A finite element method approach for the mechanobiological modeling of the osseointegration of a dental implant

Abstract

The aim of this paper is to introduce a new mathematical model using a mechanobiological approach describing the process of osseointegration at the bone–dental implant interface in terms of biological and mechanical factors and the implant surface. The model has been computationally implemented by using the finite element method. The results show the spatial–temporal patterns distribution at the bone–dental implant interface and demonstrate the ability of the model to reproduce features of the wound healing process such as blood clotting, osteogenic cell migration, granulation tissue formation, collagen-like matrix displacements and new osteoid formation. The model might be used as a methodological basis for designing a dental tool useful to predict the degree of osseointegration of dental implants and subsequent formulation of mathematical models associated with different types of bone injuries and different types of implantable devices.

Introduction

Modern implantology has evolved together with dental reconstruction [1], [2]. In the 1960s PI Branemark coined the term osseointegration to explain the acceptance and anchoring of titanium devices placed in the jaw bone [3], [4]. These titanium devices are now known as dental implants and several studies have reported advances in the original design that increase their performance [5], [6]. The osseointegration is the direct structural and functional connection between living bone and an implant surface [7]. This connection provides a binding mechanism for the incorporation of a component of non-biological material inside the human body. When a dental implant is placed into the jawbone, the so-called bone–dental implant interface or junction area is created between the biomaterial surface and the surrounding tissue. This interface may become filled with epithelial tissue, connective tissue and bone tissue as the wound healing process begins [8], [9], [10]. The proper healing of this interface consist of the anatomical reduction of the injury caused during the insertion of the implant, which is conditioned by biological factors [11], [12], patient-related factors [13], mechanical factors [14], [15], [16] and the implant surface [17], [18], [19].

The healing of the bone–dental implant interface can be summarized in four biological stages [10], [21]: (1) blood clotting, (2) osteoprogenitor cell migration, (3) granulation tissue (collagen matrix and new blood vessels) formation, and (4) new bone matrix formation. From a mechanical point of view, these healing stages depend on the forces created by the effects of molecular and cellular adhesion [19], the effects of contraction due to cell migration [22] and by bone mechanotransduction regulating new bone formation by the action of external forces [14], [23].

The implant surface modifies molecular and cellular activity at the interface, so that high roughness surfaces allow greater cells and molecules adhesion [24], [25]. This causes better tissue formation around the implant, and therefore, suitable osseointegration [4], [17]. By contrast, surfaces with low roughness do not offer enough adhesion for cells and molecules and the contraction forces exerted by cell migration may then detach the tissues being formed on the implant surface [17]. This creates a gap between the implant surface and the new tissue front line reducing the degree of osseointegration that may cause implant rejection [4], [22], [26]. Moreover, the continued presence of mechanical stimuli permits the consolidation of new bone tissue and the proper healing of the bone–dental implant interface [23], [27]. This balance between mechanical stimulation and biological healing is the main concern of mechanobiology, a field of study where the biological action of mechanical stimuli and its influence in the tissue architecture is evaluated [28].

Although much of the available knowledge on bone–dental implant interface healing comes from experimental research, quantitative results have been obtained in recent years from the development of mathematical models which numerically analyze the biological processes and the mechanical phenomena. A proper balance between experimental and computational mechanobiology therefore allows a better interpretation of experimental results and a better supply of data for new mathematical models [28]. From a biological perspective, mathematical formulations of tissue recovery in the bone–dental implant interface have been performed based on cell differentiation, cell proliferation and cell migration, and the transient extracellular matrix behavior [29], [30], [31], [32].

Although the numerical results obtained have been correlated with experimental results, none of the known formulations has considered that the bone–dental implant interface is a living entity whose properties are constantly changing due to mechanical factors [14], [23], [33]. Likewise, other authors have performed simulations of the bone–dental implant interface behavior from a mechanical approach using implant geometry and material, several bone properties and applied load levels as parameters [29], [30], [32], [34], [35], [36], [37]. Although these descriptions of the interface have not included biological variables or biochemical behaviors, the relationship between mechanical stimuli and tissue differentiation has led to adjusted results regarding experimental observations [4], [8].

Despite the unquestionable interest of these models, it has been accepted that a description of the bone–dental implant interface combining the biological stages of tissue recovery with the associated mechanical factors may lead to a mathematical model of osseointegration which is more adjusted to the physiological reality of the problem [30], [31]. This work is thus been aimed at introducing a new mathematical model of osseointegration of dental implants based on a description of the bone–dental implant interface wound healing processes.

Unlike other models, our approach considers healing as a sequential biological process mediated by mechanical factors and the implant surface. With the solution of the model we attempt to establish a mathematical relationship between the type of surface used in the dental implant and the amount of new bone formed at the interface. Computer simulations were performed using the finite element method where three types of dental implant surfaces were considered: high, average low surface roughness. The results are in qualitatively correspondence with experimental results at both spatial and temporal levels.

These results lead us to conclude that the mathematical approach here presented may be used as the methodological basis for the formulation of a further mathematical model which would be able to predict the degree of osseointegration of dental implants according to subjective patient issues [15], [16]. This model may also be suitable as an evaluation and training tool to be used by dental implants specialists. The following section describes the mechanobiological process of osseointegration at the bone–dental implant interface and the mathematical model proposed. Afterwards, the description of the simulation, the cases analyzed and the results obtained are commented. Finally we present the discussion based on the limitations of our mathematical framework and the future applications.