留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

脑组织热-力耦合行为综述

秦璇 苏丽君 万秀伟 陶泽 孙学超 卢天健

秦璇, 苏丽君, 万秀伟, 陶泽, 孙学超, 卢天健. 脑组织热-力耦合行为综述[J]. 应用数学和力学, 2024, 45(6): 670-690. doi: 10.21656/1000-0887.450143
引用本文: 秦璇, 苏丽君, 万秀伟, 陶泽, 孙学超, 卢天健. 脑组织热-力耦合行为综述[J]. 应用数学和力学, 2024, 45(6): 670-690. doi: 10.21656/1000-0887.450143
QIN Xuan, SU Lijun, WAN Xiuwei, TAO Ze, SUN Xuechao, LU Tianjian. A Review of Coupled Thermo-Mechanical Behaviors of Brain Tissue[J]. Applied Mathematics and Mechanics, 2024, 45(6): 670-690. doi: 10.21656/1000-0887.450143
Citation: QIN Xuan, SU Lijun, WAN Xiuwei, TAO Ze, SUN Xuechao, LU Tianjian. A Review of Coupled Thermo-Mechanical Behaviors of Brain Tissue[J]. Applied Mathematics and Mechanics, 2024, 45(6): 670-690. doi: 10.21656/1000-0887.450143

脑组织热-力耦合行为综述

doi: 10.21656/1000-0887.450143
基金项目: 

国家自然科学基金 12032010

江苏省研究生科研与实践创新计划 KYCX24_0543

江苏省研究生科研与实践创新计划 KYCX24_0535

详细信息
    作者简介:

    秦璇(2000—),女,博士生(E-mail: qinxuan@nuaa.edu.cn)

    通讯作者:

    卢天健(1964—),男,教授, 博士生导师(通讯作者. E-mail: tjlu@nuaa.edu.cn)

  • (我刊编委卢天健来稿)
  • 中图分类号: O34

A Review of Coupled Thermo-Mechanical Behaviors of Brain Tissue

  • (Contributed by LU Tianjian, M. AMM Editorial Board)
  • 摘要:

    脑组织是由固相与液相组成的饱和含液多孔材料,固、液、生理环境(尤其温度)之间相互作用,具体表现为脑组织内部温度场、渗流场、应力场相互影响的热-力耦合行为,故阐明脑组织的热-力耦合行为是理解大脑功能和疾病病理的关键.该文首先介绍了脑组织的传热学和力学性质,重点关注实验测量及应变率和温度的影响;其次,总结了描述脑组织热-力耦合行为的数理模型,包括力学模型、传热学模型和热-力耦合模型;最后,对该重要学科交叉领域进行了总结和展望.

    (Contributed by LU Tianjian, M. AMM Editorial Board)
    1)  (我刊编委卢天健来稿)
  • 图  1  人体不同组织的力学特性:大脑是人体最柔软的组织[1]

    Figure  1.  Mechanical properties of human tissues: brain is the softest tissue in human body [1]

    图  2  脑组织的多物理场耦合行为

    Figure  2.  Multi-physical coupling behaviors of brain tissue

    图  3  速度/应变率与脑组织剪切模量的关系[68]

    Figure  3.  Relationships between the loading velocity/strain rate and the brain shear modulus[68]

    图  4  脑组织剪切模量随温度的变化趋势:图中标注了成像平面上的两个测量区域(ROI 1和ROI 2,白色圆圈)及相应的测量结果μ1μ2[78]

       为了解释图中的颜色,读者可以参考本文的电子网页版本,后同.

    Figure  4.  The shear modulus of brain tissue changing with the temperature: 2 ROIs (the white circles) in the imagin plane and corresponding measurement results μ1 and μ2 illustrated in each image[78]

    图  5  等距保持过程中区分脑组织黏弹性和多孔弹性效应的方法示意图[110]

    Figure  5.  Schematic of the proposed method for distinguishing viscoelastic and poroelastic effects in brain tissue during the isometric hold testing [110]

