Ultrasonic propagation in cortical bone mimics

Elastic parameters characterization of multilayered structures by air-coupled ultrasonic transmission and genetic algorithm

This paper describes a non-contact method to characterize isotropic and anisotropic planar multilayer structures using a genetic algorithm. The method is based on the determination of critical angles, where the maxima of the modulus of transmission coefficient of the structure appear, and which correspond to the generation of guided waves. The optimization process minimizes the error between the reference critical angles and associated amplitudes of the transmission coefficient, with the corresponding estimated ones. The estimation of elastic parameters is demonstrated for acrylic and oak plates as well as for a bi-layered structure composed of oak and a thin layer of gesso. It is shown that to obtain satisfactory optimization results, it is necessary for guided modes of higher order than the zero ones to be taken into account. Results also show that some elastic constants such as C₃₃ and C₅₅ retrieved from the transmission coefficient are very sensitive to the optimization.

Numerical Simulation and Non-Destructive Characterization of Material Property and Defect Analysis of Cortical Bone Using Laser Ultrasound Techniques

The application of bone quality assessment has received extensive attention, and a large number of researchers continue to invest in related research activities. To get closer to the real situation, this study intends to investigate the long bones of cattle. A quantitative laser ultrasound visualization (QLUV) system was used to measure the images transmitted by the guided waves on the long bones, and the internal defects of the long bones were detected using wave propagation behavior. Then, linear scanning was performed through a laser ultrasound technique (LUT) to measure the dispersion curve of the cortical bone, and the results were compared with finite element simulations. Further, LUT was used to measure the material properties of the cortical bone in all directions. Finally, the long bones were scanned by computerized tomography to analyze the pore direction and distribution. Further, the relationship between pore direction and material properties was studied. The results showed that the obtained wave propagation image was consistent with the time-domain waveform signal and the finite element analysis results. The experimental and simulation results of wave velocity showed an error of 0.26 to 1.56% compared with the literature. The plate-shaped cortical bone showed that the phase velocity of the guided wave is higher than the circumferential direction. The defect location was identified through wave propagation behavior using the QLUV system. The elastic constant of the cortical bone was measured, and it showed the same trend as the results obtained from the tensile test in the literature. Also, the pore distribution indicated that the cortical bone porosity has the same trend as elastic constants. The elastic constants along the longitudinal direction were greater than the transversal direction. This laser ultrasound technique has been developed with an aim of having a better resolution and also as a potential application in osteoporosis conditions.

Identification of long-range ultrasonic guided wave characteristics in cortical bone by modelling

The propagation of ultrasonic guided waves in cortical bone has potential to inform medical caregivers about the condition of the bone structure. However, as waveguides, human long bones such as the tibia are complex in terms of their material behavior and their geometric features. They exhibit anisotropic elasticity and internal damping. For the first time, wave propagation is modelled in the irregular hollow tibial cross-section, which varies along its long axis. Semi-analytical, frequency domain, and time domain finite element analyses providing complimentary information about long-range wave propagation characteristics in such a waveguide are applied to the mid-diaphyseal region of a human tibia. Simulating the guided waves generated by a contact transducer, the signals received in axial transmission indicate the consistent presence of low phase velocity non-dispersive propagating modes. The guided waves capable of traveling long distances have strong potential for diagnosis of fracture healing.

Shear-Actuation and Vibrometer Reception of Penetrating Ultrasonic Guided Wave Modes in Human Tibia

The hollow long bones of the human appendicular skeleton are known to support the propagation of ultrasonic guided waves, whose potential for diagnosing bone health is being investigated. In this study, ultrasonic guided waves propagating in the diaphysis of human tibia are characterized experimentally and numerically in the frequency range around 200 kHz. The experiment involves a unique combination of omni-directional shear transducer-based excitation and detection using a 1D laser Doppler vibrometer. The cluster of phase velocities obtained from a linear array of time-history data using space-time Fourier transform is found to be in the non-dispersive low-phase velocity region of the dispersion curves obtained for a tibial cross-section. Time-domain finite element analysis revealed that the displacement components normal to the surface are significant, even though the loading is from a shear transducer. Furthermore, semi-analytical finite element analysis revealed that the wave structures of the wave modes contained within the cluster of low-phase velocity modes are consistent with the displacement profiles obtained from the time-domain analysis. The experimental results show that the low-phase velocity mode cluster has sufficient intensity to propagate axially at least 85 mm in the mid-diaphyseal region.

