Primary Stability of Dental Implants in Human Jawbones: Experiments & FE Analyses

ABSTRACT

Objectives

Primary stability (PS) is a key factor for promoting osseointegration and long‐term success of dental implants particularly for immediate loading protocols. Beyond the current assessments of PS, an accurate pre‐operative evaluation of PS would contribute to the improvement of surgical planning and treatment outcome. This study used biomechanical testing and homogenized finite element (hFE) analysis to objectively measure PS in the laboratory, and digitally estimate PS from prior μCT reconstructions.

Material and Methods

Thirty‐five bone samples extracted from the jaws of two donors were examined. Twenty‐two were finally evaluated for PS. After scanning of the samples with μCT, implants were inserted by two experienced surgeons, and various metrics such as μCT‐based bone volume fraction (BV/TV), insertion torque (IT), and resonance frequency analysis (RFA) were assessed to determine PS. Mechanical tests were conducted to measure ultimate force (UFexp) as an objective indicator of PS while the hFE simulations were performed to estimate this same ultimate force (UFsim).

Results

Higher correlation was found between UFsim and UFexp (R ² = 0.85) than between BV/TV and UFexp (R ² = 0.61), IT and UFexp (R ² = 0.50), and RFA and UFexp (R ² = 0.38). All variables demonstrated a statistically significant linear correlation with UFexp (p < 0.01).

Conclusion

UFsim turns out to be a more reliable and objective indicator of PS than IT and RFA. The hFE analysis requires prior μCT reconstructions and is currently limited by numerical convergence problems. Despite these limitations, pre‐operative hFE analysis emerges as a promising tool with a higher accuracy for estimation of PS than state of care techniques.

1. Introduction

Primary stability (PS) is essential for the success of dental implants, serving as a cornerstone for achieving osseointegration (Degidi et al. 2013; ÖStman 2008). PS refers to the immediate engagement of the implant with the surrounding bone when the implant is screwed in. The implant stability following osseointegration, when bone grows onto the implant surface over time is called secondary stability. An enhanced PS allows for immediate implant placement with immediate or early loading of the implant (Gapski et al. 2003; Seyssens, Eghbali, and Cosyn 2020; Steiner, Ferguson, and van Lenthe 2015). These loading protocols techniques contribute to time/cost savings and minimize the patient's burden by facilitating quicker recovery and reducing the number of follow‐up consultations (Kennedy et al. 2012; Marković et al. 2022). The chances of success of such procedures increase if clinicians are able to plan the osteotomy and implant placement according to objective rating of the reachable PS.

Following the assessment of the medical history and the clinical examination of the patient, a digital planning of the implantation procedure usually starts with a cone‐beam computed tomography (CBCT) often combined with an intraoral scan, providing a three dimensional view of the implantation site (Yong et al. 2021). Based on this representation, the implant is virtually positioned with respect to the neighboring anatomical structures and according to the planned prosthetic rehabilitation. In the case of statically guided surgery, these data are utilized for the fabrication of a drilling guide, which can be positioned within the oral cavity of the patient to precisely transfer the planned implant location in the surgical theatre. Subsequently, the guide is used for multiple drilling steps, aimed to hold the drill in position for preparing the implantation site (D'haese et al. 2017; Handelsman 2006). Once the osteotomy is prepared, the implant is placed, and the implantation torque (IT) can be measured through the implantation device. The whole planning and the surgery are critically dependent on determining the bone quality. An early stage assessment of bone quality of the implant site is important (Rues et al. 2021) and is usually performed by subjective classification systems and based on the surgeon's experience (Chugh et al. 2013; Juodzbalys and Kubilius 2013). Bone density or bone volume fraction (BV/TV) is the main determinant of cortical and alveolar bone mechanical properties (Carter and Hayes 1977; Lee, Kim, and Yun 2017). BV/TV is also known as a main determinant of implant primary stability (Pommer et al. 2014). Therefore, a precise and objective evaluation of bone density in vivo represents a foundation for assessment of PS prior to surgery and is highly desirable for successful treatment outcomes.

By pre‐operatively estimating the PS, dentists gain the ability to make informed decisions. This includes selecting the optimal implant position, choosing the most suitable implant design, determining the appropriate drilling sequences, and even considering the feasibility of immediate loading. From a technical perspective, PS of an implant is defined as its capacity to withstand cyclic loading up to an overload of the bone‐implant system causing damage and experiencing irreversible excessive micromotions at the interface immediately after insertion and prior to osseointegration (Ovesy, Voumard, and Zysset 2018; Voumard et al. 2019). From this point of view, the PS can then be quantified and rated by measuring the ultimate force (UF) that the implant can withstand before dislodging from the bone. Accordingly, a biomechanical testing setup was developed at the ARTORG Center to determine UF as an objective value to measure PS (Voumard et al. 2019) and a homogenized finite element (hFE) method based on a μCT reconstruction was developed to simulate this test and estimate PS digitally (Ovesy, Voumard, and Zysset 2018).