    A1  脑组织力学性质

    A1.   Mechanical properties of brain tissue

    力学性质 样品来源 数值 测试方法 测试条件 参考文献
    弹性模量
    E/kPa
    牛脑 0.35 非受限压缩法,应变率0.01 s-1 离体 [72]
    白质,牛
    灰质,牛
    1.895±0.592
    1.389±0.289
    压痕法,应变率0.004 s-1 室温,离体 [42]
    白质,大鼠
    灰质,大鼠
    0.294±0.074
    0.454±0.053
    扫描力显微镜(SFM)压痕法 室温,离体 [73]
    白质,猪
    灰质,猪
    1.787±0.186
    1.195±0.157
    压痕法 室温,离体 [74]
    牛脑,非灌注
    牛脑,灌注
    46.8±31.3
    106.4±73.9
    离心实验模拟超重 20±2 ℃,离体 [75]
    猪脑 8.12~29.46
    10.86~41.05
    16.08~60.73
    拉伸法,应变率30 s-1
    拉伸法,应变率60 s-1
    拉伸法,应变率90 s-1
    室温22 ℃,离体 [69]
    白质,猪 0.114±0.026
    2.947
    0.155
    非受限压缩法,平衡模量
    非受限压缩法,应变率2 s-1
    非受限压缩法,应变率10-6 s-1
    室温,离体 [71]
    人脑 2.704
    0.457
    非受限压缩法,应变率2 s-1
    非受限压缩法,应变率0.001 s-1
    室温,离体 [71]
    剪切模量
    G/kPa
    大鼠脑 0.412~0.453 微压痕法, 应变率1.43 s-1 离体 [76]
    大鼠脑 0.398~0.626 压痕法 在体/离体 [43]
    猪脑 0.195~0.305 振荡剪切法,应变率1 s-1 37 ℃,离体 [66]
    辐射冠,猪 0.6~1.0 压痕法,应变率0.064 s-1 室温,离体 [41]
    小脑,小鼠
    皮质,小鼠
    髓质,小鼠
    脑桥,小鼠
    2.48~3.14
    4.83~7.67
    3.81~4.32
    5.66~6.51
    微压痕法, 应变率10 s-1 室温22 ℃,离体 [63]
    白质,猪
    灰质,猪
    丘脑,猪
    中脑,猪
    0.925~1.209
    0.669~0.816
    0.943±0.109
    0.955±0.137
    压痕法 室温,离体 [61]
    胼胝体,人
    辐射冠,人
    基底神经节,人
    皮层,人
    0.33±0.18
    0.54±0.21
    0.56±0.20
    1.06±0.36
    剪切,准静态加载条件 室温,离体 [77]
    小脑,小鼠 2.11±1.26
    3.15±1.66
    3.71±1.23
    微压痕法,应变率5 s-1
    微压痕法,应变率15 s-1
    微压痕法,应变率30 s-1
    22 ℃,离体 [67]
    皮质,小鼠 4.06±1.69
    6.14±3.03
    7.05±3.92
    微压痕法,应变率5 s-1
    微压痕法,应变率15 s-1
    微压痕法,应变率30 s-1
    22 ℃,离体 [67]
    猪脑 0.311±0.055
    0.384±0.038
    0.486±0.107
    0.546±0.119
    0.645±0.071
    压痕法,应变率0.002 s-1
    压痕法,应变率0.008 s-1
    压痕法,应变率0.030 s-1
    压痕法,应变率0.061 s-1
    压痕法,应变率0.152 s-1
    室温,离体 [68]
    猪脑,冷冻保存
    猪脑,22 ℃保存
    猪脑,37 ℃保存
    1.043±0.271
    0.714±0.210
    0.497±0.156
    简单剪切,应变率30 s-1 22 ℃,离体 [59]
    猪脑 1.20
    0.84
    0.82
    0.84
    0.92
    横波弹性成像 25 ℃,离体
    37 ℃,离体
    42 ℃,离体
    45 ℃,离体
    48 ℃,离体
    [78]
    切线模量
    Et/kPa
    猪脑,冷冻保存
    猪脑,37 ℃保存
    156.7~2 242.9
    500.2~4 959.9
    SHPB高应变率单轴应力压缩实验,应变率(2 487±72) s-1 37 ℃,离体,10%应变 [60]
    存储模量
    G′/kPa
    人脑
    猪脑
    1.182~2.224
    1.727~3.757
    磁共振弹性成像 在体
    离体
    [51]
    白质,人
    灰质,人
    脑干,人
    0.453~1.903
    0.507~1.911
    1.270~5.048
    振荡剪切实验 37 ℃,离体 [79]
    白质,人
    白质,人
    白质,人
    白质,人
    0.866
    0.793
    0.764
    0.754
    流变实验 22 ℃,离体
    27 ℃,离体
    32 ℃,离体
    37 ℃,离体
    [80]
    损耗模量
    G″/kPa
    人脑
    猪脑
    0.631~1.140
    1.233±2.534
    磁共振弹性成像 在体
    离体
    [51]
    白质,人
    灰质,人
    脑干,人
    0.082~0.443
    0.124~0.456
    0.255~1.032
    振荡剪切实验 37 ℃,离体 [79]
    白质,人
    白质,人
    白质,人
    白质,人
    0.233
    0.186
    0.164
    0.152
    流变实验 22 ℃,离体
    27 ℃,离体
    32 ℃,离体
    37 ℃,离体
    [80]
    Poisson比
    ν
    牛脑 0.35 非受限压缩法,应变率0.01 s-1 离体 [72]
    人脑,非排水
    人脑,排水
    0.5
    0.496
    非受限压缩法,应变率0.01 s-1 离体 [81]
    牛脑,非灌注
    牛脑,灌注
    0.326±0.198
    0.370±0.188
    离心实验模拟超重 20±2 ℃,离体 [75]
    牛脑
    0.45~0.47
    0.67±0.05
    非受限压缩 室温(~25 ℃),离体,
    应变5%~10%
    室温(~25 ℃),离体,应变30%
    [82]
    下载: 导出CSV

    A2  脑组织热物性

    A2.   Thermal properties of brain tissue

    热物性 样品来源 数值 测试方法 测试条件 参考文献
    密度
    ρ/(kg·m-3)
    白质,马脑
    灰质,马脑
    1 038±1.1
    1 039±0.9
    离体,37 ℃ [99]

    灰质
    白质
    1 046
    1 050
    1 040
    离体,37 ℃ [100]
    比热容
    c/(J·kg-1·K-1)
    白质,人脑 3 590
    3 610
    3 640
    3 690
    DSC 离体,37 ℃
    离体,43 ℃
    离体,50 ℃
    离体,60 ℃
    [98]
    灰质,人脑 3 590
    3 650
    3 650
    3 700
    DSC 离体,37 ℃
    离体,43 ℃
    离体,50 ℃
    离体,60 ℃
    [98]
    胶质母细胞瘤 3 630
    3 790
    3 740
    3 640
    DSC 离体,37 ℃
    离体,43 ℃
    离体,50 ℃
    离体,60 ℃
    [98]

    灰质
    白质
    小脑
    3 630±74
    3 718±36
    3 525±73
    3 653
    DSC 离体,60 ℃ [100]
    人脑 4 160 DSC 离体,60 ℃ [101]
    热导率
    λ/(W·m-1·K-1)
    牛脑 0.524±0.010
    0.553±0.004
    0.563±0.005
    0.567±0.011
    0.560±0.006
    0.697±0.034
    2.005±0.057
    双针传感器 离体,22 ℃
    离体,33 ℃
    离体,41 ℃
    离体,52 ℃
    离体,66 ℃
    离体,83 ℃
    离体,97 ℃
    [88]

    灰质
    白质
    小脑
    0.51±0.02
    0.55±0.03
    0.48±0.02
    0.51±0.00
    双针传感器 离体,97 ℃ [100]
    人脑 0.49 双针传感器 离体,97 ℃ [101]
    白质,人
    灰质,人
    人脑
    0.502
    0.565
    0.528
    探针法 离体 [97]
    热扩散系数
    a/(10-6 m2·s-1)
    牛脑 0.136±0.005
    0.145±0.001
    0.147±0.001
    0.149±0.003
    0.158±0.003
    0.205±0.015
    0.373±0.014
    双针传感器 离体,22 ℃
    离体,33 ℃
    离体,41 ℃
    离体,52 ℃
    离体,66 ℃
    离体,83 ℃
    离体,97 ℃
    [88]
    白质,人
    灰质,人
    人脑
    0.134
    0.143
    0.138
    探针法 离体 [97]
    体积热容
    Cv/(MJ·m-3·K-1)
    3.86±0.06 离体,22 ℃
    3.83±0.03 离体,33 ℃
    3.83±0.04 离体,41 ℃
    牛脑 3.81±0.06 双针传感器 离体,52 ℃ [88]
    3.53±0.08 离体,66 ℃
    3.30±0.19 离体,83 ℃
    4.98±0.20 离体,97 ℃
    热膨胀系数
    αT/K-1
    海马体,大鼠 5.5×10-4
    1.37×10-3
    DIC 离体,30~40 ℃
    离体,37~40 ℃
    [102]
    狗脑 5×10-5 密度测量技术 离体,25~37 ℃ [103]
    下载: 导出CSV

