Identification of critical zones around dental implants ...

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Biomechanics Applied to Computer Assisted Surgery, 2005: ISBN: 81-308-0031-4 Editor: Yohan Payan

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Identification of critical zones around dental implants using finite element simulations Aïssa Mellal and John Botsis Ecole Polytechnique Fédérale de Lausanne (EPFL), Laboratoire de Mécanique Appliquée et d’Analyse de Fiabilité (LMAF), Faculté des Sciences et Techniques de l’Ingénieur (I2S), CH-1015 Lausanne, Switzerland

Abstract A bone-dental implant system is analyzed using finite element simulations. The objective is to predict critical zones in the implant’s vicinity, i.e. zones where bone remodelling activity is initiated, leading to bone gain or loss and zones where the risk of debonding at the bone-implant interface is high, due to tensile stresses. The onset of bone resorption, respectively formation, is then evaluated according to three remodelling criteria: (1) the von Mises strain model, (2) the strain energy density model and (3) the effective stress model; using a relationship between Correspondence/Reprint request: Dr. Aïssa Mellal, Ecole Polytechnique Fédérale de Lausanne (EPFL) Laboratoire de Mécanique Appliquée et d’Analyse de Fiabilité (LMAF), Faculté des Sciences et Techniques de l’Ingénieur (I2S), CH-1015 Lausanne, Switzerland. E-mail: [email protected]

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Aïssa Mellal & John Botsis

the mechanical stimulus and bone response (densification rate) established from in vivo observations. Two bone-implant interface conditions are considered: frictional contact surface for freshly inserted implants and common surface for integrated implants. The length of the implant was also considered as a parameter and two implant sizes (short and long) were selected. Results show that the stresses in bone around the implant are higher before integration than after; and that the stress distribution is smoother for long implants than for short ones. It is also found that freshly inserted implants induce bone remodelling activity essentially in the implant neck area, i.e. in cortical bone, but remodelling in cancellous bone is not excluded. Finally, simulations results show that over-compressed bone may lead to irreversible damage in the neck area of the non-integrated implant whereas debonding of horizontally loaded integrated implants is expected in the region under tension.

Introduction The insertion of an implant in bone induces a new mechanical environment to which bone reacts by adapting its structure (i.e. shape and density). The long-term stability of a dental implant is strongly related to its osseointegration. Freshly inserted implants have an interface with bone that allows relative displacements (frictional sliding) whereas fully integrated implants have a common interface with bone. From clinical observations, it has been noticed that in the early stage after implant insertion the osseointegrated portion of the bone-implant interface represents a small part of the whole contact surface. After a healing period of about three months, this portion may exceed 70% of the interface [1, 2]. During the healing period following implant insertion, the transition from a two contacting surfaces interface to a fully-bonded interface condition, affects the stress state around the dental implant modifying therefore the mechanical stimulus which controls bone growth or resorption. Following Wolff’s general principle that bone adapts to its mechanical environment [3], many investigators attempted to describe the process of bone remodelling using theoretical models. Most of these theories are based on experimental evidence provided by the work of Frost [4] and Pauwels [5]. The latter argued for an optimal stress level, related to the strength augmented by a safety factor, which when applied to bone would lead to a condition of no net remodelling, i.e., balanced rates of hypertrophy and atrophy. Stress levels below it would lead to net resorption, and stress levels above it would lead to net apposition. For stress levels which are much higher than the optimal stress level, there would be a bone loss through bone damage (necrosis). In 1972, Kummer described mathematically these qualitative observations by means of a cubic relationship between remodelling rate and stress [6].

