Journal of Biomechanics 47 (2014) 3562–3568

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Ultrasonic evaluation of dental implant osseointegration Romain Vayron a, Emmanuel Soffer b, Fani Anagnostou b, Guillaume Haïat a,n a b

CNRS, Laboratoire Modélisation et Simulation MultiEchelle, MSME UMR CNRS 8208, 61, Avenue du Général de Gaulle, 94010 Créteil, Cedex, France CNRS, Université Paris 7, Laboratoire de Biomécanique Biomatériaux Ostéo-Articulaires, UMR CNRS 7052, Paris, France

art ic l e i nf o

a b s t r a c t

Article history: Accepted 13 July 2014

Dental implants are widely used for oral rehabilitation. However, there remain risks of failure which are difficult to anticipate and depend on the implant osseointegration. The objective of this in vivo study is to determine the variation of the echographic ultrasonic response of a dental implant to bone healing around the implant interface. Twenty one dental implants were inserted in the femur of seven New Zealand white rabbits. Two animals were sacrificed after a healing duration of two weeks, three animals after six weeks and six animals after eleven weeks. The 10 MHz ultrasonic response of the implant was measured just after the implantation using a dedicated device positioned at the emerging surface of each dental implant. The measurements were realized again before the sacrifice with the same device. An indicator I~ was derived based on the amplitude of the rf signal obtained for each configuration. The bone–Implant Contact (BIC) ratio was determined by histological analyses. The average value of the relative variation of the indicator I~ obtained after initial surgery and after the corresponding healing period varies between 7% and 40%. A Kruskal–Wallis test (po 0.01) revealed a significant decrease of the value of the indicator I~ as function of healing time. The indicator I~ was significantly correlated (R² ¼0.45) with the BIC ratio. The results show that the ultrasonic response of a dental implant varies significantly as a function of healing time, which paves the way for the development of a new quantitative ultrasound (QUS) method in oral implantology. & 2014 Elsevier Ltd. All rights reserved.

Keywords: Dental implant Animal model Osseointegration Quantitative ultrasound

1. Introduction Dental implants (Albrektsson et al., 1988) are widely used in the clinic and have allowed considerable progresses in oral and maxillofacial surgery. However, implant failures, which may have dramatic consequences, still occur and remain difficult to anticipate. The implant stability, which is determinant for the implant success (Haiat et al., 2014), is determined by the quantity and biomechanical quality of bone tissue around the implant (Franchi et al., 2007). Despite the complexity of the phenomena involved in the osseointegration process (a phenomenon of a multi-time and multiscale nature (Mathieu et al., 2014), there is an important lack of standardization of surgical procedures used in dental implantology, in particular in the choice of the duration between implant insertion and loading with the prosthesis, which is determined empirically by the surgeons and may vary from 0 up to 6 months (Raghavendra et al., 2005). A compromise should be found in a patient specific manner between (i) an early (or even

n

Corresponding author. Tel.: þ 33 1 45 17 14 41; fax: þ33 1 45 17 14 33. E-mail address: [email protected] (G. Haïat).

http://dx.doi.org/10.1016/j.jbiomech.2014.07.011 0021-9290/& 2014 Elsevier Ltd. All rights reserved.

sometimes immediate) implant loading in order to stimulate bone remodeling phenomena around the implant via mechanical solicitations and (ii) a late implant loading in order to avoid prejudicial deterioration of the bone–implant interface (Serra et al., 2008). Meanwhile, shortening the time of implant loading with the prosthesis has become a challenge in recent implant developments (Nergiz et al., 2009; Neugebauer et al., 2009) because it allows to (i) minimize the time of social disfigurement, improving as soon as possible function, comfort and esthetics (Dierens et al., 2009), (ii) limit the treatment's cost by avoiding provisional prosthesis, which are most of the time removable so uncomfortable and unesthetic and (iii) minimize soft and hard tissues losses (Esposito et al., 2013; Guarnieri et al., 2013). As a consequence, accurate measurements of implant biomechanical stability are of interest (Atsumi et al., 2007) since they could be used to improve the surgical strategy by adapting the choice of the healing period to each patient. Assessing the implant stability is a difficult multiscale problem due to the complex heterogeneous nature of bone tissue and to remodeling phenomena (Wolff, 1892; Frost, 2003). Empirical methods based on palpation are still often used by dental surgeons to determine when the implant should be loaded because it remains difficult to monitor bone healing in vivo

