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Effects of osteocyte orientation on loading-induced interstitial fluid flow and nutrient transport in bone

骨细胞方向对负荷诱导的骨内液体流动和营养物质运输的影响

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Abstract

Changes in osteocyte spatial arrangement and orientation that are associated with aging and certain bone diseases have attracted much attention. The purpose of the current study is to demonstrate effects of osteocyte orientation on the deflection of fluid flow in bone by modeling osteocytes rotated by 0°, 30°, 45°, 60°, and 90° relative to the bone fluid flow axis. The lacuno-canalicular network was assumed to be regularly arranged and uniformly distributed and the osteon was defined as a representative cubic periodic unit cell (CPUC) at the microscale level. Calculation of canaliculi number and distribution around the osteocyte enabled estimation of osteon microstructural parameters toward the establishment of an osteon poroelastic finite element model to investigate specific loading-induced interstitial fluid flow and nutrient transport parameters in the bone under different boundary conditions and loading types. The results showed that osteocyte orientation under loading conditions approximating normal physiological loads markedly influenced predicted osteon maximum fluid pressure (p), fluid velocity (v), and fluid shear stress (τ) values. Moreover, results showing the nonuniform distribution of p and τ values within the osteon wall indicated that osteocyte orientation and canaliculi three-dimensional distribution were important parameters for predicting the degree of anisotropy of lacuno-canalicular system permeability, of anisotropy of lacuno-canalicular system permeability, while also demonstrating that osteocyte orientation had little effect on nutrient transport. Furthermore, loading type and lacuno-canalicular tortuosity effects on osteon fluid flow were greater than osteocyte orientation-associated effects. The results of this study may help researchers accurately quantify bone fluid flow behavior to enhance understanding of mechanotransduction mechanisms in bone.

摘要

与年龄或某些骨骼疾病相关的骨细胞空间排列方向的变化引起了研究者们的广泛关注. 本研究的目的是通过建立骨细胞相对于骨内流体流动轴偏转0°、30°、45°、60°和90°的骨单元多孔弹性力学模型, 证明骨细胞方向对骨内流体流动的影响. 我们假设骨陷窝-小管网络规则排列且均匀分布, 且将骨单元定义为由微观尺度水平上的代表性立方周期单元(CPUC)组成. 通过计算骨细胞周围骨小管的数量和3D分布来估算骨单元的微观结构参数(渗透率、孔隙率等), 并建立骨单元孔隙弹性有限元模型, 研究不同边界条件和载荷形式下负载诱导的骨内间质流体流动和骨内营养物质运输. 结果表明, 在接近正常生理活动的载荷条件下, 骨细胞方向对骨单元最大流体压力(p)、最大流体速度(v)和最大流体剪切应力(τ)都有显著的影响. p值和τ值在骨单元壁内呈现不均匀分布, 这说明骨细胞方向和骨小管三维分布是预测骨陷窝-小管系统渗透性各向异性程度的重要参数, 但骨细胞方向对骨内营养物质运输影响很小. 此外, 载荷形式和骨陷窝-小管弯曲度对骨单元的液体流动行为的影响大于骨细胞方向对其的影响. 这项研究的结果将有助于人们准确量化骨内液体流动行为, 并增强对骨的力传导机制的理解.

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Abbreviations

v :

Darcy fluid velocity

τ :

Fluid shear stress

CPUC:

Cubic periodic unit cell

r c :

The radius of the bone canaliculi

r o :

The radius of the osteocyte process

a 0 :

The radius of the pericellular fibers

Δ :

The effective spacing of the fibers of the pericellular matrix

q :

A dimensionless ratio between the radius of the bone canaliculus (rc) and the osteocyte process (ro)

γ :

A dimensionless length ratio between rc and the square root of the permeability of a single canaliculus \((\gamma=r_{c}/\sqrt{k_{\mathrm{p}}})\)

k p :

The permeability of the fiber-filled medium in a single canaliculus kp = 0.0572a 20 (Δ/a0)2.377

n i (i = x, y, z):

The number of canaliculi passing through each face of the CPUC perpendicular to the local osteocyte axes (x, y and z), respectively.

a, b, and c :

Semi-axes of the osteocyte lacunar ellipsoid

L :

The distance between the two lacunae, which is also the side length of CPUC

V L :

The unit volume

N Lac :

The number of the lacunae per unit volum

N :

The total number of the bone canaliculi N around each lacuna

θ :

The porosity of the lacuno-canalicular

L c :

The average length of the bone canaliculi

r Lac :

The average radius of lacunae in the radial direction

S x, S y, and S z :

The projected surface areas of the lacunar ellipsoid in the x, y, and z orientations, respectively

θ :

The osteocyte deflected θ around the x axis

K :

The permeability tensor

E r :

Radial drained Young’s modulus

E z :

Axial drained Young’s modulus

v z :

Axial drained Poisson’s ratio

M :

Biot’s modulus

α :

Biot’s effective coefficient

ρ S :

Solid density

ρ f :

Fluid density

μ :

Dynamic viscosity

R a :

Inner radius of osteon

R b :

Outer radius of osteon

C p :

Fluid compressibility

σ :

The total stress tensor

C :

The drained stiffness tensor

ε :

The total strain tensor

ζ :

The variation in fluid content

tr():

The trace operator

ρ :

The total density

ü :

The second derivative of the displacement

V :

The velocity vector

d :

The mean pore diameter

v r :

The interstitial fluid velocity

T :

The tortuosity of the flow path

w :

Harmonic displacement

f :

Harmonic frequency

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Acknowledgements

This work was supported by the Department of Science and Technology of Jilin Province (Grant No. YDZJ202201-ZYTS568), the National Natural Science Foundation of China (Grant No. 82172593), and the Doctoral Program Foundation of Jilin Medical University (Grant No. JYBS2021025LK).

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Authors and Affiliations

  1. College of Biomedical Engineering, Jilin Medical University, Jilin, 132013, China

    Weilun Yu  (于纬伦), Haoting Liu  (刘昊庭), Xuyang Huo  (霍旭阳), Fengjian Yang  (杨风健), Xiaohang Yang  (杨晓航) & Zhiyuan Chu  (楚智媛)

  2. Department of Pharmaceutics, School of Pharmacy, Jilin Medical University, Jilin, 132013, China

    Nianqiu Shi  (时念秋)

  3. College of Pharmaceutical Sciences, Yanbian University, Yanbian, 133002, China

    Nianqiu Shi  (时念秋)

  4. College of Biomedical Engineering, Taiyuan University of Technology, Taiyuan, 030024, China

    Xiaogang Wu  (武晓刚) & Weiyi Chen  (陈维毅)

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  1. Weilun Yu  (于纬伦)
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Contributions

Weilun Yu, Xuyang Huo, and Nianqiu Shi designed the research. Weilun Yu, Fengjian Yang, Xiaohang Yang, and Zhiyuan Chu wrote the first draft of the manuscript and formal analysis. Fengjian Yang, Xiaohang Yang, and Zhiyuan Chu set up the experiment set-up and processed the experiment data. Xiaogang Wu and Weiyi Chen helped inspect the manuscript. Haoting Liu revised and edited the final version.

Corresponding authors

Correspondence to Xuyang Huo  (霍旭阳) or Nianqiu Shi  (时念秋).

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Yu, W., Liu, H., Huo, X. et al. Effects of osteocyte orientation on loading-induced interstitial fluid flow and nutrient transport in bone. Acta Mech. Sin. 39, 622332 (2023). https://doi.org/10.1007/s10409-022-22332-x

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