Large-sliding contact elements accurately predict levels of bone–implant micromotion relevant to osseointegration
Introduction
The lack of initial post-operative implant stability (primary stability) is recognised as an important determinant in the aseptic loosening failure process of cementless orthopaedic implants (Maloney et al., 1989; Phillips et al., 1990; Sugiyama et al., 1989). Physiological loads giving rise to implant–bone relative micro-movements of the order of 100 or 200 μm may inhibit bone in-growth, resulting in the formation of a fibrous tissue layer around the prosthesis, and eventually promoting loosening of the implant (Maloney et al., 1989; Pilliar et al., 1986; Soballe, 1993; Sugiyama et al., 1989). An accurate evaluation of the bone–implant relative micromotion is becoming important both in pre-clinical and clinical contexts. The pre-clinical validation of new prosthetic designs often involves the evaluation of the primary stability by means of in vitro measurements (Baleani et al., 2000; Harman et al., 1995; McKellop et al., 1991; Phillips et al., 1990; Walker et al., 1987). In clinical practice primary stability is sometime assessed intra-operatively (Harris et al., 1991), and in follow-up studies Röentgen stereophotogrammetric analysis (RSA) is used to evaluate inducible micromotion (Hilding et al., 1995). Also computer-aided pre-operative planning systems are sometime connected to finite element analysis programs to predict the primary stability that would result from a given surgery (O’Toole 3rd, et al (1995), O’Toole 3rd, et al (1995)).
If the biological threshold for micro-movements is in the range 100–200 μm then, in order to be discriminative, any method used to evaluate the primary stability of a cementless implant should have an accuracy of 10–20 μm or better. Additionally, it is difficult to establish a priori the location of the maximum bone–implant micromotion; thus, such method should also be able to report the relative micromotion at each point of the interface. Unfortunately, none of the available experimental methods satisfies both requirements. Trans-cortical measurements of the interface micromotion as used in vitro, while extremely accurate, measure micromotion only at a few predefined points of the interface (Cristofolini et al.,1998). The accuracy of RSA protocols is usually higher than 100 μm (Vrooman et al., 1998) and the intra-operative torque-wrench measure the stability only at the calcar level.
On the contrary, finite element models are able to predict a complete map of the interface micromotion (Dammak et al., 1997; Tissakht et al., 1995). It is unclear, however, as to whether current finite element modelling techniques can predict the implant primary stability with the necessary accuracy. Beside the complexity of the geometry and of the constitutive equations of the biological materials, it is usually difficult to model the macro-mechanics of frictional contact at the tissue-implant interface. A variety of approaches have been used in the literature, involving different levels of complexity. The simplest physical model is unilateral frictionless contact (Van Rietbergen et al., 1993; Verdonschot et al., 1993); a more complex simulation may account for friction (Kang et al., 1993; Rubin et al., 1993); a further step, frequently simulated in in vitro experimental studies but not in numerical studies, is to account for the initial press-fit. The most used numerical representation of contact is based on the point-to-point contact model (Couteau et al., 1998; Kang et al., 1993; Rubin et al., 1993; Van Rietbergen et al., 1993; Verdonschot et al., 1993). However, more advanced methods, called point-to-face and face-to-face contact models, are also available, although rarely used in orthopaedic biomechanics (Hefzy and Singh, 1997; Mottershead et al., 1996; Tissakht et al., 1995). The validity of each of these methods depends on the fulfilment of certain conditions (e.g., gap elements are not able to cope with large shear motion). Furthermore, all non-linear modelling techniques require the identification of multiple parameters. Unfortunately none of the cited studies addressed these specific aspects. In most cases, the contact modelling technique is given as a fact and the contact parameters are assigned without any further discussion on the accuracy achieved.
The scope of the present study is to verify if any of the current finite element modelling techniques is sufficiently accurate in predicting the primary stability of a cementless prosthesis to be used to decide whether the micromotion may or may not jeopardise the implant osseointegration. Additionally, the study was designed to establish what is the minimal level of physical and numerical complexity to achieve such accuracy. To this purpose, the primary stability under torsional loads of an anatomic cementless stem, as measured in vitro, was used as a benchmark problem to comparatively evaluate the different modelling techniques and the effect of various parameters on the accuracy of the prediction.
Section snippets
Materials and methods
The primary stability of an anatomic cementless stem, as measured in vitro, was used as a benchmark problem to comparatively evaluate the different modelling techniques on the accuracy of the finite element model in predicting the measured interface micro-movements. Six composite femurs (Mod. 3103, Pacific Research Labs. Inc., Vashon Island, WA, USA) were implanted with an anatomical cementless stem (AncaFit, Cremascoli Ortho, Italy) by an expert surgeon. Each stem was press-fitted into the
Results
The face-to-face model accounting for frictional contact and initial press-fit was able to predict the micro-movements measured experimentally with an average (RMS) error of 10 μm and a peak error of 14 μm (Table 1). All the other models presented errors higher than the 20 μm assumed as accuracy threshold.
The physical model adopted to describe the bone-implant contact affected the accuracy more than the type of contact element. The best frictionless model showed average and peak errors of 38 and 50
Discussion
To verify the accuracy of the finite element models in predicting the primary stability of a cementless prosthesis it was necessary to identify a reference problem. The in vitro experiment here adopted as benchmark problem was highly repeatable, and the set-up was sufficiently accurate so that the average of the repeated measurements could be assumed as ‘true’ value for the present study. To the authors’ knowledge no other similar experiment was documented in the literature to achieve the same
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