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On the other hand, Frost [4] suggested a remodelling criterion based on a strain magnitude. He introduced a threshold strain level for the activation of bone resorption or formation and made a distinction between surface remodelling and internal remodelling. Later on, this idea was reformulated and extended by Cowin and co-workers leading to the concept of strain-adaptive elasticity [7-9]. Since then, numerous studies have been conducted to examine relevant factors that influence bone remodelling. These extensive investigations resulted in the improvement of existing theories and the development of new models with various degrees of sophistication [10-20]. For instance, Hart and Davy [21] proposed a cell biology-based model in which the remodelling rate constants are expressed in terms of biological parameters. More recently, Huiskes’ group proposed a bone adaptation model which relates bone-cell metabolism to mechanical adaptation of trabecular architecture [22, 23]. A variety of assumptions for the mechanical stimulus have been postulated in bone remodelling theories by many investigators. They included stressbased mechanical stimuli (e.g. equivalent –or von Mises– stress, maximum tensile/compressive stress, effective or –energy– stress) [5, 10, 12, 24, 25], strain-based mechanical stimuli (e.g. equivalent –or von Mises– strain, effective –or energy– strain (evaluated from the strain energy density and a local measure of the Young modulus), uniform strain, unidirectional strain, peak strain, and strain history) [5, 10, 17, 19, 21, 26] and strain energy density stimulus [11, 13]. For Hookean materials, stresses and strains are linearly related and can therefore be used interchangeably. However, as discussed by Cowin [27], the bone must sense change in functional use by ‘measuring’ the strain and not the stress. More recent studies indicate that bone remodelling is controlled predominantly by strains rather than by stresses [19, 28]. A remodelling theory that attempts to account for the mechanical objectives of the remodelling process should be therefore formulated in terms of the local bone strain rather than in terms of stress. The efficiency of these models in simulating the process of bone remodelling under mechanical loading is conditioned by their ability to reproduce experimental observations and therefore to link their parameters to measurable quantities. These models were first developed for orthopaedics, but they are equally applicable to dental implantology [29]. In this study, the stress distribution around a dental implant is analyzed through finite element simulations. The objective is to identify “critical” or “weak” zones in bone around a mechanically loaded implant. Such zones are generally locations where intensive remodelling activity may occur; locations where the risk of debonding at the bone-implant interface is high, due to tensile stresses and locations where bone is over-compressed.

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Two extreme interface conditions were considered: (1) a freshly inserted implant, i.e. before integration, and (2) a perfectly osseointegrated implant. The study was conducted for two implant lengths (short and long implant). The predictions of bone remodelling around the dental implants, before and after integration, according to three different existing criteria were verified with available data in the literature and compared. Because of the uncertainties on the parameters of selected models, only the initiation of bone remodelling was examined: location of the peak value of stimulus and sign of the remodelling change rate, i.e. resorption, homeostasis or densification without any evaluation of the bone mass change.

Materials and methods Procedure description Three-dimensional finite element analyses of statically loaded dental implants were carried out considering the effects of the following parameters on the stress distribution: (1) the bone-implant interface, which is related to the integration status of the implant in the bone matrix, (2) the implant length (i.e. short or long) and (3) the direction of load (i.e. vertical, mesio-distal or buccolingual). The results of the numerical simulations are then explored to identify locations of highest stresses, strains and strain energy densities for each load case. These data are used to evaluate bone remodelling activity and to assess the risk of debonding, respectively over-compression, with respect to the tensile, respectively compressive, stresses at the bone-implant interface. Next, the triggering of bone remodelling is examined according to three selected remodelling criteria with specific mechanical stimuli: (1) von Mises strain stimulus, (2) strain energy density (SED) stimulus and (3) effective stress stimulus. For this purpose, appropriate input data is extracted from the results of the finite element simulations. The predictions of these models are then compared and discussed.

Finite element simulations Geometry and materials A generic finite element model of a bone-implant system was constructed. The bone matrix consisted of a cancellous bone core coated with a 1mm thick cortical bone envelope. The dimensions of the core were 30 mm (length) x 20 mm (height) x 10 mm (thickness). The selected implant model was a Titanium ITI solid-screw (Straumann, Switzerland) with a total length of 15.3 mm, an insertion depth of 12 mm and a diameter of 4.1 mm for the long version. The short implant has a total length of 11.3 mm and an insertion depth of 8 mm.

