A fluid flow model in the lacunar-canalicular system under the pressure gradient and electrical field driven loads

doi:10.1007/s10483-022-2856-9

Applied Mathematics and Mechanics (English Edition) ›› 2022, Vol. 43 ›› Issue (6): 899-916.doi: https://doi.org/10.1007/s10483-022-2856-9

A fluid flow model in the lacunar-canalicular system under the pressure gradient and electrical field driven loads

Xiaogang WU^1,2, Xiyu WANG¹, Chaoxin LI¹, Zhaowei WANG¹, Yuqin SUN¹, Yang YAN¹, Yixian QIN¹, Pengcui LI², Yanqin WANG¹, Xiaochun WEI², Weiyi CHEN¹

1. College of Biomedical Engineering, Taiyuan University of Technology, Taiyuan 030024, China;
2. Shanxi Provincial Key Laboratory for Repair of Bone and Soft Tissue Injury, Taiyuan 030001, China

收稿日期:2022-02-10 修回日期:2022-04-22 发布日期:2022-06-11
通讯作者: Weiyi CHEN, E-mail:chenweiyi211@163.com
基金资助:
the National Natural Science Foundation of China (Nos. 11972242 and 11632013) and the China Postdoctoral Science Foundation (No. 2020M680913)

A fluid flow model in the lacunar-canalicular system under the pressure gradient and electrical field driven loads

Xiaogang WU^1,2, Xiyu WANG¹, Chaoxin LI¹, Zhaowei WANG¹, Yuqin SUN¹, Yang YAN¹, Yixian QIN¹, Pengcui LI², Yanqin WANG¹, Xiaochun WEI², Weiyi CHEN¹

1. College of Biomedical Engineering, Taiyuan University of Technology, Taiyuan 030024, China;
2. Shanxi Provincial Key Laboratory for Repair of Bone and Soft Tissue Injury, Taiyuan 030001, China

Received:2022-02-10 Revised:2022-04-22 Published:2022-06-11
Contact: Weiyi CHEN, E-mail:chenweiyi211@163.com
Supported by:
the National Natural Science Foundation of China (Nos. 11972242 and 11632013) and the China Postdoctoral Science Foundation (No. 2020M680913)

摘要/Abstract

摘要： The lacunar-canalicular system (LCS) is acknowledged to directly participate in bone tissue remodeling. The fluid flow in the LCS is synergic driven by the pressure gradient and electric field loads due to the electro-mechanical properties of bone. In this paper, an idealized annulus Maxwell fluid flow model in bone canaliculus is established, and the analytical solutions of the fluid velocity, the fluid shear stress, and the fluid flow rate are obtained. The results of the fluid flow under pressure gradient driven (PGD), electric field driven (EFD), and pressure-electricity synergic driven (P-ESD) patterns are compared and discussed. The effects of the diameter of canaliculi and osteocyte processes are evaluated. The results show that the P-ESD pattern can combine the regulatory advantages of single PGD and EFD patterns, and the osteocyte process surface can feel a relatively uniform shear stress distribution. As the bone canalicular inner radius increases, the produced shear stress under the PGD or P-ESD pattern increases slightly but changes little under the EFD pattern. The increase in the viscosity makes the flow slow down but does not affect the fluid shear stress (FSS) on the canalicular inner wall and osteocyte process surface. The increase in the high-valent ions does not affect the flow velocity and the flow rate, but the FSS on the canalicular inner wall and osteocyte process surface increases linearly. In this study, the results show that the shear stress sensed by the osteocyte process under the P-ESD pattern can be regulated by changing the pressure gradient and the intensity of electric field, as well as the parameters of the annulus fluid and the canaliculus size, which is helpful for the osteocyte mechanical responses. The established model provides a basis for the study of the mechanisms of electro-mechanical signals stimulating bone tissue (cells) growth.

关键词: bone canaliculi, osteocyte process, pressure gradient, electricity, fluid shear stress (FSS)

Abstract: The lacunar-canalicular system (LCS) is acknowledged to directly participate in bone tissue remodeling. The fluid flow in the LCS is synergic driven by the pressure gradient and electric field loads due to the electro-mechanical properties of bone. In this paper, an idealized annulus Maxwell fluid flow model in bone canaliculus is established, and the analytical solutions of the fluid velocity, the fluid shear stress, and the fluid flow rate are obtained. The results of the fluid flow under pressure gradient driven (PGD), electric field driven (EFD), and pressure-electricity synergic driven (P-ESD) patterns are compared and discussed. The effects of the diameter of canaliculi and osteocyte processes are evaluated. The results show that the P-ESD pattern can combine the regulatory advantages of single PGD and EFD patterns, and the osteocyte process surface can feel a relatively uniform shear stress distribution. As the bone canalicular inner radius increases, the produced shear stress under the PGD or P-ESD pattern increases slightly but changes little under the EFD pattern. The increase in the viscosity makes the flow slow down but does not affect the fluid shear stress (FSS) on the canalicular inner wall and osteocyte process surface. The increase in the high-valent ions does not affect the flow velocity and the flow rate, but the FSS on the canalicular inner wall and osteocyte process surface increases linearly. In this study, the results show that the shear stress sensed by the osteocyte process under the P-ESD pattern can be regulated by changing the pressure gradient and the intensity of electric field, as well as the parameters of the annulus fluid and the canaliculus size, which is helpful for the osteocyte mechanical responses. The established model provides a basis for the study of the mechanisms of electro-mechanical signals stimulating bone tissue (cells) growth.

Key words: bone canaliculi, osteocyte process, pressure gradient, electricity, fluid shear stress (FSS)

中图分类号:

74L15
92C10

Xiaogang WU, Xiyu WANG, Chaoxin LI, Zhaowei WANG, Yuqin SUN, Yang YAN, Yixian QIN, Pengcui LI, Yanqin WANG, Xiaochun WEI, Weiyi CHEN. A fluid flow model in the lacunar-canalicular system under the pressure gradient and electrical field driven loads[J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(6): 899-916.

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A fluid flow model in the lacunar-canalicular system under the pressure gradient and electrical field driven loads

A fluid flow model in the lacunar-canalicular system under the pressure gradient and electrical field driven loads

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