Finite element simulation of ultrasonic wave propagation in a dental implant for biomechanical stability assessment

Overview of Ultrasound in Dentistry for Advancing Research Methodology and Patient Care Quality with Emphasis on Periodontal/Peri-implant Applications

BACKGROUND

Ultrasound is a non-invasive, cross-sectional imaging technique emerging in dentistry. It is an adjunct tool for diagnosing pathologies in the oral cavity that overcomes some limitations of current methodologies, including direct clinical examination, 2D radiographs, and cone beam computerized tomography. Increasing demand for soft tissue imaging has led to continuous improvements on transducer miniaturization and spatial resolution. The aims of this study are (1) to create a comprehensive overview of the current literature of ultrasonic imaging relating to dentistry, and (2) to provide a view onto investigations with immediate, intermediate, and long-term impact in periodontology and implantology.

METHODS

A rapid literature review was performed using two broad searches conducted in the PubMed database, yielding 576 and 757 citations, respectively. A rating was established within a citation software (EndNote) using a 5-star classification. The broad search with 757 citations allowed for high sensitivity whereas the subsequent rating added specificity.

RESULTS

A critical review of the clinical applications of ultrasound in dentistry was provided with a focus on applications in periodontology and implantology. The role of ultrasound as a developing dental diagnostic tool was reviewed. Specific uses such as soft and hard tissue imaging, longitudinal monitoring, as well as anatomic and physiological evaluation were discussed.

CONCLUSIONS

Future efforts should be directed towards the transition of ultrasonography from a research tool to a clinical tool. Moreover, a dedicated effort is needed to introduce ultrasonic imaging to dental education and the dental community to ultimately improve the quality of patient care.

Assessment of dental implant stability using resonance frequency analysis and quantitative ultrasound methods

Purpose Quantitative ultrasound (QUS) and resonance frequency analyses (RFA) are promising methods to assess the stability of dental implants. The aim of this in vivo preclinical study is to compare the results obtained with these two techniques with the bone-implant contact (BIC) ratio, which is the gold standard to assess dental implant stability.Methods Twenty-two identical dental implants were inserted in the tibia and femur of 12 rabbits, which were sacrificed after different healing durations (0, 4, 8 and 13 weeks). For each implant, the ultrasonic indicator (UI) and the implant stability quotient (ISQ) were retrieved just before the animal sacrifice using the QUS and RFA techniques, respectively. Histomorphometric analyses were carried out to estimate the bone-implant contact ratio.Results UI values were found to be better correlated to BIC values (R²=0.47) compared to ISQ values (R²=0.39 for measurements in one direction and R²=0.18 for the other direction), which were shown to be dependent on the direction of measurements. Errors realized on the UI were around 3.3 times lower to the ones realized on the ISQ.Conclusions QUS provide a better estimation of dental implant stability compared to RFA. This study paves the way for the future clinical development of a medical device aiming at assessing dental implant stability in a patient-specific manner. Clinical studies should confirm these results in the future.

A finite element model for evaluating the effectiveness of the Advanced System for Implant Stability Testing (ASIST)

The Advanced system for Implant Stability Testing (ASIST) was developed to evaluate the stability of osseointegrated implants. ASIST matches the physical response with an analytical model's prediction to determine the stiffness of the bone implant interface (BII) which is then used to calculate the ASIST Stability Coefficient (ASC). In this investigation, a 3D dynamic finite element (FE) model of the ASIST experimental impact technique for bone anchored hearing aids was created. The objectives were to evaluate the analytical model's ability to capture the behavior of the implant system and to assess its effectiveness in minimising the effects of the system's geometry on the ASC scores. The models were developed on ABAQUS®, they consisted of the implant, abutment, screw, base support and impact rod. The models relied on frictional contact definitions between the system's components. The simplified "three-part" model had the implant, abutment and screw merged as one part while the "five-part" model treated them as separate components. Different interface conditions were simulated (friction coefficient range: 0-0.9) for three abutment lengths (6, 9 and 12 mm). The simulation output was the average nodal acceleration response of the rod, which was imported to the custom ASIST program in Mathematica® to obtain the ASC scores. The overall quality of the curve fits indicate that the analytical model is capable of representing the system's behavior. Moreover,ASC scores provide a reliable assessment of implant stability as they are sensitive to interface conditions and are minimally influenced by the system's geometry.