    A3  脑组织数理模型

    A3.   Mathematical models for brain tissue

    模型 内容 优点 不足
    超弹性模型 适用于脑组织等类橡胶材料,主要包括Neo-Hookean模型、Mooney-Rivlin模型、Ogden超弹性模型等 可以捕捉脑组织时间无关的拉压不对称性、非线性和大变形行为 现象学模型,不能很好地描述脑组织的时间依赖性,无法准确描述含液多孔脑组织的双相性
    黏弹性模型 描述脑组织的弹性与黏性,松弛模量采用Prony级数进行描述 可以描述脑组织的时间依赖性,预测脑组织受力后的蠕变与松弛现象 无法捕捉脑组织的拉压不对称特性,无法准确描述含液多孔脑组织的双相性
    多孔弹性模型 基于Biot理论,将脑组织看作由弹性固相和无黏液相组成的一种饱和含液多孔材料 可以考虑脑组织内部孔隙流体的影响,描述流体和固体间的相互作用 经典的Biot多孔弹性模型不含尺度,故不能准确描述固-液界面作用,且不能描述脑组织的滞回行为
    多孔黏弹性模型 结合多孔弹性与黏弹性,描述多孔材料的黏弹性行为 考虑了固相、液相之间的相互作用对时间和长度尺度的依赖性 脑组织的复杂性使得多孔黏弹性模型的建立和参数确定具有挑战性,参数确定需要更多的实验数据支持
    Pennes生物传热模型 用于描述生物组织中热传递过程的数学模型 考虑了代谢、血液灌注对传热的影响,简单、有效,具有普适性 在某些情况下过于简化,例如忽略了血管之间的相互作用、组织的各向异性以及血液流动的复杂性
    热-力耦合模型 考虑温度、饱和度、孔隙率、微观结构等因素的影响,涉及固相/液相与外界环境温度和热量的相互作用 可以描述脑组织流体流动、传热和力学变形耦合行为 存在研究空白,目前的模型大多是基于肝脏、皮肤等生物组织的热-流耦合或热-固耦合模型,缺乏热-流-固耦合模型,模型建立困难
    下载: 导出CSV
  • [1] BUDDAY S, OVAERT T C, HOLZAPFEL G A, et al. Fifty shades of brain: a review on the mechanical testing and modeling of brain tissue[J]. Archives of Computational Methods in Engineering, 2019, 27(4): 1187-1230.
    [2] GORIELY A, GEERS M G D, HOLZAPFEL G A, et al. Mechanics of the brain: perspectives, challenges, and opportunities[J]. Biomechanics and Modeling in Mechanobiology, 2015, 14(5): 931-965. doi: 10.1007/s10237-015-0662-4
    [3] PROCÈS A, LUCIANO M, KALUKULA Y, et al. Multiscale mechanobiology in brain physiology and diseases[J]. Frontiers in Cell and Developmental Biology, 2022, 10: 823857. doi: 10.3389/fcell.2022.823857
    [4] SQUIRE L R, BERG D, BLOOM F E, et al. Fundamental Neuroscience[M]. San Diego: Academic Press, 2013.
    [5] LEI Y, HAN H, YUAN F, et al. The brain interstitial system: anatomy, modeling, in vivo measurement, and applications[J]. Progress in Neurobiology, 2017, 157: 230-246. doi: 10.1016/j.pneurobio.2015.12.007
    [6] STUART G, SPRUSTON N, HÄUSSER M. Dendrites[M]. New York: Oxford University Press, 2007.
    [7] SYKOVÁ E, NICHOLSON C. Diffusion in brain extracellular space[J]. Physiological Reviews, 2008, 88(4): 1277-1340. doi: 10.1152/physrev.00027.2007
    [8] 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
    [9] BHARAT S, TECHAVIPOO U, KISS M Z, et al. Monitoring stiffness changes in lesions after radiofrequency ablation at different temperatures and durations of ablation[J]. Ultrasound in Medicine & Biology, 2005, 31(3): 415-422.
    [10] MOHAMMADI A, BIANCHI L, KORGANBAYEV S, et al. Thermomechanical modeling of laser ablation therapy of tumors: sensitivity analysis and optimization of influential variables[J]. IEEE Transactions on Biomedical Engineering, 2022, 69(1): 302-313. doi: 10.1109/TBME.2021.3092889
    [11] SINGH S, MELNIK R. Coupled thermo-electro-mechanical models for thermal ablation of biological tissues and heat relaxation time effects[J]. Physics in Medicine & Biology, 2019, 64(24): 245008.
    [12] XU F, LU T J. Introduction to Skin Biothermomechanics and Thermal Pain[M]. New York: Springer, 2011.
    [13] 卢天健, 林敏, 徐峰. 牙齿的热-力-电生理耦合行为[M]. 北京: 科学出版社, 2015.

