A Review of Coupled Thermo-Mechanical Behaviors of Brain Tissue
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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.
Abstract:The brain is the highest nerve center regulating physiological behaviors and functions. Brain tissue is a saturated porous material composed mainly of solid phase and liquid phase. Interactions between the solid phase, the liquid phase and the physiological environment (temperature in particular) are manifested in the coupled thermo-mechanical behaviors of brain tissue, and affected by internal temperature, seepage and stress fields. Characterization of the coupled thermo-mechanical behaviors of brain tissue is the key to understanding brain function and disease pathology. Firstly, the thermal and mechanical properties of brain tissue measured via different experimental methods were introduced, with a particular focus placed upon the effects of the strain rate and the temperature. Theoretical and numerical models describing the coupled thermo-mechanical behaviors of brain tissues were then summarized, including mechanical models, heat transfer models and coupled thermo-mechanical models. Finally, this important multidisciplinary field was summarized and prospected.
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Key words:
- brain tissue /
- mechanical property /
- thermophysical property /
- thermo-mechanical coupling
edited-byedited-by1) (我刊编委卢天健来稿) -
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μ1和μ2[78]
注 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]
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-122 ℃,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-122 ℃,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
500.2~4 959.9SHPB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] 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] 脑
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 690DSC 离体,37 ℃
离体,43 ℃
离体,50 ℃
离体,60 ℃[98] 灰质,人脑 3 590
3 650
3 650
3 700DSC 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 640DSC 离体,37 ℃
离体,43 ℃
离体,50 ℃
离体,60 ℃[98] 脑
灰质
白质
小脑3 630±74
3 718±36
3 525±73
3 653DSC 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] 脑
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
1.37×10-3DIC 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] 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 -
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