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低温冷冻下颅脑热-力耦合分析

陶泽 苏丽君 刘少宝

陶泽, 苏丽君, 刘少宝. 低温冷冻下颅脑热-力耦合分析[J]. 应用数学和力学, 2024, 45(6): 710-718. doi: 10.21656/1000-0887.450118
引用本文: 陶泽, 苏丽君, 刘少宝. 低温冷冻下颅脑热-力耦合分析[J]. 应用数学和力学, 2024, 45(6): 710-718. doi: 10.21656/1000-0887.450118
TAO Ze, SU Lijun, LIU Shaobao. Thermo-Mechanical Analysis of Brain Tissue During Freezing[J]. Applied Mathematics and Mechanics, 2024, 45(6): 710-718. doi: 10.21656/1000-0887.450118
Citation: TAO Ze, SU Lijun, LIU Shaobao. Thermo-Mechanical Analysis of Brain Tissue During Freezing[J]. Applied Mathematics and Mechanics, 2024, 45(6): 710-718. doi: 10.21656/1000-0887.450118

低温冷冻下颅脑热-力耦合分析

doi: 10.21656/1000-0887.450118
基金项目: 

国家自然科学基金 12032010

国家自然科学基金 11902155

详细信息
    作者简介:

    陶泽(1997—),男,博士(E-mail: ztao@nuaa.edu.cn)

    通讯作者:

    苏丽君(1994—),女,博士(通讯作者. E-mail: ljsu@nuaa.edu.cn)

    刘少宝(1988—),男,副研究员,博士,硕士生导师(通讯作者. E-mail: sbliu@nuaa.edu.cn)

  • (我刊编委刘少宝来稿)
  • 中图分类号: O343

Thermo-Mechanical Analysis of Brain Tissue During Freezing

  • (Contributed by LIU Shaobao, M.AMM Editorial Board)
  • 摘要:

    虽然大脑是人体最重要的器官,但其在低温冷冻过程中的热-力耦合机理仍不明晰. 该文考虑颅脑特殊形状、多孔弹性、脑脊液流动、颅骨约束以及冻胀效应,建立脑组织低温冷冻热-力耦合模型,通过分析冷冻过程中的温度场、相场和脑脊液冻胀产生的压力场,发现在凝固过程中脑脊液温度保持不变,而脑组织内部最大温差可达20 K. 固-液相界面厚度约0.3 mm,推进速度约0.09 mm/s. 冻胀产生的脑组织最大位移(~0.12 mm)发生在靠近头盖骨处. 固液界面处压力梯度高达500 MPa/mm,而固体和脑脊液内部压力几乎不变. 本研究可为人类大脑的低温冷冻保存策略及脑防护提供理论支撑.

    (Contributed by LIU Shaobao, M.AMM Editorial Board)
    1)  (我刊编委刘少宝来稿)
  • 图  1  颅脑简化模型

      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  1.  Idealized modeling of the human brain

    图  2  脑组织低温冷冻过程中的温度分布

    Figure  2.  Temperature distributions in the brain tissue during freezing

    图  3  脑组织低温冷冻过程中的相场

    Figure  3.  The phase field in the brain tissue during freezing

    图  4  脑组织冷冻中的位移场

    Figure  4.  The displacement field in the brain tissue during freezing

    图  5  脑组织低温冷冻过程中的压力分布

    Figure  5.  The pressure distribution in the brain tissue during freezing

    表  1  脑组织物理参数取值

    Table  1.   Values of brain physical parameters

    physical parameter value range reference value
    size riro 5 cm
    thermal conductivity of matrix λm grey matter 0.57 W/(m·K)[22]
    white matter 0.50 W/(m·K)[22]
    brain tissue 0.66 W/(m·K)[23]
    0.53 W/(m·K)
    thermal conductivity of water λw cerebrospinal fluid 0.62 W/(m·K)[22]
    plasma 0.63 W/(m·K)[22]
    blood 0.63 W/(m·K)[23]
    water 0.59 W/(m·K)[24]
    0.60 W/(m·K)
    thermal conductivity of ice λi ice 2.1 W/(m·K)[25] 2.1 W/(m·K)
    specific heat capacity of matrix cm grey matter 3.7 kJ/(kg·K)[22]
    white matter 3.6 kJ/(kg·K)[22]
    3.7 kJ/(kg·K)
    specific heat capacity of water cw cerebrospinal fluid 4.2 kJ/(kg·K)[22]
    blood 3.6 W/(m3·K)[23]
    water 4.2 kJ/(kg·K)[26]
    4.2 kJ/(kg·K)
    specific heat capacity of ice ci ice 2.1 kJ/(kg·K)[25] 2.1 kJ/(kg·K)
    density of matrix ρm grey matter 1 038 g/cm3[22]
    white matter 1 039 g/cm3[22]
    1.038 g/cm3
    density of water ρw cerebrospinal fluid 1 007 kg/m3[22]
    blood 1 050 kg/m3[23]
    1 007 kg/m3
    density of ice ρi ice 917 kg/m3[27] 900 kg/cm3
    Young’s modulus of brain Em 338.15 Pa[28] 338.15 Pa
    Young’s modulus of ice Ei 8 GPa[29] 8 GPa
    bulk modulus of water Kw 2 GPa 2 GPa
    Poisson’s ratio of brain μm 0.3[28] 0.3
    phase transition temperature of water Tf 273 K[30] 273 K
    latent heat of phase change L 334 kJ/kg[31] 334 kJ/kg
    environment temperature Te 253 K[32] 253 K
    initial temperature Ti 293 K
    saturation capacity θs 0.75~0.95[6] 0.9
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出版历程
  • 收稿日期:  2024-04-25
  • 修回日期:  2024-05-15
  • 刊出日期:  2024-06-01

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