Strain rate dependent poroelastic behavior of bovine vertebral trabecular bone

Abstract

It is widely accepted that the pressure variation of interstitial fluid is one of the most important factors in bone physiology. In order to understand the role of interstitial fluid on porous bony structure, a consideration for the biomechanical interactions between fluid and solid constituents within bone is required. In this study, a poroelastic theory was applied to investigate the elastic behavior of calf vertebral trabecular bone composed of the porous solid trabeculae and the viscous bone marrow. The poroelastic behavior of trabecular bone in a uniaxial stress condition was simulated using a commercial finite difference analysis software (FLAC, Itasca Consulting Group, USA), and tested for 5 different strain rates, i. e., 0.001, O. 01, 0.1, and 10 per second. The material properties of the calf vertebral trabecular bone were utilized from the previous experimental study. Two asymptotic poroelastic responses, the drained and undrained deformations, were predicted. From the predicted results for the simulated five strain rates, it was found that the pore pressure generation has a linearly increasing behavior when the strain rate is the highest at 10 per second, otherwise it showed a nonlinear behavior. The pore pressure generation with respect to the strain was found to be increased as the strain rate increased. The elastic moduli predicted at each strain were 208.3, 212.2, 337.6, 593. 1, and 602.2 MPa, respectively. Based on the results of the present study, it was suggested that the calf vertebral trabecular bone could be modeled as a poroelastic material and its strain rate dependent material behavior could be predicted.

Microstructure and nonlinear signatures of yielding in a heterogeneous colloidal gel under large amplitude oscillatory shear

“…Since current models for poroelastic flow [Showalter and Momken (2002); Song and Huang (2000)] do not take viscoplastic deformation of the solid network into account, we cannot make direct theoretical comparisons to our data. However, the trends we observe in our LAOS measurements, including the increase in the maximum of R 00 and the increase in normalized yield stress with increasing frequency are consistent with an increase in the viscous stress due to a resistance to drainage of fluid from the porous gel phase into the void phase under compression [Hong et al (2001)]. …”

High Strain Rate Testing of Bovine Trabecular Bone

“…Figure 3.5 displays the relationship between stiffness and strain rate for several different dynamic marrow intact test specimens for a range of volume fractions while Figure 3.6 displays the relationship between ultimate strength and strain rate for several different dynamic test specimens for a range volume fractions. According to several researchers ( [5], [15], [16], [22], [34], and [36]) experimental and modeling results conclude that the presence of marrow in trabecular bone allows the bone to absorb more energy under elevated loading rates. Therefore, failure energy density (U fail ) and failure strain ( fail ) were also examined for the dynamic test specimens.…”

“…Research has been conducted in modeling trabecular bone ( [16] and [22]) and whole bones such as vertebral bodies ( [21], [33], [34], [38], and [40]). Several studies have also focused on experimental work with trabecular bone ( [5], [10], [12], [15], [18], [23], and [37]) and vertebral bodies ( [32], [36], [39], and [41]). Other areas of biomechanics and biological material mechanical properties have also been explored but aren't necessarily relevant here.…”

“…In 2001 Lim and Hong developed an axisymmetric isotropic poroelastic model using these measured properties to predict behavior of trabecular bone at various strain rates (0.001, 0.01, 0.1, and 10 s −1 ) for drained and undrained conditions [15]. Results indicated a linear increase in pore pressure generation with strain at the highest strain rate with nonlinear pore pressure generation at other loading rates.…”

Patient-Specific Bone Multiscale Modelling, Fracture Simulation and Risk Analysis—A Survey

“…The Finite Difference Method (FDM) is simple in formulation, but exhibits some difficulties in modelling complex geometries and, for this reason, has been scarcely used for solid mechanics problems in recent years [316,317]. FDM was used by [318] to simulate bone remodelling, see Definition 19. Other numerical methods are also available, e.g., method of characteristics, finite volume method, et cetera; these are outside our paper because, to the best of the authors' knowledge, they have not yet been applied to bones.…”