基于头部运动学参数与脑损伤关系的颅脑创伤机制研究进展

张家瑞; 杜智博; 柳占立; 庄茁

doi:10.11883/bzycj-2024-0221

基于头部运动学参数与脑损伤关系的颅脑创伤机制研究进展

doi: 10.11883/bzycj-2024-0221

清华大学航天航空学院，北京 100084

基金项目: 国家重点研发计划（2020-JCJQ-ZD-254, 2022YFC3320500）

详细信息

作者简介:
张家瑞（1998－　），男，博士研究生，15862172533@163.com

通讯作者:
柳占立（1981－　），男，博士，教授，liuzhanli@mail.tsinghua.edu.cn

中图分类号: O389
计量
- 文章访问数: 51
- HTML全文浏览量: 31
- PDF下载量: 20
- 被引次数: 0
出版历程
- 收稿日期: 2024-07-04
- 修回日期: 2024-10-22
- 网络出版日期: 2024-11-05
- 刊出日期: 2024-12-01

Research progress on mechanism of craniocerebral trauma based on relationship between head acceleration and brain injury

School of Aerospace Engineering, Tsinghua University, Beijing 100084, China

摘要

摘要: 由于轻度创伤性脑损伤的复杂性和数据测量方式的局限性，直接根据脑组织损伤阈值来确定大脑的损伤状态往往并不可行。脑组织的损伤机制涉及复杂的力学、生物化学和生理学过程，且在不同个体之间存在显著差异。通过研究头部运动载荷与脑组织损伤之间的关系，研究者可以更好地理解不同类型的头部运动（如线加速度、角加速度、角速度）对脑组织的影响规律。这不仅有助于揭示颅脑创伤的力学机制，还为开发更有效的防护装具提供科学依据。但直接从头部的运动学测量评估损伤风险仍面临诸多挑战。本文详细总结和评述了与轻度创伤性脑损伤相关的冲击载荷及头部模型特点，通过综合分析头部运动学载荷与脑组织变形响应的关系，揭示包括线加速度、角加速度等载荷作用下脑组织的应力、应变响应规律，指出当前研究中存在的不足与局限性，为轻度创伤性脑损伤的预防、评估及治疗奠定理论和技术基础。
- 致伤机制 /
- 碰撞载荷 /
- 爆炸载荷 /
- 角加速度 /
- 头部模型 /
- 脑组织应变
Abstract: Due to the complexity of mild traumatic brain injury (mTBI) and the limitations of data measurement methods, it is often not feasible to directly determine the damage status of the brain based on the brain tissue damage threshold. The damage mechanism of brain tissue involves a variety of complex mechanical, biochemical, and physiological processes that vary significantly between individuals. In addition, existing measurement techniques still have limitations in temporal and spatial resolution, making it difficult to accurately capture the dynamic response of brain tissue. Therefore, establishing the relationship between head motion and brain tissue damage has become a key step in understanding the mechanical mechanism of mild traumatic brain injury. By studying the relationship between head motion and brain tissue damage, researchers can better understand the specific effects of different types of head motion (such as linear acceleration, rotational acceleration, rotational velocity) on brain tissue. This understanding not only helps reveal the basic mechanical mechanisms of mild traumatic brain injury, but also provides a scientific basis for the development of more effective protective equipment. For example, based on these findings, the design of protective helmets can be optimized to better disperse impact energy, reduce stress concentrations in brain tissue, and reduce the risk of trauma. However, there are still many challenges in assessing injury risk directly from kinematic measurements of the head. This article summarizes and reviews in detail the load characteristics related to mild traumatic brain injury and their corresponding brain tissue response, including the stress and strain effects of head kinematic parameters on brain tissue. In addition, this article also explores the head models used in studying brain injury mechanisms and their characteristics, such as high-precision finite element models and multi-scale models, which play an important role in simulating the deformation response of brain tissue. By comprehensively analyzing the relationship between head kinematic parameters and brain tissue deformation response, this article provides important reference and guidance for the prevention, assessment and treatment of mild traumatic brain injury.
- injury mechanisms /
- impact loads /
- blast loads /
- angular acceleration /
- head models /
- brain tissue strain

HTML全文

图 1 碰撞载荷下头部的加速度频谱

Figure 1. Acceleration spectrum of the head under collision loads

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图 2 可用于低频加速度测量的护齿器^[39-40]