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Constitutive laws Both cortical and spongy bone was considered as homogeneous, isotropic and linearly elastic materials. Aspects such as bone anisotropy, heterogeneity or non-linear behaviour are not included since the objective of this study is not to precisely determine the bone response but to identify the effect of interface condition on the bone response by comparison of two ideal situations (i.e. integrated vs. non-integrated implant). The elastic parameters were E = 15 GPa, ν = 0.3 for cortical bone, and E = 1 GPa, ν = 0.3 for cancellous bone [3034]. The elastic properties of the Titanium implant were E = 110 GPa and ν = 0.3 [33-35]. Bone-implant interface Before integration, i.e. for a freshly inserted implant, the bone-implant interface is modelled as two distinct surfaces. For an integrated implant, the bone and the implant are assumed to be perfectly bonded to each other and their interface is represented by a common surface. Intermediate state of osseointegration, which would necessitate the definition of a repair zone between bone and implant, is not considered. The clinical procedures indicate that before implant insertion, the bone is first tapped with the same diameter as the implant. Therefore, it is reasonable to consider that initially, the gap between implant and bone at interface is zero. The surface roughness of an implant is an important factor for its osseointegration. Implants with sand-blasted and acid-etched surface (SLA) are aimed at the best bone-implant contact in comparison with smooth surface or plasma-sprayed surface (TPS) implants [36]. In the present study, the surface roughness of the freshly inserted implants was indirectly taken into account by means of a Coulomb’s frictional interface with a friction coefficient of 0.3 [35, 37, 38]. Mechanical loading Three orthogonal static forces were applied on the top of the implants: a vertical intrusive force (V), a mesio-distal (MD) horizontal force and a buccolingual (BL) horizontal force. The intensity of forces was in the physiological range [39], i.e. 100 N for the vertical component and 30 N for the horizontal components. The loads were applied separately to identify the contribution of each component to the bone’s response. Finite element meshes Before osseointegration, vertically loaded implants are supported mainly by the threads and the lateral frictional resistance. It was then necessary in this study to model finely the helical geometry of the implant’s threads and, consequently, to construct a three-dimensional model of the whole bone-implant system.

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The finite element mesh was constructed using tetrahedral elements which permit easy mesh generating, especially with complex geometries. Linear elements (4 nodes) were used instead of 10-node quadratic elements since the latter make the calculation of contact pressure very complex. In return, linear elements require finer meshing to provide an acceptable accuracy. The system with long implant contained about 32600 elements with 6500 nodes: 8000 elements for the implant, 4600 for cortical bone and 20000 for cancellous bone (Figure 1a). The system with short implant contained about 25800 elements with 5300 nodes: 5800 elements for the implant, 4600 for cortical bone and 15400 for cancellous bone. For non-integrated implants, the bone-implant interface was modelled using non-linear frictional contact elements, which allow for relative displacements between the implant and the bone. In this case, the contact zone transfers pressure and tangential forces –due to friction- but no tension. For the simulations of fully osseointegrated implants, the interface was considered as a common surface between implant and bone (Figure 1b). (a)

(b)

before integration friction pressure

Frictional contact elements at interface after integration

Common nodes at interface

Figure 1. (a) Finite element mesh including implant, cortical and trabecular bone (b) Detail of bone-implant interface before and after integration

Mechanical stimulus for bone remodelling Bone adaptation models When subjected to a mechanical loading, bone adapts its structure by changing either its shape (i.e. geometry) or its density (or both). The change in density, also known as internal remodelling, is usually formulated using sitespecific rate equations as [14]: ∂ρ = B (φ (σ , ρ ) − F ) ∂t

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where B is a parameter that quantifies the bone gain or loss, φ is the mechanical stimulus and F is a reference value for the stimulus which defines the threshold between densification and resorption [17]. In other terms, F indicates when remodelling occurs and B indicates how much is the bone gain or loss. The triggering of bone remodelling around the loaded implant was evaluated according to three selected remodelling criteria, i.e. definitions of the mechanical stimulus. Examined models were: von Mises (or equivalent) strain stimulus, strain energy density stimulus and effective stress stimulus. The selection of these criteria was motivated by the low number of required input parameters and the ease of implementation. Since each model has its own set of parameters, it is therefore difficult to compare models’ predictions with accuracy. However, it was expected from those models to have close estimations of the solution or at least similar trends, for a given load case. Appropriate input data for evaluating the mechanical stimuli were obtained from finite element simulations. To avoid the determination of additional models’ specific parameters, we focused only on the sign of the rate equations, i.e. densification or resorption, since the objective here was not to quantify the bone gain or loss, but to determine the triggering of remodelling. The parameter B was therefore set to one for the three selected criteria. Von Mises (or equivalent) strain stimulus The von Mises (equivalent) strain is defined in terms of the principal strains ε1, ε2 and ε3 as:

ε=

[

1 (ε1 − ε 2 )2 + (ε 2 − ε 3 )2 + (ε 3 − ε1 )2 2

]

Assuming a mechanical stimulus based on the von Mises strain, the rate of change of the local stiffness modulus E, which can be correlated to the density ρ, is expressed as [10]:

