1
Bone Resorption Induced By Dental Implants with
Ceramics Crowns
Daniel Lin1, Qing Li1, Wei Li1, Pim Rungsiyakull2 and Michael Swain2
1
School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW 2006, Australia
2
Faculty of Dentistry, The University of Sydney, NSW 2006, Australia Available Online at: www.austceram.com/ACS-Journal-2009vol2.asp Abstract
The use of dental implantation to treat the problem of tooth loss is becoming more and more popular these days. However, implant-induced bone resorption remains to be a major concern in the prosthodontic clinics and research. It is hypothesised that the long-term response of the dental bones hosting a dental implant depends on the extent of bone remodelling. In most cases, the cortical bones surrounding the neck of the dental implant can resorb at a steady rate. This can be caused by either bacterial infection or occlusal overloading. Up until recently, the methods to predict dental bone resorption due to overload are scarce. In this paper, a quadratic remodelling formula was utilised to evaluate bone resorption due to occlusal overload. A 2D finite element method with a single unit implant in the mesial-distal section is considered in this study. The computational remodelling simulation was performed under overloading condition at 402N using the quadratic remodelling algorithm. The results are compared against clinical follow-up, and the effect of occlusal loading and its induced crestal bone loss was successfully predicted.
Keywords: Bone remodelling, bone resorption, ceramics crown, computer tomography, dental implant, finite element
1. Introduction
After the dental implant surgery, the resorption of the dental bones is one of the main factors that leads to biological and/or mechanical failure of implant-supported dental restorations [1]. From the biomechanics perspective, bone resorption causes the density of the bone to decrease, therefore leading to the reduction of the overall stiffness of the bone. This could worsen the stress/strain distribution and the bone’s role as the support to the implant, and in some cases, cause bacteria to be trapped in the resorbed notch area, therefore further worsening the resorption phenomenon. Clinically, two factors are primarily identified and associated with the incidence of bone resorption: (1) bacterial infection due to the plaque in the bone/implant interface [1, 2]; and (2) occlusal overload in the newly formed bones in the gap between the implant surface and the hosting bone [3], thereby damaging mineralised cellular tissues and their responses, thus preventing proper osseointegration.
The exact reason for bone resorption varies between patients and has not been pin-pointed yet [2]. In general, the crestal bone level remains more or less the same and does not change much [4]. Nevertheless, several literature studies have reported the marginal bone loss following the
dental implantation surgeries. Corn et al [5] reported the alveolar bone loss occurs at an average rate of 0.17mm per year after implantation. While Nowzari et al [6] reported the alveolar bone loss between 0.2 and 0.4mm over the first twelve months of implantation, followed by an additional 0.1mm bone loss between months 12 and 18. Overall, it can be seen that the average dental bone loss due to resorption is approximately around 0.2-0.4mm over the first twelve months, and can be said to reach a more stable status after months 12 to 18. Clinically, the bone resorption usually occurs in the cortical region surrounding the neck of the implant, as depicted in Fig. 1.Micro-damage and macro-damage may be differentiated in such a construct of artificial (implant) and natural (bone) biomaterials [7]. A certain level of micro-damage in bone tissues could promote positive bone remodelling, while excessive micro-damage may lead to certain local micro-cracking of mineralised tissues and the loss of bone strength, consequently weakening the implantation as a whole. Thereafter, the damage could reduce the magnitude of stress and strain induction in such bone tissues. Bone remodelling on the other side is a damage repair process [8-10]. Bone resorption can therefore be viewed as the result of excessive damage in the bone tissues, where the damage takes place at a rate too rapid for the bone to repair and remodel [11].
2
Figure 1: Depiction of the cortical bone loss surrounding the neck of the dental implant (12
month implantation)
McNamara et al [12] and Prendergast et al [13] have used damage based bone remodelling algorithms to predict the bone resorption, in which the bone damage is adopted as the main stimulus for remodelling. The damage-adaptive remodelling laws were proposed and the corresponding algorithms was derived to predict the bone adaptation for long bones. They found that the damage-adaptive algorithm can successfully predict the bone's adaptive behaviour in response to altered mechanical loading, provided that the nonlinear nature of damage accumulation is considered. However, none of these overloading induced resorption models has been applied to dental scenarios thus far.
Quirynen et al [14] explored a direct association between marginal bone resorption and occlusal overload. Overloading, can also lead to the accumulation of damage, which can result in the excessive fatigue failures or damage of the bones [15]. Furthermore, McNamara et al [12] proposed that, since fatigue cracking is a process driven by strain energy density, the bone remodelling algorithm based on strain energy density (SED) should be equivalent to the damage based bone remodelling algorithms, further confirming the effectiveness of using SED stimulus.