Stimulation of osteoblast differentiation with guided ultrasound waves

Background

Ultrasound induces mechanical vibration and heat, causing differentiation and proliferation in osteoblasts. All known in vitro evaluations of ultrasound are, however, performed with longitudinal ultrasound waves. We addressed a question: Do other forms of ultrasound waves, such as guided waves (longitudinal and guided flexural) transduced at a remote location, enhance differentiation of osteoblast cells?

Methods

In this study, we employed guided Lamb waves that were induced in a borosilicate glass slide (cortical bone mimic). An average energy of 10–30 mW/cm² for 20 min per day was applied to MC3T3 osteoblast-like cells, which were placed 30–75 mm distant from the transducer.

Results

The result revealed that guided waves significantly stimulated the differentiation and mineralization of MC3T3 cells. In particular, guided waves elevated mRNA expression levels of bone formation-related genes such as alkaline phosphatase, osteopontin, osteocalcin, osteoprotegerin, and bone sialoprotein on days 8 and 16. In addition, the amount of mineralization found via Alizarin red staining was increased by 157 % (p = 0.034). The amount of mineralization was found to be independent of distance from the transducer (p = 0.967).

Conclusion

We demonstrate herein that ultrasound in a form of guided Lamb waves is capable of inducing osteoblast differentiation in vitro, and it may enable the stimulation of osteoblasts in vivo over a distance from the site of ultrasound application.

Simulation of Low-Intensity Ultrasound Propagating in a Beagle Dog Dentoalveolar Structure to Investigate the Relations between Ultrasonic Parameters and Cementum Regeneration

The therapeutic effect of low-intensity pulsed ultrasound on orthodontically induced inflammatory root resorption is believed to be brought about through mechanical signals induced by the low-intensity pulsed ultrasound. However, the stimulatory mechanism triggering dental cell response has not been clearly identified yet. The aim of this study was to evaluate possible relations between the amounts of new cementum regeneration and ultrasonic parameters such as pressure amplitude and time-averaged energy density. We used the finite-element method to simulate the previously published experiment on ultrasonic wave propagation in the dentoalveolar structure of beagle dogs. Qualitative relations between the thickness of the regenerated cementum in the experiment and the ultrasonic parameters were observed. Our results indicated that the areas of the root surface with greater ultrasonic pressure were associated with larger amounts of cementum regeneration. However, the establishment of reliable quantitative correlations between ultrasound parameters and cementum regeneration requires more experimental data and simulations.

Tailoring the excitation of fundamental flexural guide waves in coated bone by phase-delayed array: two-dimensional simulations

The fundamental flexural guided wave (FFGW) enables ultrasonic assessment of cortical bone thickness. In vivo, it is challenging to detect this mode, as its power ratio with respect to disturbing ultrasound is reduced by soft tissue covering the bone. A phase-delayed ultrasound source is proposed to tailor the FFGW excitation in order to improve its power ratio. This situation is analyzed by 2D finite-element simulations. The soft tissue coating (7-mm thick) was simulated as a fluid covering an elastic plate (bone, 2-6 mm thick). A six-element array of emitters on top of the coating was excited by 50-kHz tone bursts so that each emitter was appropriately delayed from the previous one. Response was recorded by an array of receivers on top of the coating, 20-50 mm away from the closest emitter. Simulations predicted that such tailored/phase-delayed excitations should improve the power ratio of FFGW by 23 ± 5 dB, independent of the number of emitters (N). On the other hand, the FFGW magnitude should increase by 5.8 ± 0.5 dB for each doubling of N. This suggests that mode tailoring based on phase-delayed excitation may play a key role in the development of an in vivo FFGW assessment.