Ultrasonic assessment of osseointegration phenomena at the bone-implant interface using convolutional neural network

Although endosseous implants are widely used in the clinic, failures still occur and their clinical performance depends on the quality of osseointegration phenomena at the bone-implant interface (BII), which are given by bone ingrowth around the BII. The difficulties in ensuring clinical reliability come from the complex nature of this interphase related to the implant surface roughness and the presence of a soft tissue layer (non-mineralized bone tissue) at the BII. The aim of the present study is to develop a method to assess the soft tissue thickness at the BII based on the analysis of its ultrasonic response using a simulation based-convolution neural network (CNN). A large-annotated dataset was constructed using a two-dimensional finite element model in the frequency domain considering a sinusoidal description of the BII. The proposed network was trained by the synthesized ultrasound responses and was validated by a separate dataset from the training process. The linear correlation between actual and estimated soft tissue thickness shows excellent R² values equal to 99.52% and 99.65% and a narrow limit of agreement corresponding to [ -2.56, 4.32 μm] and [ -15.75, 30.35 μm] of microscopic and macroscopic roughness, respectively, supporting the reliability of the proposed assessment of osseointegration phenomena.

Quantitative ultrasound assessment of the influence of roughness and healing time on osseointegration phenomena

The evolution of bone tissue quantity and quality in contact with the surface of orthopedic and dental implants is a strong determinant of the surgical outcome but remains difficult to be assessed quantitatively. The aim of this study was to investigate the performance of a quantitative ultrasound (QUS) method to measure bone-implant interface (BII) properties. A dedicated animal model considering coin-shaped titanium implants with two levels of surface roughness (smooth, S_a = 0.49 µm and rough, S_a = 3.5 µm) allowed to work with a reproducible geometry and a planar interface. The implants were inserted in rabbit femurs and tibiae for 7 or 13 weeks. The ultrasonic response of the BII was measured ex vivo, leading to the determination of the 2-D spatial variations of bone in contact with the implant surface. Histological analysis was carried out to determine the bone-implant contact (BIC) ratio. The amplitude of the echo was significantly higher after 7 weeks of healing time compared to 13 weeks, for both smooth (p < 0.01) and rough (p < 0.05) implants. A negative correlation (R = − 0.63) was obtained between the ultrasonic response and the BIC. This QUS technique is more sensitive to changes of BII morphology compared to histological analyses.

Analytical modeling of the interaction of an ultrasonic wave with a rough bone-implant interface

Quantitative ultrasound can be used to characterize the evolution of the bone-implant interface (BII), which is a complex system due to the implant surface roughness and to partial contact between bone and the implant. The determination of the constitutive law of the BII would be of interest in the context of implant acoustical modeling in order to take into account the imperfect characteristics of the BII. The aim of the present study is to propose an analytical effective model describing the interaction between an ultrasonic wave and a rough BII. To do so, a spring model was considered to determine the equivalent stiffness K of the BII. The stiffness contributions related (i) to the partial contact between the bone and the implant and (ii) to the presence of soft tissues at the BII during the process of osseointegration were assessed independently. K was found to be comprised between 10¹³ and 10¹⁷ N/m³ depending on the roughness and osseointegration of the BII. Analytical values of the reflection and transmission coefficients at the BII were derived from values of K. A good agreement with numerical results obtained through finite element simulation was obtained. This model may be used for future finite element bone-implant models to replace the BII conditions.

Contribution to COVID-19 spread modelling: a physical phenomenological dissipative formalism

In this study, we propose an evolution law of COVID-19 transmission. An infinite ordered lattice represents population. Epidemic evolution is represented by a wave-like free spread starting from a first case as an epicentre. Free energy of the virus on a given day is defined equal to the natural logarithm of active infected cases number. We postulate a form of free energy built using thermodynamics of irreversible processes in analogy to isotherm wave propagation in solids and non-local elastic damage behaviour of materials. The proposed expression of daily free energy rate leads to dissipation of propagation introducing a parameter quantifying measures taking by governments to restrict transmission. Entropy daily rate representing disorder produced in the initial system is also explicitly defined. In this context, a simple law of evolution of infected cases as function of time is given in an iterative form. The model predicts different effects on peak of infected cases I_max and epidemic period, including effects of population size N, effects of measures taking to restrict spread, effects of population density and effect of a parameter T similar to absolute temperature in thermodynamics. Different effects are presented first. The model is then applied to epidemic spread in Tunisia and compared with data registered since the report of the first confirmed case on March 2, 2020. It is shown that the low epidemic size in Tunisia is essentially due to a low population density and relatively strict restriction measures including lockdown and quarantine.