R. Vayron et al. / Journal of Biomechanics 47 (2014) 3562–3568

(Serra et al., 2008). Accurate noninvasive quantitative methods capable of assessing the implant stability are required to guide the surgeons and hence reduce the risk of implant failure. Different approaches have been suggested to assess the implant stability in vivo. The resolution of clinical X-ray and magnetic resonance imaging (MRI) based techniques around the implant interface is limited due to distortion effects related to the presence of titanium (Shalabi et al., 2007; Gill and Shellock, 2012). X-ray and MRI based methods cannot be used per operatively to retrieve information on the bone–implant mechanical contact conditions, which plays an essential part in the implant stability (Wang et al., 2010; Arndt et al., 2012; Souffrant et al., 2012; Mathieu et al., 2014). As a consequence, biomechanical methods have been developed, their main advantage consisting in the absence of ionizing radiation, inexpensiveness, portability and noninvasiveness. The Periotest (Bensheim, Germany) is a percussion test method (Schulte et al., 1983; Van Scotter and Wilson, 1991), but its sensitivity to striking height and handpiece angulation constitute a strong limitation (Meredith et al., 1998). The most commonly used biomechanical technique is the resonance frequency analysis (RFA) (Valderrama et al., 2007), which consists in measuring (Meredith et al., 1996) the first bending resonance frequency. The RFA technique allows to assess the implant anchorage depth into bone (Meredith et al., 1997) and the stiffness of the bone–implant structure (Pattijn et al., 2007). However, the RFA cannot be used to identify directly the bone–implant interface characteristics (Aparicio et al., 2006). No correlation between the Implant Stability Quotient (ISQ) and the Bone–Implant Contact (BIC) ratio nor between ISQ and cortical thickness has been evidenced (Seong et al., 2009). The orientation and fixation of the transducer have an important effect on ISQ values (Pattijn et al., 2007). The use of quantitative ultrasound (QUS) has been suggested as an alternative method to assess the implant biomechanical stability in de Almeida et al. (2007), a work where the authors used an aluminum screw inserted in a metallic medium. The principle of the measurement relies on the dependence of the ultrasonic propagation within the implant on its boundary conditions, which are related to the bone–implant interface biomechanical properties (Mathieu et al., 2011a, 2011b, 2011c). An in vitro preliminary study was carried out by our group using implant with a simplistic geometry and consisting in titanium cylinder shaped implants (mimicking real dental implants) inserted in bone tissue. The results showed the sensitivity of the ultrasound response of the implant to the quantity of bone in contact with the implant (Mathieu et al., 2011b). Numerical simulations (Mathieu et al. 2011a) helped to understand the

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experimental results, thus quantifying the sensitivity of the technique. The sensitivity of the echographic response of a planar bone–implant interface to healing time was assessed using coinshaped implant models (Mathieu et al., 2012). More recently, significant variations of the ultrasonic response of dental implants embedded in a tricalcium silicate-based cement was shown to occur when the implant is subjected to fatigue loading (Vayron et al., 2013). Another in vitro study proved the potentiality of QUS to assess the implant primary stability (Vayron et al., in press). However, the sensitivity of the QUS response of a dental implant to healing time remains unknown and could be interesting because the ultrasonic device could be used as a decision support system in order to help the surgeon estimate the time point for implant load bearing in a patient specific manner. The aim of the present study is to investigate the sensitivity of the ultrasonic response of a dental implant to healing time. To do so, titanium dental implants were inserted in the femur of New Zealand White rabbits and different healing times (2, 6 and 11 weeks) were considered. The dependence of the ultrasonic response of the implant to healing time was investigated and compared to the BIC ratio measured with histology.

2. Material and methods 2.1. Animals Eleven New Zealand White male rabbits (Charles River, L’Arbresle, France) were used in this study (5-month-old, average weight 3.750 kg). Animals were housed in a metal hutch in an environment in accordance with the European guidelines for care and use of laboratory animals. Temperature was maintained at 19 1C and humidity at 55%. Artificial cyclic lightening and air conditioning systems were used in the animal housing facility. Commercial food and water were provided ad libitum.