    LU Tianjian, LIN Min, XU Feng. Thermo-Mechano-Electrophysiological Coupling Behaviors of Teeth[M]. Beijing: Science Press, 2015. (in Chinese)
    [14] TIAN J, HUANG G, LIN M, et al. A mechanoelectrical coupling model of neurons under stretching[J]. Journal of the Mechanical Behavior of Biomedical Materials, 2019, 93: 213-221. doi: 10.1016/j.jmbbm.2019.02.007
    [15] OCHOA D A, MIRANDA B M, CONGER B C, et al. Lunar eva thermal environment challenges[J]. SAE Transactions, 2006, 115: 492-505.
    [16] ZU EULENBURG P, VAN OMBERGEN A, TOMILOVSKAYA E S, et al. Reply to Ludwig et al: a potential mechanism for intracranial cerebrospinal fluid accumulation during long-duration spaceflight[J]. Biological Sciences, 2019, 116(41): 20265-20266.
    [17] VAN OMBERGEN A, JILLINGS S, JEURISSEN B, et al. Brain ventricular volume changes induced by long-duration spaceflight[J]. Proceedings of the National Academy of Sciences of the United States of America, 2019, 116(21): 10531-10536.
    [18] MACMANUS D B, MURPHY J G, GILCHRIST M D. Mechanical characterisation of brain tissue up to 35% strain at 1, 10, and 100/s using a custom-built micro-indentation apparatus[J]. Journal of the Mechanical Behavior of Biomedical Materials, 2018, 87: 256-266. doi: 10.1016/j.jmbbm.2018.07.025
    [19] MOHAJER N, WINTER A, GREGORY T M, et al. Experimental validation of a high-G centrifuge system using an advanced wireless human dummy[C]//Proceedings of the 2022 IEEE International Conference on Systems, Man, and Cybernetics (SMC). Prague, Czech Republic, 2022.
    [20] WANG L, YIN H, DI Y, et al. Human local and total heat losses in different temperature[J]. Physiology & Behavior, 2016, 157: 270-276.
    [21] ECKER J R, GESCHWIND D H, KRIEGSTEIN A R, et al. The barin initiative cell census consortium: lessons learned toward generating a comprehensive brain cell atlas[J]. Neuron, 2017, 96(3): 542-557. doi: 10.1016/j.neuron.2017.10.007
    [22] CHAGOVETZ A A, JENSEN R L, RECHT L, et al. Preliminary use of differential scanning calorimetry of cerebrospinal fluid for the diagnosis of glioblastoma multiforme[J]. Journal of Neuro-Oncology, 2011, 105(3): 499-506. doi: 10.1007/s11060-011-0630-5
    [23] BERTALAN G, BOEHM-STURM P, SCHREYER S, et al. The influence of body temperature on tissue stiffness, blood perfusion, and water diffusion in the mouse brain[J]. Acta Biomater, 2019, 96: 412-420. doi: 10.1016/j.actbio.2019.06.034
    [24] BARNES J M, PRZYBYLA L, WEAVER V M, et al. Tissue mechanics regulate brain development, homeostasis and disease[J]. Journal of Cell Science, 2017, 130(1): 71-82. doi: 10.1242/jcs.191742
    [25] MOMIN A, BAHRAMPOUR S, MIN H K, et al. Channeling force in the brain: mechanosensitive ion channels choreograph mechanics and malignancies[J]. Trends in Pharmacological Sciences, 2021, 42(5): 367-384. doi: 10.1016/j.tips.2021.02.006
    [26] MALEK A M, IZUMO S. Mechanism of endothelial cell shape change and cytoskeletal remodeling in response to fluid shear stress[J]. Journal of Cell Science, 1996, 109(4): 713-726. doi: 10.1242/jcs.109.4.713
    [27] TYLER W J. The mechanobiology of brain function[J]. Nature Reviews Neuroscience, 2012, 13(12): 867-878. doi: 10.1038/nrn3383
    [28] KOSER D E, THOMPSON A J, FOSTER S K, et al. Mechanosensing is critical for axon growth in the developing brain[J]. Nature Neuroscience, 2016, 19: 1592-1598. doi: 10.1038/nn.4394
    [29] RICCOBELLI D, BEVILACQUA G. Surface tension controls the onset of gyrification in brain organoids[J]. Journal of the Mechanics and Physics of Solids, 2020, 134: 103745. doi: 10.1016/j.jmps.2019.103745
    [30] NGO M T, HARLEY B A C. Progress in mimicking brain microenvironments to understand and treat neurological disorders[J]. APL Bioengineering, 2021, 5(2): 020902. doi: 10.1063/5.0043338
    [31] RASHID B, DESTRADE M, GILCHRIST M D. Inhomogeneous deformation of brain tissue during tension tests[J]. Computational Materials Science, 2012, 64: 295-300. doi: 10.1016/j.commatsci.2012.05.030
    [32] RASHID B, DESTRADE M, GILCHRIST M D. Mechanical characterization of brain tissue in tension at dynamic strain rates[J]. Journal of the Mechanical Behavior of Biomedical Materials, 2014, 33: 43-54. doi: 10.1016/j.jmbbm.2012.07.015
    [33] MILLER K, CHINZEI K. Mechanical properties of brain tissue in tension[J]. Journal of Biomechanics, 2002, 35(4): 483-490. doi: 10.1016/S0021-9290(01)00234-2
    [34] HASLACH H W, LEAHY L N, RILEY P, et al. Solid-extracellular fluid interaction and damage in the mechanical response of rat brain tissue under confined compression[J]. Journal of the Mechanical Behavior of Biomedical Materials, 2014, 29: 138-150. doi: 10.1016/j.jmbbm.2013.08.027
    [35] EL SAYED T, MOTA A, FRATERNALI F, et al. A variational constitutive model for soft biological tissues[J]. Journal of Biomechanics, 2008, 41(7): 1458-1466. doi: 10.1016/j.jbiomech.2008.02.023
    [36] YUE H, DENG J, ZHOU J, et al. Biomechanics of porcine brain tissue under finite compression[J]. Journal of Mechanics in Medicine and Biology, 2017, 17(1): 1750001. doi: 10.1142/S0219519417500014
    [37] MILLER K, CHINZEI K. Constitutive modelling of brain tissue: experiment and theory[J]. Journal of Biomechanics, 1997, 30(11): 1115-1121.
    [38] DONNELLY B R, MEDIGE J. Shear properties of human brain tissue[J]. Journal of Biomechanical Engineering, 1997, 119(4): 423-432. doi: 10.1115/1.2798289
    [39] ARBOGAST K B, MARGULIES S S. Material characterization of the brainstem from oscillatory shear tests[J]. Journal of Biomechanics, 1998, 31(9): 801-807. doi: 10.1016/S0021-9290(98)00068-2
    [40] DARVISH K K, CRANDALL J R. Nonlinear viscoelastic effects in oscillatory shear deformation of brain tissue[J]. Medical Engineering & Physics, 2001, 23(9): 633-645.
    [41] PAN C, CHEN F, ZHOU J, et al. Multiregional viscoelastic characterization of the corona radiata in the sagittal plane of the porcine brain[J]. Medical & Biological Engineering & Computing, 2018, 57(3): 615-622. doi: 10.3969/j.issn.1671-7171.2018.03.071