Ultrasonic Propagation in a Dental Implant

Ultrasound techniques can be used to characterize and stimulate dental implant osseointegration. However, the interaction between an ultrasonic wave and the implant-bone interface (IBI) remains unclear. This study-combining experimental and numerical approaches-investigates the propagation of an ultrasonic wave in a dental implant by assessing the amplitude of the displacements along the implant axis. An ultrasonic transducer was excited in a transient regime at 10 MHz. Laser interferometric techniques were employed to measure the amplitude of the displacements, which varied 3.2-8.9 nm along the implant axis. The results demonstrated the propagation of a guided wave mode along the implant axis. The velocity of the first arriving signal was equal to 2110 m.s^-1, with frequency components lower than 1 MHz, in agreement with numerical results. Investigating guided wave propagation in dental implants should contribute to improved methods for the characterization and stimulation of the IBI.

Modeling ultrasonic wave propagation in a dental implant - Bone system

The evolution of the bone-implant interface reflects the implant osseointegration and bond strength, thereby determining the overall implant stability in the jawbone. Quantitative ultrasound represents a promising alternative technique to characterize the interfacial integrity, precisely due to the fact that those waves propagate essentially along the bone-implant interface, and are therefore influenced by its state. This study reports a numerical investigation of ultrasonic wave propagation for a commercial implant-jawbone system in which the thickness and mechanical properties of the interfacial layer (corresponding to the interphase) are systematically varied through the application of a rule of mixtures, in order to mimic the evolution from a dominantly soft tissue - like medium up to a fully healed bone. A simple figure of merit is devised in terms of an RMS-like (root mean square) factor based on the implant displacements, that evolves continuously and significantly with the bone "healing" process, thereby providing unequivocal information on the nature of the investigated bone-implant interface. The results show that the wave propagation pattern is primarily dictated by the impedance mismatch rather than by the interface thickness. This study validates the concept of quantitative ultrasonic testing as a sensitive alternative to the widespread resonant frequency analysis, thereby opening the way for future sensitivity analyses that will address more refined bone-implant interface pathologies such as those observed in the clinical realm.

Elastography of the bone-implant interface

The stress distribution around endosseous implants is an important determinant of the surgical success. However, no method developed so far to determine the implant stability is sensitive to the loading conditions of the bone-implant interface (BII). The objective of this study is to investigate whether a quantitative ultrasound (QUS) technique may be used to retrieve information on compressive stresses applied to the BII. An acousto-mechanical device was conceived to compress 18 trabecular bovine bone samples onto coin-shaped implants and to measure the ultrasonic response of the BII during compression. The biomechanical behavior of the trabecular bone samples was modeled as Neo-Hookean. The reflection coefficient of the BII was shown to decrease as a function of the stress during the elastic compression of the trabecular bone samples and during the collapse of the trabecular network, with an average slope of −4.82 GPa⁻¹. The results may be explained by an increase of the bone-implant contact ratio and by changes of bone structure occurring during compression. The sensitivity of the QUS response of the BII to compressive stresses opens new paths in the elaboration of patient specific decision support systems allowing surgeons to assess implant stability that should be developed in the future.

