Poroelastic behaviors of the osteon: A comparison of two theoretical osteon models

Abstract

In the paper, two theoretical poroelastic osteon models are presented to compare their poroelastic behaviors, one is the hollow osteon model (Haversian fluid is neglected) and the other is the osteon model with Haversian fluid considered. They both have the same two types of impermeable exterior boundary conditions, one is elastic restraint and the other is displacement constrained, which can be used for analyzing other experiments performed on similarly shaped poroelastic specimens. The obtained analytical pressure and velocity solutions demonstrate the effects of the loading factors and the material parameters, which may have a significant stimulus to the mechanotransduction of bone remodeling signals. Model comparisons indicate: (1) The Haversian fluid can enhance the whole osteonal fluid pressure and velocity fields.(2) In the hollow model, the key loading factor governing the poroelastic behavior of the osteon is strain rate, while in the model with Haversian fluid considered, the strain rate governs only the velocity. (3) The pressure amplitude is proportional to the loading frequency in the hollow model, while in the model with Haversian fluid considered, the loading frequency has little effect on the pressure amplitude.

Finite Element Study of the Effect of Osteon Morphology Variation Related Ageing, Osteoporosis, or Physical Activity Level on Its Poroelastic Behaviors

“…As shown in Fig. 1, we considered the transverse isotropy and low frequency and obtained its theoretical solution in cylindrical coordinate system, and verified the validity of the corresponding finite element model 23,[25][26][27] .…”

“…fluid-solid interactions in cortical bone, and no body forces were taken into account [26][27][28][29] . The model used the transverse isotropic materials.…”

“…The height (h = 1 mm) is the same in all conditions, and the detailed geometry parameters will be given in concrete analysis. The properties of poroelastic materials of osteon are applied in Table 1 23,[26][27][28][29] .…”

“…The pore pressure and solid surface for the inner wall are considered to be zero and stress-free, respectively. As shown in Equation 1, the cyclic physiological loads are axial and symmetrical to represent longitudinal compression and its amplitude of harmonic displacement (w) and frequency (f) are 0.5 μm and 1 Hz, respectively 26,27) . The maximum axial strain (ε) amplitude is 0.001 at about 0.5 s in one cycle, however, the maximum responses of P and V occurs at about at 0.25 s 22,25) :…”

“…Based on the Biot poroelastic theory, Nguyen used analytical and finite element methods to investigate the behaviours of fluid flows in osteon 23,24) . Previous study of our group considered osteon as poroelastic materials 25) , and established mathematic and finite element model to analyse the poroelastic behaviors of osteon under different boundary conditions 26,27) , and we considered the fluid flow in osteon induced the streaming potential 28) . The poroelastic behaviors of microcracks in an osteon were evaluated 29,30) , and the direction and morphology of microcracks were fully considered 31) .…”