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北京大学学报（医学版） ›› 2025, Vol. 57 ›› Issue (1): 97-105. doi: 10.19723/j.issn.1671-167X.2025.01.015

• 论著 • 上一篇    下一篇

基于细胞生长与成骨分化的不同孔径生物支架流体力学有限元分析

胡轶博1, 吕伟佳2, 夏炜3, 刘亦洪1,*()   

  1. 1. 北京大学口腔医学院·口腔医院综合科，国家口腔医学中心，国家口腔疾病临床医学研究中心，口腔生物材料和数字诊疗装备国家工程研究中心，北京 100081
    2. 中国中医科学院西苑医院口腔科，北京 100091
    3. Department of Materials Science and Engineering, Uppsala University, Uppsala 75121，Sweden
  • 收稿日期:2024-10-02 出版日期:2025-02-18 发布日期:2025-01-25
  • 通讯作者: 刘亦洪 E-mail:kqliuyh@163.com
  • 基金资助:
    国家自然科学基金(52111530189)

Hydrodynamic finite element analysis of biological scaffolds with different pore sizes for cell growth and osteogenic differentiation

Yibo HU1, Weijia LYU2, Wei XIA3, Yihong LIU1,*()   

  1. 1. Department of General Dentistry, Peking University School and Hospital of Stomatology & National Center for Stomato-logy & National Clinical Research Center for Oral Diseases & National Engineering Research Center of Oral Biomaterials and Digital Medical Devices, Beijing 100081, China
    2. Department of Stomatology, Xiyuan Hospital of China Academy of Chinese Medical Sciences, Beijing 100091, China
    3. Department of Materials Science and Engineering, Uppsala University, Uppsala 75121, Sweden
  • Received:2024-10-02 Online:2025-02-18 Published:2025-01-25
  • Contact: Yihong LIU E-mail:kqliuyh@163.com
  • Supported by:
    the National Natural Science Foundation of China(52111530189)

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摘要：

目的: 应用流体力学有限元分析方法，建立相同孔隙率、不同孔径的三周期极小曲面(triply periodic minimal surfaces，TPMS)螺旋形(Gyroid)多孔支架模型，模拟体内微环境，通过比较不同孔径支架的流体流速、壁面剪切应力、渗透率等相关参数变化，分析不同孔径的多孔支架对细胞黏附、增殖和成骨分化的可能影响。方法: 利用nTopology软件建立3组孔径的Gyroid多孔支架模型，支架尺寸为10 mm×10 mm×10 mm，孔径大小分别为400、600、800 μm，内部结构为各向同性。利用ANSYS 2022R1软件划分为非结构四面体网格，网格总数300+万。设定边界条件，流场域入口速度分别为0.01、0.1、1 mm/s，出口压力为0 Pa。根据Navier-Stokes方程计算流体流经支架时的压力、流速、壁面剪切应力，根据达西定律(Darcy’ s law)计算渗透率，使用ANSYS 2022R1软件中的Static structural模块对上述3种孔径支架的结构模型进行抗压强度分析。结果: 当入口流速分别为0.01、0.1、1 mm/s时，壁面剪切应力与流体流速呈线性关系，流速增加会导致壁面剪切应力增大。在0.1 mm/s流速下，当流体流经孔径为400、600、800 μm的3组支架时，压力呈梯度分布并逐渐减小，入口端压力依次为0.272、0.083、0.079 Pa；平均流速依次为0.093、0.078、0.070 mm/s；平均壁面剪切应力依次为2.955、1.343、1.706 mPa；渗透率依次为0.54×10-8、1.80×10-8、1.89×10-8 m2。计算3组支架内部最适合细胞黏附、增殖与成骨分化的壁面剪切应力范围所在区域占比，其中600 μm孔径支架该剪切应力范围内的内表面面积占比最大(27.65%)，其次是800 μm孔径支架(17.30%)，400 μm孔径支架占比最小(1.95%)。400、600和800 μm孔径支架的抗压强度依次为23、26、34 MPa。结论: 3组孔径的Gyroid支架在压应力作用下，应力分布均匀；600和800 μm孔径的Gyroid支架渗透率明显高于400 μm组，600 μm孔径的支架平均壁面剪切应力最小，且内部适合细胞生长与成骨分化的壁面区域占比最大，可能更适合于细胞黏附、增殖与成骨分化。

关键词: 生物支架, 孔径, 有限元分析, 流体力学, 成骨分化

Abstract:

