Analysis of adhesion and permeability of bone scaffold with Voronoi architecture

doi:10.12307/2022.300

Abstract

Abstract: BACKGROUND: Bone tissue engineering research results have found that the adhesion and permeability of Voronoi bone scaffold are important parameters that affect bone tissue engineering scaffolds. Good adhesiveness can ensure bone cells stick to the scaffold, and promote the bone tissue regeneration. Excellent permeability can increase the transportation of nutrients and metabolic waste in the body.
OBJECTIVE: To study the adhesiveness and permeability of the bone scaffolds with Voronoi architecture.
METHODS: Taking Voronoi bone scaffold as the research object, its structure was modeled by Rhino software. The permeability and adhesion inside the bone scaffold were analyzed by means of computational fluid dynamics. The number of seed points was set to 20, 25, 30, and the scaling factors were 0.4, 0.5, 0.6, 0.7, 0.8, respectively, to explore the correspondence between the porosity and the permeability.
RESULTS AND CONCLUSION: (1) The Voronoi bone scaffold structure designed by Rhino software had an average adhesion layer thickness of 0.061-0.116 mm, which had a certain adhesion capacity. Its porosity was largely determined by the scaling factor. With the continuous increase of the scaling factor, the porosity tended to rise. Within the range of the selected structural design parameters, when the scaling factor was 0.4, the porosity of the scaffold with different seed points was the smallest, which was 33.78%, 33.87%, and 33.90%, respectively. When the scaling factor was 0.8, the porosity of the scaffold structure with different seed points was the largest, which was 84.28%, 84.35%, and 84.38%, respectively. (2) The increase in the porosity had a significant impact on the permeability of the scaffold structure. With the increases of the porosity, the permeability of the bone scaffold structure rose. In the designed scaffold structure, the permeability increased from 16.98×10-8 m2 to 82.29×10-8 m2 with the increase of the porosity. (3) The relationship between the porosity of the scaffold structure and the permeability is obtained, which provides a basis for the prediction of the permeability of the bone scaffold and the analysis of the biological performance of the complex structure bone scaffold.

Key words: bone scaffold, computational fluid dynamics, adhesion, permeability, Voronoi, bone tissue engineering, biological performance

CLC Number:

Wu Li, Huang Wei, Li Xuetao, Li Panpan, Zhang Kaihang, Shen Zhiyuan. Analysis of adhesion and permeability of bone scaffold with Voronoi architecture[J]. Chinese Journal of Tissue Engineering Research, 2022, 26(28): 4472-4476.

Figures/Tables 5

在所选支架模型范围内，不同缩放因子及种子点数下的骨支架结构在进口位置与出口位置存在较大的流速差，且出口位置平均流速要显著高于进口流速。当缩放因子为0.4、种子点数为20时，骨支架结构的孔隙率最小，为33.78%，其进口流速稳定在0.001 m/s左右，出口流速呈现出由中间到边缘逐渐减小的趋势，在中心位置流速最大为0.001 987 m/s，而在边缘位置出现了速度零点。在缩放因子为0.8、种子点数为30时，支架结构的孔隙率最大，为84.38%，其进口流速与所设进口流速相符，在0.001 m/s上下波动，而出口流速呈现出由中间到边缘逐渐减小的趋势，在中心位置流速最大为0.001 859 m/s，且中心大流速区域较前者明显增大，但在四周仍然存在速度零点，与所设无滑移的边界条件相符。 2.2 Voronoi骨支架内部压力场分布对选取的Voronoi骨支架模型进行分析，发现所选支架结构在进口处存在较大的压力，且压力沿流体流速方向逐渐下降。根据分析结果绘制图5所示的进口平均压力与孔隙率的折线图，从图中可以发现，随着缩放因子的不断增大，骨支架的孔隙率逐渐增加，支架结构的进口平均压力值整体呈现出逐渐降低的趋势，孔隙率的增加极大减少了流体内部的压力值；当种子点数分别为20，25，30时，缩放因子为0.4时骨支架结构的孔隙率最小，分别为33.78%，33.87%，33.90%，对应的平均入口压力分别为0.172 3，0.285 5，0.309 1 Pa；当缩放因子为0.8时，骨支架结构的孔隙率最大，分别为84.28%，84.35%，84.38%，对应的平均入口压力分别为0.063 8，0.071 5，0.076 2 Pa。说明随着骨支架模型孔隙率的增加，流体在渗入支架时所需的压力越小，越有利于流体的渗入。"

