.org\/10.1016\/j.jbiomech.2013.02.014","journal-title":"J Biomech"},{"issue":"2","key":"3692_CR59","doi-asserted-by":"publisher","first-page":"175","DOI":"10.5254\/1.3538422","volume":"70","author":"OH Yeoh","year":"1997","unstructured":"Yeoh OH (1997) On the Ogden strain-energy function. Rubber Chem Technol 70(2):175\u2013182. https:\/\/doi.org\/10.5254\/1.3538422","journal-title":"Rubber Chem Technol"},{"issue":"4","key":"3692_CR60","doi-asserted-by":"publisher","first-page":"483","DOI":"10.1016\/S0021-9290(01)00234-2","volume":"35","author":"K Miller","year":"2002","unstructured":"Miller K, Chinzei K (2002) Mechanical properties of brain tissue in tension. J Biomech 35(4):483\u2013490. https:\/\/doi.org\/10.1016\/S0021-9290(01)00234-2","journal-title":"J Biomech"},{"issue":"6","key":"3692_CR61","doi-asserted-by":"publisher","first-page":"1158","DOI":"10.1016\/j.jbiomech.2011.01.019","volume":"44","author":"T Kaster","year":"2011","unstructured":"Kaster T, Sack I, Samani A (2011) Measurement of the hyperelastic properties of ex vivo brain tissue slices. J Biomech 44(6):1158\u20131163. https:\/\/doi.org\/10.1016\/j.jbiomech.2011.01.019","journal-title":"J Biomech"},{"issue":"1","key":"3692_CR62","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1007\/s10237-005-0007-9","volume":"5","author":"F Velardi","year":"2006","unstructured":"Velardi F, Fraternali F, Angelillo M (2006) Anisotropic constitutive equations and experimental tensile behavior of brain tissue. Biomech Model Mechanobiol 5(1):53\u201361. https:\/\/doi.org\/10.1007\/s10237-005-0007-9","journal-title":"Biomech Model Mechanobiol"},{"issue":"11","key":"3692_CR63","doi-asserted-by":"publisher","first-page":"1163","DOI":"10.1089\/089771503770802853","volume":"20","author":"A Gefen","year":"2003","unstructured":"Gefen A, Gefen N, Zhu Q, Raghupathi R, Margulies SS (2003) Age-dependent changes in material properties of the brain and braincase of the rat. J Neurotrauma 20(11):1163\u20131177. https:\/\/doi.org\/10.1089\/089771503770802853","journal-title":"J Neurotrauma"},{"issue":"13","key":"3692_CR64","doi-asserted-by":"publisher","first-page":"2136","DOI":"10.1016\/j.jbiomech.2009.05.041","volume":"42","author":"M Shafieian","year":"2009","unstructured":"Shafieian M, Darvish KK, Stone JR (2009) Changes to the viscoelastic properties of brain tissue after traumatic axonal injury. J Biomech 42(13):2136\u20132142. https:\/\/doi.org\/10.1016\/j.jbiomech.2009.05.041","journal-title":"J Biomech"},{"issue":"1","key":"3692_CR65","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1002\/mrm.1910370107","volume":"37","author":"KP Whittall","year":"1997","unstructured":"Whittall KP, Mackay AL, Graeb DA, Nugent RA, Li DK, Paty DW (1997) In vivo measurement of T2 distributions and water contents in normal human brain. Magn Reson Med 37(1):34\u201343. https:\/\/doi.org\/10.1002\/mrm.1910370107","journal-title":"Magn Reson Med"},{"key":"3692_CR66","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmbbm.2020.104240","volume":"115","author":"F Eskandari","year":"2021","unstructured":"Eskandari F, Shafieian M, Aghdam MM, Laksari K (2021) Mind the gap: a mechanobiological hypothesis for the role of gap junctions in the mechanical properties of injured brain tissue. J Mech Behav Biomed Mater 115:104240. https:\/\/doi.org\/10.1016\/j.jmbbm.2020.104240","journal-title":"J Mech Behav Biomed Mater"},{"issue":"1","key":"3692_CR67","doi-asserted-by":"publisher","first-page":"154","DOI":"10.1016\/j.expneurol.2007.01.023","volume":"205","author":"Y Deng","year":"2007","unstructured":"Deng Y, Thompson BM, Gao X, Hall ED (2007) Temporal relationship of peroxynitrite-induced oxidative damage, calpain-mediated cytoskeletal degradation and neurodegeneration after traumatic brain injury. Exp Neurol 205(1):154\u2013165. https:\/\/doi.org\/10.1016\/j.expneurol.2007.01.023","journal-title":"Exp Neurol"},{"issue":"3","key":"3692_CR68","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1111\/j.1440-1819.1997.tb02379.x","volume":"51","author":"G Kanayama","year":"1997","unstructured":"Kanayama G, Takeda M, Morihara T, Miyamae Y, Shinozaki K, Nishikawa T, Niigawa H, Nishimura T (1997) Temporal and regional profiles of cytoskeletal protein accumulation in the rat brain following traumatic brain injury. Psychiatry Clin Neurosci 51(3):157\u2013165. https:\/\/doi.org\/10.1111\/j.1440-1819.1997.tb02379.x","journal-title":"Psychiatry Clin Neurosci"},{"key":"3692_CR69","doi-asserted-by":"publisher","first-page":"194","DOI":"10.1016\/j.jmbbm.2018.02.002","volume":"80","author":"SA Yousefsani","year":"2018","unstructured":"Yousefsani SA, Shamloo A, Farahmand F (2018) Micromechanics of brain white matter tissue: a fiber-reinforced hyperelastic model using embedded element technique. J Mech Behav