Linear Poroelastic Cancellous Bone Anisotropy: Trabecular Solid Elastic and Fluid Transport Properties

Abstract

The mechanical performance of cancellous bone is characterized using experiments which apply linear poroelasticity theory. It is hypothesized that the anisotropic organization of the solid and pore volumes of cancellous bone can be physically characterized separately (no deformable boundary interactive effects) within the same bone sample. Due to its spongy construction, the in vivo mechanical function of cancellous or trabecular bone is dependent upon fluid and solid materials which may interact in a hydraulic, convective fashion during functional loading. This project provides insight into the organization of the tissue, ie., the trabecular connectivity, by defining the separate nature of this biphasic performance. Previous fluid flow experiments [Kohles et al., 2001, Journal of Biomechanics, 34(11), pp. 1197-1202] describe the pore space via orthotropic permeability. Ultrasonic wave propagation through the trabecular network is used to describe the solid component via orthotropic elastic moduli and material stiffness coefficients. The linear poroelastic nature of the tissue is further described by relating transport (fluid flow) and elasticity (trabecular load transmission) during regression analysis. In addition, an empirical relationship between permeability and porosity is applied to the collected data. Mean parameters in the superior-inferior (SI) orientation of cubic samples (n=20) harvested from a single bovine distal femur were the largest (p<0.05) in comparison to medial-lateral (ML) and anterior-posterior (AP) orientations: Apparent elastic modulus (2,139 MPa), permeability (4.65x10(-10) m2), and material stiffness coefficient (13.6 GPa). A negative correlation between permeability as a predictor of structural elastic modulus supported a parametric relationship in the ML (R2=0.4793), AP (R2=0.3018), and SI (R2=0.6445) directions (p<0.05).

Fabric dependence of wave propagation in anisotropic porous media

“…Predictions of the intrinsic permeability are shown in Figure 1b, and exhibit a large variability that coincides with studies reporting experimental measurements of the permeability κ 0 (1 × 10 −12 – 1 × 10 −7 m 2 ) on cancellous bone (Lim and Hong, 2000; Grimm and J. L. Williams, 1997b; Nauman et al, 1999; Kohles et al, 2001; Kohles and Roberts, 2002; Baroud et al, 2004; Beaudoin et al 1991; Li et al 1987). The variability of the intrinsic permeability in porous media is due to the dependence of the permeability on the porosity (Grimm and J. L. Williams, 1997b; Nauman et al, 1999) and the microstructure of the sample (Nauman et al, 1999; Kohles et al, 2001; Kohles and Roberts, 2002; Baroud et al, 2004). …”

Biomechanical considerations on tooth-implant supported fixed partial dentures

“…The existence of trabecular rods–plates and the pores that are filled with a viscous fluid form a matter with a complex mechanical response during loading. 108–110 The big difference between the bulk modulus of the solid and the fluid phases, as well as the minute local deformations, as a result has a biphasic mechanical response to external loads, which may be expressed by a poroelastic model. 61,110 Trabecular bone is an anisotropic material and a reformation of the equations of anisotropic poroelasticity has been presented by Thompson and Willis.…”

“…108–110 The big difference between the bulk modulus of the solid and the fluid phases, as well as the minute local deformations, as a result has a biphasic mechanical response to external loads, which may be expressed by a poroelastic model. 61,110 Trabecular bone is an anisotropic material and a reformation of the equations of anisotropic poroelasticity has been presented by Thompson and Willis. 111 However, for simplicity reasons, the equations presented by Cowin 61 were for an isotropy case, and the isotropic stress–strain relationship is expressed as…”

Mechanical and flow characterization of Sponceram® carriers: Evaluation by homogenization theory and experimental validation

“…Measurement of the scaffold permeability could be based on those tests conceived for bone. In this sense, gravity‐induced pressure systems have been used to measure the permeability of human13 and bovine14 cancellous bone using oil and water as fluid, respectively. Scaffold permeability data have been published in several papers using pumped water,15, 16 with a gravity‐induced pressure using water,17, 18 or using compressed air 19.…”