    [42] 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
    [43] GEFEN A, GEFEN N, ZHU Q, et al. Age-dependent changes in material properties of the brain and braincase of the rat[J]. Journal of Neurotrauma, 2003, 20(11): 1163-1177. doi: 10.1089/089771503770802853
    [44] BRADFIELD C, VOO L, DREWRY D, et al. Dynamic strain fields of the mouse brain during rotation[J]. Biomech Model Mechanobiol, 2024, 23(2): 397-412. doi: 10.1007/s10237-023-01781-8
    [45] MENARD K P, MENARD N. Dynamic Mechanical Analysis[M]. CRC Press, 2020.
    [46] PENG Y Y, DUSSAN D D, NARAIN R. Polymer Science and Nanotechnology[M]. Elsevier, 2020.
    [47] DEWALL R J. Ultrasound elastography: principles, techniques, and clinical applications[J]. Critical Reviews in Biomedical Engineering, 2013, 41(1): 1-19. doi: 10.1615/CritRevBiomedEng.2013006991
    [48] GENNISSON J L, DEFFIEUX T, FINK M, et al. Ultrasound elastography: principles and techniques[J]. Diagnostic and Interventional Imaging, 2013, 94(5): 487-495. doi: 10.1016/j.diii.2013.01.022
    [49] OZTURK A, GRAJO J R, DHYANI M, et al. Principles of ultrasound elastography[J]. Abdom Radiol (NY), 2018, 43(4): 773-785. doi: 10.1007/s00261-018-1475-6
    [50] KRUSE S A, ROSE G H, GLASER K J, et al. Magnetic resonance elastography of the brain[J]. Neuroimage, 2008, 39(1): 231-237. doi: 10.1016/j.neuroimage.2007.08.030
    [51] WEICKENMEIER J, KURT M, OZKAYA E, et al. Magnetic resonance elastography of the brain: a comparison between pigs and humans[J]. Journal of the Mechanical Behavior of Biomedical Materials, 2018, 77: 702-710. doi: 10.1016/j.jmbbm.2017.08.029
    [52] STREITBERGER K J, SACK I, KREFTING D, et al. Brain viscoelasticity alteration in chronic-progressive multiple sclerosis[J]. PLoS One, 2012, 7(1): e29888. doi: 10.1371/journal.pone.0029888
    [53] HAMHABER U, KLATT D, PAPAZOGLOU S, et al. In vivo magnetic resonance elastography of human brain at 7 t and 1.5 t[J]. Journal of Magnetic Resonance Imaging, 2010, 32(3): 577-583. doi: 10.1002/jmri.22294
    [54] HRAPKO M, VAN DOMMELEN J A, PETERS G W, et al. The influence of test conditions on characterization of the mechanical properties of brain tissue[J]. Journal of Biomechanical Engineering, 2008, 130(3): 031003. doi: 10.1115/1.2907746
    [55] VELARDI F, FRATERNALI F, ANGELILLO M. Anisotropic constitutive equations and experimental tensile behavior of brain tissue[J]. Biomechanics and Modeling in Mechanobiology, 2005, 5(1): 53-61.
    [56] ZHU Z, JIANG C, JIANG H. A visco-hyperelastic model of brain tissue incorporating both tension/compression asymmetry and volume compressibility[J]. Acta Mechanica, 2019, 230(6): 2125-2135. doi: 10.1007/s00707-019-02383-1
    [57] MILLER K. Method of testing very soft biological tissues in compression[J]. Journal of Biomechanics, 2005, 38(1): 153-158. doi: 10.1016/j.jbiomech.2004.03.004
    [58] ESKANDARI F, SHAFIEIAN M, AGHDAM M M, et al. Tension strain-softening and compression strain-stiffening behavior of brain white matter[J]. Annals of Biomedical Engineering, 2021, 49(1): 276-286. doi: 10.1007/s10439-020-02541-w
    [59] RASHID B, DESTRADE M, GILCHRIST M D. Influence of preservation temperature on the measured mechanical properties of brain tissue[J]. Journal of Biomechanics, 2013, 46(7): 1276-1281. doi: 10.1016/j.jbiomech.2013.02.014
    [60] ZHANG J, YOGANANDAN N, PINTAR F A, et al. Effects of tissue preservation temperature on high strain-rate material properties of brain[J]. Journal of Biomechanics, 2011, 44(3): 391-396. doi: 10.1016/j.jbiomech.2010.10.024
    [61] VAN DOMMELEN J A W, VAN DER SANDE T P J, HRAPKO M, et al. Mechanical properties of brain tissue by indentation: interregional variation[J]. Journal of the Mechanical Behavior of Biomedical Materials, 2010, 3(2): 158-166. doi: 10.1016/j.jmbbm.2009.09.001
    [62] PRANGE M T, MARGULIES S S. Regional, directional, and age-dependent properties of the brain undergoing large deformation[J]. Journal of Biomechanical Engineering, 2002, 124(2): 244-252. doi: 10.1115/1.1449907
    [63] MACMANUS D B, PIERRAT B, MURPHY J G, et al. Region and species dependent mechanical properties of adolescent and young adult brain tissue[J]. Scientific Reports, 2017, 7(1): 13729. doi: 10.1038/s41598-017-13727-z
    [64] ELKIN B S, ILANKOVAN A, MORRISON B. Age-dependent regional mechanical properties of the rat hippocampus and cortex[J]. Journal of Biomechanical Engineering, 2010, 132(1): 011010. doi: 10.1115/1.4000164
    [65] RASHID B, DESTRADE M, GILCHRIST M D. Temperature effects on brain tissue in compression[J]. Journal of the Mechanical Behavior of Biomedical Materials, 2012, 14: 113-118. doi: 10.1016/j.jmbbm.2012.04.005
    [66] GARO A, HRAPKO M M, DOMMELEN V, et al. Towards a reliable characterisation of the mechanical behaviour of brain tissue: the effects of post-mortem time and sample preparation[J]. Biorheology, 2007, 44(1): 51-58.
    [67] MACMANUS D B, PIERRAT B, MURPHY J G, et al. Dynamic mechanical properties of murine brain tissue using micro-indentation[J]. Journal of Biomechanics, 2015, 48(12): 3213-3218. doi: 10.1016/j.jbiomech.2015.06.028
    [68] QIAN L, ZHAO H, GUO Y, et al. Influence of strain rate on indentation response of porcine brain[J]. Journal of the Mechanical Behavior of Biomedical Materials, 2018, 82: 210-217. doi: 10.1016/j.jmbbm.2018.03.031
    [69] RASHID B, DESTRADE M, GILCHRIST M D. Mechanical characterization of brain tissue in tension at dynamic strain rates[J]. Journal of the Mechanical Behavior of Biomedical Materials, 2014, 33: 43-54. doi: 10.1016/j.jmbbm.2012.07.015
    [70] MILLER K, CHINZEI K, ORSSENGO G, et al. Mechanical properties of brain tissue in-vivo: experiment and computer simulation[J]. Journal of Biomechanics, 2000, 33(11): 1369-1376. doi: 10.1016/S0021-9290(00)00120-2
