Presentation of a Mathematical Model to Predict Longterm Behaviour of Implants and their Prosthesis based on Probabilistic Fatigue

Prados-Privado M^1,2*, Bea JA² and Prados-Frutos JC^1,2

¹Department of Medicine and Surgery, Faculty of Health Sciences, Rey Juan Carlos University, Madrid, Spain

²Applied Modelling and Instrumentation Group, Aragón Institute of Engineering Research, University of Zaragoza, Zaragoza, Spain

*Corresponding author: Prados-Privado M, Department of Medicine and Surgery, Faculty of Health Sciences, Rey Juan Carlos University, Spain

Received: January 19, 2017; Accepted: February 15, 2017; Published: February 17, 2017

Abstract

A key element for the success of a dental implant and its superstructures is related to bite forces, quality and quantity of jaw bones and implant design, among others. The goal of this study was to analyze load distribution in implantsupported dentures using probabilistic fatigue. 3D models were created employing the CAD software. An oblique load of 150 N with a 30° inclination in the linguo-buccal direction was applied. Calculations of stresses of the prosthesis and the bone were made. Then, the fatigue life (mean and variance) and the probability of failure were obtained.

Keywords: Finite element method; Probabilistic fatigue; Dental prosthesis

Introduction

A key element for the success of a dental implant and its superstructures is related to bite forces, quality and quantity of jaw bones, implant design, implant surface texture and surgical procedures [1,2]. As Li detailed in his study [3], implant diameter and implant length are well accepted as an important factor in success because they directly influence the primary stability. Clinical observations indicate that the most common cause of implant failure is incomplete osseointegration [4]. Other two potential causes of implant failure are parafunctional habits and excessive occlusal forces [5] and the passive fit and seal between the implant and its abutment components [4].

The quality of the bone varies strongly depending on the anatomic region in the mandible [3,6]. Density of bone is an essential factor in treatment planning and clinical success and it determines the surgical approach, the implant design and the healing time [7,8]. Cortical thickness tends to decrease as its moves to the posterior region of the mandible but increase its trabecular porosity. Some clinical phenomenon can be understood with a good knowledge of the bone density in different areas of the maxilla and mandible [9]. Some studies have described the close relationship between the bone density and the success of dental implants where dental implants placed in low-density areas have a higher failure rate [9,10]. According to Chugh’s study [9], the density in the maxilla and mandible increases progressively from the midline to the posterior region because of the stress distribution.

Type of loading, material and geometric characteristic of the implant, bone-implant interface and the quantity and quality of the surrounding bone have influence on the load transfer from implants to surrounding bone [1,11,12].

The use of finite element method in the analysis of implant biomechanics furnishes many advantages in the simulation of complex clinical situations. This method makes possible, from a bioengineering point of view, to design and analyze dental implants with geometry that minimize the peak bone stress [11].

The aim of the present research was to evaluate the biomechanical behavior in the bone around the implant as well as to assess the stress transfer in the implant and it superstructures using a threedimensional finite element analysis and predict the long-term behavior of the whole structure.

Material and Methods

Finite element model

3D models were created employing the CAD software Solid works 2016 [Dassault Systemes, Solid Works Corp., Concord, MA, USA]. Dental implants were provided by the manufacturer and bone geometries were created employing Solid Works.

A D2 bone type [13] was simulated and their characteristics were obtained from Vootla and coworkers [14]. Dimensions used in the bone geometry ensure avoid any undesired boundary effects shows in Figure 1. Figure 2 details the prosthesis model analyzed in this study.

Figure 1: Lingual vision of the finite element model employed in the present study.

    
    
    Figure 1:  Lingual vision of the finite element model employed in the present
study.

Figure 2: Dental prosthesis model.

    
    
    Figure 2:  Dental prosthesis model.

Material properties

Implants and abutments were made from Ti6Al4V, as the manufactured provided. The elastic properties of the titanium alloy and bone used in the models were taken from the literature. All materials were modeled with linear, elastic, isotropic and homogeneous properties [1]. The elastic modulus and Poisson’s ratio of the titanium alloy was 100GPa and 0.3, respectively [15]. Young’s modulus and Poisson’s ratio of the bridge was 218GPa and 0.33, respectively [16]. Bone properties were taken from [17] and they are summarized in Table 1.

Table 1: Elastic properties of materials employed in the study (E: Elastic modulus, μ: Poisson’s ratio).




  
    Material
    E (GPa)
    μ
  
  
    Titanium
    103
    0.31
  
  
    CrCo
    218
    0.33
  
  
    Cortical bone
    13.7
    0.3
  
  
    Cancellous bone
    4
    0.3



Table 1: Elastic properties of materials employed in the study (E: Elastic modulus,
μ: Poisson’s ratio).

Boundary and loading conditions

The model was subjected to a rigid fixation restriction in the lower maxilla. An ideal osseo integrated screw implants was simulated. An oblique load of 150 N with a 30° inclination in the linguo-buccal direction was applied [18].

Probabilistic fatigue

Physical magnitudes employed in fatigue problems are usually deterministic. However, there are a lot of uncertainties that can seriously compromise the usefulness and validity of the system. Geometrical and material properties or applied loads in the structure are some of them, which are clearly justified in some problems as, dental implants.

The model proposed in this study is based on probabilistic finite element method and Markov chains [19]. The main difference between this model and other studies available in the literature is that we consider the uncertainties of the most important factors in this phenomenon and we include them in the mathematical model. Finite element analysis obtains the stress and strain distribution considering that loads and material properties do not have uncertainties. However, the probabilistic model employed in this study keeps in mind that these variables are random. The reader is referred to Prados-Privado et al. [20] for further details about the mathematical model.

Table 2 shows the force employed here obtained from [16] and the Young’s modulus and Poisson’s ratio of titanium, which have been considered as Gaussian random variables.

	Force	Young’s modulus
Mean	150 N	100 GPa
Variance	10N²	20 GPa²

Mean fatigue life [million cycles]	Variance fatigue life [million cycles²]
115	72

Presentation of a Mathematical Model to Predict Longterm Behaviour of Implants and their Prosthesis based on Probabilistic Fatigue

Abstract

Introduction

Material and Methods

Finite element model

Material properties

Boundary and loading conditions

Probabilistic fatigue

Results and Discussion

Conclusion

Acknowledgment

References

Material	E (GPa)	μ
Titanium	103	0.31
CrCo	218	0.33
Cortical bone	13.7	0.3
Cancellous bone	4	0.3