Objective: The triply periodic minimal surface (TPMS) Gyroid porous scaffolds were built with identical porosity while varying pore sizes were used by fluid mechanics finite element analysis (FEA) to simulate the in vivo microenvironment. The effects of scaffolds with different pore sizes on cell adhesion, proliferation, and osteogenic differentiation were evaluated through calculating fluid velocity, wall shear stress, and permeability in the scaffolds. Methods: Three types of gyroid porous scaffolds, with pore sizes of 400, 600 and 800 μm, were established by nTopology software. Each scaffold had dimensions of 10 mm × 10 mm × 10 mm and isotropic internal structures. The models were imported to the ANSYS 2022R1 software, and meshed into over 3 million unstructured tetrahedral elements. Boun- dary conditions were set with inlet flow velocities of 0.01, 0.1, and 1 mm/s, and outlet pressure of 0 Pa. Pressure, velocity, and wall shear stress were calculated as fluid flowed through the scaffolds using the Navier-Stokes equations. At the same time, permeability was determined based on Darcy' s law. The compressive strength of scaffolds with different pore sizes was evaluated by ANSYS 2022R1 Static structural analysis. Results: A linear relationship was observed between the wall shear stress and fluid velocity at inlet flow rates of 0.01, 0.1 and 1 mm/s, with increasing velocity leading to higher wall shear stress. At the flow velocity of 0.1 mm/s, the initial pressures of scaffolds with pore sizes of 400, 600 and 800 μm were 0.272, 0.083 and 0.079 Pa, respectively. The fluid pressures were gradually decreased across the scaffolds. The average flow velocities were 0.093, 0.078 and 0.070 mm/s, the average wall shear stresses 2.955, 1.343 and 1.706 mPa, permeabilities values 0.54×10-8 1.80×10-8 and 1.89×10-8 m2 in the scaffolds with pore sizes of 400, 600 and 800 μm. The scaffold surface area proportions according with optimal wall shear stress range for cell growth and osteogenic differentiation were calcula-ted, which was highest in the 600 μm scaffold (27.65%), followed by the 800 μm scaffold (17.30%) and the 400 μm scaffold (1.95%). The compressive strengths of the scaffolds were 23, 26 and 34 MPa for the 400, 600 and 800 μm pore sizes. Conclusion: The uniform stress distributions appeared in all gyroid scaffold types under compressive stress. The permeabilities of scaffolds with pore sizes of 600 and 800 μm were significantly higher than the 400 μm. The average wall shear stress in the scaffold of 600 μm was the lowest, and the scaffold surface area proportion for cell growth and osteogenic differentiation the largest, indicating that it might be the most favorable design for supporting these cellular activities.

Key words: Biological scaffolds, Pore size, Finite element analysis, Fluid mechanics, Osteogenic differentiation

中图分类号: 

  • R782.4

表1

3组支架主要参数"

Scaffold Porosity/% Pore size/μm Strut size/μm Volume of porous scaffold/mm3 Surface area/mm2 Specific surface area/(mm2/mm3)
P400 68.98 400 260 310.2 3590.94 11.58
P600 70.76 600 390 292.4 2366.90 8.09
P800 71.53 800 510 284.7 1755.36 6.17

图1

3组支架结构示意图"

图2

流场域和网格示意图"

图3

抗压强度分析时边界条件设置示意图"

图4

入口速度0.1 mm/s时3组支架的压力分布云图"

表2

不同流速下流体流经3组支架时的平均流速和最大流速"

Inlet velocity/(mm/s) P400 P600 P800
Average velocity/(mm/s) Maximum velocity/(mm/s) Average velocity/(mm/s) Maximum velocity/(mm/s) Average velocity/(mm/s) Maximum velocity/(mm/s)
0.01 0.009 0.032 0.008 0.033 0.007 0.033
0.1 0.093 0.312 0.078 0.330 0.070 0.331
1 0.939 3.168 0.792 3.273 0.704 3.279

图5

入口速度0.1 mm/s时3组支架的流速分布云图"

表3

不同入口流速下3组支架的平均壁面剪切应力和最大壁面剪切应力"

Inlet velocity/(mm/s) P400 P600 P800
Average wall shear stress/mPa Maximum wall shear stress/mPa Average wall shear stress/mPa Maximum wall shear stress/mPa Average wall shear stress/mPa Maximum wall shear stress/mPa
0.01 0.295 1.499 0.134 0.508 0.170 0.616
0.1 2.955 13.885 1.343 5.097 1.706 6.123
1 29.935 138.447 13.715 51.738 17.326 63.048

图6

3组支架的壁面剪切应力云图"

图7

3组支架的应力分布云图"

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ISSN 1671-167X
CN 11-4691/R
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