Numerical analysis of fluid field changes in articular cartilage with micro-defects under compressive load

doi:10.3969/j.issn.2095-4344.0387

Abstract

Abstract:

BACKGROUND: Mechanical study of articular cartilage has been focused on the deformation of solid phase, and there are few studies on interstitial flow. While interstitial flow is the core mechanism for maintaining the
normal mechanical and physiological functions of cartilage.
OBJECTIVE: To study the changes of cartilage fluid field of articular cartilage with micro-defects under compressive load, and to provide theoretical basis for better understanding of mechanical mechanism of cartilage injury.
METHODS: The two-dimensional numerical model of fiber-reinforced and porous-viscoelasticity articular cartilage was established to simulate and parameterize the process of interstitial flow under compressive load. The variation of fluid field distribution of articular cartilage with micro-defects was obtained.
RESULTS AND CONCLUSION: The increase in interstitial fluid pressure at the bilateral bottom corners of defect sites under compressive load increased the bearing capacity and prevented further damage. The reduction in the interstitial fluid pressure on the bilateral defects and the acceleration in the interstitial flow would promote the damage deteriorating to the surrounding area. In addition, due to stress concentration at the bilateral bottom corners of the defect and interstitial fluid pressure difference, it would make interstitial fluid flowed from the center stress of stress concentration into surrounding area. Our results show that injured cartilage has a self-regulating ability to delay damage.

中国组织工程研究杂志出版内容重点：组织构建；骨细胞；软骨细胞；细胞培养；成纤维细胞；血管内皮细胞；骨质疏松；组织工程

Key words: Cartilage, Articular, Hydrodynamics, Computer Simulation, Tissue Engineering

CLC Number:

R318

Li Xiao-ming1, 2, Men Yu-tao1, 2, Zhang Chun-qiu1, 2. Numerical analysis of fluid field changes in articular cartilage with micro-defects under compressive load [J]. Chinese Journal of Tissue Engineering Research, 2018, 22(32): 5117-5122.

Figures/Tables 2

该文主要从间质液压力、间质液流速以及间质液流动轨迹等力学性能来研究微缺损关节软骨的流体场变化。 2.1 间质液压力在软骨承受压缩载荷过程中，首先做出反应的并不是关节软骨的固体基质，而是软骨组织内液相的间质液，称之为间质液压效应[34-36]。这种效应与它的多孔特性是密切相关的。由于关节软骨内部的孔隙极小，导致它的渗透率只有10-15 m4/Ns，当关节软骨刚受到压力时，软骨组织中的间质液不能快速地从承载区流出，反而形成了液压来承受软骨表面的压力。又由于渗透率的变化缓慢，所以这种液压效应可以维持很长一段时间。这样不但很大程度上分担了软骨表面的载荷，阻碍了软骨发生大的变形，而且减少了软骨表面间固体部分的接触，从而保证了摩擦系数在关节在运动过程始终可以保持的很低[37-39]。因此，研究关节软骨损伤后间质液压的分布状况对于骨关节炎的治疗和预防具有重要意义。图3为微缺损关节软骨不同压缩时间下的间质液压和孔隙率的分布云图，其中0-1 s为线性加载过程，1-3 601 s为恒定加载过程。从图3A可以看出整个加载过载中间质液压的最大值始终位于缺损底部的两侧底角处，这是由于此处存在挤压应力，使得缺损处的孔隙率变小(见图3B)，更大程度上的限制了间质流动，进而在此处形成了极高的间质液压。孔隙率变小导致的间质流动受阻，一方面减少了软骨细胞代谢所需营养物质及其分泌的各种生物分子的流失；另一方面间质液压的增大，使得此处的承载能力提高，进而可以阻碍损伤向深处扩展，这其实可以看作是关节软骨在损伤后作出的自我保护。此外，从图3A可以看出缺损边缘处间质液压较低，这是由于缺损边缘处基质被拉伸，孔隙率变大，间质流动加快，从而间质液压变小。由上述分析可知，孔隙率变大，间质流动加快，间质压力变小，不利于软骨自身的修复，反而会进一步促使损伤的扩展。从图3A中可以看出在线性加载过程中，关节软骨整体的间质压力随着时间的推移逐渐增大，这是由于随着载荷的增大，软骨内部压力梯度也逐渐增大，间质流动有加快的趋势，而软骨内部极小的孔隙率却限制了这种趋势，进而在软骨内形成的间质压力也逐渐增大；在恒定加载过程中，关节软骨整体的间质压力随着时间的推移逐渐减小，这是由于随着时间的推移软骨间质液逐渐流出，间质液压效果衰竭，载荷逐步转由固相部分承担。在这个过程中，胶原纤维和基质开始承受载荷，与软骨表层平行走向的胶原纤维就像鼓面的蒙皮一样，使软骨面上载荷的分布趋于均匀。 2.2 间质液流速图4显示了微缺损关节软骨不同压缩时间下的间质流速变化云图，从图中可以看出在线性加载阶段，关节软骨整体的间质流速随着时间的推移逐渐增大，这是由于随着载荷的增大，软骨内部压力梯度也逐渐增大，进而间质液的流动速度也逐渐增大；在恒定加载过程中，关节软骨整体的间质流速随着时间的推移逐渐减小，这一"

