1. Influence of Flow-Independent Viscoelasticity
Orthopaedic Biomechanics
Influence of Flow-Independent Viscoelasticity
and Flow-Dependent Poroelasticity in Preconditioning of Articular Cartilage
S.M. Hosseini, W. Wilson, K. Ito, C.C. van Donkelaar
Introduction
Analyzing mechanics of biological materials such as cartilage is challenging. These inhomogeneous and anisotropic tissues behave non-linearly and time-dependently. In cartilage, time dependent behavior is due to flow- dependent and independent viscoelasticity. These characteristics make tissue preconditioning necessary. Preconditioning is commonly explained by the fact that residual strains inside the tissue need to be leveled out before reliable measurements can be performed.
Aim
To provide a mechanistic explanation for preconditioning by exploring separate and combined time-dependent effects of poroelastic fluid flow and viscoelastic deformation.
Materials and Methods
A composition-based fibril-reinforced, poroviscoelastic swelling model already developed for studying articular cartilage has been used [1]. Cartilage plugs were modeled as axisymmetric with a radius and thickness of 1 mm. To apply load, two different rigid nonporous indenters have been used, a round indenter (IND) (Φ=0.8 mm) and a plate (unconfined compression-UC). In the first step the tissue swells and equilibrates in 0.15 M saline solution, then after equilibrating in 5% compression a series of strain-relaxation-unstrain between 5% and 10% has been applied to the tissue (Fig. 1) with different recovery time (RT) in each simulations (Table 1).
Table 1: Recovery times (s).
Figure 1: Indenter displacement , dash lines shows recovery times.
To study flow- dependent and independent viscoelasticity, zero collagen fiber viscoelasticity and zero pore pressure for the whole tissue have been defined respectively. Also simulations with both effects present have been done .
Results
Normalized difference between first and second peak values against RT shows (Fig. 2 and Fig. 3): 1st, when only matrix viscoelasticity is considered, first peak is larger than second one; this is opposite when there is only matrix poroelasticity. 2nd, flow-dependent poroelastic effects dominates under UC; flow-independent viscoelasticity dominates under IND. 3rd, effects induced by fluid-independent matrix viscoelasticity are effective over a wider RT range. 4th, when both flow- dependent and independent effects are included, it takes longer to reach equilibrium compared to when either one of them is present alone.
Figure 2: Normalized difference between the first and second peak values as a function of the recovery time, Left: UC, Right: IND.
Figure 3: Normalized difference of subsequent peak values for all cycles.
Discussion
Total tissue response is the result of a complex time-dependent interaction of a viscoelastic collagen network reinforcing a poroelastic tissue. During repeated loading, collagen viscoelasticity and fluid flow have opposite effects partly masking each other. Their relative importance depends on the load nature, UC vs. IND, and on load protocol. Importantly, rather than eliminating residual stress from tissue during preconditioning, results show that initial loading cycles introduce residual stresses in the tissue.
References
[1] Wilson, W, et al J Orthop Res (24) pp 60 80
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/ Department of Biomedical Engineering