∂E = B (ε − ε 0 ) ∂t where B quantifies the bone gain or loss and ε0 is a reference value for the threshold of remodelling. The sign of densification rate determines if there is a bone gain (i.e. when ε >ε0) or a bone loss (i.e. when ε ε 0 max

Based on previously published experimental data, the stimulus window [ε0 min, ε0 max] was set to 150-2000 µm/m limits which are considered as clinically realistic upper and lower bounds [40]. The value of B was set to one. Note that instead of a unique value for ε0 defining the limit between resorption and densification, Frost [41] introduced the concept of a ‘lazy zone’ defined by an interval [ε0-, ε0+] in which no bone gain or loss occurs. Below the lower bound of this interval, the densification rate is negative, meaning that bone is resorbing; and beyond the upper bound, the densification rate is positive, meaning that bone is growing. Strain energy density (SED) stimulus The strain energy density criterion (SED) assumes that the density change rate, representing bone densification or resorption, is expressed as a function of the variation of strain energy density due to the mechanical loading [11] : ∂ρ = C (U − U n ) ∂t

where U = 1 σ ij ε ij is the strain energy density, σij and εij are the components 2 of the local stress and strain tensors respectively. Un is a site-specific measure of strain energy density playing the role of a limit between densification and resorption; and C is a parameter that quantifies bone gain or loss. This criterion is formulated in an equivalent form [13, 19] as:

⎞ ⎛U ∂ρ = B ⎜⎜ − k ⎟⎟ ∂t ⎠ ⎝ρ where B/ρ and ρ k correspond to C and Un respectively. A lazy zone, in which no net change of bone density occurs may separate the domains of bone densification and bone resorption. Therefore, the remodelling rate expressed as the variation of bone density as a function of a strain energy density stimulus is given by:

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⎧ ⎛U ⎞ ⎪ B ⎜ − (1 + s ) k ⎟ ⎠ ⎪ ⎝ρ ∂ρ ⎪ 0 =⎨ ∂t ⎪ ⎪ B ⎛⎜ U − (1 − s ) k ⎞⎟ ⎪⎩ ⎝ ρ ⎠

if if if

U

> (1 + s ) k

ρ

(1 − s ) k ≤ U

U

ρ

≤ (1 + s ) k

< (1 − s ) k

ρ

where s, in percent, defines the lazy zone’s extent beside the threshold k. The input parameters were taken from previous published studies [11, 13, 19] as s = 10%, k = 0.004 J/g and B = 1. The lazy zone defined by the interval

[(1 − s) k , (1 + s) k ] is therefore in the range: 0.0036 ≤ ρ U

≤ 0.0044 .

The density was estimated using the correlation E = 3790 ρ 3 between the elastic modulus and the density [42]: ρ = 0.64 g/cm3 for cancellous bone ( E = 1 GPa ) and ρ = 1.58 g/cm3 for cortical bone ( E = 15 GPa ). Effective stress stimulus The effective stress σ is a scalar which indicates the “magnitude” of the stress tensor σ and is defined by: σ = 2 EU

where E is the local stiffness modulus and U is the strain energy density. A mechanical stimulus based on the effective stress was proposed by Carter [10] as: 1

⎛ ⎞m ψ b = ⎜⎜ ∑ ni σ im ⎟⎟ ⎝ day ⎠

where n is the number of loading cycles (stress stimuli) per day and the subscript i denotes the simultaneous loads applied to bone; the stress exponent m is an empirical constant which acts as a weighting factor for the relative importance of stress magnitude and number of stimuli. However, in this study, in view of comparison with other criteria, the stress stimulus was calculated separately for each load case. The remodelling rate expressed as the variation of bone density as a function of the effective stress stimulus, and including a lazy zone, is given by:

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⎧ B (ψ b − (1 + s)ψ bAS ) ∂ρ ⎪ 0 =⎨ ∂t ⎪ ⎩ B (ψ b − (1 − s)ψ bAS )

if if if

ψ b > (1 + s)ψ bAS (1 − s)ψ bAS ≤ ψ b ≤ (1 + s)ψ bAS ψ b < (1 − s)ψ bAS

ψ bAS is referred to as the ‘attracter state stimulus’ which is the normal stress stimulus, i.e. producing no net bone mass change. The advantage of this criterion is that it uses a scalar quantity (i.e. the effective stress) but all the components of the stress tensor are included by means of the strain energy density. Based on previously published data [12, 24, 43], the ‘attracter state stimulus’ ψbAS was calculated using the following assumption: applying a 100 N load onto the dental implant and considering a compressed area of about 10 mm 2 induces an average effective stress of σ = 10 MPa ; setting n = 500 stimulations/day and m = 4 leads to ψ bAS = 47 MPa . The other parameters were s = 10% and B = 1. The obtained equilibrium range (ψbAS ± s) is therefore: 42.3 ≤ ψ b ≤ 51.7 (MPa)

