Abstract
Introduction
Novel hydrogel implants, TRUFIT® bone plugs, have been developed by Smith & Nephew to replace worn-out cartilage surfaces, restoring mobility and relieving joint pain. There is limited information, however, on the biomechanical properties of the implants. Therefore, appropriate mechanical testing and modelling must be carried out to assess their mechanical properties for load bearing applications.
In this study, compressive properties of TRUFIT® bone and dual layer implants were examined under selected physiological loading conditions. The bone layer of the implant was also modelled using a biphasic poroviscoelastic (BPVE) material constitutive law and the results from the model are compared with those from the experiments.
Materials and Methods
TRUFIT® CB plugs, with diameters of 11 and 5mm, were sectioned to obtain single layer bone and dual layer samples, with an aspect ratio of 0.86. Specimens were tested in confined and unconfined compressions at two constant strain rates of 0.002/sec (walking) and 0.1/sec (impact) [1-3] on a MTS servo-hydraulic test machine equipped with a bionix envirobath. All samples were tested in phosphate buffered saline (PBS) solution at 37 °C. A preload of 0.1 MPa was applied and preconditioning (10 cycles of 0.008 strain) at a constant strain rate of 0.005 sec−1 [4] was used. The compressive modulus was calculated from the slope of the linear part of the stress-strain curve. In addition, whilst stress relaxation tests were performed on the bone samples in unconfined compression up to 5% strain, at a strain rate of 0.01/s (running) [1-2].
Biphasic Modelling
The bone implant was modelled as a biphasic poroviscoelastic (BPVE) material assuming constant permeability and linear viscoelasticty. An axisymmetric finite element model of the implant in unconfined compression was built using FEBio [5], with 8-node tri-linear displacement and pore pressure elements. The governing equations for linear BPVE theory are summarized in [6]. Six material coefficients were obtained to describe the model, as shown in Table 1. E and µ are the Young's modulus and Poisson coefficient of the solid matrix; k is the hydraulic permeability; G∗, t1 and t2 represent the discrete relaxation spectrum magnitude and time relaxation constants used to describe the intrinsic viscoelastic nature of the solid matrix. The Young's modulus of the solid matrix was calculated from the equilibrium stress versus strain in the linear range. The Poisson coefficient of the porous solid matrix was determined also from 3D in situ step-wise compressive tests using Digital Volume Correlation. Permeability measurements were performed, where steady state flow rate versus pressure gradient was measured and the hydraulic permeability was calculated using the Darcy's law. An inverse iterative FE technique was used to identify the remaining coefficients from the stress relaxation experiments.
Results & discussion
The compressive moduli are summarized in Fig 1. The preliminary results seem to suggest that strain rate seems to have a dominant effect on compressive modulus. Higher strain rate would always result in higher modulus. On the other hand, the influence of confinement seems to be small. Higher moduli were observed for bones. Smaller sized (5mm) bone samples seem to have a higher modulus at both strain rates. For plugs, significantly higher modulus was found for 5mm samples in walking but similar results were obtained in impact.
Fig. 2 shows a typical curve fitting exercise of the BPVE model using the experimentally determined stress relaxation curve (R2=0.95), from which model parameters were obtained. The BPVE model is able to account for the initial, transient and stationary regime of stress relaxation. Moreover, the model is able to reproduce the monotonic unconfined compressive responses at two strain rates (walking and impact), as illustrated in Fig. 3.
Acknowledgements
The authors would like to thank Smith & Nephew for providing the samples.