It is noted that currently it is very challenging (if not impossible) to predict the amount of bone resorption caused by bacterial infection. However, there is one recent study by Li et al [16], where the bone resorption due to occlusal overloading could be predicted by using a modified quadratic formula based on the strain energy density stimulus. However, Li et al did not superficially focus on the bone resorption phenomenon in the cortical neck. The insights of their paper would allow us to investigate the downsides of implant treatment, which will serve as a foundation for future exploration on this topic.
2. Methods and Procedures
2.1 Theoretical model for bone resorption
In order to perform the bone resorption simulations, the bone remodelling equation is needed. In Li et al’s [16] study, a quadratic formula was added to incorporate the overload related resorption as: 2 ) ( ) (U k D U k B dt d
(1)where the values for B =1.0g/cm³, k=0.004J/g, D=60(g/cm³)³/MPa² per time unit, U and ρ are the strain energy and the bone density respectively, as used by following early studies in [17].
Li et al [16] attempted to relate density change to stress stimulus through a unified cubic Young’s modulus-density relationship: 3
C E (2)where C is a constant with the value of 3790MPa(g.cm-3)-2. However, according to Lin et al [18], the relationship between Young’s modulus and density for the cortical and cancellous bone is not necessarily identical. In continuum mechanics, the mechanical stress tensor consists of six independent components [19]. As a result, the implication of using mechanical stress tensor into bone remodelling algorithm is only theoretically meaningful. In finite element analysis, it may not be realistic since it needs to involve the determination of all the remodelling reference values on different planes; while such data are not fully available currently. For this reason, strain energy density in Eq. (1) is considered appropriate for computational bone remodelling, because it provides an accumulated quantity that eliminates the individual magnitudes and directions when using the stress tensor components.
In Eq. (1), the solution to the quadratic equation would lead to the two roots, which can be referred to as the two new thresholds. These two critical values divide the entire remodelling process into three regions: under-load (disuse) resorption, bone apposition, and overload resorption, as illustrated in Fig. 2.
Cortical bones surrounding the neck of the implant Cortical bones surrounding
3
Figure 2: Quadratic remodelling algorithms Eq. (1) was implemented into the computational bone remodelling simulation in the commercial finite element program [20, 21]. The initial bone density is 1.74g/cm³ for the cortical bone and 0.9g/cm³ for the cancellous bone [22]. It is assumed that the initial bone density and Young’s modulus are uniform in both the bony tissues. In the finite element analysis, since it is impossible to assign zero Young’s modulus value to the elements, a very low value was embedded in the Python program, where if the bone resorbed completely, the elements with “zero” density would be assigned a low density of 0.0001g/cm³ computationally, thereby simulating the “near” disappearance of bony tissues due to bone resorption.
2.2 2D Finite Element Model
The model was constructed from a computer tomography (CT) scan, together with a single unit titanium implant and a ceramic crown embedded in the cortical bone with thickness of approximately 2mm surrounding the cancellous bone. However, in order to accurately predict the resorption in the cortical bones surrounding the neck of the dental implant. A highly dense finite element mesh was generated, to better capture bone resorption progression in more detail. As shown in Fig. 3, the finite element model comprises in total 62884 3-node triangular elements, featuring 60170 3-3-nodes triangular elements in the cortical regions. The loading applied to the implant represents a higher range of magnitude of 402N at an inclination angle of 1.32˚ to simulate the scenario of occlusal overload, according to Dincer et al’s study [23].
The clamped boundary conditions were applied to both sides of the mesial-distal sectional plane stress model [1, 24-27], as in Fig. 3. The interface between the cortical and cancellous bones, the crown and implant are considered to be in perfect bonding, while the interface between the implant and the cortical and cancellous bones is modelled as a frictional contact with a friction coefficient of 1.0, shear modulus of 120MPa and the maximum shear strength of 18MPa [28, 29]. The material properties used in the model are summarised in Table 1 [22, 30, 31].
Table 1: The Material properties for the finite element model
Parts Young’s modulus (GPa) Poisson’s ratio
Crown 100 0.33
Titanium implant 110 0.33
Cortical bone 18 0.33
Cancellous bone 1.8 0.33
Figure 3: Illustration of 2D finite element model used for bone resorption simulation
U/ρ dρ/dt Bone growth overload underload Critical Load 1 Critical Load 2 Quadratic remodeling formula
U/ρ dρ/dt Bone growth overload underload Critical Load 1 Critical Load 2 Quadratic remodeling formula
420N
1.32
˚
crown
implant
Cortical
bone
Cancellous bone
420N
1.32
˚
crown
implant
Cortical
bone
Cancellous bone
4 2.3 Bone remodelling calculation
The bone remodelling simulation use the same procedure as described in our previous studies [18, 21], in which ABAQUS was employed for finite element calculation and a user-subroutine in Python script was used for the bone remodelling calculations. The Python program implemented in this study contains the quadratic term as defined in Eq. (1). The program aims to predict the crestal bone loss due to occlusal overloading. In all the analyses, 12 iterations were performed to match the X-ray images from our clinical follow-up study. Therefore, each of the iterations simulates one month of bone remodelling.