Figure 2. Mouthguards used for low-frequency acceleration measurement^[39-40]

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图 3 爆炸载荷下头部的加速度频谱

Figure 3. Acceleration spectrum of the head under collision loads

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图 4 脑组织剪切模量的应变率依赖性^[59]

Figure 4. Strain rate dependence of shear modulus of brain tissue^[59]

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图 5 脑组织的非线性应力-应变关系^[59]

Figure 5. Nonlinear stress-strain relationship of brain tissue^[59]

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图 6 无法复现尸体模型数据的无脑脊液头部有限元模型^{[74, 76]}

Figure 6. Finite element models of head without cerebrospinal fluid that cannot reproduce cadaveric model data^{[74, 76]}

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图 7 三维头部有限元模型的前3阶频率对应模态^[84]

Figure 7. The first three frequencies of the 3D finite element head model^[84]

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图 8 脑损伤分析的多尺度框架^[96]

Figure 8. Multiscale framework for brain injury analysis^[96]

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图 9 爆炸载荷下头部最大线加速度、最大角加速度和与脑组织最大主应变的线性关系^[49]

Figure 9. The linear relationship between the maximum linear acceleration, maximum angular acceleration of head and the maximum principal strain of brain tissue under blast load^[49]

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图 10 基于头部角速度曲线通过数据驱动方法预测脑组织应变分布^[100]

Figure 10. Prediction of brain tissue strain distribution using a data-driven approach based on head angular velocity curves^[100]

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参考文献(104)

