3-D finite element model of the impaction of a press-fitted femoral stem under various biomechanical environments.

BACKGROUND: Uncemented femoral stem insertion into the bone is achieved by applying successive impacts on an inserter tool called "ancillary". Impact analysis has shown to be a promising technique to monitor the implant insertion and to improve its primary stability. METHOD: This study aims to provide a better understanding of the dynamic phenomena occurring between the hammer, the ancillary, the implant and the bone during femoral stem insertion, to validate the use of impact analyses for implant insertion monitoring. A dynamic 3-D finite element model of the femoral stem insertion via an impaction protocol is proposed. The influence of the trabecular bone Young's modulus (Et), the interference fit (IF), the friction coefficient at the bone-implant interface (µ) and the impact velocity (v0) on the implant insertion and on the impact force signal is evaluated. RESULTS: For all configurations, a decrease of the time difference between the two first peaks of the impact force signal is observed throughout the femoral stem insertion, up to a threshold value of 0.23 ms. The number of impacts required to reach this value depends on Et, v0 and IF and varies between 3 and 8 for the set of parameters considered herein. The bone-implant contact ratio reached after ten impacts varies between 60% and 98%, increases as a function of v0 and decreases as a function of IF, µ and Et. CONCLUSION: This study confirms the potential of an impact analyses-based method to monitor implant insertion and to retrieve bone-implant contact properties.

Effect of collagen fibril orientation on the anisotropic properties of peri-implant bone.

In orthopedic and dental surgery, the implantation of biomaterials within the bone to restore the integrity of the treated organ has become a standard procedure. Their long-term stability relies on the osseointegration phenomena, where bone grows onto and around metallic implants, creating a bone-implant interface. Bone is a highly hierarchical material that evolves spatially and temporally during this healing phase. A deeper understanding of its biomechanical characteristics is needed, as they are determinants for surgical success. In this context, we propose a multiscale homogenization model to evaluate the effective elastic properties of bone as a function of the distance from the implant, based on the tissue's structure and composition at lower scales. The model considers three scales: hydroxyapatite foam (nanoscale), ultrastructure (microscale), and tissue (mesoscale). The elastic properties and the volume fraction of the elementary constituents of bone matrix (mineral, collagen, and water), the orientation of the collagen fibril relative to the implant surface, and the mesoscale porosity constitute the input data of the model. The effect of a spatiotemporal variation in the collagen fibrils' orientation on the bone anisotropic properties in the proximity of the implant was investigated. The findings revealed a strong variation of the components of the effective elasticity tensor of the bone as a function of the distance from the implant. The effective elasticity appears to be primarily sensitive to the porosity (mesoscale) rather than to the collagen fibrils' orientation (sub-micro scale). However, the orientation of the fibrils has a significant influence on the isotropy of the bone. When analyzing the symmetry properties of the effective elasticity tensor, the ratio between the isotropic and hexagonal components is determined by a combination of the porosity and the fibrils' orientation. A decrease in porosity leads to a decrease in bone isotropy and, in turn, an increase in the impact of the fibrils' orientation. These results demonstrate that the collagen fibril orientation should be taken into account to properly describe the effective elastic anisotropy of bone at the organ scale.

Characterization of the concentration of agar-based soft tissue mimicking phantoms by impact analysis.

In various medical fields, a change of soft tissue stiffness is associated with its physio-pathological evolution. While elastography is extensively employed to assess soft tissue stiffness in vivo, its application requires a complex and expensive technology. The aim of this study is to determine whether an easy-to-use method based on impact analysis can be employed to determine the concentration of agar-based soft tissue mimicking phantoms. Impact analysis was performed on soft tissue mimicking phantoms made of agar gel with a mass concentration ranging from 1% to 5%. An indicator Δt is derived from the temporal variation of the impact force signal between the hammer and a small beam in contact with the sample. The results show a non-linear decrease of Δt as a function of the agar concentration (and thus of the sample stiffness). The value of Δt provides an estimation of the agar concentration with an error of 0.11%. This sensitivity of the impact analysis based method to the agar concentration is of the same order of magnitude than results obtained with elastography techniques. This study opens new paths towards the development of impact analysis for a fast, easy and relatively inexpensive clinical evaluation of soft tissue elastic properties.

