## 1 Introduction  
Bone tissue is mainly composed of hydroxyapatite and collagen. The structure of cortical bone contains multi-scale microcanals or micropores that are filled with tissue fluid. When a cortical bone is subjected to stresses, the resulting strains acting as a driving force that can cause flows of the tissue fluid through the microcanals, during which streaming potentials arise simultaneously [1]. Moreover, the resultant strain can induce polarized electric charges or potential in the bone due to the piezoelectric effect of bone collagens [2]. The two types of stress generated potentials (SGPs) may be related to the growth of bone cells, which stimulates the interest to study the electromechanical properties of bone [3; 4; 5]. The bone growth and absorption process is known as remodeling. [PERSON] et al. concluded that bone remodeling is sensitive to changes in the magnitudes of mechanical strain, the number of mechanical loading cycles, the distribution of loading, the rate of strain and the rate of fluid stress [6]. To explore the role of SGPs, attempts have been made to apply the SGPs to orthopedics for enhancing bone growth. [PERSON] and [PERSON] [7] studied the healing process of bone fractures using a pulsed electromagnetic field device. Literature [8; 9; 10; 11] showed that piezoelectric potentials can enhance bone regeneration and remodeling. For example, [PERSON] et al. demonstrated that an external microcurrent (10 \(\mu\)A) can modulate the homeostasis of bone remodeling [12]. Thus, studying the electromechanical properties of bone not only help us understand the nature of bone materials, but also have clinical significance. When a bone is subjected to deformation caused by stresses, the deformation can lead to bone fluid flows in the microcanals, and then streaming potentials are induced in the microcanals. Owing to the fact that the structure of the microcanals in bone are very complicated, with diameters ranging from tens of nanometers to tens of micrometers, the characteristics of the fluid flowing and the corresponding streaming potentials are still not fully understood [13; 14], though the streaming potentials may play a role in influencing the remodeling of bone cells [15]. [PERSON] [16] obtained the streaming potentials in the intraosseous of a cortical bone experimentally and the results indicated that streaming potentials are induced by fluid pressure gradient. The classical theory of streaming potential is available if and only if the fluid flows in a straight capillary with equal diameter [1; 17]. Based on this understanding, a classical formula of the streaming potential is given by  
\[\phi=\frac{P\varepsilon\zeta}{\mu\lambda_{b}} \tag{1}\]  
where \(\varepsilon\), \(\mu\) and \(\lambda_{b}\) represent the electric permittivity, dynamic viscosity and bulk conductivity of the fluid respectively. The symbol \(P\) is externally applied pressure and \(\zeta\), known as Zeta potential, is the potential at the slipping plane, which refers to the plane where the fluid velocity decreases to zero. The \(\zeta\) represents the electric charges density on the capillary's inner surface in a certain extent. Equation (1) indicates that streaming potential is independent of canal's length [18; 19] and can be affected by the physical characteristics of electric permittivity, dynamic viscosity and bulk conductivity of the fluid. Many factors can, indeed, affect the streaming potentials in bone, because of the hierarchical and interconnected structure of the microcanals [20]. For example, a simulation demonstrates that the key loading factor governing streaming potential is the strain rate ranging from \(10^{-4}\) to \(10^{-3}\) s\({}^{-1}\)[18], and an experimental result shows that streaming potential decreases with increasing pressure-gradient rate [21]. The presence of interconnected pores in the bulk of hydroxyapatite specimens result in additional variations of the internal zeta potentials and the pore conductivities [22].