[1]	HANLON E M, BIR C A. Real-time head acceleration measurement in girls’ youth soccer [J]. Medicine and Science in Sports and Exercise, 2012, 44(6): 1102–1108. DOI: 10.1249/MSS.0b013e3182444d7d.
[2]	HOLBOURN A H S. Mechanics of head injuries [J]. The Lancet, 1943, 242(6267): 438–441. DOI: 10.1016/S0140-6736(00)87453-X.
[3]	FORERO RUEDA M A, CUI L, GILCHRIST M D. Finite element modelling of equestrian helmet impacts exposes the need to address rotational kinematics in future helmet designs [J]. Computer Methods in Biomechanics and Biomedical Engineering, 2011, 14(12): 1021–1031. DOI: 10.1080/10255842.2010.504922.
[4]	ROWSON S, DUMA S M, BECKWITH J G, et al. Rotational head kinematics in football impacts: an injury risk function for concussion [J]. Annals of Biomedical Engineering, 2012, 40(1): 1–13. DOI: 10.1007/s10439-011-0392-4.
[5]	HARDY W N, KHALIL T B, KING A I. Literature review of head injury biomechanics [J]. International Journal of Impact Engineering, 1994, 15(4): 561–586. DOI: 10.1016/0734-743X(94)80034-7.
[6]	JONES M. Biomechanics of primary traumatic head injury [M]// WHITWELL H, MILROY C, DU PLESSIS D. Forensic Neuropathology. 2nd ed. Boca Raton: CRC Press, 2021: 45-54. DOI: 10.1201/9781003158035.
[7]	ONO K, KIKUCHI A, NAKAMURA M, et al. Human head tolerance to sagittal impact reliable estimation deduced from experimental head injury using subhuman primates and human cadaver skulls [J]. SAE Transactions, 1980: 3837-3866. DOI: 10.4271/801303.
[8]	NISHIMOTO T, MURAKAMI S. Relation between diffuse axonal injury and internal head structures on blunt impact [J]. Journal of Biomechanical Engineering, 1998, 120(1): 140–147. DOI: 10.1115/1.2834294.
[9]	ANDERSON R W G, BROWN C J, BLUMBERGS P C, et al. Impact mechanics and axonal injury in a sheep model [J]. Journal of Neurotrauma, 2003, 20(10): 961–974. DOI: 10.1089/089771503770195812.
[10]	BAILES J E, PETRAGLIA A L, OMALU B I, et al. Role of subconcussion in repetitive mild traumatic brain injury: a review [J].Journal of Neurosurgery, 2013, 119(5): 1235–1245. DOI: 10.3171/2013.7.JNS121822.
[11]	HUME P A, THEADOM A, LEWIS G N, et al. A comparison of cognitive function in former rugby union players compared with former non-contact-sport players and the impact of concussion history [J]. Sports Medicine, 2017, 47(6): 1209–1220. DOI: 10.1007/s40279-016-0608-8.
[12]	THUNNAN D J, BRANCHE C M, SNIEZEK J E. The epidemiology of sports-related traumatic brain injuries in the United States: recent developments [J]. Journal of Head Trauma Rehabilitation, 1998, 13(2): 1–8. DOI: 10.1097/00001199-199804000-00003.
[13]	CUNNINGHAM J, BROGLIO S, WILSON F. Influence of playing rugby on long-term brain health following retirement: a systematic review and narrative synthesis [J]. BMJ Open Sport and Exercise Medicine, 2018, 4(1): e000356. DOI: 10.1136/bmjsem-2018-000356.
[14]	FITZPATRICK A C, NAYLOR A S, MYLER P, et al. A three-year epidemiological prospective cohort study of rugby league match injuries from the European Super League [J]. Journal of Science and Medicine in Sport, 2018, 21(2): 160–165. DOI: 10.1016/j.jsams.2017.08.012.
[15]	SOICA A, TARULESCU S. Impact phase in frontal vehicle-pedestrian collisions [J]. International Journal of Automotive Technology, 2016, 17(3): 387–397. DOI: 10.1007/s12239-016-0040-y.
[16]	GILSON L, RABET L, IMAD A, et al. Experimental and numerical assessment of non-penetrating impacts on a composite protection and ballistic gelatine [J]. International Journal of Impact Engineering, 2020, 136: 103417. DOI: 10.1016/j.ijimpeng.2019.103417.
[17]	LIU H, KANG J Y, CHEN J, et al. Intracranial pressure response to non-penetrating ballistic impact: an experimental study using a pig physical head model and live pigs [J]. International Journal of Medical Sciences, 2012, 9(8): 655–664. DOI: 10.7150/ijms.5004.