Propagation of time-reversed Lamb waves in bovine cortical bone in vitro

The present study aims to investigate the propagation of time-reversed Lamb waves in bovine cortical bone in vitro. The time-reversed Lamb waves were successfully launched at 200 kHz in 18 bovine tibiae through a time reversal process of Lamb waves. The group velocities of the time-reversed Lamb waves in the bovine tibiae were measured using the axial transmission technique. They showed a significant correlation with the cortical thickness and tended to follow the theoretical group velocity of the lowest order antisymmetrical Lamb wave fairly well, consistent with the behavior of the slow guided wave in long cortical bones.

Excitation of ultrasonic Lamb waves using a phased array system with two array probes: phantom and in vitro bone studies

Long bones are good waveguides to support the propagation of ultrasonic guided waves. The low-order guided waves have been consistently observed in quantitative ultrasound bone studies. Selective excitation of these low-order guided modes requires oblique incidence of the ultrasound beam using a transducer-wedge system. It is generally assumed that an angle of incidence, θi, generates a specific phase velocity of interest, co, via Snell's law, θi=sin(-1)(vw/co) where vw is the velocity of the coupling medium. In this study, we investigated the excitation of guided waves within a 6.3-mm thick brass plate and a 6.5-mm thick bovine bone plate using an ultrasound phased array system with two 0.75-mm-pitch array probes. Arranging five elements as a group, the first group of a 16-element probe was used as a transmitter and a 64-element probe was a receiver array. The beam was steered for six angles (0°, 20°, 30°, 40°, 50°, and 60°) with a 1.6-MHz source signal. An adjoint Radon transform algorithm mapped the time-offset matrix into the frequency-phase velocity dispersion panels. The imaged Lamb plate modes were identified by the theoretical dispersion curves. The results show that the 0° excitation generated many modes with no modal discrimination and the oblique beam excited a spectrum of phase velocities spread asymmetrically about co. The width of the excitation region decreased as the steering angle increased, rendering modal selectivity at large angles. The phenomena were well predicted by the excitation function of the source influence theory. The low-order modes were better imaged at steering angle ⩾30° for both plates. The study has also demonstrated the feasibility of using the two-probe phased array system for future in vivo study.

Influence of cortical bone thickness on the ultrasound velocity

OBJECTIVE

An experimental in vitro study was carried out to evaluate the influence of cortical bone thickness on ultrasound propagation velocity.

METHODS

Sixty bone plates were used, made from bovine femurs, with thickness ranging from 1 to 6 mm (10 of each). The ultrasound velocity measurements were performed using a device specially designed for this purpose, in an underwater acoustic tank and with direct contact using contact gel. The transducers were positioned in two ways: on opposite sides, with the bone between them, for the transverse measurement; and parallel to each other, on the same side of the bone plates, for the axial measurements.

RESULTS

In the axial transmission mode, the ultrasound velocity speed increased with cortical bone thickness, regardless of the distance between the transducers, up to a thickness of 5 mm, then remained constant thereafter. There were no changes in velocity when the transverse measures were made.

CONCLUSION

Ultrasound velocity increased with cortical bone thickness in the axial transmission mode, until the thickness surpasses the wavelength, after which point it remained constant.

LEVEL OF EVIDENCE

Experimental Study.

Analysis of ultrasonic waves propagating in a bone plate over a water half-space with and without overlying soft tissue

Recent in vitro studies have shown that guided waves can characterize bone properties. However, for clinical applications to be viable, the soft-tissue layer should be considered. This study examined the effect of soft tissue on guided waves using a bovine bone plate over a water half-space and overlaid by a 4-mm gelatin-based soft-tissue mimic. The data (with and without soft tissue) clearly show a high-frequency, fast-propagating wave packet and a low-frequency, delayed phase group. The presence of soft tissue attenuates the signals significantly and increases mode density and number as predicted by theory. The data retain higher frequency content than the bone-plate data at large offsets. Using theoretical dispersion curves, the guided modes can be identified with mode 1 (similar to the A0 Lamb mode) minimally affected by the addition of soft tissue. There is infiltration of high-frequency, late-arriving energy within the low-velocity guided-wave regime. Results of travel-time calculation suggest that P-wave and PP-reflections/multiples within the soft tissue may be responsible for the high-frequency oscillations.