Pre‐operatively, CBCT images can be technically used to measure BV/TV or bone density, which are considered as indicators of bone quality and UF (Pommer et al. 2014; Voumard et al. 2019). In clinical routine, PS is mostly rated during and/or post‐surgery by implantation torque (IT) and resonance frequency analysis (RFA), respectively. IT related PS assessment is done by observing the peak IT measured during implant insertion (Rabel, Köhler, and Schmidt‐Westhausen 2007). RFA‐based PS rating is performed by generating acoustic waves through the implant and analyzing its resonance frequency (Makary et al. 2012). Voumard et al. (2019), showed that for homogenous bone samples and one implant type those values correlate well with UF, while IT outperformed BV/TV and RFA. Yet, the correlation strength between those parameters and UF has not been evaluated in human jaws using the testing protocol by Voumard et al. (2019) or the simulation method of Ovesy, Voumard, and Zysset (2018). Furthermore, it is believed that PS is also influenced by the implant geometry and the drilling sequence (dos Santos, Elias, and Cavalcanti Lima 2011).

Therefore, the present study aims to: (1) assess the homogeneity and distribution of BV/TV across different locations in the human jaw; (2) compare clinical mechanical parameters such as maximum intraoperative IT or RFA against the robust experimental UF parameter (UFexp); (3) investigate the correlation between BV/TV and UFexp; and (4) use a computational model that allow the comparison between UF simulated (UFsim) and UFexp in human jaws.

2. Materials and Methods

2.1. Human Bone Samples

Two cadaver human heads (male donors aged 82 and 86 years, Figure 1) were obtained with informed consent and full compliance with international ethical standards from the Institute of Anatomy at the University of Bern. A total of 35 implants were planned based on cone‐beam computed tomography (CBCT) images by two experienced dental surgeons. The implant locations were chosen to correspond to clinically significant areas, such as the roots of extracted teeth, while ensuring a sufficient minimum distance of 12 mm between neighboring implants. To extract the separate bone samples (n = 35), any soft tissue and additional bony structures, such as the ramus mandible, were removed. The dental surgeons extracted the remaining teeth and flatten the surface where a tooth was extracted with a milling machine to ensure bone level placement of the implants (Figure 2).

FIGURE 1.

Overview of the sequence steps performed from the extracted samples of an 82‐year‐old human jaw (n = 19) and an 86‐year‐old human jaw (n = 16): from extractions and μCT scan, to experimental test and simulation prediction of primary stability. Only n = 22 samples were valid for prediction as 3 samples had to be excluded by the experiment and 10 by simulation.

FIGURE 2.

Left: Tooth extraction and flattening by milling of the anatomical samples, when a tooth has been extracted. Middle: In PMMA embedded bone sample that did not require milling. After pilot drilling, the anatomical samples were cut in segments for each implant site and embedded in PMMA, for final drilling, implant placement, and mechanical testing. Right: Setup of the mechanical tests.

2.2. Experimental Procedure

Planning, drilling and implantation of variable‐thread tapered implants (NobelActive (NA); Nobel Biocare AB; Göteborg, Sweden) were performed manually by two dentists as described in Table 1 in dry conditions at room temperature using an Osseocare implantology device (Nobel Biocare). For drilling rotational speed (max 2000 rpm prescribed by Osseocare) and feeding rate were applied by the surgeons according to their clinical experience and were not recorded. After each drilling step the holes were cleaned with a water jet.

TABLE 1.

Overview of the drilling protocol and its respective implant.

Pilot drill	Main drill	Implant	Abutment
Twist drill	Twist step drill	NobelActive Internal NP	Snappy abutment
ø2 mm	ø2.4–2.8 mm	ø3.5 mm	4.0, 1.5 (NP)
	ø2.8–3.2 mm	Length = 13 mm

Pilot drilling was conducted down to a depth of 13 mm on the intact maxillae and mandibulae. Following, the jaws were cut (facial to buccal) using a diamond bandsaw (EXAKT, EXAKT Advanced Technologies GmbH, Norderstedt, Germany) into 35 separate samples, each approximately 12 mm in width along the sagittal plane (with 6 mm to each cutting side from the center of the pilot osteotomy) and embedded into polymethylmethacrylate (PMMA). To track the anatomical orientation, a small notch was created both in the sample and in the polymerized PMMA, ensuring visibility in the μCT scans. Subsequently, main drilling to a length of 13 mm was performed using the two twist step drill sequentially independently of the final implant position and/or bone quality. Finally, implants were inserted until its top surface was aligned with the bone surface, according to the implant manual (rotation speed: 25 rpm, max. torque: 70 Ncm). Insertion torque of the implantation was measured with a load cell (M‐2025, Lorenz Messtechnik GmbH, Germany) and peak value (IT) was computed. Three samples with a relatively high BV/TV reached the maximum torque threshold and had to be inserted by hand to be fully seated. Therefore, they were excluded for predicting primary implant stability. Directly after implantation, the implant stability quotient (ISQ) was measured using RFA with the smartpeg and the Osstell ISQ device (Integration Diagnostics, Sweden). It measures the vibration frequency of the implant and assigned it to an ISQ scale from 1 to 100 as a rating of the stability of an implant. According to the manufacturer, high stability is demonstrated for values > 70 ISQ, medium stability by 60–69 ISQ and low stability by < 60 ISQ.

