Abstract
In order to demonstrate the influence of the boundary conditions in experimental biomechanical investigations of arthrodesis implants two different models were investigated. As basic model, a simplified finite element model of the cortical bone was used in order to compare the stress values with (Model 1) and without (Model 2) allowing horizontal displacements of the load application point. The model without constraints of horizontal displacements showed considerably higher stress values at the point of failure. Moreover, this investigation shows that the boundary conditions (e.g. constraints) have to be carefully considered, since simplifications of the reality with experimental tests cannot always be avoided.
1 Introduction
It is commonly known that boundary conditions in biomechanical investigations can substantially influence their results. Therefore, in each case it has to be ensured that the boundary conditions provide at least an approximation of the reality, as the whole complexity of the reality can be modelled neither in theoretical models nor in biomechanical experiments. This is mainly true for biomechanical experimental tests of osteosynthesis implants.
In this case, comparing biomechanical measurements of stiffness and failure load of two upper ankle arthrodesis methods had to be carried out: the screw arthrodesis and the arthrodesis using osteosynthesis plates. The test device allows the measurement of the stiffness and the failure load of the arthrodetic ankle joint with dynamical load in varus/valgus and plantar-/dorsiflexion direction. The force and the displacement of selected marker points at the bone are measured. In this paper, the question is asked which boundary conditions have to be realized by the test device. A test device is described by Richter et al [1] which allows a similar ankle joint load.
A test device allowing a dynamical loading of the ankle arthrodesis was designed and tested with artificial bones. Under certain boundary conditions which are described more in detail below, an early failure of the artificial bones at an unexpected point was observed. The reasons for this failure were found in the boundary conditions, which will be shown in this study by a simplified finite element model.
Schematic representation of the bone test device with the main dimensions in mm
2 Material and methods
The test device which was used in our study consists of the tibia fixation, which is performed by embedding the proximal end in bone cement and fixation in the lower specimen holder of the test device (Fig. 1). The calcaneus is also embedded and fixed in the opposed specimen holder with a lever arm, thus the ankle joint is tested in overhead position using a finite element model. The model (Fig. 2) is formed by a conic hollow cylinder which represents the artificial bone, with rigid restraints at the lower surface. The dimensions are similar to the artificial bone; however the approximately triangular tibial cross section was represented by a circular ring. The ratio of the inner to outer diameter is set to a value of 0.55 [2], which realizes the highest specific strength of hollow bones
For sake of simplicity, the material properties of the bone are defined linear elastically, with a Young’s modulus value of E=17 GPa and a Poisson ration of ν =0.3 for cortical bone. The analysis was performed nonlinear statically by the finite element system ABAQUS with a load of 100N.
The upper embedding and the horizontal lever for load application by the testing machine are represented by rigid links (Multiple Point Constraints, MPC). Hence, the load is directly applied to the pivot point of the mechanical testing device, which is linked by the MPCs to all nodes of the upper surface of the bone model. In Model 1, the load is applied by a horizontal sled, allowing a horizontal displacement of the load application point and hence a horizontal movement of the artificial bone, according to Richter et al. [1]. In Model 2, the sled was removed and all tests were performed with horizontal blocking of the displacement of the load application point.
3 Results and discussion
In the preliminary experiments with artificial bones an early bone failure was observed (Fig. 3). The artificial bones failed immediately over the embedding cement with a load level of 200 N. Hence, the failure of the ankle joint arthrodesis could not be investigated within these tests. Therefore, the sled was removed and all subsequent tests were performed with horizontal blocking of the displacement of the load application point.
The early artificial bone failure did not occur after this modification, and the ankle joint arthrodesis were tested properly.
For determination of the reason of the bone failure the v. Mises stress values are shown as contour plots. Model 1 shows a maximum value of 3.88 MPa in the range of the lower rigid restraint (compression stress side), while the maximum value in Model 2 occurs at the tension stress side and is with 0.98 MPa considerably lower (Fig. 4). Thus, the higher v. Mises stress values seems to be the reason for the early bone failure for Model 1.
Finite element models with Multiple Point Constraints (MPC) and boundary conditions.
Artificial bone in the test device (left), artificial bone after failure (right)
For normal stress evaluation, the vertical stress Syy is displayed along a path in the xy-plane of the lower rigid restraint (Fig. 5). It can be seen that the absolute values of the normal stress with Model 2 are lower compared to Model 1, while the normal stress direction is inverse to that of Model 1. These results from the additional horizontal constraint are causing less stress to pass through the bone model than without this constraint.
With the determination of the reason of the early bone failure, it remains to be clarified which boundary conditions are closer to the reality. It has to be considered that the rigid restraint of the tibia proximal end is a very rough simplification of the reality. However for a better comparability of the experimental result values of the different bone groups the simplification was accepted.
Contour plots of v. Mises stress in MPa for Model 1 and Model 2
Diagrams of v. Mises stress and of the vertical normal stress in MPa along the path in the region of fixed restraint
The simulation of the reality could be improved and the force maximum at the rigid restraint could be avoided using a moment-free bearing of the tibia in the knee joint and the establishment of the equilibrium by additional single forces at the physiological force application points of the muscles. However, this would require a technical complexity of the experiments which seems to be a major challenge for biomechanical tests of arthrodesis systems.
4 Conclusion
The boundary conditions required for biomechanical tests have to be carefully considered with respect to the goal of the investigations, as they have a considerable influence on the results. All biomechanical tests on artificial bones have to be performed under the same boundary conditions. Therefore, it is necessary to test the practicality of the boundary conditions and testing device in preliminary experiments.
Author's Statement
Conflict of interest: Authors state no conflict of interest. Material and Methods: Informed consent: Informed consent has been obtained from all individuals included in this study. Ethical approval: The research related to human use has been complied with all the relevant national regulations, institutional policies and in accordance the tenets of the Helsinki Declaration, and has been approved by the authors’ institutional review board or equivalent committee.
References
[1] Richter M, Evers J, Waehnert D, Deorio JK, Pinzur M, Schulze M, Zech S, Ochman S. Biomechanical comparison of stability of tibiotalocalcaneal arthrodesis with two different intramedullary retrograde nails. Foot Ankle Surg. 2014 Mar; 20 (1):14-9. 10.1016/j.fas.2013.08.003Search in Google Scholar PubMed
[2] Richard HA, Kullmer G: Biomechanik. Grundlagen und Anwendungen auf den menschlichen Bewegungsapparat. Wiesbaden Springer Vieweg 2013.Search in Google Scholar
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