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流-固耦合作用下小尺寸肾结石引发的输尿管疼痛响应

刘勇岗 苏丽君

刘勇岗, 苏丽君. 流-固耦合作用下小尺寸肾结石引发的输尿管疼痛响应[J]. 应用数学和力学, 2024, 45(6): 735-752. doi: 10.21656/1000-0887.450095
引用本文: 刘勇岗, 苏丽君. 流-固耦合作用下小尺寸肾结石引发的输尿管疼痛响应[J]. 应用数学和力学, 2024, 45(6): 735-752. doi: 10.21656/1000-0887.450095
LIU Yonggang, SU Lijun. Responses of Ureteral Pain Caused by Small-Sized Kidney Stones Under Fluid-Structure Coupling[J]. Applied Mathematics and Mechanics, 2024, 45(6): 735-752. doi: 10.21656/1000-0887.450095
Citation: LIU Yonggang, SU Lijun. Responses of Ureteral Pain Caused by Small-Sized Kidney Stones Under Fluid-Structure Coupling[J]. Applied Mathematics and Mechanics, 2024, 45(6): 735-752. doi: 10.21656/1000-0887.450095

流-固耦合作用下小尺寸肾结石引发的输尿管疼痛响应

doi: 10.21656/1000-0887.450095
基金项目: 

国家自然科学基金(重点项目) 12032010

详细信息
    通讯作者:

    刘勇岗(1991—),男,讲师,博士(通讯作者. E-mail: lyg@yau.edu.cn)

  • 中图分类号: O347

Responses of Ureteral Pain Caused by Small-Sized Kidney Stones Under Fluid-Structure Coupling

  • 摘要:

    肾结石引发的输尿管疼痛长期折磨着人类,严重影响着人们的生活质量. 然而,目前临床上由于缺乏肾结石与输尿管相互作用的定量分析,泌尿医师无法针对不同患者制定精准的个性化治疗及镇痛方案. 针对该问题,以小尺寸肾结石为例,基于耦合Euler-Lagrange(CEL)算法的流-固耦合有限元方法分析了进入输尿管管腔内的小尺寸肾结石与输尿管的相互作用规律,并基于已建立的输尿管疼痛模型,对由输尿管内小尺寸肾结石引发的输尿管疼痛进行了定量化研究. 有限元分析结果表明,当结石直径小于输尿管内径时,结石会在输尿管壁蠕动作用下与输尿管发生动态接触,造成输尿管内壁上出现动态应力. 随着输尿管壁蠕动幅度增大,结石的移动速度增大,且结石与输尿管接触的概率减小,同时输尿管壁上的接触应力也会降低. 将应力结果输入输尿管疼痛模型计算对应的中心传输神经元细胞膜电位,结果表明,疼痛水平随时间的变化与动态应力随时间的变化趋势类似,在应力交替变化的情况下,疼痛程度并不会随应力降为零应力而降低至疼痛阈值以下,表现出疼痛程度与应力水平不对等的特征. 该研究所得结果可以结合当前临床上已有的医学影像技术和计算机领域的大数据与人工智能等技术,有望为个性化精准诊断结石患者病况并定量化评估患者疼痛程度,从而制定个性化治疗方案的精准医疗临床策略提供理论基础.

  • 图  1  人体泌尿系统

    Figure  1.  The human urinary system

    图  2  输尿管解剖结构(横截面)[7]

      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  2.  The anatomical structure of the ureter (cross-section)[7]

    图  3  输尿管壁的解剖结构及机械力刺激引起的痛觉信号传递

    Figure  3.  The anatomical structure of the ureteral wall and the pain signal transmission caused by mechanical stimulation

    图  4  疼痛统一模型示意图

    Figure  4.  Schematic diagram of the holistic pain model

    图  5  基于疼痛统一模型的输尿管疼痛量化模型

    Figure  5.  The quantitative model for the ureteral pain based on the holistic pain model

    图  6  输尿管中不同尺寸肾结石示意图

    Figure  6.  Schematic diagram of kidney stones with different sizes in the ureter lumen