Biophysical characterization of low-frequency ultrasound interaction with dental pulp stem cells

Background

Low-intensity ultrasound is considered an effective non-invasive therapy to stimulate hard tissue repair, in particular to accelerate delayed non-union bone fracture healing. More recently, ultrasound has been proposed as a therapeutic tool to repair and regenerate dental tissues. Our recent work suggested that low-frequency kilohertz-range ultrasound is able to interact with dental pulp cells which could have potential to stimulate dentine reparative processes and hence promote the viability and longevity of teeth.

Methods

In this study, the biophysical characteristics of low-frequency ultrasound transmission through teeth towards the dental pulp were explored. We conducted cell culture studies using an odontoblast-like/dental pulp cell line, MDPC-23. Half of the samples underwent ultrasound exposure while the other half underwent ‘sham treatment’ where the transducer was submerged into the medium but no ultrasound was generated. Ultrasound was applied directly to the cell cultures using a therapeutic ultrasound device at a frequency of 45 kHz with intensity settings of 10, 25 and 75 mW/cm² for 5 min. Following ultrasound treatment, the odontoblast-like cells were detached from the culture using a 0.25% Trypsin/EDTA solution, and viable cell numbers were counted. Two-dimensional tooth models based on μ-CT 2D images of the teeth were analyzed using COMSOL as the finite element analysis platform. This was used to confirm experimental results and to demonstrate the potential theory that with the correct combination of frequency and intensity, a tooth can be repaired using small doses of ultrasound. Frequencies in the 30 kHz–1 MHz range were analyzed. For each frequency, pressure/intensity plots provided information on how the intensity changes at each point throughout the propagation path. Spatial peak temporal average (SPTA) intensity was calculated and related to existing optimal spatial average temporal average (SATA) intensity deemed effective for cell proliferation during tooth repair.

Results

The results demonstrate that odontoblast MDPC-23 cell numbers were significantly increased following three consecutive ultrasound treatments over a 7-day culture period as compared with sham controls underscoring the anabolic effects of ultrasound on these cells. Data show a distinct increase in cell number compared to the sham data after ultrasound treatment for intensities of 10 and 25 mW/cm² (p < 0.05 and p < 0.01, respectively). Using finite element analysis, we demonstrated that ultrasound does indeed propagate through the mineralized layers of the teeth and into the pulp chamber where it forms a ‘therapeutic’ force field to interact with the living dental pulp cells. This allowed us to observe the pressure/intensity of the wave as it propagates throughout the tooth. A selection of time-dependent snapshots of the pressure/intensity reveal that the lower frequency waves propagate to the pulp and remain within the chamber for a while, which is ideal for cell excitation. Input frequencies and pressures of 30 kHz (70 Pa) and 45 kHz (31 kPa), respectively, with an average SPTA of up to 120 mW/cm² in the pulp seem to be optimal and agree with the SATA intensities reported experimentally.

Conclusions

Our data suggest that ultrasound can be harnessed to propagate to the dental pulp region where it can interact with the living cells to promote dentine repair. Further research is required to analyze the precise physical and biological interactions of low-frequency ultrasound with the dental pulp to develop a novel non-invasive tool for dental tissue regeneration.

Study of factors affecting the magnitude and nature of ultrasound exposure with in vitro set-ups

Therapeutic ultrasound is a clinically applied method to improve fracture healing and holds great potential as a manipulator of biologic material relevant to tissue engineering approaches. Unfortunately, the cell stimulating property of ultrasound is not known, which inhibits the optimal use of this technique. Additionally, many in vitro studies in this field use ultrasound configurations that are vulnerable to errors during calibration and use. These errors arise from the structural simplicity and incomplete characterization of these configurations. In this study, pulse-echo ultrasound, laser Doppler vibrometry and Schlieren imaging were applied to noninvasively characterize common in vitro experimental configurations. Fine wire thermocouple measurements were conducted to characterize any possible temperature rise during the ultrasound exposures. The results quantified the frequency dependent sound transmission through culture wells and the standing wave effect within the cell volume. These effects can cause uncertainty of up to 700% in the actual ultrasound exposure experienced by the cell. A temperature rise of 2.7°C was measured from an ultrasound configuration commonly used in vitro ultrasound studies. Furthermore, wave mode conversion in culture wells was observed, emphasizing the complexity of these sonications. Similar type Lamb waves have been observed in bone in vivo. Thus, Lamb waves may be a mechanism for stimulating the cells.