2.2. Dental implants Twenty one grade 5, Ti–Al6V4 titanium alloy, 10 mm long and 4.2 mm diameter conical dental implants were used in the present study. The implants were manufactured by Implant Diffusion International (Montreuil, France) under the reference IdCam 1042.

2.3. Surgical procedure Each dental implant was placed in each femur of the rabbits following the procedure described by Pearce et al. (2007), as shown in Fig. 1A. A conical cavity (10mm deep and 4.0-mm wide) was created in the lateral condyle in a stepwise fashion, using color-coded, 10-mm-length surgical drills (1.5–4.0 mm diameter; Implants Diffusion International, Paris, France). These cavities were thoroughly rinsed with isotonic saline to remove bone fragments prior to the insertion of the titanium implants.

Dental Implant

Ultrasonic Transducer

Healing Abtument

Bone Tissue Soft Tissue Fig. 1. (A) Insertion of the implant during initial surgery and (B) configuration of the in vivo ultrasonic measurement.

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R. Vayron et al. / Journal of Biomechanics 47 (2014) 3562–3568

Two (respectively three and six) rabbits were sacrificed at 2 weeks (respectively 6 and 11) after initial implant surgery. The aforementioned duration corresponds to the healing time considered for each implant and was chosen based on previous studies considering the same surgical procedure (Pearce et al., 2007; Soffer et al., 2010). Note that for one rabbit (2 weeks of healing time), only one implant could be inserted due to a lack of primary stability for the other implant, leading to the removal of the implant during the initial surgery.

2.4. Ultrasonic device The ultrasonic device is composed of a 5 mm diameter planar ultrasonic contact monoelement transducer (V129SM, Panametrics, Waltham, MA, USA) generating a broadband ultrasonic pulse propagating perpendicularly to its active surface. The ultrasonic probe is used in echographic mode and its center frequency is equal to 10 MHz, with a frequency bandwidth approximately equal to 6–14 MHz. The probe is placed in contact with the circular top surface of the healing abutment emerging from the femur. The healing abutment used in this study is made of the same Ti–Al6V4 titanium alloy as the one used for the dental implant. A commercial healing abutment manufactured by Implant Diffusion International (Montreuil, France) was used. Its upper surface was machined in order to obtain a planar interface, which improves the contact conditions between the healing abutment and the transducer. The same healing abutment was used for all experiments. Note that the healing abutment should be made with the same material as the one used for the implant in order to allow optimal energy transmission from the abutment into the implant. Ultrasonic coupling gel is placed on the active surface of the transducer in order to prevent the presence of air bubbles, which may disrupt ultrasonic measurements (see Fig. 1). The ultrasonic probe is linked to an analyzer (model 5052 UA, Panametrics, Waltham, MA, USA) via a coaxial cable. A 12-bit acquisition card (Spectrum M3i.3242, Grosshansdorf, Germany) records the radiofrequency (rf) signal obtained from the analyzer with a sampling frequency equal to 100 MHz (see Fig. 2).

2.5. Experimental protocol First, the ultrasonic response of the implant was measured just after the implant insertion during the initial surgery (at a time denoted t0 in what follows). The second measurement was realized just before the rabbits were euthanized, i.e. after 2, 6, 11 weeks of healing time (at a time denoted t þ in what follows). Each ultrasonic measurement was carried out 10 times in order to assess the reproducibility of the measurements. The comparison of the ultrasonic response of the implant (i) at time t0 and t þ and (ii) for different healing durations allows to estimate the effect of healing time on the ultrasonic response of the implant.

2.6. Signal processing and analysis Based on the analysis of all rf signals corresponding to the ultrasonic response of the implant, a duration equal to 60 ms was chosen for the time window used in the signal processing method, which corresponds to a compromise between a sufficient duration in order to obtain valuable information and the requirement of a sufficient signal to noise ratio for all rf signals. Based on the method developed in (Mathieu et al. 2011b, Vayron et al., in press, Vayron et al., 2013), an indicator I~ was devised to quantitatively estimate the average amplitude of the signal before 60 ms. To do so, the first step consist in determining the averaged amplitude I of the envelop S(t) of the rf signal s(t), which was determined using the absolute value of the Hilbert transform as follows: N

I ¼ ∑ SðiT s Þ;