Debonding of coin-shaped osseointegrated implants: Coupling of experimental and numerical approaches.

While cementless implants are now widely used clinically, implant debonding still occur and is difficult to anticipate. Assessing the biomechanical strength of the bone-implant interface can help improving the understanding of osseointegration phenomena and thus preventing surgical failures. A dedicated and standardized implant model was considered. The samples were tested using a mode III cleavage device to assess the mechanical strength of the bone-implant interface by combining experimental and numerical approaches. Four rough (Sa = 24.5 µm) osseointegrated coin-shaped implants were left in sheep cortical bone during 15 weeks of healing time. Each sample was experimentally rotated at 0.03°/sec until complete rupture of the interface. The maximum values of the torque were comprised between 0.48 and 0.72 N m, while a significant increase of the normal force from 7-12 N to 31-43 N was observed during the bone-implant interface debonding, suggesting the generation of bone debris at the bone-implant interface. The experimental results were compared to an isogeometric finite element model describing the adhesion and debonding phenomena through a modified Coulomb's law, based on a varying friction coefficient to represent the transition from an unbroken to a broken bone-implant interface. A good agreement was found between numerical and experimental torques, with numerical friction coefficients decreasing from 8.93 to 1.23 during the bone-implant interface rupture, which constitutes a validation of this model to simulate the debonding of an osseointegrated bone-implant interface subjected to torsion.

Detection of periprosthetic fractures around the femoral stem by resonance frequency analysis: An in vitro study.

Periprosthetic femoral bone fractures are frequent complications of Total Hip Arthroplasty (THA) and may occur during the insertion of uncemented Femoral Stems (FS), due to the nature of the press-fit fixation. Such fracture may lead to the surgical failure of the THA and require a revision surgery, which may have dramatic consequences. Therefore, an early detection of intra-operative fractures is important to avoid worsening the fracture and/or to enable a peroperative treatment. The aim of this in vitro study is to determine the sensitivity of a method based on resonance frequency analysis of the bone-stem-ancillary system for periprosthetic fractures detection. A periprosthetic fracture was artificially created close to the lesser-trochanter of 10 femoral bone mimicking phantoms. The bone-stem-ancillary resonance frequencies in the range (2-12) kHz were measured on an ancillary instrumented with piezoelectric sensors, which was fixed to the femoral stem. The measurements were repeated for different fracture lengths from 4 to 55 mm. The results show a decrease of the resonance frequencies due to the fracture occurrence and propagation. The frequency shift reached up to 170 Hz. The minimum fracture length that can be detected varies from 3.1±1.7 mm to 5.9±1.9 mm according to the mode and to the specimen. A significantly higher sensitivity (p = 0.011) was obtained for a resonance frequency around 10.6 kHz, corresponding to a mode vibrating in a plane perpendicular to the fracture. This study opens new paths toward the development of non-invasive vibration-based methods for intra-operative periprosthetic fractures detection.

Using an Instrumented Hammer to Predict the Rupture of Bone Samples Subject to an Osteotomy.

Osteotomies are common procedures in maxillofacial and orthopedic surgery. The surgeons still rely on their proprioception to control the progression of the osteotome. Our group has developed an instrumented hammer that was shown to provide information on the biomechanical properties of the tissue located around the osteotome tip. The objective of this study is to determine if this approach may be used to predict the rupture of a bone sample thanks to an instrumented hammer equipped with a force sensor. For each impact, an indicator τ is extracted from the signal corresponding to the variation of the force as a function of time. A linear by part regression analysis is applied to the curve corresponding to the variation of τ as a function of the distance d between the tip of the osteotome and the end of the sample. The experiments were conducted with plywood and bovine trabecular bone samples. The results show that τ starts increasing when the value of d is lower than 2.6 mm on average, which therefore corresponds to a typical threshold detection distance between the osteotome tip and the sample end. These findings open new paths for the development of this instrumented surgical hammer.