    [71] SU L, QI B, YIN J, et al. Compressive response of white matter in the brain at low strain rates[J]. International Journal of Mechanical Sciences, 2024, 277: 109415. doi: 10.1016/j.ijmecsci.2024.109415
    [72] CHENG S, BILSTON L E. Unconfined compression of white matter[J]. Journal of Biomechanics, 2007, 40(1): 117-124. doi: 10.1016/j.jbiomech.2005.11.004
    [73] CHRIST A F, FRANZE K, GAUTIER H, et al. Mechanical difference between white and gray matter in the rat cerebellum measured by scanning force microscopy[J]. Journal of Biomechanics, 2010, 43(15): 2986-2992. doi: 10.1016/j.jbiomech.2010.07.002
    [74] KASTER T, SACK I, SAMANI A. Measurement of the hyperelastic properties of ex vivo brain tissue slices[J]. Journal of Biomechanics, 2011, 44(6): 1158-1163. doi: 10.1016/j.jbiomech.2011.01.019
    [75] GUILLAUME A, OSMONT D, GAFFIE D, et al. Effects of perfusion on the mechanical behavior of the brain-exposed to hypergravity[J]. Journal of Biomechanics, 1997, 30(4): 383-389. doi: 10.1016/S0021-9290(96)00153-4
    [76] FINAN J D, ELKIN B S, PEARSON E M, et al. Viscoelastic properties of the rat brain in the sagittal plane: effects of anatomical structure and age[J]. Annals of Biomedical Engineering, 2011, 40(1): 70-78.
    [77] 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
    [78] LIU Y L, LI G Y, HE P, et al. Temperature-dependent elastic properties of brain tissues measured with the shear wave elastography method[J]. Journal of the Mechanical Behavior of Biomedical Materials, 2017, 65: 652-656. doi: 10.1016/j.jmbbm.2016.09.026
    [79] CHATELIN S, VAPPOU J, ROTH S, et al. Towards child versus adult brain mechanical properties[J]. Journal of the Mechanical Behavior of Biomedical Materials, 2012, 6: 166-173. doi: 10.1016/j.jmbbm.2011.09.013
    [80] FORTE A E, GENTLEMAN S M, DINI D. On the characterization of the heterogeneous mechanical response of human brain tissue[J]. Biomechanics and Modeling in Mechanobiology, 2016, 16(3): 907-920.
    [81] 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
    [82] ESKANDARI F, RAHMANI Z, SHAFIEIAN M. The effect of large deformation on Poisson's ratio of brain white matter: an experimental study[J]. Proceedings of the Institution of Mechanical Engineers (Part H): Journal of Engineering in Medicine, 2021, 235(4): 401-407. doi: 10.1177/0954411920984027
    [83] WANG J, ZHANG Y, JIANG Z, et al. Mechanical behavior and constitutive equations of porcine brain tissue considering both solution environment effect and strain rate effect[J]. Mechanics of Advanced Materials and Structures, 2024, 31(10): 2115-2129. doi: 10.1080/15376494.2022.2150917
    [84] KIYATKIN E A. Brain temperature homeostasis: physiological fluctuations and pathological shifts[J]. Frontiers in Bioscience: a Journal and Virtual Library, 2010, 15: 73. doi: 10.2741/3608
    [85] WANG H, WANG B, NORMOYLE K P, et al. Brain temperature and its fundamental properties: a review for clinical neuroscientists[J]. Frontiers in Neuroscience, 2014, 8: 307.
    [86] LOPRESTO V, ARGENTIERI A, PINTO R, et al. Temperature dependence of thermal properties of ex vivo liver tissue up to ablative temperatures[J]. Physics in Medicine and Biology, 2019, 64(10): 105016. doi: 10.1088/1361-6560/ab1663
    [87] SILVA N P, BOTTIGLIERI A, CONCEIÇÃO R C, et al. Characterisation of ex vivo liver thermal properties for electromagnetic-based hyperthermic therapies[J]. Sensors, 2020, 20(10): 3004. doi: 10.3390/s20103004
    [88] MOHAMMADI A, BIANCHI L, ASADI S, et al. Measurement of ex vivo liver, brain and pancreas thermal properties as function of temperature[J]. Sensors, 2021, 21(12): 4236. doi: 10.3390/s21124236
    [89] BHATTACHARYA A, MAHAJAN R L. Temperature dependence of thermal conductivity of biological tissues[J]. Physiological Measurement, 2003, 24(3): 769-783. doi: 10.1088/0967-3334/24/3/312
    [90] CHOI J, MORRISSEY M, BISCHOF J C. Thermal processing of biological tissue at high temperatures: impact of protein denaturation and water loss on the thermal properties of human and porcine liver in the range 25~80 ℃[J]. Journal of Heat Transfer, 2013, 135(6): 061302. doi: 10.1115/1.4023570
    [91] HAYES L J, VALVANO J W. Steady-state analysis of self-heated thermistors using finite elements[J]. Journal of Biomechanical Engineering, 1985, 107(1): 77-80. doi: 10.1115/1.3138524
    [92] VALVANO J W, COCHRAN J R, DILLER K R. Thermal conductivity and diffusivity of biomaterials measured with self-heated thermistors[J]. International Journal of Thermophysics, 1985, 6(3): 301-311. doi: 10.1007/BF00522151
    [93] VALVANO J W, ALLEN J T, BOWMAN H F. The simultaneous measurement of thermal conductivity, thermal diffusivity, and perfusion in small volumes of tissue[J]. Journal of Biomechanical Engineering, 1984, 106(3): 192-197. doi: 10.1115/1.3138482
    [94] CLAS S D, DALTON C R, HANCOCK B C. Differential scanning calorimetry: applications in drug development[J]. Pharmaceutical Science & Technology Today, 1999, 2(8): 311-320.
    [95] BIANCHI L, CAVARZAN F, CIAMPITTI L, et al. Thermophysical and mechanical properties of biological tissues as a function of temperature: a systematic literature review[J]. International Journal of Hyperthermia, 2022, 39(1): 297-340. doi: 10.1080/02656736.2022.2028908
    [96] GILL P, MOGHADAM T T, RANJBAR B. Differential scanning calorimetry techniques: applications in biology and nanoscience[J]. Journal of Biomolecular Techniques, 2010, 21(4): 167-193.
    [97] COOPER T E, TREZEK G J. A probe technique for determining the thermal conductivity of tissue[J]. Journal of Heat Transfer, 1972, 94(2): 133-140. doi: 10.1115/1.3449883
    [98] SANO F, WASHIO T, MATSUMAE M. Measurements of specific heat capacities required to build computer simulation models for laser thermotherapy of brain lesions[J]. The Tokai Journal of Experimental and Clinical Medicine, 2019, 44(4): 80-84.
    [99] WEBB A I, WEAVER B M. The density of equine tissue at 37 ℃[J]. Research in Veterinary Science, 1979, 26(1): 71-75. doi: 10.1016/S0034-5288(20)30944-9