Correlations between ultrasonic guided wave velocities and bone properties in bovine tibia in vitro

Correlations between ultrasonic guided wave velocities and bone properties were investigated in bovine tibia in vitro. The velocities of the first arriving signal and the slow guided wave, termed V(FAS) and V(SGW), along the long axis of the tibia were measured at 200 kHz in 20 bovine tibiae using the axial transmission technique. V(FAS) yielded significant negative correlation coefficients of -0.54 to -0.66 with the bone properties. In contrast, V(SGW) yielded strong positive correlation coefficients of 0.68-0.84. The best univariate predictor of V(FAS) and V(SGW) was the cortical thickness yielding adjusted squared correlation coefficients of 0.41 and 0.69, respectively.

Impact of attenuation on guided mode wavenumber measurement in axial transmission on bone mimicking plates

Robust signal processing methods adapted to clinical measurements of guided modes are required to assess bone properties such as cortical thickness and porosity. Recently, an approach based on the singular value decomposition (SVD) of multidimensional signals recorded with an axial transmission array of emitters and receivers has been proposed for materials with negligible absorption, see Minonzio et al. [J. Acoust. Soc. Am. 127, 2913-2919 (2010)]. In presence of absorption, the ability to extract guided mode degrades. The objective of the present study is to extend the method to the case of absorbing media, considering attenuated plane waves (complex wavenumber). The guided mode wavenumber extraction is enhanced and the order of magnitude of the attenuation of the guided mode is estimated. Experiments have been carried out on 2 mm thick plates in the 0.2-2 MHz bandwidth. Two materials are inspected: polymethylacrylate (PMMA) (isotropic with absorption) and artificial composite bones (Sawbones, Pacific Research Laboratory Inc, Vashon, WA) which is a transverse isotropic absorbing medium. Bulk wave velocities and bulk attenuation have been evaluated from transmission measurements. These values were used to compute theoretical Lamb mode wavenumbers which are consistent with the experimental ones obtained with the SVD-based approach.

Ultrasound propagation velocity and broadband attenuation can help evaluate the healing process of an experimental fracture

Ultrasonometry seems to have a future for the evaluation of fracture healing. Ultrasound propagation velocity (USPV) significantly decreases at the same time that bone diameter decreases as healing takes place, thus approaching normal values. In this investigation, both USPV and broadband ultrasound attenuation (BUA) were measured using a model of a transverse mid-diaphyseal osteotomy of sheep tibiae. Twenty-one sheep were operated and divided into three groups of seven, according to the follow-up period of 30, 60, and 90 days, respectively. The progress of healing of the osteotomy was checked with monthly conventional radiographs. The animals were killed at the end of the period of observation of each group, both operated-upon and intact tibiae being resected and submitted to the measurement of underwater transverse and direct contact transverse and longitudinal USPV and BUA at the osteotomy site. The intact left tibia of the 21 animals was used for control, being examined on a symmetrical diaphyseal segment. USPV increased while BUA decreased with the progression of healing, with significant differences between the operated and untouched tibiae and between the periods of observation, for most of the comparisons. There was a strong negative correlation between USPV and BUA. Both USPV and BUA directly reflect and can help predict the healing of fractures, but USPV alone can be used as a fundamental parameter. Ultrasonometry may be of use in clinical application to humans provided adequate adaptations can be developed.