3 Results and Discussion
3.1 Bone resorption results
It is observed that the implementation of the quadratic remodelling algorithm resulted in the resorption of cortical bone surrounding the neck of the dental implant, when the implant is applied with an excessive occlusal load as shown in Fig. 4, where the bone density contours are depicted at the intervals of every four months, from month 0 to month 12 in the cortical neck next to the dental implant.
In the contours shown in Fig. 4, the blue areas represent the resorbed cortical tissue. The snapshots clearly indicate that, the cortical bone adjacent to the dental implant neck undergoes resorption rapidly in the first four months. At month eight, the rate of resorption in the cortical bone seemed to have slowed down somehow.
Furthermore, it is observed that the resorption of bone is not even on both sides of the cortical bones in this 2D model. This is due to the lateral force component from the occlusal load. This also indicates the effect of lateral force on the crestal bone loss. The amount of bone resorption is approximately 0.8mm (the cortical bone thickness is 2mm). This result is higher than the recorded clinical data of 0.2-0.4mm bone loss over a 12 month period as in Nowzari et al’s [6]. Therefore, it appears that the implementation of the quadratic algorithm produces a more excessive bone resorption. However, one should notice that in this study, a very high occlusal overload (indicating the upper range of load) was applied to the model, in order to deliberately simulate the condition of drastic overloading.
In the clinical scenarios, the patients may not always chew food at such a high level force. Therefore, the result of excessive bone resorption should not be a surprise.
The resorption will worsen the stress/strain concentration and will not relieve the overloading in the local region. As a result, the excessive bone resorption could not be avoided. However, the maximum cortical bone density attained is 2.0g/cm³, and this signifies that while the bone resorbs due to overloading the bony tissues in the other regions, far from the bonded overloaded areas of the cortical bone, can still remodel positively.
Another interesting phenomenon is the presence of resorption zones take a V-shaped appearance, and almost parallel the shape of the dental implant neck. This suggests that the shape and the taper angle of the dental implant neck can impact the dental bone remodelling and the osseointegration process. Such an observation indicates the potential that bone resorption due to overload could possibly be manipulated by varying the taper of the dental implant neck during the initial design procedure. The activity of bone remodelling can be easily seen in Fig. 1. It should be noted that the cortical bones surround the implant neck suffered from a high degree of bone resorption, where the height of the cortical ridge becomes lower than its original level. However, the cancellous bone demonstrated bone density augmentation from the X-Ray examination. A visual comparison between the X-ray photos and the density contours from the computational simulations showed a fairly good agreement. In the contours from computational results, the cortical bone surrounding the implant neck resorbs substantially over the 12 month remodelling, forming a V-shaped area at the resorbed cortical bones in Fig. 4. In the X-ray photo in Fig. 1, the bone resorbed in a similar fashion. However, it is noted that the X-ray photo did not exhibit bone resorption as great as in the computational simulation. Furthermore, it is uncertain whether the patient who received the dental implantation treatment was consistently subjected to excessive occlusal loading. As a result, this clinical follow-up of bone resorption may or may not be exactly the same as the simulation condition. Based on these comparisons, nevertheless, a deduction can be made to confirm the implication of implementing the quadratic remodelling formula for bone resorption simulation.
5
Figure 4: Bone density contours for overloading case, in the bones next to the neck of the dental implant (blue indicates the resorbed areas)
3.3 Bone resorption/remodelling
The average bone density in the cortical neck next to the dental implant, the peri-implant cancellous bone density and their related average strain energy density will be discussed in more detail.
Fig. 5 shows both the average density in the cortical bone neck next to the implant and the average strain energy density in this region over the period of 12 months.
Figure 5: Average density and SED for cortical bones surrounding the implant neck
The average cortical bone densities around the implant neck showed the signs of rapid resorption in the first 8 months. In months 11 and 12, the amount of bone resorption seems to slow down somehow, indicating the incoming approach to a stable status. This result presents certain similarities to the clinical follow-up data and literature, where both the results illustrate a rapid sign of bone resorption in the first year of implantation. However, in the case of clinical data, the reports often suggested a continual resorption after the first year of implantation at a constant rate around 0.1-0.2 mm per year [6], of which develops a slower
resorption and a lower magnitude than those in the first 12 months, while the computational results seems to predict a status approaching nearly zero bone resorption after 12 month. A suitable explanation could be that in the case of clinical trial, after resorption has reached a significant level, (e.g. after 12 months) in the bone next to the implant neck, the gap between the bone and the implant provides room for bacterial infection. The infection would further the bone resorption process, leading to additional bone loss mainly due to biological rather than mechanical causes in this stage. As a result, the bone loss phenomenon may continue. In the computer simulation, the effect of bacterial infection is absent due to the difficulty of implementing such biological infection in the existing biomechanical finite element model.