During the preparation, three high‐resolution μCT measurements were acquired after pilot drilling (stage 1), after main drilling (stage 2) and after implantation (stage 3). The images were acquired using the uCT100 device (Scanco Medical, Brüttisellen, energy: 70 kV, intensity: 114 μA, integration time: 300 ms, voxel size: 24.5 μm). The μCT reconstructions from stage 1 were segmented with an OTSU threshold and a hollow cylinder (Ø 6 × 13 mm) was defined around the pilot drill osteotomy on the segmented image to retrieve the pre‐operative BV/TV. BV/TV was defined as the ratio of the volume occupied by bone (bone volume: BV) to the total volume (TV) of a predefined region of interest (ROI) and is given in %.

Prior to mechanical testing and in case the implant insertion torque reached 35 Ncm or higher, the abutment was tightened manually to 35 Ncm. Otherwise, the abutment was tightened to 80% of the reached implant insertion torque. The samples were then randomly mechanically tested in four different anatomical loading directions: Distal‐mesial, buccal‐lingual, mesial‐distal, lingual‐buccal. The mechanical tests were performed as described in (Voumard et al. 2019) to measure ultimate force (UFexp) as an objective indicator of PS. Shortly, this test configuration is an adaptation of the standard ISO 14801, where implants are tested under a 30° loading configuration to mimic biting forces. In this study, a cyclic displacement‐controlled loading protocol with increasing amplitude was used instead of a load‐driven fatigue protocol. After three pre‐conditioning cycles between 0.04 mm deformation and zero load, the samples were loaded stepwise up to 2.56 mm by doubling the previous displacement amplitudes and performing three repetitions per step.

Axial forces were measured by a load cell (662‐04D, MTS, USA). Finally, stiffness (K) and ultimate force (UFexp) were computed for each sample using a custom MATLAB script. K was analyzed in the second cycle of the force displacement curve. To get UFexp each sample underwent displacement‐controlled cyclic testing with increasing forces until failure (UFexp) was detected (Figure 3, bottom left).

FIGURE 3.

Top left: Registered μCT images to localize implant position and narrowing down of the ROI. The cropped image was segmented and used for BV/TV mapping. Top right: Structure of the simulation with the boundary conditions. The displacement for the mechanical testing was along the z‐axis with a 30° inclination of the implant. Bottom: Force displacement curve of the experiment (left) and simulation (right). The red point denotes the ultimate force.

2.3. FE Simulation

To reliably design the simulation as close as possible to the experiment, it was essential to determine the precise location of the implant within the bone. This information was critical for identifying the region of interest (ROI), for BV/TV mapping and ensuring the correct assembly of the bone and implant parts in the finite element analysis (FEA). To achieve this, the μCT images of stage 1 and stage 3 were registered to each other (Figure 3, top left). This registration process pinpointed the final position of the implant within the μCT image of stage 1. Once the implant's location was established, the image featuring the pilot osteotomy was oriented so that the anatomical loading direction aligns with the y‐axis of the simulation's global coordinate system. Subsequently, the ROI was delineated around the implant's location to map the local BV/TV from the μCT image to the hFE mesh (Figure 3, top left). The final geometry of the stepped drill was included into the BV/TV mapping process, which aimed to determine the material properties of each finite element representing the bone. This mapping involved correlating the segmented ROI from the μCT image with the FE mesh, ensuring that the bone's material characteristics were accurately modeled based on the varying BV/TV detected within the scan. The BV/TV for an element was determined by calculating the number of bone voxels within a sphere (Arias‐Moreno et al. 2019), centered at the element's location of the center of gravity in the μCT image. This value was then divided by the total number of elements (both bone and non‐bone) within the sphere. In other words, if there were mainly bone voxels within that sphere, the corresponding element was defined to have material properties of high BV/TV. On the other hand, an element located within the bone marrow had properties of a lower BV/TV. An isotropic trabecular orientation was assumed for each element.

The implant's geometry was simplified to a rotationally symmetric shape (Figure 3, top right), but closely mimicking the thread pattern of the NobelActive implant (3.5 mm × 13.0 mm). It was positioned within the osteotomy included in the bone ROI, which precisely matched the dimensions of the final twist step drill leading to the initial overclosure between the contact bodies, implant and bone. This arrangement results in an initial overlap between the contacting entities (implant and bone), thereby establishing an initial press‐fit condition. The press fit was specified with the Abaqus/Standard interference fit options with an automatic shrink fit using general surface‐to‐surface contact. At the initial step of the simulation, the interference fit forces the bone's surface (slave‐surface) to adapt to the contour of the implant (master‐surface), aiming to reproduce the typical mechanical interaction in actual implant placement scenarios.

The size of the volume representing the bone in the hFE model was deliberately selected to establish a minimum spacing of 2 mm between the implant's outer surface and the bone's boundary. This approach was aligned with methodologies from prior research, aiming to reduce computational demands while ensuring methodological consistency (Ovesy, Voumard, and Zysset 2018; Ovesy, Indermaur, and Zysset 2019). Additionally, it was designed to guarantee that the region of interest (ROI) was comprehensively populated with bone material from the sample, preventing the presence of PMMA at the boundaries to avoid including another material in the model than bone. The selected size represents a balanced compromise, bridging the gap between the actual dimensions of the bone sample and the scale of the computational model. This choice ensured both the integrity of the simulation's biomechanical relevance and the efficiency of its computational execution.