Influence of the biomechanical environment on the femoral stem insertion and vibrational behavior: a 3-D finite element study.

The long-term success of cementless surgery strongly depends on the implant primary stability. The femoral stem initial fixation relies on multiple geometrical and material factors, but their influence on the biomechanical phenomena occurring during the implant insertion is still poorly understood, as they are difficult to quantify in vivo. The aim of the present study is to evaluate the relationship between the resonance frequencies of the bone-implant-ancillary system and the stability of the femoral stem under various biomechanical environments. The interference fit IF, the trabecular bone Young's modulus [Formula: see text] and the bone-implant contact friction coefficient [Formula: see text] are varied to investigate their influence on the implant insertion phenomena and on the system vibration behavior. The results exhibit for all the configurations, a nonlinear increase in the bone-implant contact throughout femoral stem insertion, until the proximal contact is reached. While the pull-out force increases with [Formula: see text], IF and [Formula: see text], the bone-implant contact ratio decreases, which shows that a compromise on the set of parameters could be found in order to achieve the largest bone-implant contact while maintaining sufficient pull-out force. The modal analysis on the range [2-7] kHz shows that the resonance frequencies of the bone-implant-ancillary system increase with the bone-implant contact ratio and the trabecular bone Young's modulus, with a sensitivity that varies over the modes. Both the pull-out forces and the vibration behavior are consistent with previous experimental studies. This study demonstrates the potential of using vibration methods to guide the surgeons for optimizing implant stability in various patients and surgical configurations.

Modeling the debonding process of osseointegrated implants due to coupled adhesion and friction.

Cementless implants have become widely used for total hip replacement surgery. The long-term stability of these implants is achieved by bone growing around and into the rough surface of the implant, a process called osseointegration. However, debonding of the bone-implant interface can still occur due to aseptic implant loosening and insufficient osseointegration, which may have dramatic consequences. The aim of this work is to describe a new 3D finite element frictional contact formulation for the debonding of partially osseointegrated implants. The contact model is based on a modified Coulomb friction law by Immel et al. (2020), that takes into account the tangential debonding of the bone-implant interface. This model is extended in the direction normal to the bone-implant interface by considering a cohesive zone model, to account for adhesion phenomena in the normal direction and for adhesive friction of partially bonded interfaces. The model is applied to simulate the debonding of an acetabular cup implant. The influence of partial osseointegration and adhesive effects on the long-term stability of the implant is assessed. The influence of different patient- and implant-specific parameters such as the friction coefficient [Formula: see text], the trabecular Young's modulus [Formula: see text], and the interference fit [Formula: see text] is also analyzed, in order to determine the optimal stability for different configurations. Furthermore, this work provides guidelines for future experimental and computational studies that are necessary for further parameter calibration.

Mechanical micromodeling of stress-shielding at the bone-implant interphase under shear loading.

Inserting a titanium implant in the bone tissue may modify its physiological loading and therefore cause bone resorption, via a phenomenon called stress-shielding. The local stress field around the bone-implant interphase (BII) created under shear loading may be influenced by different parameters such as the bone-implant contact (BIC) ratio, the bone Young's modulus, the implant roughness and the implant material. A 2-D finite element model was developed to model the BII and evaluate the impact of the aforementioned parameters. The implant roughness was described by a sinusoidal function (height 2Δ, wavelength λ), and different values of the BIC ratio were simulated. A heterogeneous distribution of the maximum shear stress was evidenced in the periprosthetic bone tissue, with high interfacial stress for low BIC ratios and low implant roughness and underloaded regions near the roughness valleys. Both phenomena may lead to stress-shielding-related effects, which were concentrated within a distance lower than 0.8λ from the implant surface. Choosing an implant material with mechanical properties matching those of bone tissue leads to a homogenized shear stress field and could help to prevent stress-shielding effects. Finally, the equivalent shear modulus of the BII was derived to replace its complex behavior with a simpler analytical model in future studies. Schematic illustrations of the 2-D finite element model used in the present study and spatial variation of the maximal shear stress in the periprosthetic bone tissue for different implant roughness and bone-implant contact ratios.