[18]	FREITAS C J, BIGGER R P, SCOTT N, et al. Composite materials dynamic back face deflection characteristics during ballistic impact [J]. Journal of Composite Materials, 2014, 48(12): 1475–1486. DOI: 10.1177/0021998313487934.
[19]	OUKARA A, NSIAMPA N, ROBBE C, et al. Assessment of non-lethal projectile head impacts [J]. Human Factors and Mechanical Engineering for Defense and Safety, 2017, 1(1): 3. DOI: 10.1007/s41314-016-0001-2.
[20]	National Research Council, Division on Engineering and Physical Sciences, Board on Army Science and Technology, et al. Review of Department of Defense test protocols for combat helmets [R]. Washington: The National Academies Press, 2014. DOI: 10.17226/18621.
[21]	GURDJIAN E S, GURDJIAN E S. Cerebral contusions: re-evaluation of the mechanism of their development [J]. The Journal of Trauma: Injury, Infection, and Critical Care, 1976, 16(1): 35–51. DOI: 10.1097/00005373-197601000-00005.
[22]	GURDJIAN E S, HODGSON V R, THOMAS L M, et al. Significance of relative movements of scalp, skull, and intracranial contents during impact injury of the head [J]. Journal of Neurosurgery, 1968, 29(1): 70–72. DOI: 10.3171/jns.1968.29.1.0070.
[23]	KING A I, YANG K H, ZHANG L, et al. Is head injury caused by linear or angular acceleration? [C]//Proceedings of the International Research Conference on the Biomechanics of Impacts. Lisbon, Portugal: IRCOBI, 2003: 1–12.
[24]	GENNARELLI T A, THIBAULT L E. Biomechanics of acute subdural hematoma [J]. The Journal of Trauma: Injury, Infection, and Critical Care, 1982, 22(8): 680–686. DOI: 10.1097/00005373-198208000-00005.
[25]	KLEIVEN S, PELOSO P M, HOLST H. The epidemiology of head injuries in Sweden from 1987 to 2000 [J]. Injury Control and Safety Promotion, 2003, 10(3): 173–180. DOI: 10.1076/icsp.10.3.173.14552.
[26]	KLEIVEN S. Why most traumatic brain injuries are not caused by linear acceleration but skull fractures are [J]. Frontiers in Bioengineering and Biotechnology, 2013, 1: 15. DOI: 10.3389/fbioe.2013.00015.
[27]	MCCUEN E, SVALDI D, BREEDLOVE K, et al. Collegiate women’s soccer players suffer greater cumulative head impacts than their high school counterparts [J]. Journal of Biomechanics, 2015, 48(13): 3720–3723. DOI: 10.1016/j.jbiomech.2015.08.003.
[28]	CACCESE J B, LAMOND L C, BUCKLEY T A, et al. Reducing purposeful headers from goal kicks and punts may reduce cumulative exposure to head acceleration [J]. Research in Sports Medicine, 2016, 24(4): 407–415. DOI: 10.1080/15438627.2016.1230549.
[29]	REYNOLDS B B, PATRIE J, HENRY E J, et al. Comparative analysis of head impact in contact and collision sports [J]. Journal of Neurotrauma, 2017, 34(1): 38–49. DOI: 10.1089/neu.2015.4308.
[30]	LAMOND L C, CACCESE J B, BUCKLEY T A, et al. Linear acceleration in direct head contact across impact type, player position, and playing scenario in collegiate women’s soccer players [J]. Journal of Athletic Training, 2018, 53(2): 115–121. DOI: 10.4085/1062-6050-90-17.
[31]	NEVINS D, HILDENBRAND K, KENSRUD J, et al. Laboratory and field evaluation of a small form factor head impact sensor in un-helmeted play [J]. Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology, 2018, 232(3): 242–254. DOI: 10.1177/1754337117739458.
[32]	CHRISMAN S P D, EBEL B E, STEIN E, et al. Head impact exposure in youth soccer and variation by age and sex [J]. Clinical Journal of Sport Medicine, 2019, 29(1): 3–10. DOI: 10.1097/JSM.0000000000000497.
[33]	HARRISS A, JOHNSON A M, WALTON D M, et al. Head impact magnitudes that occur from purposeful soccer heading depend on the game scenario and head impact location [J]. Musculoskeletal Science and Practice, 2019, 40: 53–57. DOI: 10.1016/j.msksp.2019.01.009.
[34]	MYER G D, FOSS K B, THOMAS S, et al. Altered brain microstructure in association with repetitive subconcussive head impacts and the potential protective effect of jugular vein compression: a longitudinal study of female soccer athletes [J]. British Journal of Sports Medicine, 2019, 53(24): 1539–1551. DOI: 10.1136/bjsports-2018-099571.