The aforementioned signal processing method was carried out for all implants and for t0 and t þ . The minimum and maximum values of I (respectively noted Imin and Imax) obtained for all measurements was determined. Then, the indicator I~ , corresponding to a percentage, was defined as follows: 100ðI  I min Þ : I~ ¼ ðI max  Imin Þ

ð2Þ

A value of I~ equal to 0% (respectively 100%) corresponds to the measurement with the lowest (respectively highest) signal amplitude. The aforementioned definition of the indicator I~ constitutes a simple way of obtaining a score proportional to the signal amplitude comprised between 0% and 100% for all measurements realized with all implants at times t0 and t þ . 2.7. Histology After the ultrasonic measurements, the samples were prepared for histological analysis. Due to problems encountered during the resin hardening process, only 13 samples could be analyzed with histology (3 samples with 2 weeks of healing time, 3 samples with 6 weeks of healing time and 7 samples with 11 weeks of healing time). A procedure described in detail by Soffer et al. (2006) and Chevallier et al. (2009) for nondecalcified histology was used. Histological images were analyzed by classical microscopy in order to evaluate the percentage of the implant surface in intimate contact with mineralized bone tissue, which was assessed manually. Moreover, the average and standard deviation values of the BIC ratio were calculated over one section of the samples. 2.8. Statistical analysis A χ² test was realized in order to check the nature of the distribution of the data corresponding to the values of the indicator I~ . Moreover, a Kruskal–Wallis test was performed to evaluate the effect of the corresponding healing time on the indicator I~ . Tukey–Kramer tests were performed to evaluate the difference between the values of I~ obtained with different healing times (2, 6 and 11 weeks). Analysis of variance analyses (ANOVA) and Tukey–Kramer tests were performed to evaluate the difference between the values of BIC ratio obtained with different healing times (2, 6 and 11 weeks).

3. Results Fig. 3 shows two superimposed representative rf signals obtained the day of the implantation (black curve) and after 11 weeks of healing time (gray curve). As shown in Fig. 3, both rf signals exhibit a decay of their amplitudes as a function of time. Moreover, Fig. 3 shows that the amplitude of the rf signal obtained at time t þ is lower than that obtained at time t0. This figure is obtained for the rabbit #8 (right leg). The corresponding average and standard deviation values of I~ at time t0 are equal to 53.36715.48%. The average and standard deviation values of I~ at time t þ are equal to 16.737 9.79%. Table 1 shows the results obtained for the mean value and standard deviation of I~ at time t0 and t þ for all implants and the

ð1Þ

i¼1

where N ¼6000 is chosen to consider the entire rf signal and Ts ¼0.01 ms corresponds to the sampling period.

Ultrasonic Probe Healing Abutment

PC + PCI Transient Recorder Analyser

Dental Titanium Implant BoneTissue

Indicator Fig. 2. Schematic description of the in vivo ultrasonic experimental set-up. The titanium dental implant is inserted in the femur of New Zealand White male rabbits.

Fig. 3. Time gated rf signals obtained the day of the implantation (black line) and after 11 weeks of healing time (gray line).

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Table 1 Average and standard deviation of the indicator I~, difference and ANOVA tests between t0 and t þ for each rabbit and each leg (RL for right leg and LL for left leg). Healing time

2 Weeks

Rabbit number

1 2

6 Weeks

3 4 5

11 Weeks

6 7 8 9 10 11

Implant location

Average7 standard deviation of I~ (%) at t0

Average7 standard deviation of I~ (%) at t þ

Average variation of I~

Average of variation for the healing time

ANOVA p-Value

F-statistic

7.06

 10

6.07  10 7.41  10  2 6.00  10  4

153.79 3.59 17.07

RL LL RL

86.767 5.82 26.677 6.15 34.29 7 5.68

50.79 7 6.72 31.5 7 5.21 44.247 5.07

35.97  4.83  9.95

RL LL RL LL RL LL

79.337 16.74 59.067 11.02 70.767 9.04 38.79 7 14.37 70.117 7.92 39.767 12.32

17.2 7 12.10 9.317 7.35 34.89 7 16.93 58.577 12.41 35.517 6.26 7.82 7 4.00

62.13 49.75 35.87  19.48 34.6 31.94

32.47

5.57  10  7 5.43  10  10 4.83  10  4 4.21  10  4 2.57  10  9 3.53  10  7

74.52 172.83 25.35 19.61 117.39 60.78

RL LL RL LL RL LL RL LL RL LL RL LL

77.247 15.35 85.917 15.32 50.487 10.57 47.94 7 14.67 53.36 7 15.48 80.25 7 10.76 35.88 7 6.22 72.667 4.97 48.167 10.32 86.217 9.08 36.337 11.74 46.83 7 8.09