Ultrasonic Evaluation of the Bone-Implant Interface.

While implant surgical interventions are now routinely performed, failures still occur and may have dramatic consequences. The clinical outcome depends on the evolution of the biomechanical properties of the bone-implant interface (BII). This chapter reviews studies investigating the use of quantitative ultrasound (QUS) techniques for the characterization of the BII.First, studies on controlled configurations evidenced the influence of healing processes and of the loading conditions on the ultrasonic response of the BII. The gap of acoustical properties at the BII increases (i) during healing and (ii) when stress at the BII increases, therefore inducing a decrease of the reflection coefficient at the BII.Second, an acoustical model of the BII is proposed to better understand the parameters influencing the interaction between ultrasound and the BII. The reflection coefficient is shown to decrease when (i) the BII is better osseointegrated, (ii) the implant roughness decreases, (iii) the frequency of QUS decreases and (iv) the bone mass density increases.Finally, a 10 MHz device aiming at assessing dental implant stability was validated in vitro, in silico and in vivo. A comparison between QUS and resonance frequency analysis (RFA) techniques showed a better sensitivity of QUS to changes of the parameters related to the implant stability.

Modal Analysis of the Ancillary During Femoral Stem Insertion: A Study on Bone Mimicking Phantoms.

The femoral stem primary stability achieved by the impaction of an ancillary during its insertion is an important factor of success in cementless surgery. However, surgeons still rely on their proprioception, making the process highly subjective. The use of Experimental Modal Analysis (EMA) without sensor nor probe fixation on the implant or on the bone is a promising non destructive approach to determine the femoral stem stability. The aim of this study is to investigate whether EMA performed directly on the ancillary could be used to monitor the femoral stem insertion into the bone. To do so, a cementless femoral stem was inserted into 10 bone phantoms of human femurs and EMA was carried out on the ancillary using a dedicated impact hammer for each insertion step. Two bending modes could be identified in the frequency range [400-8000] Hz for which the resonance frequency was shown to be sensitive to the insertion step and to the bone-implant interface properties. A significant correlation was obtained between the two modal frequencies and the implant insertion depth (R2 = 0.95 ± 0.04 and R2 = 0.94 ± 0.06). This study opens new paths towards the development of noninvasive vibration based evaluation methods to monitor cementless implant insertion.

Validation of an Instrumented Hammer for Rhinoplasty Osteotomies: A Cadaveric Study.

Background: Osteotomies during rhinoplasty are usually based on surgeon's proprioception to determine the number, energy, and trajectory of impacts. Objective: The first objective was to detect the occurrence of fractures. The second objective was to determine when the thicker frontal bone was encountered by the osteotome. Materials and Methods: An instrumented hammer was used to measure the impact force during lateral osteotomies on nine human anatomic specimens. A prediction algorithm was developed using machine learning techniques, to detect the occurrence of fractures, and the proximity of the osteotome to the frontal bone. Results: The algorithm was able to predict the occurrence of fractures and the proximity to the frontal bone with a prediction rate of 83%, 91%, and 93% when allowing for an error of 0, 1, and 2 impacts, respectively. The location of the osteotome in the frontal bone was predicted with an error of 7.7%. Conclusion: An osteotomy hammer measuring the impact force when performing lateral osteotomies can predict the occurrence of fractures and the proximity to the frontal bone, providing the surgeon with instant feedback.

Anatomical subject validation of an instrumented hammer using machine learning for the classification of osteotomy fracture in rhinoplasty.