Numerical and experimental simulation of the effect of long bone fracture healing stages on ultrasound transmission across an idealized fracture

The effect of various stages of fracture healing on the amplitude of 200 kHz ultrasonic waves propagating along cortical bone plates and across an idealized fracture has been modeled numerically and experimentally. A simple, water-filled, transverse fracture was used to simulate the inflammatory stage. Next, a symmetric external callus was added to represent the repair stage, while a callus of reducing size was used to simulate the remodeling stage. The variation in the first arrival signal amplitude across the fracture site was calculated and compared with data for an intact plate in order to calculate the fracture transmission loss (FTL) in decibels. The inclusion of the callus reduced the fracture loss. The most significant changes were calculated to occur from the initial inflammatory phase to the formation of a callus (with the FTL reducing from 6.3 to between 5.5 and 3.5 dB, depending on the properties of the callus) and in the remodeling phase where, after a 50% reduction in the size of the callus, the FTL reduced to between 2.0 and 1.3 dB. Qualitatively, the experimental results follow the model predictions. The change in signal amplitude with callus geometry and elastic properties could potentially be used to monitor the healing process.

Measurement of the dispersion and attenuation of cylindrical ultrasonic guided waves in long bone

Osteoporotic bones are likely to have less cortical bone than healthy bones. The velocities of guided waves propagating in a long cylindrical bone are very sensitive to bone properties and cortical thickness (CTh). This work studies the dispersion and attenuation of ultrasonic guided waves propagating in long cylindrical bone. A hollow cylinder filled with a viscous liquid was used to model the long bone and then to calculate the theoretical phase and group velocities, as well as the attenuation of the waves. The generation and selection of guided wave modes were based on theoretical dispersive curves. The phase velocity and attenuation of cylindrical guided wave modes, such as L(0,1), L(0,2) and L(0,3), were measured in bovine tibia using angled beam transducers at various propagation distances ranging from 75 to 160 mm. The results showed that the phase velocity of the L(0,2) guided wave mode decreased with an increase in CTh. The attenuation of the low cylindrical guided wave modes was a nonlinear function that increased with propagation distance and mode order. The L(0,2) mode had a different attenuation for each CTh. The experimental results were in good agreement with the predicted values. Cylindrical guided waves of low-frequency and low-order have been shown to demonstrate more dispersion and less attenuation and should, therefore, be used to evaluate long bone.

The effect of boundary conditions on guided wave propagation in two-dimensional models of healing bone

Guided wave propagation has recently drawn significant interest in the ultrasonic characterization of bone. In this work, we present a two-dimensional computational study of ultrasound propagation in healing bones aiming at monitoring the fracture healing process. In particular, we address the effect of fluid loading boundary conditions on the characteristics of guided wave propagation, using both time and time-frequency (t-f) signal analysis techniques, for three study cases. In the first case, the bone was assumed immersed in blood which occupied the semi-infinite spaces of the upper and lower surfaces of the plate. In the second case, the bone model was assumed to have the upper surface loaded by a 2mm thick layer of blood and the lower surface loaded by a semi-infinite fluid with properties close to those of bone marrow. The third case, involves a three-layer model in which the upper surface of the plate was again loaded by a layer of blood, whereas the lower surface was loaded by a 2mm layer of a fluid which simulated bone marrow. The callus tissue was modeled as an inhomogeneous material and fracture healing was simulated as a three-stage process. The results clearly indicate that the application of realistic boundary conditions has a significant effect on the dispersion of guided waves when compared to simplified models in which the bone's surfaces are assumed free.

Modeling the impact of soft tissue on axial transmission measurements of ultrasonic guided waves in human radius

Recent in vitro and simulation studies have shown that guided waves measured at low ultrasound frequencies (f=200 kHz) can characterize both material properties and geometry of the cortical bone wall. In particular, a method for an accurate cortical thickness estimation from ultrasound velocity data has been presented. The clinical application remains, however, a challenge as the impact of a layer of soft tissue on top of the bone is not yet well established, and this layer is expected to affect the dispersion and relative intensities of guided modes. The present study is focused on the theoretical modeling of the impact of an overlying soft tissue. A semianalytical method and finite-difference time domain simulations were used. The models developed were shown to predict consistently real in vivo data on human radii. As a conclusion, clinical guided wave data are not consistent with in vitro data or related in vitro models, but use of an adequate in vivo model, such as the one introduced here, is necessary. A theoretical model that accounts for the impact of an overlying soft tissue could thus be used in clinical applications.