The implant was modeled as a rigid shell with element type R3D8. For meshing, an approximate global seed size of 1 mm was utilized, resulting in 534 elements. The homogenized trabecular bone was meshed with a global seed size of 0.6 mm. Additionally, the geometry of the osteotomy was refined using a local seed size of 0.4 mm for the arc and 0.2 mm along the drill axis. This resulted in 11,780 linear hexahedral elements of type C3D8 with a similar size around the implants used in (Ovesy, Voumard, and Zysset 2018).

An anisotropic elastic‐viscoplastic damage model from (Schwiedrzik and Zysset 2013) was chosen in the finite element simulations in order to take into account the non‐linear behavior of the bone material at large strains. It was applied in the finite element package Abaqus (Abaqus 6.21 Dassault Systems, Vélizy‐Villacoublay) using the same user material subroutine as described in (Ovesy, Voumard, and Zysset 2018). Shortly, this model simulates the behavior of an elastoplastic material with a quadric yield surface, whose parameters depend on BV/TV. The post‐yield behavior is modelled without hardening or softening, but with densification that represents the progressive compaction of the trabeculae. The damage variable is a scalar function of the cumulated plastic strain and reduces all components of the stiffness matrix (Ovesy, Voumard, and Zysset 2018).

The boundaries of the bone model were constrained, with the outer side walls below the implant shoulder and bottom surface fixed in all directions to simulate the rigid and immobile embedding. Furthermore, the orientation of the assembled model was carefully aligned with the anatomical loading direction employed during the experimental phase, using the Z‐axis to apply the vertical displacement. The interaction between the implant surface and bone was established as a unilateral interface. A separable surface‐to‐surface contact was defined to characterize this interface, incorporating both normal and tangential contact interactions. Normal contact was complemented by a frictional force acting tangentially, with a coefficient of friction (μ) set to 0.3, a value previously adopted (Ovesy, Voumard, and Zysset 2018). Additionally, a slip tolerance of 0.05 was adopted as described in (Ovesy, Voumard, and Zysset 2018). An interference fit condition, simulating initial press fit between the implant and bone, was specified at the start of the simulation. The upper part of the bone mesh was modelled like a funnel. This was performed for two reasons: (i) To take into account the bone structures that are higher than the implant shoulder. (ii) To ensure that there is no interaction between the outer part of the implant and the mesh during loading. The cyclic loading protocol was implemented by applying a displacement at a reference node. This node, located 11 mm above the implant shoulder, was kinematically linked to the implant. The displacement regimen involved incremental movements of the reference node to maximum displacements of 0.04, 0.08, 0.16, and 0.32 mm in the z‐direction for each loading cycle, with freedom of motion along the other two axes. Simulations were executed using the finite element software package Abaqus/Standard (version 6.21, Dassault Systèmes, Vélizy‐Villacoublay). Computations were carried out on the University of Bern's Linux cluster (UBELIX), utilizing 8 CPUs with 5 GB of memory each. An implicit simulation approach was employed, with the average processing time for a single sample being approximately 30 min.

K was assessed during the descending phase of the first loading step, which corresponded to a displacement of 0.4 mm. UFsim was determined by selecting the maximal force achieved during the simulation (Figure 3, bottom right). The inclusion criteria for simulations in the results were contingent upon the achievement of a force plateau, ensuring the consistency and reliability of the data. Out of the 32 remaining samples for the experiment, the simulation did not converge for 10 of them. The convergence problems occurred randomly and were not related to either high or low BV/TV samples. The stiffness was not evaluated further, as the elastic behavior of the screw and the abutment were not considered in the simulation.

2.4. Statistics for PS Prediction and Model Validation

To assess the efficacy of each individual predictor variable (BV/TV, IT, RFA, and UFsim), in forecasting PS (UFexp serving as the response or dependent variable), an initial step involved fitting either a linear or power regression model.

Power model: ${\mathit{UF}}_{\mathit{\text{pred}}}\left(x\right)={\mathit{Ax}}^B\left[N\right].$

Linear model: ${\mathit{UF}}_{\mathit{\text{pred}}}\left(x\right)=A+B\bullet x\left[N\right].$

The determination of whether to apply a linear or power model was primarily based on the normality of residuals distribution. If a power regression model was deemed more appropriate, indicating a non‐linear relation in the original variables, the natural logarithm was applied to the variables which allowed for the transformation of the non‐linear relationship into a linear format in the logarithmic space, thereby enabling the application of linear regression techniques to model relationships that are inherently non‐linear relationships in the original variables.

The predictive capability of each variable in providing insight into PS was evaluated, by each models' root mean square error (RMSE), standard deviation (SD) and coefficient of variation (CV_SD).

3. Results

3.1. Anatomical BV/TV Distribution (N = 35)

For each of the 35 extracted sample the BV/TV is represented in Figure 4 according to its anatomical location for both of the human donors using a color distribution scheme ranging from low (yellow) to high BV/TV (red). The BV/TV ranged from 17% to a high 72%. The colored images show a clear difference between the two donors. The jaw M86 shows on average a higher BV/TV (47.3% ± 14.7%) than jaw M82 (30.3% ± 8.3%). However, the differences between the jaws of the two donors are smaller for the maxilla than for the mandible. Mandibular BV/TV exceeds maxillary BV/TV in both donors: Mandible: M82 = 33.3% ± 9.5%, M86 = 55.7% ± 10.1%. Maxilla: M82 = 27.6% ± 6.5%, M86 = 33.2% ± 9.0%. Additionally, there is a noticeable trend where BV/TV is highest in the molars, although it is not necessarily symmetrically distributed between the two lateral sides. The BV/TV is uneven distributed along the pilot drill osteotomy. A clear trend towards lower BV/TV in the apical and higher BV/TV in the coronal part is visible.