Osteotomies during rhinoplasty are usually based on the surgeon's proprioception to determine the number and the strength of the impacts. The aim of this study is to determine whether a hammer instrumented with a force sensor can be used to classify fractures and to determine the location of the osteotome tip. Two lateral osteotomies were realized in nine anatomical subjects using an instrumented hammer recording the evolution of the impact force. Two indicators τ and λ were derived from the signal, and video analysis was used to determine whether the osteotome tip was located in nasal or frontal bone as well as the condition of the bone tissue around the osteotome tip. A machine-learning algorithm was used to predict the condition of bone tissue after each impact. The algorithm was able to predict the condition of the bone after the impacts with an accuracy of 83%, 91%, and 93% when considering a tolerance of 0, 1, and 2 impacts, respectively. Moreover, in nasal bone, the values of τ and λ were significantly lower (p < 10-10) and higher (p < 10-4) than in frontal bone, respectively. This study paves the way for the development of the instrumented hammer as a decision support system.

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.

Determinants of the primary stability of cementless acetabular cup implants: A 3D finite element study.

Primary stability of cementless implants is crucial for the surgical success and long-term stability. However, primary stability is difficult to quantify in vivo and the biomechanical phenomena occurring during the press-fit insertion of an acetabular cup (AC) implant are still poorly understood. The aim of this study is to investigate the influence of the cortical and trabecular bone Young's moduli Ec and Et, the interference fit IF and the sliding friction coefficient of the bone-implant interface µ on the primary stability of an AC implant. For each parameter combination, the insertion of the AC implant into the hip cavity and consequent pull-out are simulated with a 3D finite element model of a human hemi-pelvis. The primary stability is assessed by determining the polar gap and the maximum pull-out force. The polar gap increases along with all considered parameters. The pull-out force shows a continuous increase with Ec and Et and a non-linear variation as a function of µ and IF is obtained. For µ > 0.6 and IF > 1.4 mm the primary stability decreases, and a combination of smaller µ and IF lead to a better fixation. Based on the patient's bone stiffness, optimal combinations of µ and IF can be identified. The results are in good qualitative agreement with previous studies and provide a better understanding of the determinants of the AC implant primary stability. They suggest a guideline for the optimal choice of implant surface roughness and IF based on the patient's bone quality.

Using an impact hammer to perform biomechanical measurements during osteotomies: Study of an animal model.

Osteotomies are common surgical procedures used for instance in rhinoplasty and usually performed using an osteotome impacted by a mallet. Visual control being difficult, osteotomies are often based on the surgeon proprioception to determine the number and energy of each impact. The aim of this study is to determine whether a hammer instrumented with a piezoelectric force sensor can be used to (i) follow the displacement of the osteotome and (ii) determine when the tip of the osteotome arrives in frontal bone, which corresponds to the end of the osteotomy pathway. Seven New Zealand White rabbit heads were collected, and two osteotomies were performed on their left and right nasal bones using the instrumented hammer to record the variation of the force as a function of time during each impact. The second peak time τ was derived from each signal while the displacement of the osteotome tip D was determined using video motion tracking. The results showed a significant correlation between τ and D (ρ2 = 0.74), allowing to estimate the displacement of the osteotome through the measurement of τ. The values of τ measured in the frontal bone were significantly lower than in the nasal bone (p<10-10), which allows to determine the transition between the nasal and frontal bones when τ becomes lower than 0.78 its initial averaged value. Although results should be validated clinically, this technology could be used by surgeons in the future as a decision support system to help assessing the osteotome environment.

Neutron microtomography to investigate the bone-implant interface-comparison with histological analysis.