[35]	RICH A M, FILBEN T M, MILLER L E, et al. Development, validation and pilot field deployment of a custom mouthpiece for head impact measurement [J]. Annals of Biomedical Engineering, 2019, 47(10): 2109–2121. DOI: 10.1007/s10439-019-02313-1.
[36]	TOLEA B, RADU A I, BELES H, et al. Influence of the geometric parameters of the vehicle frontal profile on the pedestrian’s head accelerations in case of accidents [J]. International Journal of Automotive Technology, 2018, 19(1): 85–98. DOI: 10.1007/s12239-018-0009-0.
[37]	NAUNHEIM R S, BAYLY P V, STANDEVEN J, et al. Linear and angular head accelerations during heading of a soccer ball [J]. Medicine & Science in Sports & Exercise, 2003, 35(8): 1406–1412. DOI: 10.1249/01.MSS.0000078933.84527.AE.
[38]	JONES C M, AUSTIN K, AUGUSTUS S N, et al. An instrumented mouthguard for real-time measurement of head kinematics under a large range of sport specific accelerations [J]. Sensors, 2023, 23(16): 7068. DOI: 10.3390/s23167068.
[39]	LIU Y Z, DOMEL A G, YOUSEFSANI S A, et al. Validation and comparison of instrumented mouthguards for measuring head kinematics and assessing brain deformation in football impacts [J]. Annals of Biomedical Engineering, 2020, 48(11): 2580–2598. DOI: 10.1007/s10439-020-02629-3.
[40]	O’CONNOR K L, ROWSON S, DUMA S M, et al. Head-impact-measurement devices: a systematic review [J]. Journal of Athletic Training, 2017, 52(3): 206–227. DOI: 10.4085/1062-6050.52.2.05.
[41]	REYNOLDS B B, PATRIE J, HENRY E J, et al. Practice type effects on head impact in collegiate football [J]. Journal of Neurosurgery, 2016, 124(2): 501–510. DOI: 10.3171/2015.5.JNS15573.
[42]	HORROCKS C L. Blast injuries: biophysics, pathophysiology and management principles [J]. BMJ Military Health, 2001, 147(1): 28–40. DOI: 10.1136/jramc-147-01-03.
[43]	OWENS B D, KRAGH JR J F, WENKE J C, et al. Combat wounds in operation Iraqi freedom and operation enduring freedom [J]. The Journal of Trauma: Injury, Infection, and Critical Care, 2008, 64(2): 295–299. DOI: 10.1097/TA.0b013e318163b875.
[44]	Defense and Veterans Brain Injury Center. DoD worldwide numbers for TBI [R]. Defense and Veterans Brain Injury Center, 2018.
[45]	CHAMPION H R, HOLCOMB J B, YOUNG L A. Injuries from explosions: physics, biophysics, pathology, and required research focus [J]. The Journal of Trauma: Injury, Infection, and Critical Care, 2009, 66(5): 1468–1477. DOI: 10.1097/TA.0b013e3181a27e7f.
[46]	WOOD G W, PANZER M B, SHRIDHARANI J K, et al. Attenuation of blast pressure behind ballistic protective vests [J]. Injury Prevention, 2013, 19(1): 19–25. DOI: 10.1136/injuryprev-2011-040277.
[47]	YOUNG L, RULE G T, BOCCHIERI R T, et al. When physics meets biology: low and high-velocity penetration, blunt impact, and blast injuries to the brain [J]. Frontiers in Neurology, 2015, 6: 89. DOI: 10.3389/fneur.2015.00089.
[48]	GULLOTTI D M, BEAMER M, PANZER M B, et al. Significant head accelerations can influence immediate neurological impairments in a murine model of blast-induced traumatic brain injury [J]. Journal of Biomechanical Engineering, 2014, 136(9): 091004. DOI: 10.1115/1.4027873.
[49]	SARVGHAD-MOGHADDAM H, REZAEI A, ZIEJEWSKI M, et al. Correlative analysis of head kinematics and brain’s tissue response: a computational approach toward understanding the mechanisms of blast TBI [J]. Shock Waves, 2017, 27(6): 919–927. DOI: 10.1007/s00193-017-0749-1.
[50]	MAO H J, UNNIKRISHNAN G, RAKESH V, et al. Untangling the effect of head acceleration on brain responses to blast waves [J]. Journal of Biomechanical Engineering, 2015, 137(12): 124502. DOI: 10.1115/1.4031765.
[51]	LOCKHART P, CRONIN D, WILLIAMS K, et al. Investigation of head response to blast loading [J]. The Journal of Trauma: Injury, Infection, and Critical Care, 2011, 70(2): E29–E36. DOI: 10.1097/TA.0b013e3181de3f4b.