32.3 7 6.99 7.81 7 4.02 11.687 7.65 177 7.95 16.737 9.79 28.337 13.66 24.47 4.83 21.05 7 9.20 34.08 7 8.48 23.517 4.60 8.777 7.20 15.88 7 7.49

44.94 78.1 38.8 30.94 36.63 51.92 11.48 51.61 14.08 62.7 27.56 30.95

39.96

3.47  10  7 6.73  10  12 2.27  10  8 1.09  10  5 9.10  10  6 1.63  10  7 2.18  10  4 6.65  10  12 4.6  10  3 1.51  10  13 5.82  10  6 5.38  10  8

68.77 243.14 88.50 35.01 38.84 77.02 21.23 243.48 10.66 379.69 40.02 78.85

three healing durations. For all implants except for one implant with a healing time equal to 2 weeks, the value of I~ obtained at t0 is significantly different than that obtained at time t þ . The χ² test realized considering all data pooled shows that the data are normally distributed (p ¼1.6  10  5). When pooling all data at t0 and t þ together, the Kruskal–Wallis test shows a significant effect of healing time on the indicator I~ (p ¼ 8  10  52, F¼110). When considering the three implants with a healing time equal to 2 weeks, the value of I~ increased significantly for one implant between t0 and t þ , while it decreased significantly for another implant and no significant variation was obtained for the last implant. When considering implants with healing times of 6 weeks, the values of I~ obtained at time t0 were significantly higher than that obtained at time t þ for all implants except for one implant. For all implants with healing times of 13 weeks, the values of I~ obtained at time t0 were significantly higher than that obtained at time t þ . A Tukey–Kramer analysis (see Table 2) revealed that the values of the indicator I~ obtained for samples with 2 weeks of healing time were significantly different from those obtained for 6 and 11 weeks of healing time. Moreover, the values obtained for the indicator I~ are significantly different for the samples with 6 weeks of healing time compared with the samples with 11 weeks of healing time. Fig. 4 shows three representative images of the histological analysis obtained at the three healing times considered (2, 6 and 11 weeks). These images were used to estimate the BIC ratio. At two weeks of healing time, the average BIC ratio is equal to 30.4 72.8%. At 6 weeks of healing time (11 weeks, respectively), the BIC ratio is equal to 51.371.8% (respectively 50.7 79.4%). The ANOVA test of the 13 implants considered showed a significant effect of healing time on the BIC ratio (p-value ¼ 1.61  10  2 and F-statistic ¼6.42). A Tukey–Kramer test revealed that the obtained values of the BIC ratio for samples at 2 weeks of healing time are significantly different from those obtained for 6 and 11 weeks of healing time. However, the results are not statistically different for samples with six and 11 weeks of healing time. Fig. 5 shows the variation of the indicator I~ as function of the BIC ratio, together

Table 2 Mean deviations and 95% confidence intervals for indicator I between 2, 6 and 11 weeks of healing time. Ĩ (arbitrary unit) gaps between different healing time Mean

2 vs 6 Weeks of healing time 2 vs 11 Weeks of healing time 6 vs 11 Weeks of healing time

Inferior boundary of the 95% confidence interval for the true mean

Superior boundary of the 95% confidence interval for the true mean

15.56

7.58

23.53

22.13

15.00

29.26

6.58

0.82

12.33

with a linear regression analysis. The results show that the indicator I~ decreases significantly as a function of the BIC ratio (correlation coefficient R²¼ 0.45).

4. Discussion To the best of our knowledge, this study constitutes the first attempt to investigate the dependence of the ultrasonic response of a dental implant as a function of healing time. The average decrease of the indicator I~ as a function of healing time obtained at 6 and 11 weeks can be explained by the combination of two phenomena. First, the BIC ratio is known to increase as a function of healing time with the present animal model (Seong et al., 2011; Aboushelib et al., 2013; Kang et al., 2013), which is confirmed by the results obtained herein with histology. When the bone–implant interface is debonded (i.e. when the implant is in contact with fibrous tissue or liquid), a stronger gap of mechanical properties is obtained at the implant interface, thus explaining that the transmission coefficient at the implant external interface is lower (Mathieu et al., 2012; Vayron et al., in press, 2014) than when bone tissue is in intimate contact

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Fig. 4. Histological images for (a) 2, (b) 6 and (c) 11 weeks of healing duration. The implant corresponds to the black regions and mineralized bone tissue to the gray part of the image. The BIC ratio is equal to 30.1% at 2 weeks, 49.6% at 6 weeks and 58.2% at 11 weeks of healing time.