A review on the latest advancements in the non-invasive evaluation/monitoring of dental and trans-femoral implants

Dental implants and transcutaneous prostheses (trans-femoral implants) improve the quality of life of millions of people because they represent the optimal treatments to edentulism and amputation, respectively. The clinical procedures adopted by surgeons to insert these implants are well established. However, there is uncertainty on the outcomes of the post-operation recovery because of the uncertainty associated with the osseointegration process, which is defined as the direct, structural and functional contact between the living bone and the fixture. To guarantee the long-term survivability of dental or trans-femoral implants doctors sometimes implement non-invasive techniques to monitor and evaluate the progress of osseointegration. This may be done by measuring the stability of the fixture or by assessing the quality of the bone-fixture interface. In addition, care providers may need to quantify the structural integrity of the bone-implant system at various moments during the patients recovery. The accuracy of such non-invasive methods reduce recovery and rehabilitation time, and may increase the survival rate of the therapies with undisputable benefits for the patients. This paper provides a comprehensive review of clinically-approved and emerging non-invasive methods to evaluate/monitor the osseointegration of dental and orthopedic implants. A discussion about advantages and limitations of each method is provided based on the outcomes of the cases presented. The review on the emerging technologies covers the developments of the last decade, while the discussion about the clinically approved systems focuses mostly on the latest (2017-2018) findings. At last, the review also provides some suggestions for future researches and developments in the area of implant monitoring.

Biomechanical behaviours of the bone-implant interface: a review

In recent decades, cementless implants have been widely used in clinical practice to replace missing organs, to replace damaged or missing bone tissue or to restore joint functionality. However, there remain risks of failure which may have dramatic consequences. The success of an implant depends on its stability, which is determined by the biomechanical properties of the bone-implant interface (BII). The aim of this review article is to provide more insight on the current state of the art concerning the evolution of the biomechanical properties of the BII as a function of the implant's environment. The main characteristics of the BII and the determinants of implant stability are first introduced. Then, the different mechanical methods that have been employed to derive the macroscopic properties of the BII will be described. The experimental multi-modality approaches used to determine the microscopic biomechanical properties of periprosthetic newly formed bone tissue are also reviewed. Eventually, the influence of the implant's properties, in terms of both surface properties and biomaterials, is investigated. A better understanding of the phenomena occurring at the BII will lead to (i) medical devices that help surgeons to determine an implant's stability and (ii) an improvement in the quality of implants.

Reflection of an ultrasonic wave on the bone-implant interface: Effect of the roughness parameters

Quantitative ultrasound can be used to characterize the evolution of the bone-implant interface (BII), which is a complex system due to the implant surface roughness and to partial contact between bone and the implant. The aim of this study is to derive the main determinants of the ultrasonic response of the BII during osseointegration phenomena. The influence of (i) the surface roughness parameters and (ii) the thickness W of a soft tissue layer on the reflection coefficient r of the BII was investigated using a two-dimensional finite element model. When W increases from 0 to 150 μm, r increases from values in the range [0.45; 0.55] to values in the range [0.75; 0.88] according to the roughness parameters. An optimization method was developed to determine the sinusoidal roughness profile leading to the most similar ultrasonic response for all values of W compared to the original profile. The results show that the difference between the ultrasonic responses of the optimal sinusoidal profile and of the original profile was lower to typical experimental errors. This approach provides a better understanding of the ultrasonic response of the BII, which may be used in future numerical simulation realized at the scale of an implant.

Flexible Transparent Electrodes Based on Gold Nanomeshes

The transmittance, conductivity, and flexibility are the crucial properties for the development of next-generation flexible electrodes. Achieving a good trade-off between transmittance and conductivity of flexible electrodes has been a challenge because the two properties are inversely proportional. Herein, we reveal a good trade-off between transmittance and conductivity of gold nanomesh (AuNM) can be achieved through appropriately increasing the AuNM thickness no more than 40 nm, the mean free path of electrons in Au metal. The further flexibility investigation indicates that the AuNM electrodes with mesh structure show higher tolerance than the Au bulk film, and the AuNM electrodes with smaller inter-aperture wire width can accommodate more tensile strains than a counterpart with bigger inter-aperture wire width. The simulated results based on finite element analysis (FEA) show good agreement with experimental results, which indicates the fabrication method of versatile nanosphere lithography (NSL) is reliable. These results established a promising approach toward next-generation large-scale flexible transparent AuNM electrodes for flexible electronics.