[52]	SIEGMUND G P, KING D J, LAWRENCE J M, et al. Head/neck kinematic response of human subjects in low-speed rear-end collisions [C]//Proceedings of the 41st Stapp Car Crash Conference. Orlando: SAE, 1997: 3877–3905.
[53]	DIONNE J P, LEVINE J, MAKRIS A. Acceleration-based methodology to assess the blast mitigation performance of explosive ordnance disposal helmets [J]. Shock Waves, 2018, 28(1): 5–18. DOI: 10.1007/s00193-017-0737-5.
[54]	GANPULE S, ALAI A, PLOUGONVEN E, et al. Mechanics of blast loading on the head models in the study of traumatic brain injury using experimental and computational approaches [J]. Biomechanics and Modeling in Mechanobiology, 2013, 12(3): 511–531. DOI: 10.1007/s10237-012-0421-8.
[55]	SIEGMUND G P, SANDERSON D J, INGLIS J T. Gradation of neck muscle responses and head/neck kinematics to acceleration and speed change in rear-end collisions [C]//48th Stapp Car Crash Conference. Vancouver: SAE, 2004. DOI: 10.4271/2004-22-0018.
[56]	ONO K, KANEOKA K, WITTEK A, et al. Cervical injury mechanism based on the analysis of human cervical vertebral motion and head-neck-torso kinematics during low speed rear impacts [C]//Proceedings of the 1997 41st Stapp Car Crash Conference. Lake Buena Vista: SAE, 1997: 3859-3876.
[57]	ESCARCEGA J D, KNUTSEN A K, ALSHAREEF A A, et al. Comparison of deformation patterns excited in the human brain in vivo by harmonic and impulsive skull motion [J]. Journal of Biomechanical Engineering, 2023, 145(8): 081006. DOI: 10.1115/1.4062809.
[58]	BUDDAY S, SOMMER G, BIRKL C, et al. Mechanical characterization of human brain tissue [J]. Acta Biomaterialia, 2017, 48: 319–340. DOI: 10.1016/j.actbio.2016.10.036.
[59]	BUDDAY S, NAY R, DE ROOIJ R, et al. Mechanical properties of gray and white matter brain tissue by indentation [J]. Journal of the Mechanical Behavior of Biomedical Materials, 2015, 46: 318–330. DOI: 10.1016/j.jmbbm.2015.02.024.
[60]	KYRIACOU S K, MOHAMED A, MILLER K, et al. Brain mechanics for neurosurgery: modeling issues [J]. Biomechanics and Modeling in Mechanobiology, 2002, 1(2): 151–164. DOI: 10.1007/s10237-002-0013-0.
[61]	BUDDAY S, STEINMANN P, KUHL E. Physical biology of human brain development [J]. Frontiers in Cellular Neuroscience, 2015, 9: 257. DOI: 10.3389/fncel.2015.00257.
[62]	FRANCESCHINI G, BIGONI D, REGITNIG P, et al. Brain tissue deforms similarly to filled elastomers and follows consolidation theory [J]. Journal of the Mechanics and Physics of Solids, 2006, 54(12): 2592–2620. DOI: 10.1016/j.jmps.2006.05.004.
[63]	WARD C C, THOMPSON R B. The development of a detailed finite element brain model [C]//19th Stapp Car Crash Conference. SAE, 1975: 3238–3252. DOI: 10.4271/751163.
[64]	HOSEY R. A homeomorphic finite element model of the human head and neck [J]. Finite Elements in Biomechanics, 1982.
[65]	NICOLLE S, LOUNIS M, WILLINGER R. Shear properties of brain tissue over a frequency range relevant for automotive impact situations: new experimental results [C]//48th Stapp Car Crash Conference. Strasbourg: SAE, 2004. DOI: 10.4271/2004-22-0011.
[66]	PETERS G W M, MEULMAN J H, SAUREN A A H J. The applicability of the time/temperature superposition principle to brain tissue [J]. Biorheology, 1997, 34(2): 127–138. DOI: 10.1016/S0006-355X(97)00009-7.
[67]	KLEIVEN S, HARDY W N. Correlation of an FE model of the human head with local brain motion-consequences for injury prediction [C]//46th Stapp Car Crash Conference. SAE, 2002. DOI: 10.4271/2002-22-0007.
[68]	HORGAN T J, GILCHRIST M D. The creation of three-dimensional finite element models for simulating head impact biomechanics [J]. International Journal of Crashworthiness, 2003, 8(4): 353–366. DOI: 10.1533/ijcr.2003.0243.
[69]	GHAJARI M, HELLYER P J, SHARP D J. Computational modelling of traumatic brain injury predicts the location of chronic traumatic encephalopathy pathology [J]. Brain, 2017, 140(2): 333–343. DOI: 10.1093/brain/aww317.