    [100] MCINTOSH R L, ANDERSON V. A comprehensive tissue properties database provided for the thermal assessment of a human at rest[J]. Biophysical Reviews and Letters, 2011, 5(3): 129-151.
    [101] XU X, TIKUISIS P, GIESBRECHT G. A mathematical model for human brain cooling during cold-water near-drowning[J]. Journal of Applied Physiology (1985), 1999, 86(1): 265-272. doi: 10.1152/jappl.1999.86.1.265
    [102] DAGRO A M, LI H, DILEONARDI A M, et al. Nonlinearity of the coefficient of thermal expansion in brain tissue[J]. Journal of the Mechanical Behavior of Biomedical Materials, 2021, 123: 104779. doi: 10.1016/j.jmbbm.2021.104779
    [103] MENDEZ J, KEYS A, ANDERSON J T, et al. Density of fat and bone mineral of the mammalian body[J]. Metabolism-Clinical and Experimental, 1960, 9(5): 472-477.
    [104] SALCMAN M, MORIYAMA E, ELSNER H J, et al. Cerebral blood flow and the thermal properties of the brain: a preliminary analysis[J]. Journal of Neurosurgery, 1989, 70(4): 592-598. doi: 10.3171/jns.1989.70.4.0592
    [105] JIANG Q, CHOPP M, ZHANG Z G, et al. The effect of hypothermia on transient focal ischemia in rat brain evaluated by diffusion- and perfusion-weighted NMR imaging[J]. Journal of Cerebral Blood Flow and Metabolism, 1994, 14(5): 732-741. doi: 10.1038/jcbfm.1994.94
    [106] BIRG T, ORTOLANO F, WIEGERS E J A, et al. Brain temperature influences intracranial pressure and cerebral perfusion pressure after traumatic brain injury: a center TBI study[J]. Neurocrit Care, 2021, 35(3): 651-661. doi: 10.1007/s12028-021-01294-1
    [107] ROSSI S, ZANIER E R, MAURI I, et al. Brain temperature, body core temperature, and intracranial pressure in acute cerebral damage[J]. Journal of Neurol Neurosurg Psychiatry, 2001, 71(4): 448-454. doi: 10.1136/jnnp.71.4.448
    [108] WEX C, ARNDT S, BRANDSTÄDTER K, et al. Biomechanical characterization of material properties of porcine liver after thermal treatment[J]. Soft Materials, 2014, 12(4): 411-419. doi: 10.1080/1539445X.2014.936559
    [109] GUAN F J, ZHANG G J, JIA X H, et al. Study on the effect of sample temperature on the uniaxial compressive mechanical properties of the brain tissue[J]. Applied Bionics and Biomechanics, 2021, 2021: 9986395.
    [110] SU L, WANG M, YIN J, et al. Distinguishing poroelasticity and viscoelasticity of brain tissue with time scale[J]. Acta Biomaterialia, 2023, 155: 423-435. doi: 10.1016/j.actbio.2022.11.009
    [111] KIM B, LEE S B, LEE J, et al. A comparison among Neo-Hookean model, Mooney-Rivlin model, and Ogden model for chloroprene rubber[J]. International Journal of Precision Engineering and Manufacturing, 2012, 13(5): 759-764. doi: 10.1007/s12541-012-0099-y
    [112] SACCOMANDI G, VERGORI L. Generalised Mooney-Rivlin models for brain tissue: a theoretical perspective[J]. International Journal of Non-Linear Mechanics, 2019, 109: 9-14. doi: 10.1016/j.ijnonlinmec.2018.09.008
    [113] PAMIDI M R, ADVANI S H. Nonlinear constitutive relations for human brain tissue[J]. Transactions of the ASME, 1978, 100(1): 44-48.
    [114] OGDEN R W. Large deformation isotropic elasticity-on the correlation of theory and experiment for incompressible rubberlike solids[J]. A Mathematical and Physical Sciences, 1972, 326(1567): 565-584.
    [115] WILLIAM O R. Large deformation isotropic elasticity: on the correlation of theory and experiment for compressible rubberlike solids[J]. Proceedings of the Royal Society of London, 1972, 328(1575): 567-583.
    [116] MIHAI L A, BUDDAY S, HOLZAPFEL G A, et al. A family of hyperelastic models for human brain tissue[J]. Journal of the Mechanics and Physics of Solids, 2017, 106: 60-79. doi: 10.1016/j.jmps.2017.05.015
    [117] PREVOST T P, BALAKRISHNAN A, SURESH S, et al. Biomechanics of brain tissue[J]. Acta Biomaterialia, 2011, 7(1): 83-95. doi: 10.1016/j.actbio.2010.06.035
    [118] FALLENSTEIN G T, HULCE V D, MELVIN J W. Dynamic mechanical properties of human brain tissue[J]. Journal of Biomechanics, 1969, 2(3): 217-226. doi: 10.1016/0021-9290(69)90079-7
    [119] CALHOUN M A, BENTIL S A, ELLIOTT E, et al. Beyond linear elastic modulus: viscoelastic models for brain and brain mimetic hydrogels[J]. ACS Biomaterials Science & Engineering, 2019, 5(8): 3964-3973.
    [120] HOSSEINI-FARID M, RAMZANPOUR M, ZIEJEWSKI M, et al. A compressible hyper-viscoelastic material constitutive model for human brain tissue and the identification of its parameters[J]. International Journal of Non-Linear Mechanics, 2019, 116: 147-154. doi: 10.1016/j.ijnonlinmec.2019.06.008
    [121] WHITTALL K P, MACKAY A L, GRAEB D A, et al. In vivo measurement of T2 distributions and water contents in normal human brain[J]. Magnetic Resonance in Medicine, 1997, 37(1): 34-43. doi: 10.1002/mrm.1910370107
    [122] KACZMAREK M, SUBRAMANIAM R P, NEFF S R. The hydromechanics of hydrocephalus: steady-state solutions for cylindrical geometry[J]. Bulletin of Mathematical Biology, 1997, 59(2): 295-323. doi: 10.1007/BF02462005
    [123] PEÑA A, BOLTON M D, WHITEHOUSE H, et al. Effects of brain ventricular shape on periventricular biomechanics: a finite-element analysis[J]. Neurosurgery, 1999, 45(1): 107-116.
    [124] MOW V C, KUEI S C, LAI W M, et al. Biphasic creep and stress relaxation of articular cartilage in compression? Theory and experiments[J]. Journal of Biomechanical Engineering, 1980, 102(1): 73-84. doi: 10.1115/1.3138202
    [125] ANGELI S, STYLIANOPOULOS T. Biphasic modeling of brain tumor biomechanics and response to radiation treatment[J]. Journal of Biomechanics, 2016, 49(9): 1524-1531. doi: 10.1016/j.jbiomech.2016.03.029
    [126] WANG R, SARNTINORANONT M. Biphasic analysis of rat brain slices under creep indentation shows nonlinear tension-compression behavior[J]. Journal of the Mechanical Behavior of Biomedical Materials, 2019, 89: 1-8. doi: 10.1016/j.jmbbm.2018.08.043