Results The bone response to the applied mechanical loads is analyzed through the stress/strain distributions in the whole bone matrix. The results are presented in terms of von Mises stresses which permit to evaluate, in any location, the “magnitude” of the stress since this norm is calculated from the three principal stresses of the local stress tensor. In figures 2 and 3, are presented the von Mises stress distributions around the long and short implants before and after osseointegration. For each load case, due to the high contrast between the stresses in cortical bone and the stresses in cancellous bone, the results are presented separately for each material. In figure 4, the von Mises stresses for the long and the short implants are compared at the bone-implant interface in the median plane for the vertical and MD load cases and in the bucco-lingual plane for the BL load case. Figure 5 shows distributions of the tensile and compressive stresses for a long implant horizontally loaded in the mesio-distal plane. Figure 6 plots the distribution of von Mises strains which are used for the evaluation of remodelling trigger levels. In figure 7, are presented the predictions of bone mass change (gain, loss or constant) according to the three selected remodelling criteria. Table 1 summarizes the main results of the finite element analyses (von Mises -equivalent- stress/strain, strain energy density, effective stress, maximum compressive/tensile stresses), which serve as input data for remodelling algorithms. Table 2 lists the values of mechanical stimuli calculated from the FE analysis output according to the selected remodelling criteria.

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Table 1. Maximum stresses, strains and strain energy density in bone before and after integration Effective Compressive Tensile Equivalent Equivalent SED Stress Strain Stress Stress Stress U (kPa) (MPa) (MPa) σequ (MPa) εequ (µm/m) σ (MPa) vertical 5.30 2130 8.49 4.12 2.59 3.07 mesio-distal before 15.35 906 8.71 16.16 15.3 8.52 bucco-lingual 14.23 829 9.19 16.60 14 8.52 vertical 10.92 881 6.42 13.88 12.8 5.04 mesio-distal after 8.17 498 4.44 11.54 10.8 11 bucco-lingual 11.14 645 6.58 14.05 7.99 7.91 Note 1: values in italics are measured in cancellous bone (E = 1 GPa) and obtained for non-osseointegrated implants loaded vertically, all other values are measured in cortical bone (E = 15 GPa), near the implant neck. Note 2: maximum values of stresses and strains were obtained from the whole bone matrix and may therefore not necessarily appear on the plotted results since only half of the 3-D structure is represented in figures 2 to 6. Load case

Osseointegration

(a)

(b)

Figure 2. Von Mises stresses around a long implant: (a) before osseointegration (b) after osseointegration

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Stress distributions around implants before and after integration Effect of implant integration status on the stress distribution The results show that, in the case of non-integrated long implants, debonding induces stress concentrations in all load cases (Figure 2a). For vertical loading, the forces are transferred to cancellous bone but the stresses are concentrated in the implant thread vicinity because the lateral face of the implant supports only a small portion of the load by friction and the implant is therefore mainly supported by the thread. The horizontal loading shows that the bone is over-compressed on one side (direction of force) whereas the opposite side undergoes very low stresses. Also, for horizontally loaded implants, their rigidity being much higher than the rigidity of bone, an effect of lever arm is noticed. The bone matrix is compressed locally in the implant neck area and in the area at the bottom opposite side of the implant. After osseointegration, the stresses are more smoothly distributed because tensions are transferred by the interface and thus the compressions on one side are counter-balanced by tensions on the other side, leading to a certain ‘symmetry’ with respect to the implant’s vertical axis (Figure 2b). In this case, the whole surface of the implant contributes to the load transfer to the bone. As shown in Table 1, the maximum von Mises stresses are lower, except for the vertical load case, in which the integrated implant is perfectly attached to the bone and generates therefore tension stresses in the surrounding cortical bone. Effect of implant length on the stress distribution The distribution of von Mises stresses around the short implant shows a similar trend to the long implant either before integration or after (figure 3). However, for short implants, bone undergoes higher stresses than for long implants (figure 4). Indeed, long implants have a larger contact surface with bone than short implants. The load is then transferred from implant to bone over a larger surface, leading to lower stresses. Maximum compressive/tensile stresses Maximum tensile stresses occur in cortical bone (except for non-integrated vertically loaded implants). For integrated implants, the highest value is observed at the opposite side of the compressed area (diametrically opposed locations); whereas for non-integrated implants, the peak tensile stress is observed on the lateral sides (figure 5). For the non-integrated long implant, the maximum tensile stress was 8.52 MPa and the maximum compressive stress was 15.3 MPa (Table 1). The corresponding stresses for the integrated implant were 11 and 12.8 MPa, respectively. Maximum computed compressive stresses in cortical and cancellous bone, i.e. 15.3 and 2.6 MPa respectively, are well below the