[70]	WITTEK A, MILLER K, KIKINIS R, et al. Patient-specific model of brain deformation: application to medical image registration [J]. Journal of Biomechanics, 2007, 40(4): 919–929. DOI: 10.1016/j.jbiomech.2006.02.021.
[71]	YANG S C, TANG J S, NIE B B, et al. Assessment of brain injury characterization and influence of modeling approaches [J]. Scientific Reports, 2022, 12(1): 13597. DOI: 10.1038/s41598-022-16713-2.
[72]	CHENG L Y, RIFAI S, KHATUA T, et al. Finite element analysis of diffuse axonal injury [C]//International Congress and Exposition. SAE, 1990. DOI: 10.4271/900547.
[73]	DIMASI F, TONG P, MARCUS J H, et al. Simulated head impacts with upper interior structures using rigid and anatomic brain models [M]//OÑATE E, PERIAUX J, SAMUELSSON A. The Finite Element Method in the 1990’s: A Book Dedicated to O. C. Zienkiewicz. Berlin: Springer, 1991: 333–345. DOI: 10.1007/978-3-662-10326-5_34.
[74]	KUIJPERS A H W M, CLAESSENS M H A, SAUREN A A H J. The influence of different boundary conditions on the response of the head to impact: a two-dimensional finite element study [J]. Journal of Neurotrauma, 1995, 12(4): 715–724. DOI: 10.1089/neu.1995.12.715.
[75]	NAHUM A M, SMITH R, WARD C C. Intracranial pressure dynamics during head impact [C]//21st Stapp Car Crash Conference. San Diego: SAE, 1977. DOI: 10.4271/770922.
[76]	CLAESSENS M H A, SAUREN A A H J, WISMANS J S H M. Modeling of the human head under impact conditions: a parametric study [C]//41st Stapp Car Crash Conference. Orlando: SAE, 1997: 3829–3848. DOI: 10.4271/973338.
[77]	KIMPARA H, NAKAHIRA Y, IWAMOTO M, et al. Head injury prediction methods based on 6 degree of freedom head acceleration measurements during impact [J]. International Journal of Automotive Engineering, 2011, 2(2): 13–19. DOI: 10.20485/jsaeijae.2.2_13.
[78]	MAO H J, ZHANG L Y, JIANG B H, et al. Development of a finite element human head model partially validated with thirty five experimental cases [J]. Journal of Biomechanical Engineering, 2013, 135(11): 111002. DOI: 10.1115/1.4025101.
[79]	MILLER L E, URBAN J E, STITZEL J D. Development and validation of an atlas-based finite element brain model [J]. Biomechanics and Modeling in Mechanobiology, 2016, 15(5): 1201–1214. DOI: 10.1007/s10237-015-0754-1.
[80]	LI X G. Subject-specific head model generation by mesh morphing: a personalization framework and its applications [J]. Frontiers in Bioengineering and Biotechnology, 2021, 9: 706566. DOI: 10.3389/fbioe.2021.706566.
[81]	ZHOU Z, LI X G, KLEIVEN S. Fluid-structure interaction simulation of the brain-skull interface for acute subdural haematoma prediction [J]. Biomechanics and Modeling in Mechanobiology, 2019, 18(1): 155–173. DOI: 10.1007/s10237-018-1074-z.
[82]	BÉKÉSY G V. Vibration of the head in a sound field and its role in hearing by bone conduction [J]. The Journal of the Acoustical Society of America, 1948, 20(6): 749–760. DOI: 10.1121/1.1906433.
[83]	FRANKE E K. Response of the human skull to mechanical vibrations [J]. The Journal of the Acoustical Society of America, 1956, 28(6): 1277–1284. DOI: 10.1121/1.1908622.
[84]	FONVILLE T R, SCAROLA S J, HAMMI Y, et al. Resonant frequencies of a human brain, skull, and head [M]//PRABHU R, HORSTEMEYER M. Multiscale Biomechanical Modeling of the Brain. Amsterdam: Elsevier, 2022: 239–254. DOI: 10.1016/B978-0-12-818144-7.00006-2.
[85]	LAKSARI K, KURT M, BABAEE H, et al. Mechanistic insights into human brain impact dynamics through modal analysis [J]. Physical Review Letters, 2018, 120(13): 138101. DOI: 10.1103/PhysRevLett.120.138101.
[86]	LJUNG C. A model for brain deformation due to rotation of the skull [J]. Journal of Biomechanics, 1975, 8(5): 263–274. DOI: 10.1016/0021-9290(75)90078-0.
[87]	BAYLY P V, MASSOUROS P G, CHRISTOFOROU E, et al. Magnetic resonance measurement of transient shear wave propagation in a viscoelastic gel cylinder [J]. Journal of the Mechanics and Physics of Solids, 2008, 56(5): 2036–2049. DOI: 10.1016/j.jmps.2007.10.012.