FIGURE 4.

Left: Evaluated samples according to their anatomical location. The color scheme indicates average BV/TV of each sample ranging from 15% (yellow) to 75% (red). Right: Box plot of the BV/TV distribution along the osteotomy of the pilot drill. Samples marked with * or × correspond to the excluded samples by the experiment or the simulation, respectively.

3.2. Descriptive Statistics of Primary Stability (N = 22)

A descriptive statistical analysis was conducted on the remaining 22 samples selected for predicting UFexp. This analysis included the mean value (μ), standard deviation (SD), and the minimal (min) and maximal (max) values, all summarized in Table 2. Overall, the reduced sample size demonstrates consistent trends in BV/TV distribution compared to the whole sample set. The maxillary BV/TV remains within the same range for both donors M82 and M86 and mandibular BV/TV is about 29% smaller for M82 compared to M86. Overall, the mandible of M86 exhibits the highest mean values across the variables of BV/TV, IT, RFA, UFexp, and UFsim.

TABLE 2.

Overview of the average values of each measurement grouped by donor, maxilla and mandibula.

	M82								M86
ID	Maxilla (OK, n = 4)				Mandibula (UK, n = 5)				Maxilla (OK, n = 6)				Mandibula (UK, n = 7)
Location	μ	SD	Min	Max	μ	SD	Min	Max	μ	SD	Min	Mix	μ	SD	Min	Max
BV/TV (%)	31.3	4.0	28	37	37.2	10.7	28	52	33.2	9.0	20	44	52.1	8.9	37	60
IT (Ncm)	23.0	3.9	20	28	33.9	9.4	23	45	22.5	12.1	6.9	42	53.4	18.8	25	70
RFA (ISQ)	71.6	6.9	62	79	76.2	4.0	70	80	76.3	3.6	70	81	80.0	3.0	75	84
UFexp (N)	126.9	38.9	84	163	288.2	179.0	140	596	199.6	125.3	78	370	401.7	195.9	168	788
UFsim (N)	230.9	55.4	178	309	312.3	214.1	155	659	226.1	74.3	124	330	459.3	154.1	260	763

However, no clear pattern or trend emerges between BV/TV, IT, RFA, and UFexp (Table 2). For instance, both the average mandibular RFA of M82 and the maxillary RFA of M86 align closely at 76 ISQ. By contrast, BV/TV is 11%, IT is 34% and UFexp is 31%, higher for the mandibula of M82 than for the maxilla of M86. Conversely, when comparing the average maxillary BV/TV and IT of M86 with M82, RFA is 6% lower, and UFexp is 36% smaller for M82, highlighting the variability and complexity in the relationships between these metrics.

The best relationship can be seen between UFsim and UFexp, where UFexp is on average 17% smaller than UFsim (Table 2). The highest discrepancies between UFsim and UFexp are observed in the maxilla of M82, where the UFsim is on average 45% larger than UFexp. Conversely, the lowest difference between UFexp and UFsim is found for the mandible of M82, with a difference of about 7%. For M86, the difference in UFsim and UFexp falls within the same range, approximately 12%.

3.3. Regressions to Predict PS

Models were fitted to predict UFexp. IT, RFA and BV/TV exhibited the best fit using a power model (Figure 5). All three models exhibit a significant relationship (p ≤ 0.001) between the independent and dependent variables, with RFA showing the lowest significance. On the other hand, they reach relatively low R², ranging from 0.38 (RFA model) to 0.60 (BV/TV model), indicating low linear relation to UFexp as well high variation, which is also underlined by the elevated RMSE and CV_SD (Table 3).

FIGURE 5.

Linear regression plot of each model with the 95% confidence interval (dashed line). The x‐ and y‐axis are transformed to the log scale for the power models.

TABLE 3.

Parameter overview of the fitted models to predict PS defined by UFexp.

Model	R 2	p	RMSE (N)	CV_SD (%)	A	B
BV/TV	0.62	7.891e‐06	123.1	99.46	0.469	5.437
IT	0.56	4.221e‐05	130.4	91.76	10.76	2.425
RFA	0.36	1.966e‐03	142.3	104.3	7.54e‐10	441.4
UFsim	0.85	8.468e‐10	67.05	61.00	−48.26	0.995

In contrary to the values BV/TV, IT and RFA, UFsim demonstrated the best fit with a simple linear regression model. For visual comparison of the models with each other, the x‐ and y‐axis is given in the log space for the power models, allowing for a linear fit with the 95% confidence interval for visualization (Figure 5). The parameters of each model are summarized in Table 3.

The UFsim model (p = 8e‐10) exhibits a two to three times higher significance level compared to the other models. The same is observed for the R², the UFsim model demonstrates a substantially higher R² of 0.85 compared to the other models. Additionally, the UFsim model has the lowest RMSE and CV_SD compared to the other models, as underlined in Figure 2, where the UFsim model exhibits the least variation around the fitted line. Moreover, the RMSE of the UFsim model is on average 51%, and its CV_SD is 36% lower than those of the other models.

