压力与电场协同作用下具有初级纤毛和胶原小丘的骨细胞的力学响应研究

王岩; 李朝鑫; 董浩; 禹健豪; 燕杨; 武晓刚; 王艳芹; 李鹏翠; 卫小春; 陈维毅

doi:10.1007/s10409-022-09004-x

Mechanosensation of osteocyte with collagen hillocks and primary cilia under pressure and electric field stimulation

doi: 10.1007/s10409-022-09004-x

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

Funds:

the National Natural Science Foundation of China Grant

and China Postdoctoral Science Foundation Grant

Corresponding authors: Corresponding authors. E-mail addresses: wuxiaogang@tyut.edu.cn (Xiaogang Wu); chenweiyi@tyut.edu.cn (Weiyi Chen).; Corresponding authors. E-mail addresses: wuxiaogang@tyut.edu.cn (Xiaogang Wu); chenweiyi@tyut.edu.cn (Weiyi Chen).

摘要

摘要: 骨细胞内的力学传感器是骨细胞感知周围力学环境变化的最重要的细胞器. 为了评估骨陷窝-骨小管系统(LCS)内胶原小丘、细胞突触和初级纤毛作为力学传感器的生物力学效应, 我们利用COMSOL Multiphysics软件开发了一种压力-电场-结构相互作用的骨细胞模型, 以描述在流体流动和电场刺激下LCS中胶原小丘, 初级纤毛以及细胞突触作为骨细胞中力学传感器的力学感应效果. 分析了LCS中的力学信号(孔隙压力、流体速度、应力、变形)并且研究了胶原小丘弹性模量的变化、细胞突触的数量和位置、初级纤毛的长度和位置对骨细胞内力学传感器的力学敏感性以及骨细胞总体多孔弹性响应的影响. 结果表明, 初级纤毛和胶原小丘的存在将会导致骨细胞部分位置产生明显的应力集中(比骨细胞体其他位置的应力大1~2个数量级). 相比于细胞突触沿骨细胞短轴方向生长, 沿长轴方向生长可以刺激骨细胞产生更大的应力. 当初级纤毛位于骨细胞顶部时, 初级纤毛基底的应力比初级纤毛位于骨细胞底部时大8 Pa. 然而, 胶原小丘和初级纤毛的存在并不影骨细胞整体的力学信号分布. 所建立的模型可用于在多尺度水平上研究骨力学信号的传导机制.
Abstract: Mechanosensors are the most important organelles for osteocytes to perceive the changes of surrounding mechanical environment. To evaluate the biomechanical effectiveness of collagen hillock, cell process and primary cilium in lacunar-canalicular system (LCS), we developed pressure-electricity-structure interaction models by using the COMSOL Multiphysics software to characterize the deformation of collagen hillocks- and primary cilium-based mechanosensors in osteocyte under fluid flow and electric field stimulation. And mechanical signals (pore pressure, fluid velocity, stress, deformation) were analyzed in LCS. The effects of changes in the elastic modulus of collagen hillocks, the number and location of cell processes, the length and location of primary cilia on the mechanosensitivity and the overall poroelastic responses of osteocytes were studied. These models predict that the presence of primary cilium and collagen hillocks resulted in significant stress amplifications (one and two orders of magnitude larger than osteocyte body) on the osteocyte. The growth of cell process along the long axis could stimulate osteocyte to a higher level than along the short axis. The Mises stress of the basal body of primary cilia near the top of osteocyte is 8 Pa greater than that near the bottom. However, the presence of collagen hillocks and primary cilium does not affect the mechanical signal of the whole osteocyte body. The established model can be used for studying the mechanism of bone mechanotransduction at the multiscale level.
- Osteocyte /
- Cell Process /
- Primary Cilium /
- Collagen Hillock /
- Finite Element

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1. Idealized finite element model of LCS inclusion osteocyte body under pressure-electricity synergic driven.

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2. Selected points for statistical data of each osteocyte structure.

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3. Time responses of pressure and electric field.

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4. Maximum displacement curve of osteocyte body with t.

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5. Comparison of mechanical signals of osteocyte without and with collagen hillocks in LCS. a Distribution of stress of osteocyte without collagen hillocks. b Distribution of stress of cell with collagen hillocks. c Distribution of displacement of osteocyte without collagen hillocks. d Distribution of displacement of osteocyte with collagen hillocks. e Distribution of pore pressure of cell without collagen hillocks; f Distribution of pore pressure of cell with collagen hillocks. g Distribution of pore flow rate of cell without collagen hillocks; h Distribution of pore flow rate of cell with collagen hillocks.

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6. Comparison of mechanical signals of reference line of the cell without and with collagen hillocks in LCS. a Distribution of stress of reference line of the cell without and with collagen hillocks. b Distribution of displacement of reference line of the cell without and with collagen hillocks. c Distribution of pore pressure of reference line of the cell without and with collagen hillocks. d Distribution of pore flow rate of reference line of the cell without and with collagen hillocks.

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7. The influence of the presence and absence of collagen hillocks on cell processes. a Mises stress nephogram of the x-z section with or without collagen hillocks. b The total displacement nephogram of the x-z section with or without collagen hillocks. c Comparison of the Mises stress of the AB line segment of the two hillocks with or without collagen hillocks. d Comparison of the total displacement of the AB line segment of the two hillocks with or without collagen hillock. e The influence of the presence or absence of collagen hillocks on the Mises stress near 1-3 hillocks. f The influence of the presence or absence of collagen hillocks on the total displacement near 1-3 hillocks.