[88]	MARGULIES S S, THIBAULT L E. An analytical model of traumatic diffuse brain injury [J]. Journal of Biomechanical Engineering, 1989, 111(3): 241–249. DOI: 10.1115/1.3168373.
[89]	MASSOUROS P G, BAYLY P V, GENIN G M. Strain localization in an oscillating Maxwell viscoelastic cylinder [J]. International Journal of Solids and Structures, 2014, 51(2): 305–313. DOI: 10.1016/j.ijsolstr.2013.09.022.
[90]	MASSOUROS P G, GENIN G M. The steady-state response of a Maxwell viscoelastic cylinder to sinusoidal oscillation of its boundary [J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2008, 464(2089): 207–221. DOI: 10.1098/rspa.2007.0081.
[91]	CHRISTENSEN R M, GOTTENBERG W G. The dynamic response of a solid, viscoelastic sphere to translational and rotational excitation [J]. Journal of Applied Mechanics, 1964, 31(2): 273–278. DOI: 10.1115/1.3629597.
[92]	COTTER C S, SMOLARKIEWICZ P K, SZCZYRBA I N. A viscoelastic fluid model for brain injuries [J]. International Journal for Numerical Methods in Fluids, 2002, 40(1/2): 303–311. DOI: 10.1002/fld.287.
[93]	WAN Y, FANG W Q, CARLSEN R W, et al. A finite rotation, small strain 2D elastic head model, with applications in mild traumatic brain injury [J]. Journal of the Mechanics and Physics of Solids, 2023, 179: 105362. DOI: 10.1016/j.jmps.2023.105362.
[94]	GABLER L F, CRANDALL J R, PANZER M B. Development of a second-order system for rapid estimation of maximum brain strain [J]. Annals of Biomedical Engineering, 2019, 47(9): 1971–1981. DOI: 10.1007/s10439-018-02179-9.
[95]	MCBIRNEY S, HOCH E. Toward a unified multiscale computational model of the human body’s immediate responses to blast-related trauma: proceedings and expert findings from a U. S. department of defense international state-of-the-science meeting [J]. Rand Health Quarterly, 2023, 10(4): 11.
[96]	MONTANINO A, LI X G, ZHOU Z, et al. Subject-specific multiscale analysis of concussion: from macroscopic loads to molecular-level damage [J]. Brain Multiphysics, 2021, 2: 100027. DOI: 10.1016/j.brain.2021.100027.
[97]	LIU Y K, CHANDRA K B, VON ROSENBERG D U. Angular acceleration of viscoelastic (Kelvin) material in a rigid spherical shell: a rotational head injury model [J]. Journal of Biomechanics, 1975, 8(5): 285–292. DOI: 10.1016/0021-9290(75)90080-9.
[98]	HOSSEINI-FARID M, AMIRI-TEHRANI-ZADEH M S, RAMZANPOUR M, et al. The strain rates in the brain, brainstem, dura, and skull under dynamic loadings [J]. Mathematical and Computational Applications, 2020, 25(2): 21. DOI: 10.3390/mca25020021.
[99]	CARLSEN R W, FAWZI A L, WAN Y, et al. A quantitative relationship between rotational head kinematics and brain tissue strain from a 2-D parametric finite element analysis [J]. Brain Multiphysics, 2021, 2: 100024. DOI: 10.1016/j.brain.2021.100024.
[100]	WU S J, ZHAO W, GHAZI K, et al. Convolutional neural network for efficient estimation of regional brain strains [J]. Scientific Reports, 2019, 9(1): 17326. DOI: 10.1038/s41598-019-53551-1.
[101]	WU S J, ZHAO W, JI S B. Real-time dynamic simulation for highly accurate spatiotemporal brain deformation from impact [J].Computer Methods in Applied Mechanics and Engineering, 2022, 394: 114913. DOI: 10.1016/j.cma.2022.114913.
[102]	ZHAN X H, LIU Y Z, RAYMOND S J, et al. Rapid estimation of entire brain strain using deep learning models [J]. IEEE Transactions on Biomedical Engineering, 2021, 68(11): 3424–3434. DOI: 10.1109/TBME.2021.3073380.
[103]	ZHAN X H, LI Y H, LIU Y Z, et al. Machine-learning-based head impact subtyping based on the spectral densities of the measurable head kinematics [J]. Journal of Sport and Health Science, 2023, 12(5): 619–629. DOI: 10.1016/j.jshs.2023.03.003.
[104]	ZHAN X H, LIU Y Z, CECCHI N J, et al. AI-based denoising of head impact kinematics measurements with convolutional neural network for traumatic brain injury prediction [J]. IEEE Transactions on Biomedical Engineering, 2024, 71(9): 2759–2770. DOI: 10.1109/TBME.2024.3392537.