从图中可以发现，由于进口位置处无复杂的孔隙结构及较广泛的流体接触，使得在进口处流体与支架内壁接触位置速度为0的区域层厚度为0，而在支架内部由于复杂孔结构对流体的阻碍作用及支架内壁对流体的黏滞作用，使各截面层均存在一定厚度的速度为0的区域，由于骨支架内部孔结构的随机性及孔大小的不同分布，因此在支架内部不同截面层速度为0的区域层也在不断变化，来回波动。其中当种子点数为20时，各截面速度为零区域层的平均厚度在0.061-0.116 mm之间；当种子点数为25时，各截面速度为零区域层的平均厚度在0.061-0.113 mm之间；当种子点数为30时，各截面速度为零区域层的平均厚度在0.063-0.096 mm之间。在所选骨支架结构中，所有骨支架结构的平均滞留层厚度值均在0.061-0.116 mm之间波动，说明所设计支架结构具有一定的黏附能力。人骨细胞胞体长轴的直径大约为0.02 mm、短轴的直径大约0.01 mm，而此次实验的滞留层厚度(0.061-0.116 mm)大于骨细胞的直径，所以滞留层中可以包含部分骨细胞，在实际应用时能够促进细胞在支架内壁的附着，对支架生物性能的研究具有一定的影响意义。 2.4 Voronoi骨支架渗透率分析渗透率是描述复杂微孔结构骨支架渗透能力的重要参数，可用评判骨支架运送细胞、营养物质及代谢废物的能力，对于雷诺数Re ≤ 10的层流运动，根据达西定律可以得到流体在多空介质中的渗透率计算公式为：式中，k 为渗透率(m2)，v 为进口流速(m/s)，μ为流体黏度(Pa·s)，L为沿入口流向长度(mm)，Δp 为沿入口流向压力差(Pa)。实验的雷诺数为9.84 < 10，可应用达西定律对所选骨支架模型进行渗透率的计算。对支架模型进行渗透率分析，取入口平均压力与支架出口位置处的平均压力差进行计算，得到各骨支架模型的渗透率。在种子点数为30时，支架结构的渗透率在16.98×10-8-68.90×10-8 m2之间；在种子点数为25时，支架结构的渗透率在18.39×10-8 -73.43×10-8 m2之间；在种子点数为20时，支架结构的渗透率在30.47×10-8 -82.29×10-8 m2之间，在不同种子点数时，随缩放因子的不断增加，支架结构的孔隙率在逐渐增加，相应的支架结构的渗透率也在增加。骨支架结构的渗透率是衡量支架结构生物性能的重要指标，而孔隙率是反映支架内部孔隙多少的量，当骨支架结构孔隙率较大时其内部的孔隙结构较多，液体在流经支架时遇到的阻碍作用较小，有利于液体进入支架内部，提高骨支架结构的渗透作用；相反，当骨支架结构孔隙率件小时其内部的孔隙结构也相应较少，液体在流经支架时遇到的阻碍作用较大，不利于液体在支架内部的流通，显著降低支架结构的渗透作用。因此孔隙率与支架结构的渗透率存在较大的联系，为了进一步观察两者之间的联系，根据上文所得数据绘制了图7所示的骨支架渗透率与孔隙率之间的关系图，并对孔隙率与渗透率之间的关系进行了拟合。"

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