方面是由于随着时间的推移软骨间质液逐渐流出，软骨内部的间质液不再饱和，另一方面随着时间的推移载荷开始转由固相的胶原纤维承担，软骨间质液受到的压力梯度也逐渐减小，进而导致间质流速逐渐减小。此外，在图中还可以看出在整个加载过程中，软骨缺损边缘的间质流速始终大于周边未缺损部位，这是由于此处存在应力集中，压力梯度大于未缺损部位，同时应力集中使得该出产生了大变形，孔隙率变大，这使得缺损边缘的间质流速增大，进而加速了软骨细胞代谢所需营养物质及其分泌的各种生物分子的流失。图5为恒定加载过程中软骨间质液的最大流速变化情况。当线性加载结束时，关节软骨的间质流速达到最大值1.67×10-6 mm/s，而在整个恒定加载过程中，间质流速呈现出指数形式的衰减趋势，这种逐渐趋于平缓的衰减趋势反映出了间质液压效应和固相变形的互补过程。即在线性加载阶段，由于间质液的快速响应机制使得间质流速产生了一个峰值，但在恒定加载过程中，随着间质液的减少，关节软骨开始产生变形，而软骨的变形会压缩软骨内部的蛋白多糖类分子，从而软骨内部的孔隙率减小，孔隙的减小又会反过来阻碍间质液的流出。这种互补机制既能实现营养物质的传递又能延长液相承担载荷的时间。 2.3 间质液流动轨迹图6是整个加载过程中各个时刻对应的间质流动的方向，从图6A中可以看出整个加载过程中关节软骨未缺损部位的间质流动方向始终朝向软骨两侧，并且随着时间的推移，间质流动的范围由中间向两侧逐渐缩小，最终集中在软骨的两侧区域，这是由于随着时间的推移软骨间质液逐渐向外流出导致的。从图6B(缺口局部放大5倍)中可以看出整个加载过程中缺损部位软骨间质液的流动轨迹表现出现很大的不同，具体表现为软骨间质液始终以缺损底部的两侧底角处的应力集中处为中心向四周流动，尤其向软骨表面和中间的间质流动更为明显，这是由于应力集中处的间质液压高于四周区域(见图6A)，由于液压差的存在，软骨间质液自然从高压处流向低压处，而表面和中间的间质流动更为明显是因为缺损边缘处基质的孔隙率较大(见图3B)。这种现象加速了软骨细胞代谢所需营养物质及其分泌的各种生物分子的流失。"

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