Abstract
A refinement technique is proposed for developing finite element models capable of simulating peri-implant bone conditions for bone types II, III, and IV at various degrees of osseointegration. The refined models feature a transition region between bone (cortical and cancellous) and implant and designate it partially to fully osseointegrated by assigning corresponding fractions of the bulk bone’s elastic properties to this region. Bone is assumed to be transversely isotropic. The refined technique is implemented in a case study, in which osseointegrated (25–100%) peri-implant bone, type II, III, or IV with an implant attached, is loaded with a 100 MPa occlusal load. The biomechanics of this peri-implant bone was simulated and analysed. Results showed that the less dense bone must support higher stress and strain, especially at the cortical region. Higher degree of osseointegration induced higher stress but lower strain. Both the bone type and the osseointegration condition significantly affected the stress–strain relation. For minimum stress and strain, denser and more osseointegrated peri-implant bone is desirable. When bone failure criteria were set, based on the yield strength and strain of the bone, a higher degree of osseointegration was needed for the less dense peri-implant bone to be considered safe.
The success of dental implants depends on factors involving biological and biomechanics as well as clinical practice. An implant functions as a load bearing structure, so an implant must withstand and transfer external load acting on it to the peri-implant bone. From this view, the biomechanics of the corresponding peri-implant bone is key in the evaluation of the implant’s reliability and efficiency. For satisfactory performance, an implant needs to withstand the loads and the bone tissue must support the transferred loads without failure.
Osseointegration of an implant to its respective peri-implant bone determines the stability and long term success of the implant. Osseointegrated implant activates adequate support from properly remodelled and maintained peri-implant bone. Quantitative clinical assessments revealed that osseointegration does not occur fully. Within the peri-implant bone, certain areas show no bone-to-implant contact, so osseointegration never reaches 100%. Therefore, the effects of a partially osseointegrated peri-implant bone on the performance of the implant need to be investigated.
The finite element method is generally considered to be an acceptable tool to simulate the biomechanics of a peri-implant bone. After generating the implant and bone models, assigning material properties, and applying loads and boundary conditions, stress and strain can be calculated based on the preset governing equations and their subset algorithms. Model parameters can be simplified because the finite element method is inherently an approximation tool. A common simplification in simulating peri-implant bone biomechanics is the assumption of full osseointegration or no osseointegration. Considering the clinical reality of osseointegration mentioned above, a refinement technique capable of representing partial osseointegration is needed. Through the refinement, the numerical analysis is expected to represent the physical reality of an implantation better.
Previous work aiming to refine the numerical simulation of bone–implant interaction for various osseointegration conditions is lacking. Amongst the few references, the approach reported by Papavasiliou et al. suggests that the osseointegrated portion of the bone must be assigned the properties of cortical and cancellous bones whereas the non-osseointegrated portion should be assigned the properties of connective tissue with very low stiffness. The arrangements of partial osseointegration conditions (25–100%) were proposed to be locally alternating, coronal only, apical only, facial only or lingual only. Another approach proposed a transition region between the implant and the bulk structure of peri-implant bones, to represent the conditions of bones during the healing process. A similar technique was applied by van Staden et al. by applying a blood and bone interface filling around implant threads when simulating the implant insertion process. The latter two approaches indicate that peri-implant bone contains an area which does not have the same properties as the bulk counterpart, although partial osseointegration is not mentioned specifically.
In this study, a refinement technique is proposed, expected to represent peri-implant bone conditions better. Adopting the approaches that introduce a bone–implant transition region, this technique assigns a fraction of the bone properties to the transition region to represent partial osseointegration. The refined technique is proposed for application to various bone types and for bones which do not perfectly integrate to an implant even after the healing period and when the crown is fixed on top of the implant. Whilst acknowledging the anisotropy of bones, the bone is approximated as a transversely isotropic material. A case study is given to show that the refined technique is implementable. From this study, the stress and strain in a peri-implant bone induced by occlusal load are simulated, and the influence of the degree of osseointegration is analysed.
Materials and methods
Geometric model
The first step of the numerical analysis is to draw three-dimensional geometric models of the jaw bone and the prescribed implant. A detailed model of a patient’s jaw bone can be generated using computed axial tomography (CT scan) for conversion into a computer aided drawing (CAD) Image. In place of using CT data, a jaw bone model can also be generated based on the Lekholm and Zarb classification for bone types II, III, and IV. The general guideline is to have a thick cortical bone for bone type II and a thin one for bone types III and IV.
Within the jaw bone, a transition region is introduced. The transition region is the jaw bone section adjacent to the implant; it lies beyond the outermost geometry of the implant (usually up to 0.5 mm from the implant’s inner diameter and proportionally towards its apical region). The transition region covers both cortical and cancellous bones, consisting of implant–cortical and implant–cancellous transition region portions.
A detailed implant model can be obtained from the manufacturer, generated by using a coordinate measuring machine, or it can be generated arbitrarily, as in the case of new implant designs.
Material properties
A set of material elastic properties are assigned to the jaw bone models. Ideally, the properties should represent the anisotropy of bone. Bone is considered anisotropic because it shows different mechanical properties when measured in different directions (in the same sample). Approximation may be applicable however because the elastic moduli of a cortical bone in buccolingual and infero-superior directions are not significantly different and those of a cancellous bone in buccolingual and messiodistal directions are similar. Thus, bone can be assumed to be transversely isotropic. With this approximation assumption, only five independent elastic properties instead of nine for an orthotropic material (independence in all three directions but symmetry about each perpendicular axis) or the full 21 for anisotropic materials need to be derived from the generalized Hooke’s law. By definition, this approximation of transverse isotropy better represents the reality of a bone’s anisotropy than the commonly applied assumption of isotropy (only two independent elastic properties required: Poisson’s ratio and Young’s modulus). In an isotropic material, the properties are considered uniform in all directions, which is not the case for the mandible. Nonetheless, this assumption is often assigned to jaw bone models for simplicity.
With respect to the bone type, the assigned elastic properties may apply to bone type II, III, or IV. Following the definition, the properties should represent high density cancellous bone, low density cancellous bone, and cortical bone.
The properties assigned to the bone–implant transition region are acquired from the properties of bulk cortical and cancellous bones. Various degrees of osseointegration are featured in this transition region. The assumption of perfect osseointegration applies when the transition region has 100% bulk properties. Partial osseointegration is represented by fractional values of the bulk’s elastic and shear moduli at constant Poisson’s ratio.
Case study
As an example of the above refinement technique, a case study of mandibular peri-implant bones of types II, III, and IV loaded with 380 N occlusal load is analysed. Each bone type is analysed for conditions of 25%, 50%, 75%, and full osseointegration.
The jaw bone is modelled arbitrarily ( Fig. 1 a ) and intended to resemble an edentulous posterior mandible. The thickness of the cortical layer is adjusted according to the Lekholm and Zarb bone specification, in which a thick cortical bone (as in bone type II) is modelled as having 2 mm thickness whilst a thin cortical bone (for bone types III and IV) is modelled as having 1 mm thickness ( Table 1 ).