Ultrasound transmission loss across transverse and oblique bone fractures: an in vitro study

An axial transmission technique has been used to investigate the changes in the first arrival time and signal amplitude of 200 kHz ultrasonic waves travelling across different fracture geometries. Results taken from intact bovine femora were compared with those produced when a transverse and an oblique fracture were simulated. The arrival time and signal amplitude displayed a different variation with receiver position for the two geometries and a given fracture gap width. A comparison between this work and a previous study suggested that the marrow does not play a significant role in the mechanisms causing the change in arrival time and signal amplitude. Numerical modelling revealed that an oblique fracture caused a reduction in the extra time delay of the propagating wave compared with the transverse case, but a decrease in the corresponding signal amplitude, i.e., greater signal loss. The angle of the oblique fracture was investigated and results suggested that decreasing the fracture angle relative to the wave propagation direction caused a decrease in the extra time delay and an increase in signal loss. These findings are important for determining the sensitivity of systems for monitoring fracture healing using ultrasound arrival time and signal amplitude. (E-mail: spd@inorbit.com).

Ultrasonic guided waves in bone

Recent progress in quantitative ultrasound (QUS) has shown increasing interest toward measuring long bones by ultrasonic guided waves. This technology is widely used in the field of nondestructive testing and evaluation of different waveguide structures. Cortical bone provides such an elastic waveguide and its ability to sustain loading and resist fractures is known to be related to its mechanical properties at different length scales. Because guided waves could yield diverse characterizations of the bone's mechanical properties at the macroscopic level, the method of guided waves has a strong potential over the standardized bone densitometry as a tool for bone assessment. Despite this, development of guided wave methods is challenging, e.g., due to interferences and multiparametric inversion problems. This paper discusses the promises and challenges related to bone characterization by ultrasonic guided waves.

Ultrasonic monitoring of bone fracture healing

Quantitative ultrasound has attracted significant interest in the evaluation of bone fracture healing. Animal and clinical studies have demonstrated that the propagation velocity across fractured bones can be used as an indicator of healing. Researchers have recently employed computational methods for modeling wave propagation in bones, aiming to gain insight into the underlying mechanisms of wave propagation and to further enhance the monitoring capabilities of ultrasound. In this paper, we review the relevant literature and present the current status of knowledge.

Modelling the effects of different fracture geometries and healing stages on ultrasound signal loss across a long bone fracture

The effect on the signal amplitude of ultrasonic waves propagating along cortical bone plates was modelled using a 2D Finite Difference code. Different healing stages, represented by modified fracture geometries were introduced to the plate model. A simple transverse and oblique fracture filled with water was introduced to simulate the inflammatory stage. Subsequently, a symmetric external callus surrounding a transverse fracture was modelled to represent an advanced stage of healing. In comparison to the baseline (intact plate) data, a large net loss in signal amplitude was produced for the simple transverse and oblique cases. Changing the geometry to an external callus with different mechanical properties caused the net loss in signal amplitude to reduce significantly. This relative change in signal amplitude as the geometry and mechanical properties of the fracture site change could potentially be used to monitor the healing process.

An in vitro study of ultrasound signal loss across simple fractures in cortical bone mimics and bovine cortical bone samples

Measurements have been performed on Sawbones and bovine cortical bone samples at 200 kHz using an axial transmission technique to investigate the factors that determine how ultrasonic waves propagate across a simulated fracture. The peak amplitude of the first arrival signal (FAS) was studied. Results taken from intact specimens were compared with those produced when a simple transverse fracture was introduced. These fracture simulation experiments were found to be consistent with Finite Difference modelling of the experimental conditions. The peak amplitude showed a characteristic variation across the fracture caused by interference between reradiated and scattered/diffracted waves at the fracture site and a net Fracture Transmission Loss (FTL). For small fracture gaps, the change in amplitude was sensitive to the presence of the fracture. This sensitivity suggests that this parameter could be a good quantitative indicator for the fracture healing process assuming the relative change in this parameter brought about by healing is measurable.