    [127] MILLER K, CHINZEI K. Modelling of brain tissue mechanical properties: bi-phasic versus single-phase approach[C]//Proceedings of the 3rd International Symposium on Computer Methods in Biomechanics and Biomedical Engineering. 1997.
    [128] BIOT M A. General theory of three-dimensional consolidation[J]. Journal of Applied Physics, 1941, 12(2): 155-164. doi: 10.1063/1.1712886
    [129] LI X, VON HOLST H, KLEIVEN S. Influence of gravity for optimal head positions in the treatment of head injury patients[J]. Acta Neurochirurgica, 2011, 153(10): 2057-2064. doi: 10.1007/s00701-011-1078-2
    [130] JU G, CAI M, LI J, et al. Parameter-robust multiphysics algorithms for Biot model with application in brain edema simulation[J]. Mathematics and Computers in Simulation, 2020, 177: 385-403. doi: 10.1016/j.matcom.2020.04.027
    [131] CHEN X, TI F, LI M, et al. Theory of fluid saturated porous media with surface effects[J]. Journal of the Mechanics and Physics of Solids, 2021, 151: 104392. doi: 10.1016/j.jmps.2021.104392
    [132] TI F, CHEN X, LI M, et al. Cylindrical compressible liquid inclusion with surface effects[J]. Journal of the Mechanics and Physics of Solids, 2022, 161: 104813. doi: 10.1016/j.jmps.2022.104813
    [133] CHATELIN S, CONSTANTINESCO A, WILLINGER R. Fifty years of brain tissue mechanical testing: from in vitro to in vivo investigations[J]. Biorheology, 2010, 47(5/6): 255-276.
    [134] MAK A F. The apparent viscoelastic behavior of articular cartilage-the contributions from the intrinsic matrix viscoelasticity and interstitial fluid flows[J]. Journal of Biomechanical Engineering, 1986, 108(2): 123-130. doi: 10.1115/1.3138591
    [135] BLOOM F E. Fundamental Neuroscience[M]. Academic Press, 2014: 3-13.
    [136] ROSSMANN C, HAEMMERICH D. Review of temperature dependence of thermal properties, dielectric properties, and perfusion of biological tissues at hyperthermic and ablation temperatures[J]. Critical Reviews in Biomedical Engineering, 2014, 42(6): 467-492. doi: 10.1615/CritRevBiomedEng.2015012486
    [137] PENNES H H. Analysis of tissue and arterial blood temperatures in the resting human forearm[J]. Journal of Applied Physiology, 1998, 85(1): 5-34. doi: 10.1152/jappl.1998.85.1.5
    [138] WEINBAUM S, XU L X, ZHU L, et al. A new fundamental bioheat equation for muscle tissue, part Ⅰ: blood perfusion term[J]. Journal of Biomechanical Engineering, 1997, 119(3): 278-288. doi: 10.1115/1.2796092
    [139] WEINBAUM S, JIJI L M. A new simplified bioheat equation for the effect of blood flow on local average tissue temperature[J]. Journal of Biomechanical Engineering, 1985, 107(2): 131-139. doi: 10.1115/1.3138533
    [140] BAISH J W. Formulation of a statistical model of heat transfer in perfused tissue[J]. Journal of Biomechanical Engineering, 1994, 116(4): 521-527. doi: 10.1115/1.2895804
    [141] MA W, LIU W, LI M. Analytical heat transfer model for targeted brain hypothermia[J]. International Journal of Thermal Sciences, 2016, 100: 66-74. doi: 10.1016/j.ijthermalsci.2015.09.014
    [142] SULEMAN M, RIAZ S. Computational modeling of poroelastic brain tumor therapy during heat transfer carrying temperature-dependent blood perfusion[J]. Medical Engineering & Physics, 2022, 103: 103792.
    [143] ELWASSIF M M, KONG Q, VAZQUEZ M, et al. Bio-heat transfer model of deep brain stimulation-induced temperature changes[J]. Journal of Neural Engineering, 2006, 3(4): 306. doi: 10.1088/1741-2560/3/4/008
    [144] XU F, SEFFEN K A, LU T J. Non-Fourier analysis of skin biothermomechanics[J]. International Journal of Heat and Mass Transfer, 2008, 51(9): 2237-2259.
    [145] LI X, ZHONG Y, JAZAR R, et al. Thermal-mechanical deformation modelling of soft tissues for thermal ablation[J]. Bio-Medical Materials and Engineering, 2014, 24(6): 2299-2310. doi: 10.3233/BME-141043
    [146] BAI B, ZHOU R, CAI G, et al. Coupled thermo-hydro-mechanical mechanism in view of the soil particle rearrangement of granular thermodynamics[J]. Computers and Geotechnics, 2021, 137: 104272. doi: 10.1016/j.compgeo.2021.104272
    [147] CUI W, POTTS D M, ZDRAVKOVIĆ L, et al. An alternative coupled thermo-hydro-mechanical finite element formulation for fully saturated soils[J]. Computers and Geotechnics, 2018, 94: 22-30. doi: 10.1016/j.compgeo.2017.08.011
    [148] HASHEMI A, SUTMAN M, MEDERO G M. A review on the thermo-hydro-mechanical response of soil-structure interface for energy geostructures applications[J]. Geomechanics for Energy and the Environment, 2023, 33: 100439. doi: 10.1016/j.gete.2023.100439
    [149] HASHEMI A, SUTMAN M. Thermo-hydro-mechanical behaviour of partially saturated fine-grained soils in the context of energy geostructures[J]. Geomechanical for Energy and the Environment, 2022, 33: 100439.
    [150] SCARINGI G, LOCHE M. A thermo-hydro-mechanical approach to soil slope stability under climate change[J]. Geomorphology, 2022, 401: 108108. doi: 10.1016/j.geomorph.2022.108108
    [151] WU W, LI X, CHARLIER R, et al. A thermo-hydro-mechanical constitutive model and its numerical modelling for unsaturated soils[J]. Computers and Geotechnics, 2004, 31(2): 155-167. doi: 10.1016/j.compgeo.2004.02.004
    [152] KEANGIN P, WESSAPAN T, RATTANADECHO P. Analysis of heat transfer in deformed liver cancer modeling treated using a microwave coaxial antenna[J]. Applied Thermal Engineering, 2011, 31(16): 3243-3254. doi: 10.1016/j.applthermaleng.2011.06.005
    [153] BENEVENTO M, ALPÁR A, GUNDACKER A, et al. A brainstem-hypothalamus neuronal circuit reduces feeding upon heat exposure[J]. Nature, 2024, 628: 826-834. doi: 10.1038/s41586-024-07232-3
    [154] SHI L, MYERS K. A finite porous-viscoelastic model capturing mechanical behavior of human cervix under multi-step spherical indentation[J]. Journal of the Mechanical Behavior of Biomedical Materials, 2023, 143: 105875. doi: 10.1016/j.jmbbm.2023.105875
  • 加载中
图(5) / 表(3)
计量
  • 文章访问数:  69
  • HTML全文浏览量:  23
  • PDF下载量:  22
  • 被引次数: 0
出版历程
  • 收稿日期:  2024-05-15
  • 修回日期:  2024-06-05
  • 刊出日期:  2024-06-01

目录

    /

    返回文章
    返回