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(a)

(b)

Figure 3. Von Mises stresses around a short implant: (a) before osseointegration (b) after osseointegration

compressive strength of these materials, i.e. 100-200 MPa [44] and 5-6 MPa [45] respectively. However, the 11 MPa maximum tensile stress computed at the bone-implant interface exceeds clearly experimental measurements on bone-implant bonding. Indeed, depending on the implant surface texture the tensile strength vary between 1 and 7.6 MPa [46-48]. These high stresses may therefore cause debonding in the zones under tension.

Evaluation of bone remodelling triggering Predictions on bone remodelling onset due to the applied loads are performed for the three selected criteria, i.e. von Mises, strain energy density and effective stress models. For each remodelling criterion, the value of the corresponding mechanical stimulus calculated from FE output (Table 2) is

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Figure 4. Stress profile along the implant-bone interface in the median MD plane for vertical and mesio-distal load cases and in the BL median plane for the bucco-lingual load case

(a)

(b)

Tension Horizontal Load

Horizontal Load

Compression

Compression Tension

Tension

Figure 5. Tensile and compressive stresses around a long implant and locations of peak tensile stresses and peak compressive stresses: (a) before osseointegration (b) after osseointegration.

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(a)

(b)

Figure 6. Von Mises strains around a long implant: (a) before integration (b) after integration Table 2. Mechanical stimuli for selected remodelling criteria. The sign indicates the bone mass change: (+) for bone gain, (–) for bone loss and (0) for no net mass change (lazy zone) Load case vertical mesio-distal bucco-lingual vertical mesio-distal bucco-lingual

Osseointegration before

after

Equivalent strain stimulus εequ (µm/m) 2130 (–) 906 (+) 829 (+) 881 (+) 498 (+) 645 (+)

SED Stimulus U/ρ 1.33E-02 (+) 5.51E-03 (+) 5.82E-03 (+) 4.06E-03 (0) 2.81E-03 (–) 4.16E-03 (0)

Effective stress stimulus ψ 19.5 (–) 76.4 (+) 78.5 (+) 65.6 (+) 54.6 (+) 66.4 (+)

compared to the limits of the criterion to obtain a prediction on bone remodelling (densification, resorption, or equilibrium state with no net bone mass change) as shown in figure 7. The trigger value for bone remodelling according to a given criterion is evaluated at the location where the maximum value of the mechanical stimulus was obtained. However, bone remodelling for lower values in other locations is not excluded. Von Mises (equivalent) strain criterion The application of this remodelling criterion leads to ossification in all cases except for non-integrated implants loaded vertically. For this latter case, predicted resorption is due to over-compression (Table 2 and figure 7). Lowest values of equivalent strain (~500 µm/m) are obtained for integrated implants loaded horizontally in the MD plane.

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Aïssa Mellal & John Botsis Integration status Load case densification

resorption

resorption (overload)

Before After

Vertical Horizontal MD Horizontal BL

εequ [µm/m] 0

2000

150

resorption

equivalent strain stimulus 3000

densification (1+s) k

(1-s) k

U/ρ [kPa/g/cm ] 3

15

4.4 0

3.6

resorption

strain energy density stimulus

densification (1+s) ψb (1-s) ψb 51.7

0

42.3

ψb [MPa/day] 100

effective stress stimulus

Figure 7. Bone remodelling triggering predictions for the three tested stimuli

For this stimulus, no “lazy” zone was defined. However, results show that all calculated stimulus values exceed largely the threshold value of 150 microstrains, i.e. an interval of ±10% or even ±20% will have no influence on the results leading to the same predictions. Strain energy density criterion The evaluation of bone remodelling using the strain energy density (SED) as mechanical stimulus predicts bone densification in all load cases except for integrated implants loaded horizontally in the MD plane. The highest densification rates are obtained for vertically loaded non-integrated implants (Table 2 and figure 7). Effective stress criterion The evaluation of bone remodelling using this criterion leads to bone resorption for the vertically loaded non-integrated implant and to densification for all other cases (Table 2 and figure 7).