Therefore, in the present computational calculations, after the cortical bones next to the implant has resorbed to a significantly low level (i.e. approximately zero density and modulus), the stress and strain energy fields in this region will no longer affect the resorption process further (except for the new stress concentration). Instead, the infection of bacteria may dominate the resorption process. This hypothesis may point out a new topic of research for the future, where the protocol can incorporate the biological factors, such as bacterial infection, into the remodelling algorithms. A possible way could be to use the concentrations of oxygen and bacteria to model osteoclast recruitment around the implant neck. This is beyond the scope of this paper.
The average strain energy density progression followed a similar pattern to the crestal bone resorption. This is expected, as the bone resorbs due to overloading, the amount of strain in this region undergoes a rapid reduction. This leads to the reduction of the overall strain energy in these related elements of the model.
Start
Month 4
Month 8
Month 12
Start
Month 4
Month 8
Month 12
Peri-implant cortical bone remodleing response
0.0 0.4 0.8 1.2 1.6 2.0 0 2 4 6 8 10 12 Number of month bo ne de nsi ty (g /c m ^ 3 ) 0 500 1000 1500 2000 2500 s tr a in e n e rg y d e n s it y (J /g ) average cortical bone density average cortical SED
Peri-implant cortical bone remodelling response Peri-implant cortical bone remodleing response
0.0 0.4 0.8 1.2 1.6 2.0 0 2 4 6 8 10 12 Number of month bo ne de nsi ty (g /c m ^ 3 ) 0 500 1000 1500 2000 2500 s tr a in e n e rg y d e n s it y (J /g ) average cortical bone density average cortical SED
6 Unlike the plot of bone density, the strain energy density sharply declines in the first two months. The rate of SED declination slows down until month 7, followed by a very rapid reduction in SED values again until month 9, when the SED value approaches zero, this is because at month 12, the bones in these regions have almost completely resorbed away, and have disappeared from the model.
The sudden slow down of strain energy density rate between months 2 and 7 is an indication that the dental bones are resorbing very rapidly in this time period. One of the main features of the quadratic algorithm is that the quadratic term can accommodate the bone resorption. Specifically, in months 2-7 the overload caused the bone to resorb very quickly, and this leads to the stiffness of the bones around the implant neck to reduce.
In this paper, the following major assumptions were made which could cause the inaccuracies of the results:
1.) The initial density values in the bones were assumed to be uniform.
2.) The presence of bacterial infection is absent.
3.) The external geometrical morphology of the oral bones remains unchanged, while in reality the oral bones undergo physical morphology due to remodelling/resorption.
These three assumptions remain to be the biggest obstacles to accurately predict crestal bone loss. The first assumption can be overcome by constructing the multimaterial finite element model, with mesh and material properties completely determined by the CT grey scales. However, such technique requires specialised facilities and program of which could be cost inefficient. The assumption of non-existence of bacterial infection in the gap between the implant/bone interfaces could be very difficult to overcome. This is because to do so would require the introduction of substantial biological modelling algorithms into the growth of dental bacteria infection from dental implant surgery. A vast input from both the theoretical biology and computational mechanics communities will be needed. This could create a new opportunity for the future research. Finally, the issue of surface bone remodelling is currently a topic still under investigation, where the information related to computational resorption simulation is scarce. Although the quadratic resorption algorithm is offering the capability of predicting bone resorption in an internal remodelling basis, the limitations and assumptions need to be improved to more precisely model the crestal resorption in the future.
4. Conclusion
This paper has successfully implemented the quadratic remodelling/resorption algorithm to the prediction of crestal bone resorption due to occlusal overload. Comparison with clinical x-ray photos shows a good agreement in the pattern of crestal bone loss. However, the degree of bone resorption in the computational analysis is slightly more excessive than the clinical literature data, indicating the consequence of continuous overloading in the remodelling simulation. These results indicate further biological data on crestal bone region is needed in order to predict crestal bone loss more accurately.
In conclusion, while the assumptions made in this study could contribute to inaccuracies in the computational results. The numerical predictions presented in this paper can serve as a starting point for the future development of dental implant induced crestal bone loss prediction. Consequently, the negative perspectives of implantology could be better understood and controlled.
5. Acknowledgements
This study was supported by Australian Research Council and the first author is grateful.
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