60

y= -0.77x+ 60.08 R² = 0.45

Indicator I

~

50 40 30 20 10 0 20

30

50

40

60

70

BIC% Fig. 5. Variation of the indicator I~ as function of the BIC ratio. The triangles represent the samples with 2 weeks of healing time, the squares represent the samples with 6 weeks of healing time and the circles represent the samples with 11 weeks of healing time.

with the implant. Therefore, energy leakage of the ultrasonic wave out of the implant (which acts as a wave guide; Mathieu et al., 2011a, 2011b) is lower when the bone–implant interface is debonded, which explains the slower decrease of the ultrasonic energy as a function of time recorded by the sensor. Second, the biomechanical properties of newly formed bone tissue around implants (such as the apparent Young's modulus; Vayron et al., 2012, the hardness; Vayron et al., 2011, the ultrasonic velocity; Mathieu et al., 2011c and mass density; Vayron et al., 2014) are known to increase as a function of healing time, which may be explained by the bone tissue remodeling and progressive mineralization. This increase of mechanical properties as a function of healing time induces a lower impedance gap between the implant and the surrounding bone tissue, leading in turn to higher ultrasound energy leakage. In summary, the coupling of the increase of the BIC ratio and of bone mechanical properties

leads to a cumulative effect inducing a decrease of the reflection coefficient at the bone–implant interface as a function of time and thus to a significant decrease of the indicator I~ vs healing time. For two weeks of healing duration, the results shown in Table 1 indicate that the average value of the indicator I~ increases for one sample, decreases for another sample and does not vary significantly for the other sample. These apparently contradictory results may be compared with previous clinical studies obtained with the Osstell device, showing that a decrease of the ISQ was obtained during the first 4 weeks after initial surgery (Glauser et al., 2004; Balshi et al., 2005; Huwiler et al., 2007; Sohn et al., 2010). However, additional implants should be considered for two weeks of healing time. The histological analyses showed a significant increase of the BIC ratio according to healing time in agreement with the literature (Biasotto et al., 2005; Park et al., 2008; Blanco et al., 2011). Several limitations may explain (i) the significant but relatively weak correlation between BIC ratio and I~ and (ii) the absence of significant difference for the BIC ratio obtained between 6 and 13 weeks of healing time. First, only 13 samples were analyzed and more samples should be analyzed in the future. Second, histology only allows the estimation of bone tissue in contact with the implant in a given plane while the real data of interest should be assessed in 3D. Third, the implant ultrasonic response does not only depend on the BIC ratio but also on the mechanical properties of bone tissue in direct contact with the implant, which cannot be estimated using histology. Several works need to be realized to comfort our approach. First, the understanding of propagation phenomena in the bone– implant system should be achieved using numerical simulations. Second, the reproducibility of the measurements should be improved using a fully integrated transducer allowing to reduce positioning errors of the transducer relatively to the implant axis. Third, the measurements should be realized in vivo for different

R. Vayron et al. / Journal of Biomechanics 47 (2014) 3562–3568

healing durations for the same implant in order to determine the variation of the indicator as a function of healing time for one given implant. However, we choose to realize the measurements only before the sacrifice in order not to disrupt the osseointegration phenomena. Fourth, this study should be conducted on a large animal model and in oral environment such as in beagle dog. Fifth, the use of Osstell should be conducted in parallel to compare both approaches. Sixth, the relatively low number of rabbits used in the present study constitutes a limitation. We decided to consider more rabbits for higher consolidation points in order to maximize bone healing and to increase the chances of success of the study.

Conflict of interest statement There is no conflict of interest.

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Ultrasonic evaluation of dental implant osseointegration.

Dental implants are widely used for oral rehabilitation. However, there remain risks of failure which are difficult to anticipate and depend on the im...
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