Resonant frequency analysis of dental implants

Dental implant stability influences the decision on the determination of the duration between implant insertion and loading. This work investigates the resonant frequency analysis by means of a numerical model. The investigation is done numerically through the determination of the eigenfrequencies and performing steady state response analyses using a commercial finite element package. A peri-implant interface, of simultaneously varying stiffness, density and layer thickness is introduced in the numerical 3D model in order to probe the sensitivity of the eigenfrequencies and steady state response to an evolving weakened layer, in an attempt to identify the bone reconstruction around the implant. For the first two modes, the resonant frequency is somewhat insensitive to the healing process, unless the weakened layer is rather large and compliant, like in the very early stages of the implantation. A "Normalized Healing Factor" is devised in the spirit of the Implant Stability Quotient, which can identify the healing process especially at the early stages after implantation. The sensitivity of the resonant frequency analysis to changes of mechanical properties of periprosthetic bone tissue seems relatively weak. Another indicator considering the amplitude as well as the resonance frequency might be more adapted to bone healing estimations. However, these results need to be verified experimentally as well as clinically.

Clinical Assessment of Dental Implant Stability During Follow-Up: What Is Actually Measured, and Perspectives

The optimization of loading protocols following dental implant insertion requires setting up patient-specific protocols, customized according to the actual implant osseointegration, measured through quantitative, objective methods. Various devices for the assessment of implant stability as an indirect measure of implant osseointegration have been developed. They are analyzed here, introducing the respective physical models, outlining major advantages and critical aspects, and reporting their clinical performance. A careful discussion of underlying hypotheses is finally reported, as is a suggestion for further development of instrumentation and signal analysis.

Reflection of an ultrasonic wave on the bone-implant interface: A numerical study of the effect of the multiscale roughness

Quantitative ultrasound is used to characterize and stimulate osseointegration processes at the bone-implant interface (BII). However, the interaction between an ultrasonic wave and the implant remains poorly understood. This study aims at investigating the sensitivity of the ultrasonic response to the microscopic and macroscopic properties of the BII and to osseointegration processes. The reflection coefficient R of the BII was modeled for different frequencies using a two-dimensional finite element model. The implant surface roughness was modeled by a sinusoidal function with varying amplitude h and spatial frequency L. A soft tissue layer of thickness W was considered between bone tissue and the implant in order to model non-mineralized fibrous tissue. For microscopic roughness, R is shown to increase from around 0.55 until 0.9 when kW increases from 0 to 1 and to be constant for kW > 1, where k is the wavenumber in the implant. These results allow us to show that R depends on the properties of bone tissue located at a distance comprised between 1 and 25 μm from the implant surface. For macroscopic roughness, R is highly dependent on h and this dependence may be explained by phase cancellation and multiple scattering effects for high roughness parameters.

Updates on ultrasound research in implant dentistry: a systematic review of potential clinical indications

OBJECTIVES

Ultrasonography has shown promising diagnostic value in dental implant imaging research; however, exactly how ultrasound was used and at what stage of implant therapy it can be applied has not been systematically evaluated. Therefore, the aim of this review is to investigate potential indications of ultrasound use in the three implant treatment phases, namely planning, intraoperative and post-operative phase.

METHODS

Eligible manuscripts were searched in major databases with a combination of keywords related to the use of ultrasound imaging in implant therapy. An initial search yielded 414 articles, after further review, 28 articles were finally included for this systematic review.

RESULTS

Ultrasound was found valuable, though at various development stages, for evaluating (1) soft tissues, (2) hard tissues (3) vital structures and (4) implant stability. B-mode, the main function to image anatomical structures of interest, has been evaluated in pre-clinical and clinical studies. Quantitative ultrasound parameters, e.g. sound speed and amplitude, are being developed to evaluate implant-bone stability, mainly in simulation and pre-clinical studies. Ultrasound could be potentially useful in all three treatment phases. In the planning phase, ultrasound could evaluate vital structures, tissue biotype, ridge width/density, and cortical bone thickness. During surgery, it can provide feedback by identifying vital structures and bone boundary. At follow-up visits, it could evaluate marginal bone level and implant stability.

CONCLUSIONS

Understanding the current status of ultrasound imaging research for implant therapy would be extremely beneficial for accelerating translational research and its use in dental clinics.

Evaluation of dental implant stability in bone phantoms: Comparison between a quantitative ultrasound technique and resonance frequency analysis

BACKGROUND

Resonance frequency analyses and quantitative ultrasound methods have been suggested to assess dental implant primary stability.