Discussion The FE simulations lead to coherent distributions of the stresses and strains around the mechanically loaded implant either before or after

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integration. However the absolute predicted values should be considered only as indicators since many assumptions were made in this analysis (e.g. the homogeneity and isotropy of bone material, simple geometry, isolated implant) to focus exclusively on the investigated topics (i.e. interface status effect, implant length effect and prediction of bone remodelling). The high values of computed tensile stresses, in comparison with tensile strength of interface bonding, were obtained for an isolated implant surrounded by bone. In real situations, these tensile stresses are significantly attenuated due to the vicinity of neighbouring teeth which support a portion of the load and therefore redistribute the stresses more uniformly. On the other hand, peak values of compressive stresses are below materials’ strength but resorption due to over-compression may take place (e.g. non-integrated vertically loaded implant): pathologic overload leading to irreversible bone damage. To evaluate the mechanical stimuli, only peak values were considered. Their location is not necessarily the same from one criterion to another, which means that the predicted zones of remodelling initiation are not necessarily the same according to the three criteria. Certain contradictions between remodelling criteria have been revealed: 1/

2/

3/

For the integrated implant, two criteria (effective stress and equivalent strain) predict densification for all load cases, whereas SED criterion predicts resorption and homeostasis at best (see figure 7). For the non-integrated implant loaded vertically, von Mises strain criterion predicts resorption due to overload, SED criterion predicts densification and effective stress stimulus leads to resorption. But in this last case, the highest value of effective stress is obtained in cortical bone (implant neck area) whereas the maximum values of von Mises strain and SED are obtained in cancellous bone (figure 2a and Table 1). Thus, for a complete comparison, bone remodelling should be evaluated according to these criteria in the whole bone matrix instead of punctual comparisons. For the equivalent strain stimulus, a stimulus window of 150-2000 µm/m was chosen, and considered as clinically realistic, according to Rong’s assumption [40]. On the other hand, in Frost’s model, it is suggested that strains below 200 µm/m initiate resorption, strains of between 200 and ~2000 µm/m maintain bone architecture, strains of between ~2000 and 4000 µm/m initiate lamellar bone deposition and strains beyond 4000 µm/m cause damage initiating woven bone deposition [20]. This may be due to the fact that Frost’s data correspond to axial strains and cannot therefore be directly compared to equivalent strains calculated from a three dimensional strain tensor.

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The comparison to in vivo data is highly affected by the availability of experimental data, its biological variability and the coherence of theoretical models’ parameters with experimentally measured quantities. These aspects are discussed in [49] and [50] in more detail.

Conclusion The effects of bone-implant interface conditions on the stress distribution have been investigated using a three-dimensional finite element analysis. It has been shown that for an integrated dental implant, stresses in bone are lower and more smoothly distributed than for a freshly inserted implant. Long implants, with larger contact surface with bone, permit a better load transfer than short implants either before or after osseointegration. The stress distribution directly affects bone remodelling in the implant’s vicinity [16] and higher stresses before osseointegration favour bone adaptation. However, overcompressed bone may cause irreversible damage. Additionally, high tensile stresses near the bone-implant interface may lead to debonding. Bone remodelling triggering has been checked for peak values of equivalent strain, effective stress and strain energy density. The initiation is generally found in cortical bone in the implant neck area. This fact doesn’t mean that the cancellous bone doesn’t undergo bone remodelling, but simply indicates where remodelling first occurs and where the highest activity is located. If a complete map of bone remodelling is needed, the evaluation must be carried out for the whole FE model. The comparison of the three remodelling models’ predictions shows generally a good agreement with minor exceptions due essentially to the definition of each model’s bounds (e.g. lazy zone, stimulus window). The quantitative differences points out the need for experimental validation of these models and for calibration of their parameters to specific bone tissues. Provided these conditions are met, the finite element simulations can be used as a non-invasive diagnosis tool for practitioners to predict “weak” zones (debonding, resorption, over-compression) as well as bone remodelling activation around dental implants.

References 1.

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