    图  7  结石与输尿管三维CEL有限元建模

    Figure  7.  The 3D CEL finite element modeling of stones and ureters

    图  8  结石与输尿管三维CEL有限元模型

    Figure  8.  The 3D CEL finite element model for stones and ureters

    图  9  蠕动状态下输尿管管壁上间距为Δz的两质点的运动状态示意

    Figure  9.  The schematic of the motion state of 2 mass points with distance Δz in the ureter wall under the peristaltic state

    图  10  三维CEL模型输尿管壁结点位移载荷施加

    Figure  10.  Application of node displacement loads for the 3D CEL model of ureteral wall

    图  11  输尿管管壁蠕动振幅比φ=0.2时结石运动的位移-时间曲线

    Figure  11.  The displacement-time curve of kidney stone movement under φ=0.2

    图  12  输尿管管壁蠕动振幅比φ=0.2时,结石与管壁接触引起的管壁应力状态变化

    Figure  12.  The changes in stresss states of the ureter wall caused by the contact between the stone and the ureter wall under dimensionless peristaltic amplitude of ureteral wall φ=0.2

    图  13  输尿管管壁蠕动振幅比φ=0.4时,对应的结石的位移-时间曲线与管壁接触面上最大主应力云图

    Figure  13.  The curve of the kidney stone displacement vs. the time and the maximum principal stress distribution on the contact surface of the ureter wall under the dimensionless peristaltic amplitude of ureteral wall φ=0.4

    图  14  输尿管管壁蠕动振幅比φ=0.6时对应的结石在管腔中的相对位置与结石运动的位移-时间曲线

    Figure  14.  The kidney stone location in the ureter lumen and the curve of the kidney stone displacement vs. the time under the dimensionless peristaltic amplitude of ureteral wall φ=0.6

    图  15  小尺寸结石引发输尿管疼痛响应的量化计算

    Figure  15.  Quantitative calculations of ureteral pain responses caused by small-sized stones

    表  1  尿液介质本构材料参数

    Table  1.   Constitutive parameters of the urinary liquid

    quantity value
    dynamic viscosity μ/(MPa·s) 10-5
    initial density ρf0/(t/mm3) 10-9
    sound speed in urinary liquid cf0/(mm/s) 1.5×106[31]
    material constant Γ0 0[32]
    material constant s 0[32]
    下载: 导出CSV

    表  2  人类输尿管的4参数Fung超弹性模型本构参数[34]

    Table  2.   Constitutive parameters of the 4-parameter Fung hyperelastic model for human ureter[34]

    parameter C/MPa Aθθθθ Azzzz Aθθzz
    value 0.405 6 0.709 1 0.185 6 0.889 2
    下载: 导出CSV

    表  3  三维CEL模型输尿管黏弹性部分的Prony级数参数

    Table  3.   Prony parameters of the viscoelastic part of the ureter in the 3D CEL model

    number of terms i gi ki τi/s
    1 0.28 0 5.63
    2 0.20 0 69.65
    下载: 导出CSV

    表  4  三维CEL模型的基准参数

    Table  4.   Datum parameters of the 3D CEL model

    parameter value
    inner radius of ureter Rin/mm 20
    outer radius of ureter Rout/mm 36
    amplitude of peristaltic wave Aw/mm 4
    wavelength of peristaltic wave λ/mm 200
    wave speed of peristaltic wave c/(mm/s) 200
    kinematic viscosity of urinary liquid ν/(mm2/s) 400
    density of urinary liquid ρl/(t/mm3) 10-9
    radius of kidney stone Rs/mm 20
    density of kidney stone ρs/(t/mm3) 2×10-9
    下载: 导出CSV

    表  5  三维CEL模型的基准无量纲参数

    Table  5.   Datum dimensionless parameters for the 3D CEL models

    parameter value
    dimensionless size of kidney stone ξ 1.0
    Reynolds number Re 1.0
    dimensionless thickness of ureter wall η 1.8
    dimensionless peristaltic amplitude of ureter wall φ 0.2
    peristaltic wave number of ureter wall β 0.1
    dimensionless density of kidney stone ψ 2.0
    下载: 导出CSV
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  • 收稿日期:  2024-04-11
  • 修回日期:  2024-05-28
  • 刊出日期:  2024-06-01

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