PURPOSE

The purpose of this study was to compare the results obtained using these two techniques applied to the same dental implants inserted in various bone phantoms.

MATERIALS AND METHODS

Different values of trabecular bone density and cortical thickness were considered to assess the effect of bone quality on the respective indicators (UI and ISQ). The effect of the implant insertion depth and of the final drill diameter was also investigated.

RESULTS

ISQ values increase and UI values decrease as a function of trabecular density, cortical thickness and the screwing of the implant. When the implant diameter varies, the UI values are significantly different for all final drill diameters (except for two), while the ISQ values are similar for all final drill diameters lower than 3.2 mm and higher than 3.3 mm. The error on the estimation of parameters with the QUS device is between 4 and 8 times lower compared to that made with the RFA technique.

CONCLUSIONS

The results show that ultrasound technique provides a better estimation of different parameters related to the implant stability compared to the RFA technique.

Comparison of Resonance Frequency Analysis and of Quantitative Ultrasound to Assess Dental Implant Osseointegration

Dental implants are widely used in the clinic. However, there remain risks of failure, which depend on the implant stability. The aim of this paper is to compare two methods based on resonance frequency analysis (RFA) and on quantitative ultrasound (QUS) and that aim at assessing implant stability. Eighty-one identical dental implants were inserted in the iliac crests of 11 sheep. The QUS and RFA measurements were realized after different healing times (0, 5, 7, and 15 weeks). The results obtained with the QUS (respectively RFA) method were significantly different when comparing two consecutive healing time for 97% (respectively, 18%) of the implants. The error made on the estimation of the healing time when analyzing the results obtained with the QUS technique was around 10 times lower than that made when using the RFA technique. The results corresponding to the dependence of the ISQ versus healing time were significantly different when comparing two directions of RFA measurement. The results show that the QUS method allows a more accurate determination of the evolution of dental implant stability when compared to the RFA method. This study paves the way towards the development of a medical device, thus providing a decision support system to dental surgeons.

Finite element analysis of dental implants with validation: to what extent can we expect the model to predict biological phenomena? A literature review and proposal for classification of a validation process

A literature review of finite element analysis (FEA) studies of dental implants with their model validation process was performed to establish the criteria for evaluating validation methods with respect to their similarity to biological behavior. An electronic literature search of PubMed was conducted up to January 2017 using the Medical Subject Headings “dental implants” and “finite element analysis.” After accessing the full texts, the context of each article was searched using the words “valid” and “validation” and articles in which these words appeared were read to determine whether they met the inclusion criteria for the review. Of 601 articles published from 1997 to 2016, 48 that met the eligibility criteria were selected. The articles were categorized according to their validation method as follows: in vivo experiments in humans (n = 1) and other animals (n = 3), model experiments (n = 32), others’ clinical data and past literature (n = 9), and other software (n = 2). Validation techniques with a high level of sufficiency and efficiency are still rare in FEA studies of dental implants. High-level validation, especially using in vivo experiments tied to an accurate finite element method, needs to become an established part of FEA studies. The recognition of a validation process should be considered when judging the practicality of an FEA study.

Assessment of the biomechanical stability of a dental implant with quantitative ultrasound: A three-dimensional finite element study

Dental implant stability is an important determinant of the surgical success. Quantitative ultrasound (QUS) techniques can be used to assess such properties using the implant acting as a waveguide. However, the interaction between an ultrasonic wave and the implant remains poorly understood. The aim of this study is to investigate the sensitivity of the ultrasonic response to the quality and quantity of bone tissue in contact with the implant surface. The 10 MHz ultrasonic response of an implant used in clinical practice was simulated using an axisymmetric three-dimensional finite element model, which was validated experimentally. The amplitude of the echographic response of the implant increases when the depth of a liquid layer located at the implant interface increases. The results show the sensitivity of the QUS technique to the amount of bone in contact with the implant. The quality of bone tissue around the implant is varied by modifying the bone biomechanical properties by 20%. The amplitude of the implant echographic response decreases when bone quality increases, which corresponds to bone healing. In all cases, the amplitude of the implant response decreased when the dental implant stability increased, which is consistent with the experimental results.