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8. The influence of the change of the elastic modulus E_CN of the collagen hillocks on the stress and the total displacement. a The reference line stress distribution of different E_CN; b the reference line displacement distribution of different E_CN.

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9. Three LCS models with changes in the direction and number of bone canaliculus and cell processes. Model 1: only a pair of bone canaliculus and cell processes grow in the direction of the osteocyte’s long axis; model 2: only a pair of bone canaliculus and cell processes grow in the direction of the osteocyte’s short axis; model 3: two pairs of bone canaliculus and cell processes grow together in the long axis and short axis .

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10. The effect of changes in the direction and number of bone canaliculus and cell processes on mechanical signals. a The stress distribution of osteocyte in model 1; b the stress distribution of osteocyte in model 2; c the displacement distribution of osteocyte in model 1; d the displacement distribution of osteocyte in model 2.

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11. The mechanical signals distribution of each part of different models. a Mises stress; b total displacement; c pore pressure; d pore flow rate.

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12. a The stress nephogram of the primary cilium at the cross-section. b The selection point on the primary cilium. c The stress distribution on the selected point of primary cilium. d The displacement distribution on the selected point of primary cilium.

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13. a The nephogram of fluid shear rate of osteocyte body. b The location distribution of 4 groups of primary cilia.

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14. Maximum deflection of primary cilia at different locations and the corresponding load.

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15. Location 1: Primary cilia are 0 μm from the central axis of osteocyte; Location 2: Primary cilia are 2 μm from the central axis of osteocyte; Location 3: Primary cilia are 4 μm from the central axis of bone cell; Location 4: Primary cilia are 6 μm from the central axis of osteocyte.

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16. The mechanical signals of each part of osteocytes when primary cilia in different locations. a Stress, b total displacement, c pore pressure, d pore flow rate.

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17. The mechanical signals of each part of osteocytes when the length of primary cilia is different. a Stress, b total displacement, c pore pressure, d pore flow rate.

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18. The Mises stress of various parts of osteocyte: Collagen hillock: the average Mises stresses for collagen hillocks with different elastic moduli. Basal body: the average Mises stress for the basal body of primary cilia of different lengths.

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Table 1. The sizes of osteocyte model [28]

Components (μm)	Value	Implication
X_cytoplasm	14	The long axis of the cytoplasm
Y_cytoplasm	8	The short axis of the cytoplasm
H_nucleus	4	The height of the cytoplasm
X_nucleus	7	The long axis of the nucleus
Y_nucleus	4	The short axis of the nucleus
H_nucleus	3	The height of the nucleus
D_pc	0.2	The diameter of primary cilium
L_pc	0.4	The length of primary cilium

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Table 2. Cytoplasmic parameters [31]

Components	Value	Components	Value
Elastic modulus E (Pa)	360	Liquid density $ρ_{l} ({kg m}^{- 3})$	992.52
Poisson’s ratio $ν_{s}$	0.38	Dynamic viscosity $μ (Pa s)$	0.001
Solid density $ρ_{s} ({kg m}^{- 3})$	800	Compressibility $χ_{f} (1 {Pa}^{- 1})$	4.35×10⁻¹⁰
Permeability $κ (m^{2})$	1×10⁻¹⁸	Relaxation time $τ_{v} (s)$	40
Porosity $ε_{p}$	0.2	Shear modulus $G_{v} (Pa)$	33.3

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Table 3. Nuclear parameters [31]

Components	Value	Components	Value
Elastic modulus E (Pa)	1440	Liquid density $ρ_{l} ({kg m}^{- 3})$	992.52
Poisson’s ratio $ν_{s}$	0.38	Dynamic viscosity $μ (Pa s)$	0.001
Solid density $ρ_{s} ({kg m}^{- 3})$	2000	Compressibility $χ_{f} (1 {Pa}^{- 1})$	4.35×10⁻¹⁰
Permeability $κ (m^{2})$	1×10⁻²⁰	Relaxation time $τ_{v} (s)$	5
Porosity $ε_{p}$	0.1	Shear modulus $G_{v} (Pa)$	666.67

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Mechanosensation of osteocyte with collagen hillocks and primary cilia under pressure and electric field stimulation

doi: 10.1007/s10409-022-09004-x

Corresponding authors: Corresponding authors. E-mail addresses: wuxiaogang@tyut.edu.cn (Xiaogang Wu); chenweiyi@tyut.edu.cn (Weiyi Chen).; Corresponding authors. E-mail addresses: wuxiaogang@tyut.edu.cn (Xiaogang Wu); chenweiyi@tyut.edu.cn (Weiyi Chen).

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Mechanosensation of osteocyte with collagen hillocks and primary cilia under pressure and electric field stimulation

doi: 10.1007/s10409-022-09004-x

Corresponding authors: Corresponding authors. E-mail addresses: wuxiaogang@tyut.edu.cn (Xiaogang Wu); chenweiyi@tyut.edu.cn (Weiyi Chen).; Corresponding authors. E-mail addresses: wuxiaogang@tyut.edu.cn (Xiaogang Wu); chenweiyi@tyut.edu.cn (Weiyi Chen).

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