4. Discussion

4.1. Summary of the Study

In this study, the experimental framework developed by Voumard et al. (2019) and the simulation method introduced by Ovesy, Voumard, and Zysset (2018) for assessing PS of dental implants were successfully applied to human jaw bone. The samples showed a realistic heterogeneous BV/TV distribution and, implant planning was performed by experienced dentists. PS was objectively quantified by evaluating UFexp through mechanical testing. Using UFexp as reference, a comparative analysis was conducted between the clinically established parameters (IT and RFA) and the two newly introduced pre‐operative indicators of PS, specifically BV/TV and UFsim using pre‐operative μCT imaging.

4.2. Main Findings

4.2.1. Representative Human Mandibular and Maxillary Bone Samples

In our samples, the average BV/TV ranged from 17% to 72%, which is an extremely broad spectrum compared to previous experimental studies (Rokn et al. 2018; Voumard et al. 2019) using human vertebral bone (7%–17%) or bovine trabecular bone from the proximal tibia (13%–48%). However, it remains consistent with reported BV/TV range of the trabecular core found in the maxilla 13%–73% (Fanuscu and Chang 2004; González‐García and Monje 2013) and mandible 30%–70% (Akça et al. 2006; González‐García and Monje 2013).

4.2.2. Heterogeneity of Bone Around the Implant

Our research corroborates findings from previous studies indicating the heterogeneous character of bone present in the human mandible and maxilla (Lee, Kim, and Yun 2017; MacMillan 1926; Misch, Qu, and Bidez 1999; Parfitt 1962). Our results showed that, there were differences in BV/TV within and between the maxilla and mandible as well in the coronal, mid and apical region along the tooth. The two donors displayed a trend where BV/TV are generally higher in the mandible than in the maxilla as well higher in the coronal than in the apical region. The quality of bone varies with its anatomical position in the jaw and along the root of the tooth. Another study (Lee, Kim, and Yun 2017), described that the different orientation and intensities of external force might exist at each site, are the reason for this observation. Moreover, the maxilla exhibits significantly higher density in the anterior region compared to the middle or distal regions, as documented by Misch, Qu, and Bidez (1999), a difference also attributable to the distinct biomechanical functions of these structures, as suggested by MacMillan (1926) and Parfitt (1962). Consistent with the literature on bone density changes post‐tooth loss or extraction (Atwood 1963; Bodic et al. 2005; Carlsson and Persson 1967), our study observed a reversible decrease in BV/TV; specifically, M82, primarily edentulous, had a lower average BV/TV compared to M86. This heterogeneity in BV/TV distribution, within a single donor, along the tooth and across anatomical locations (Figure 4), underscores the complex variability inherent to bone density and its implications for dental treatment planning. It emphasizes the disparity between homogeneous synthetic bone samples, utilized in primary implant stability tests to replace real bone samples (Wu et al. 2012) and underscores the importance of using authentic bone samples for more realistic assessments.

4.2.3. BV/TV as a Key Element of PS

BV/TV is recognized as the critical determinant of bone quality (Carter and Hayes 1977), as well for trabecular (Musy et al. 2017) or cortical (Cai et al. 2019) bone strength, which is also underlined by the findings of this study. Additionally, the results of this study among others show, that BV/TV plays an important role in predicting PS of implants (Pommer et al. 2014; Voumard et al. 2019). This underscores the importance of BV/TV in both the structural integrity of bone and its suitability for successful implant integration. Classification of bone quality and its relation to oral implantology is not a new concept and has existed for more than 53 years. Since then, different bone classification system were proposed. For instance, in 1988, Misch proposed four bone density groups (D1, D2, D3, and D4) based on macroscopic bone characteristics (Misch 1990; Misch, Qu, and Bidez 1999). Furthermore, Bilhan et al. (2010) and others mentioned that elevated bone quality and presence of cortical bone is important for good PS, which is believed being influenced by implant‐related factors, such as pre‐drilling and implant geometry too.

4.2.4. IT

The insights from such studies have led to the adoption of more quantitative techniques, such as IT measurement and RFA, for more accurate assessment of PS intra‐ and post‐operatively, respectively, beside subjective bone quality classification systems. These methodologies provide a more objective basis for evaluating PS during or after implant placement and predicting the likelihood of successful osseointegration. Elevated IT is believed to generate higher clinical PS (Rabel, Köhler, and Schmidt‐Westhausen 2007; Voumard et al. 2019). This is further supported by our findings, which revealed a significant linear relationship between IT and UFexp. Nevertheless, our results showed also that the correlation between IT values and PS is marked by a relatively low R² and a high CV_SD, indicating that IT may not capture all factors influencing PS. Furthermore, peak IT value alone could be misleading the PS judgment, since it is influenced by the design of the implant system (Rabel, Köhler, and Schmidt‐Westhausen 2007), the size of the pre‐drilled osteotomy used for implant placement and seems to be influenced by the cortical layer (Bilhan et al. 2010). The latter might be the main reason for the high CV_SD and RMSE using IT to predict UFexp. Furthermore, a very narrow pre‐drilled osteotomy (a practice called under‐preparation) significantly increases the IT compared to a larger osteotomy, although this increase does not correlate with an expected rise in the UFexp or PS. In extreme cases, the excessive pressure from an overly large implant can damage or even generate a crack in the surrounding bone, leading to decreased PS. Additionally, our research underscores a notable correlation between BV/TV and PS within the human jaw, suggesting that bone quality has a more significant impact on implant stability than mechanical insertion parameters like IT. Nonetheless, when uniform conditions are maintained—specifically, when the same implant size, type, and drilling protocol are utilized—IT proves to be strongly related to PS. This demonstrates IT's utility in assessing PS under controlled circumstances, though it falls short in comparing PS across different implant systems and protocols, making a universal IT value for PS assessment impractical. This limitation highlights the necessity of maintaining consistent conditions when evaluating an implant's PS, ensuring that the assessment compensates for variations in implant geometry or drilling protocol.