Bone properties and especially its microstructure around implants are crucial to evaluate the osseointegration of prostheses in orthopaedic, maxillofacial and dental surgeries. Given the intrinsic heterogeneous nature of the bone microstructure, an ideal probing tool to understand and quantify bone formation must be spatially resolved. X-ray imaging has often been employed, but is limited in the presence of metallic implants, where severe artifacts generally arise from the high attenuation of metals to x-rays. Neutron tomography has recently been proposed as a promising technique to study bone-implant interfaces, thanks to its lower interaction with metals. The aim of this study is to assess the potential of neutron tomography for the characterisation of bone tissue in the vicinity of a metallic implant. A standardised implant with a bone chamber was implanted in rabbit bone. Four specimens were imaged with neutron tomography and subsequently compared to non-decalcified histology to stain soft and mineralised bone tissues, used here as a ground-truth reference. An intensity-based image registration procedure was performed to place the 12 histological slices within the corresponding 3D neutron volume. Significant correlations (p < 0.01) were obtained between the two modalities for the bone-implant contact (BIC) ratio (R = 0.77) and the bone content inside the chamber (R = 0.89). The results indicate that mineralised bone tissue can be reliably detected by neutron tomography. However, theBICratio and bone content were found to be overestimated with neutron imaging, which may be explained by its sensitivity to non-mineralised soft tissues, as revealed by histological staining. This study highlights the suitability of neutron tomography for the analysis of the bone-implant interface. Future work will focus on further distinguishing soft tissues from bone tissue, which could be aided by the adoption of contrast agents.

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.

Stress shielding at the bone-implant interface: Influence of surface roughness and of the bone-implant contact ratio.

Short and long-term stabilities of cementless implants are strongly determined by the interfacial load transfer between implants and bone tissue. Stress-shielding effects arise from shear stresses due to the difference of material properties between bone and the implant. It remains difficult to measure the stress field in periprosthetic bone tissue. This study proposes to investigate the dependence of the stress field in periprosthetic bone tissue on (i) the implant surface roughness, (ii) the material properties of bone and of the implant, (iii) the bone-implant contact ratio. To do so, a microscale two-dimensional finite element model of an osseointegrated bone-implant interface was developed where the surface roughness was modeled by a sinusoidal surface. The results show that the isostatic pressure is not affected by the presence of the bone-implant interface while shear stresses arise due to the combined effects of a geometrical singularity (for low surface roughness) and of shear stresses at the bone-implant interface (for high surface roughness). Stress-shielding effects are likely to be more important when the bone-implant contact ratio value is low, which corresponds to a case of relatively low implant stability. Shear stress reach a maximum value at a distance from the interface comprised between 0 and 0.1 time roughness wavelength λ and tend to 0 at a distance from the implant surface higher than λ, independently from bone-implant contact ratio and waviness ratio. A comparison with an analytical model allows validating the numerical results. Future work should use the present approach to model osseointegration phenomena.

Effect of the Acoustic Impedance Mismatch at the Bone-Soft Tissue Interface as a Function of Frequency in Transcranial Ultrasound: A Simulation and In Vitro Experimental Study.

The transcranial Doppler (TCD) ultrasound is a method that uses a handheld low-frequency (2-2.5 MHz), pulsed Doppler phased array probe to measure blood velocity within the arteries located inside the brain. The problem with TCD lies in the low ultrasonic energy penetrating inside the brain through the skull, which leads to a low signal-to-noise ratio. This is due to several effects, including phase aberration, variations in the speed of sound in the skull, scattering, the acoustic impedance mismatch, and absorption of the three-layer medium constituted by soft tissues, the skull, and the brain. The goal of this article is to study the effect of transmission losses due to the acoustic impedance mismatch on the transmitted energies as a function of frequency. To do so, wave propagation was modeled from the ultrasonic transducer into the brain. This model calculates transmission coefficients inside the brain, leading to a frequency-dependent transmission coefficient for a given skin and bone thickness. This approach was validated experimentally by comparing the analytical results with measurements obtained from a bone phantom plate mimicking the skull. The average position error of the occurrence of the maximum amplitude between the experiment and analytical result was equivalent to a 0.06-mm error on the skin thickness given a fixed bone thickness. The similarity between the experimental and analytical results was also demonstrated by calculating correlation coefficients. The average correlation between the experimental and analytical results came out to be 0.50 for a high-frequency probe and 0.78 for a low-frequency probe. Further analysis of the simulation showed that an optimized excitation frequency can be chosen based on skin and bone thicknesses, thereby offering an opportunity to improve the image quality of TCD.