Biomed Mater 80:194\u2013202. https:\/\/doi.org\/10.1016\/j.jmbbm.2018.02.002","journal-title":"J Mech Behav Biomed Mater"},{"key":"3692_CR70","doi-asserted-by":"publisher","DOI":"10.3389\/fmech.2021.685519","volume":"7","author":"M Kazempour","year":"2021","unstructured":"Kazempour M, Kazempour A, Baniassadi M, Remond Y, Baghani M (2021) Numerical investigation of axonal damage for regular and irregular axonal distributions. Front Mech Eng 7:685519. https:\/\/doi.org\/10.3389\/fmech.2021.685519","journal-title":"Front Mech Eng"},{"key":"3692_CR71","unstructured":"Eskandari F, Shafieian M, Aghdam MM, Laksari K (2019) Mechanical properties of brain white matter under repetitive loading condition: introducing a mechanical damage function, Proceedings of the 26th National and 4th International Iranian Conference on Biomedical Engineering, Tehran, Iran, November 2019. Available at: https:\/\/www.researchgate.net\/publication\/337828117_Mechanical_Properties_of_Brain_White_Matter_under_Repetitive_Loading_Condition_Introducing_a_Mechanical_Damage_Function"},{"issue":"4","key":"3692_CR72","doi-asserted-by":"publisher","first-page":"642","DOI":"10.1016\/j.jbiomech.2011.12.023","volume":"45","author":"K Laksari","year":"2012","unstructured":"Laksari K, Shafieian M, Darvish K (2012) Constitutive model for brain tissue under finite compression. J Biomech 45(4):642\u2013646. https:\/\/doi.org\/10.1016\/j.jbiomech.2011.12.023","journal-title":"J Biomech"},{"issue":"14","key":"3692_CR73","doi-asserted-by":"publisher","first-page":"3070","DOI":"10.1016\/j.jbiomech.2007.03.019","volume":"40","author":"A Nekouzadeh","year":"2007","unstructured":"Nekouzadeh A, Pryse KM, Elson EL, Genin GM (2007) A simplified approach to quasi-linear viscoelastic modeling. J Biomech 40(14):3070\u20133078. https:\/\/doi.org\/10.1016\/j.jbiomech.2007.03.019","journal-title":"J Biomech"},{"issue":"16","key":"3692_CR74","doi-asserted-by":"publisher","first-page":"2795","DOI":"10.1016\/j.jbiomech.2013.09.001","volume":"46","author":"X Jin","year":"2013","unstructured":"Jin X, Zhu F, Mao H, Shen M, Yang KH (2013) A comprehensive experimental study on material properties of human brain tissue. J Biomech 46(16):2795\u20132801. https:\/\/doi.org\/10.1016\/j.jbiomech.2013.09.001","journal-title":"J Biomech"},{"key":"3692_CR75","doi-asserted-by":"publisher","DOI":"10.1016\/j.jbiomech.2021.110260","volume":"117","author":"MT Begonia","year":"2021","unstructured":"Begonia MT, Knapp AM, Prabhu RK, Liao J, Williams LN (2021) Shear-deformation based continuum-damage constitutive modeling of brain tissue. J Biomech 117:110260. https:\/\/doi.org\/10.1016\/j.jbiomech.2021.110260","journal-title":"J Biomech"}],"container-title":["Medical & Biological Engineering & Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11517-026-03692-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11517-026-03692-z","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11517-026-03692-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T00:04:04Z","timestamp":1791245044000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11517-026-03692-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10,5]]},"references-count":75,"alternative-id":["3692"],"URL":"https:\/\/doi.org\/10.1007\/s11517-026-03692-z","relation":{},"ISSN":["0140-0118","1741-0444"],"issn-type":[{"value":"0140-0118","type":"print"},{"value":"1741-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,10,5]]},"assertion":[{"value":"3 July 2026","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 September 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 October 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"Bovine brain tissues used in this study were sourced from a commercial slaughterhouse as waste materials from animals slaughtered for human consumption. No animals were euthanized specifically for this research. As the study involved only ex vivo tissue testing and did not involve live animals or human subjects, institutional ethical review and approval were not required.","order":1,"name":"Ethics","label":"Ethical approval","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"During the preparation of this work, artificial intelligence language models were used to assist with paraphrasing and improving readability. After utilizing these tools, we reviewed and edited the content as necessary and assume full responsibility for the final content of the published article.","order":2,"name":"Ethics","label":"Declaration of generative AI in scientific writing","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no competing interests to declare that are relevant to the content of this article.","order":3,"name":"Ethics","label":"Conflict of interest","group":{"name":"EthicsHeading","label":"Declarations"}}]}}