4.2.5. RFA

The efficacy of RFA as a sole method for evaluating PS has been questioned by numerous studies, including our own findings. While RFA does exhibit a significant linear relationship with the UFexp, its predictive accuracy for UFexp is compromised, as indicated by high RMSE high CV_SD, and a low R². Furthermore, RFA measurements from different implant systems are not directly comparable, casting doubt on the sufficiency of RFA as a universal tool for assessing PS (Bilhan et al. 2010). A study conducted on human jaws revealed a weak correlation between RFA and removal torque, with the latter being used as a measure of PS (Brouwers et al. 2009). Moreover, the exact relationship between RFA and bone density has not yet been fully characterized (Brouwers et al. 2009; Rabel, Köhler, and Schmidt‐Westhausen 2007) and does not always show correlation with peak IT value or bone density (Daher et al. 2021; Feng et al. 2023). Simultaneously, the relationship between RFA and IT as well as RFA and BV/TV remains controversial (Açil et al. 2017). Nevertheless, follow‐up measurements, exceedingly low RFA values after one or two months seem to be a reliable indicator of increased risk of failure (Glauser et al. 2004). RFA is necessarily influenced by implant design and bone anchorage during insertion (Feng et al. 2023). Like for IT, also for RFA there are existing studies, which show a good relationship to PS (Voumard et al. 2019). Those studies typically rely on homogeneous bone samples obtained from bovine tibia, porcine ribs or human vertebrae. However, our results show that when tests are conducted on the more heterogeneous human jawbone, these values demonstrate high variability in predicting PS. Highlighting once more the variability of human bone structures found in maxillae, mandibles and its axial heterogeneity. This points to the need for a multifaceted approach to accurately gauge PS, beyond the limitations of individual metrics like bone classification systems, IT or RFA.

4.2.6. Imaging of BV/TV

BV/TV derived from μCT images can be used to identify bone quality (Lee, Kim, and Yun 2017), but such techniques cannot be used on patients due to the high radiation dose needed for their acquisition. Recently this concept becomes more interesting, since low dose cone beam CT (CBCT) systems have been widely used to 3D reconstruct the skeletal jaw for dental treatment planning (Yong et al. 2021). Evaluation of bone patterns gained from CBCT images might be used for automated bone classification and removing subjectivity in validation bone quality. Despite limitations, pre‐operative CBCT images might enable to estimate PS for treatment planning.

Furthermore, there is a significant correlation between IT and the position of cortical bone‐to‐implant contact (CBIC), surface area of CBIC and BV/TV (Feng et al. 2023). Nevertheless, BV/TV itself was not sufficient to describe the mechanical properties of bone (Lee, Kim, and Yun 2017). Specialists considered bone quality to be an important parameter for implant treatment outcome, but there is no consensus neither on what bone quality means nor on how to assess bone quality (Lindh et al. 2014). Architecture (Tb.Th—Trabecular thickness, Tb.Sp—Trabecular spacing), density (BV/TV, BS/TV—bone surface fraction), bulk (TV, BV, BS), and trabecular orientation (Rincón‐Kohli and Zysset 2009), can potentially influence the primary stability of dental implants. Such techniques could form the basis for more reliable and standardized bone quality assessment procedures that could eventually be incorporated into CBCT‐based planning software (Nicolielo et al. 2018). The understanding of the relationship between those factors to bone microarchitecture might reveal important aspects of its mechanical properties, essential for implant success (Gomes de Oliveira et al. 2012). This is potentially possible with explicit computer simulations based on μCT images (Ovesy, Indermaur, and Zysset 2019).

4.2.7. Experimental PS Assessment

Nevertheless, IT is still often used as indicator for PS to validate new techniques to assess PS. This does not make sense, given that IT as well as RFA measurements cannot be directly compared across varying implant systems and drilling protocols. BV/TV alone seem not reliable enough as PS assessment value. To overcome this problem, Voumard et al. (2019) developed an experimental approach to measure PS robust and objectively, aimed for comparing PS among different implant systems and drilling protocols. This method involves assessing the UF that can be applied to an implant before the surrounding bone structure collapses. This setup provides for the first time a standardized way to evaluate and compare the PS of various implant systems and drilling techniques on samples with varying bone quality.

4.2.8. hFE

Our simulation approach enables virtual measurement of UF, facilitating a more reliable pre‐operative prediction of PS that surpasses the constraints of conventional clinical parameters such as bone quality classification, IT, and RFA. This computer‐based UFsim integrates crucial factors omitted by standard PS prediction methods. Specifically, our simulation accounts for the size of the final drill, incorporates the specific geometry of the implant, and accurately represents the heterogeneous BV/TV distribution within the considered bone, thus offering a comprehensive measure of PS as indicated by the UF value.

The UFsim in this study yielded values that align closely with the experimental data range. This alignment is supported by a high R² = 0.85 and a linear regression model slope of 1, indicating a strong correlation with experimental outcomes. Furthermore, employing our UFsim as a PS prediction tool significantly improves accuracy, reducing the RMSE and CV_SD by half when compared to BV/TV, IT, and RFA. Such a high level of concordance highlights the effectiveness of our hFE method in pre‐operatively predicting UFexp, thereby showcasing its potential utility in pre‐operative assessment of PS for surgical planning. This demonstrates not only the accuracy of our simulation in reflecting real‐world scenarios but also its value as a tool for enhancing the predictability and success of implant procedures, offering a more reliable basis for surgical planning than currently used clinical parameters.

4.3. Limitations

The present study faces several limitations, including a relatively small sample size of 35, which was further reduced to 22 samples gained from only two elderly donors. Generally, elderly individuals tend to have lower BV/TV (Kavitha et al. 2016) than the younger population, representing a worst‐case scenario for reaching high PS and successful implant fixation. Our study successfully captured a wide range of BV/TV (17%–72%), providing a solid foundation for validation to demonstrate that the hFE model is capable of capturing PS in a broad variation of BV/TV. However, we cannot exclude that younger patients may exhibit BV/TV values beyond that range in some anatomical locations.

Only one implant geometry and drilling protocol was used as our study focusses on the primary stability conferred by the surrounding bone. Nevertheless, the assumptions underlying the hFE analysis are identical for any implant and the present study could be repeated with alternative implant sizes and shapes. In fact, the hFE analysis can be used to compare different implant designs by using the exact same bone samples, which is an exclusivity of computational models.

Our methodology did not account for any healing period following tooth extraction, samples which were manually inserted since they exceeded the limits of the protocol were excluded, and some of the bone surfaces were artificially flattened by milling, which does not perfectly mirror clinical scenarios. This has no influence on the PS prediction, as the same conditions apply to experiments and simulations. However, all plannings, preparations and implantations were conducted by two experienced dentists, marking the first instance of such measurements being performed on human jaws.

The use of virtual insertion in the hFE model, implemented through an interference fit, may underestimate the real extent of damage often seen in clinical settings, as it cannot account for damage due to shear forces. Nevertheless, this limitation appears to have a minor impact on the UFsim outcomes demonstrated in absolute values that closely approximate to the experimental data range and might be the cause of the 17% elevated UFsim compared to UFexp. The study also faced simulation convergence issues that can be caused by highly deformed elements and the lack of softening in the material model.

The simulation and BV/TV measurement relied on μCT images, which introduces a disparity from actual pre‐operative conditions by representing a partially unrealistic scenario. Nevertheless, for the purposes of the homogenized simulation approach, the μCT was coarsened to the size of the hFE mesh. This can be seen as an averaging of the μCT resolution to the resolution of CBCT image and shows that the hFE method may also be used for images with lower resolution, such as CBCT images.

5. Conclusion

The emergence and adoption of the immediate implant placement strategy, followed by immediate loading, has attracted a greater interest in pre‐operative assessment of PS. However, currently there is no reliable method to accomplish this pre‐operatively. The qualitative state of care methods are not convincing, especially when tested in heterogeneous jaw bone (Abrahamsson, Linder, and Lang 2009; Manresa, Bosch, and Echeverría 2014). An objective and quantitative measurement method of PS was applied to human jaws and compared with current clinical intra‐ and postoperative methods. It shows that these results differ from results gained with homogenous bone samples (Voumard et al. 2019) and suggests that the heterogeneous characteristics of human jaw bone have a great impact on IT and RFA values. Although the data set is too limited to develop a robust predictive model for PS, it provides valuable insights into the expected accuracy and variability of specific PS indicators, underscoring the potential for pre‐operative evaluation of PS using simulation‐based methods. Lastly, the UFsim derived from hFE serves as a more accurate predictor of PS than other assessed variables, such as pre‐operative BV/TV, IT measured during or RFA measured after implantation. Once developed for a specific implant system, such hFE models could be integrated into a digital planning software. This integration would enable automatic estimation of PS based on the patient's bone condition, given by the CBCT image and implant position.

Author Contributions

Patrik Wili: writing – original draft, visualization, data curation, validation, methodology, conceptualization, investigation, software. Cedric Rauber: validation, writing – review and editing, data curation, visualization. Amal Saade: writing – review and editing, project administration. Salomé Bliggenstorfer: writing – review and editing, investigation. Valentina Ramirez‐Garmendia: writing – review and editing, investigation. Ramon Schweizer: project administration, writing – review and editing. Ainara Irastorza‐Landa: project administration, writing – review and editing, conceptualization. Vivianne Chappuis: resources, writing – review and editing, supervision. Philippe Zysset: supervision, writing – review and editing, resources, conceptualization, methodology, funding acquisition.

Ethics Statement

The human jaws were obtained from donors to the Institute of Anatomy of the University of Bern with informed consent.

Conflicts of Interest

The authors declare no conflicts of interest.

Data Availability Statement

The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions.