Waves In Bone Research Articles

Ultrasonic Guided Waves in Bone: A Decade of Advancement in Review.

The use of guided wave ultrasonography as a means to assess cortical bone quality has been a significant practice in bone quantitative ultrasound for more than 20 years. In this article, the key developments within the technology of ultrasonic guided waves (UGW) in long bones during the past decade are documented. The covered topics include data acquisition configurations available for measuring bone guided waveforms, signal processing techniques applied to bone UGW, numerical modeling of ultrasonic wave propagation in cortical long bones, formulation of inverse approaches to extract bone properties from observed ultrasonic signals, and clinical studies to establish the technology's application and efficacy. The review concludes by highlighting specific challenging problems and future research directions. In general, the primary purpose of this work is to provide a comprehensive overview of bone guided-wave ultrasound, especially for newcomers to this scientific field.

Estimating dispersion relations of ultrasonic guided waves in bone using a modified matrix pencil algorithm

Guided wave ultrasound technology is well recognized for non-destructive testing. The technology is increasingly applied in bone characterization and imaging to evaluate bone strength and fracture risk. Cortical bone with porous microstructure induces substantial dispersion and attenuation effects on ultrasonic guided waves (UGW). Estimating frequency-dependent propagation characteristics of co-excited wave modes is significant to studying UGW propagation and developing wave-based approaches. This work implements a modified matrix pencil method to simultaneously compute modal wavenumber and attenuation coefficient from dispersive bone UGW signals with improved convergence rate and noise reduction ability. The dispersion estimation is formulated as a matrix pencil or generalized eigenvalue problem with Loewner matrices. The extracted eigenvalues are estimated complex wavevectors, in which the wavenumber and attenuation can be deduced from the real and imaginary components respectively. The performance of the proposed algorithm is demonstrated with low signal-to-noise-ratio synthetic and experimental datasets acquired using axial-transmission measurement settings. The computed dispersive features are validated via comparison with the theoretically calculated dispersion curves by semi-analytical finite-element simulation. The dispersive wave properties are accurately reconstructed in a computationally efficient manner and can be further utilized for bone parametric analyses and subsequently clinical bone health assessment.

Single Versus Multi-channel Dispersion Analysis of Ultrasonic Guided Waves Propagating in Long Bones.

Ultrasonic guided wave techniques have been applied to characterize cortical bone for osteoporosis assessment. Compared with the current gold-standard X-ray-based diagnostic methods, ultrasound-based techniques pose some advantages such as compactness, low cost, lack of ionizing radiation, and their ability to detect the mechanical properties of the cortex. Axial transmission technique with a source-receiver offset is employed to acquire the ultrasound data. The dispersion characteristics of the guided waves in bones are normally analyzed in the transformed domains using the dispersion curves. The transformed domain can be time-frequency map using a single channel or wavenumber-frequency (or phase velocity-frequency) map with multi-channels. In terms of acquisition effort, the first method is more cost- and time-effective than the latter. However, it remains unclear whether single-channel dispersion analysis can provide as much quantitative guided-wave information as the multi-channel analysis. The objective of this study is to compare the two methods using numerically simulated and ex vivo data of a simple bovine bone plate and explore their advantages and disadvantages. Both single- and multi-channel signal processing approaches are implemented using sparsity-constrained optimization algorithms to reinforce the focusing power. While the single-channel data acquisition and processing are much faster than those of the multi-channel, modal identification and analysis of the multi-channel data are straightforward and more convincing.

Theoretical model of guided waves in a bone-mimicking plate coupled with soft-tissue layers

Quantitative ultrasound has shown a significant promise in the assessment of bone characteristics in the recent reports. However, our understanding of wave interaction with bone tissues is still far from complete since the propagation of ultrasonic waves in bones is a very challenging topic due to their multilayer nature. The aim of the current study is to develop a theoretical model for guided waves in a bone-mimicking plate coupled with two soft-tissue layers. Here, the bone plate is modeled as an isotropic solid layer while the soft tissues are modeled as fluid layers. Based on the boundary conditions set for the three-layered structure, a characteristic equation is obtained which results in dispersion curves of the phase and group velocities. New expressions for free guided waves propagating in the trilayered plate are introduced. The amplitudes of wave modes generated by time-harmonic loads applied in the plate are theoretically computed by reciprocity consideration. As an example of calculation, the normalized amplitudes of the lowest wave modes are presented. The obtained results and equations discussed in this study could be, in general, useful for further applications in the area of bone quantitative ultrasound.

Characterization of shear waves in cortical bone using the axial transmission technique

A quantitative ultrasound technique with the advantages of an axial transmission measurement was applied in this study for the characterization of ultrasonic waves in the MHz range. This study focuses on the evaluation and effective detection of shear waves in bone plates. Subsequently, wave propagation in a homogeneous and isotropic bone model is analyzed using the finite-difference time-domain, (FDTD) method. A comparative analysis is presented between the experimental measurements and simulation results. Ultrasound generated and detected at different incident angles, revealed that longitudinal or shear waves can be observed depending on the angle. Wave velocity measurements in the anisotropic medium of the bone plate showed good agreement with the FDTD isotropic model results, suggesting that isotropic models could give a reliable estimation for measurements performed in the axial direction of the cortical bone. Finally, this study confirmed the possibility of shear wave detection using the axial transmission technique.

Influence of guided waves in bone on pulse-inversion contrast-enhanced ultrasound.

Guided waves generated from bone cortex inevitably act on microbubbles flowing through skeletal muscle capillaries in contrast-enhanced ultrasound (CEUS) and might influence the image quality. However, the action mechanism underlying the guided waves influence is still unknown, especially under contrast pulse-inversion transmission mode. This study aimed to clarify the influence of guided waves on pulse-inversion CEUS, which was investigated via in vitro infusion experiments. Tibia guided waves were detected at pulse-inversion transmission and then characterized by using a short-time Fourier transform energy distribution. Using results at normal incidence as a baseline, the influence of guided wave dispersion on the contrast and resolution of pulse-inversion CEUS was investigated at an oblique incidence through continuous microbubbles infusion experiments in a vessel-tibia flow phantom. Frequency-dispersive property of tibia guided waves was observed at phases 0° and 180°, which improved the contrast of CEUS and reduced its resolution. Pulse-inversion CEUS balanced the contrast enhancement and resolution degeneration induced by guided waves. By contrast, contrast-to-tissue ratio of pulse-inversion CEUS increased by up to 109.1±13.2% (P<0.05) due to guided waves and its resolution was up to 0.9±0.1 times that of baseline. Alterations of contrast and resolution in pulse-inversion CEUS induced by guided waves might provide an additional assessment for the capillary perfusion in the skeletal muscle near the bone cortex.

Vibro-acoustic stimulating ultrasonic guided waves in long bone

Ultrasonic guided wave is sensitive to waveguide microstructure and material property, which has great potential applications in long cortical bone evaluation. Due to the multimodal dispersion effect, low-frequency guided wave is usually used to avoid multimode overlapping and simplify the signal processing. However, the traditional low-frequency ultrasound transducer is usually designed on a large-scale (around several millimeters), leading to relatively low-spatial resolution. In response to such a technique limit, an ultrasound-stimulated vibro-acoustic method is introduced to excite low-frequency ultrasonic guided waves. There are two excitation ways of the ultrasound-stimulated vibro-acoustic method, i.e., a single amplitude-modulated (AM) beam and confocal beam excitation. In the case of the single beam excitation, a high-frequency signal is modulated by using a low-frequency amplitude. In addition, low-frequency vibration can also be produced by a confocal transducer, where two beams are close to the center frequency and focus on a small region. In this way, the frequency difference between two beams can be selected to generate the arbitrary low-frequency excitation in a given bandwidth on the focus point. In this paper, we first introduce the theory of ultrasonic guided wave in the plate and the basic principle of ultrasound-stimulated acoustic emission. Second, the three-dimensional finite element method is used to simulate the phenomena of the low-frequency ultrasonic guided waves excited by the ultrasound-stimulated vibro-acoustic method. Two Gaussian-function enveloped tone-burst signals close to the center frequencies of 5 MHz are used to excite 150 kHz low-frequency guided wave in a 3 mm-thick bone plate. An ex-vivo bovine bone plate is involved in the experiments to test the feasibility of the proposed method. The axial transmission ultrasonic guided waves are recorded at eight different propagation distances. The time-frequency representation method is used to analyze the dispersive guided waves. The results indicate that both the two confocal beams and the single AM beam are capable of stimulating low-frequency ultrasonic guided waves in the bone plate. The first two fundamental guided wave modes, i.e., symmetrical S0 and asymmetrical A0 are observed in the bone plate. Similar spectrum can be obtained in the two different excitation ways. In the simulation and experiment, two wave packets can be separated in the distance-time diagram of the received signals. Good agreement can be found between the results of time-frequency representation and the theoretical group dispersion curves. This study can enhance the spatial resolution of measuring ultrasonic guided wave in long bone, and improve the flexibility of excitation with arbitrary frequency in a given bandwidth. The study can be helpful for developing the new clinical techniques of using low-frequency guided waves for long cortical bone assessment.

1F25 脛骨におけるガイド波骨密度計測を想定した多孔質丸棒の音速と密度の推定(GS1-2:硬組織の力学(2))

1F25 脛骨におけるガイド波骨密度計測を想定した多孔質丸棒の音速と密度の推定(GS1-2:硬組織の力学(2))

On ultrasound waves guided by bones with coupled soft tissues: A mechanism study and in vitro calibration

The influence of soft tissues coupled with cortical bones on precision of quantitative ultrasound (QUS) has been an issue in the clinical bone assessment in conjunction with the use of ultrasound. In this study, the effect arising from soft tissues on propagation characteristics of guided ultrasound waves in bones was investigated using tubular Sawbones phantoms covered with a layer of mimicked soft tissue of different thicknesses and elastic moduli, and an in vitro porcine femur in terms of the axial transmission measurement. Results revealed that presence of soft tissues can exert significant influence on the propagation of ultrasound waves in bones, leading to reduced propagation velocities and attenuated wave magnitudes compared with the counterparts in a free bone in the absence of soft tissues. However such an effect is not phenomenally dependent on the variations in thickness and elastic modulus of the coupled soft tissues, making it possible to compensate for the coupling effect regardless of the difference in properties of the soft tissues. Based on an in vitro calibration, this study proposed quantitative compensation for the effect of soft tissues on ultrasound waves in bones, facilitating development of high-precision QUS.

3P5-31 Electromagnetic Response Exited by Amplitude-Modulated Ultrasonic Waves in Bones(Poster Session)

3P5-31 Electromagnetic Response Exited by Amplitude-Modulated Ultrasonic Waves in Bones(Poster Session)

Shock wave therapy for femoral head necrosis—Pressure measurements inside the femoral head

There is a persisting need for effective therapies of femoral head necrosis, a common bone disease. Promising clinical results have been stated for the treatment with extracorporeal shock waves (ESW). However, the effective remaining pressure in the target region inside the femoral head has never been determined. Aim of this study was to investigate whether ESW are able to propagate through bone without an excessive loss of pressure. The remaining ESW pressure generated by an electromagnetic device after passing a certain intraosseous distance within the femoral head was measured. Standardized holes were drilled in porcine femora and the absorption in relation to reference measurements in degassed water was determined. The results showed continuous attenuation of shock waves in bone. After a clinical relevant intraosseous distance of 10 mm an ESW pressure of ∼50% remained. In conclusion, ESW have the potential to reach necrotic regions with therapeutic pressure levels and to effectively treat femoral head necrosis.

Role of absorption mechanisms for ultrasound attenuation in cancellous bone: Macroscopic modeling and experiment.

Evaluation of the relative contribution of physical mechanisms responsible for attenuation of ultrasonic wave in cancellous bone is one of the crucial issues from the point of view of modeling elastic wave propagation and related model-based identification of the structural and mechanical properties of bone material. Considering trabecular bone as a porous material filled with fluid, the wave attenuation may stem from (i) intrinsic absorption in the fluid and solid phase, (ii) friction at the fluid-solid interface, as well as (iii) wave scattering by inhomogeneities (pores/trabeculaes). The commonly used for modeling ultrasound propagation in cancellous bone of the macroscopic Biot’s theory will be discussed in context of its potential applicability for prediction of wave parameters: phase velocity and attenuation coefficient as functions of frequency. Since the model was introduced for long wavelength range, the scattering effects are neglected, and the analysis will be focused on the absorption mechanisms responsible for attenuation of ultrasonic waves in bone material. The suitability of the model will be verified by comparison of results of sensitivity analysis of the model with in vitro experimental ultrasonic data obtained for cancellous bones filled with different fluids.

Velocity dispersion of guided waves propagating in a free gradient elastic plate: Application to cortical bone

The classical linear theory of elasticity has been largely used for the ultrasonic characterization of bone. However, linear elasticity cannot adequately describe the mechanical behavior of materials with microstructure in which the stress state has to be defined in a non-local manner. In this study, the simplest form of gradient theory (Mindlin Form-II) is used to theoretically determine the velocity dispersion curves of guided modes propagating in isotropic bone-mimicking plates. Two additional terms are included in the constitutive equations representing the characteristic length in bone: (a) the gradient coefficient g, introduced in the strain energy, and (b) the micro-inertia term h, in the kinetic energy. The plate was assumed free of stresses and of double stresses. Two cases were studied for the characteristic length: h=10(-4) m and h=10(-5) m. For each case, three subcases for g were assumed, namely, g>h, g<h, and g=h. The values of g and h were of the order of the osteons size. The velocity dispersion curves of guided waves were numerically obtained and compared with the Lamb modes. The results indicate that when g was not equal to h (i.e., g not equal h), microstructure affects mode dispersion by inducing both material and geometrical dispersion. In conclusion, gradient elasticity can provide supplementary information to better understand guided waves in bones.

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.

Model study on assessment of bone by ultrasonic guided waves through a varying layer of soft tissue

Propagation parameters of ultrasonic guided waves in long bones are sensitive to changes of the cortical thickness, which is one of bone parameters affected by osteoporosis. Meanwhile, the guided waves in bone can be masked by the longitudinal waves in the overlying soft tissues, especially in obese patients. The goal of this study was to explore a possibility to minimize the effect of soft tissue on quantitative assessment of propagation parameters of axial guided waves in long bones. Phantoms and animal bone fragments modeling the axial gradients of the cortical thickness in the human proximal tibia were used. The specimens were covered by a layer of soft tissue of varied thickness. Ultrasonic signals were acquired in the pulse mode at 0.1 MHz by the surface transmission. The specimens were scanned lengthwise and the acquired signals were plotted versus the scanned distance. Analysis of the obtained waveform profiles along the tested specimens allowed quantitative evaluation of the variations of the cortical thickness despite the presence of a 5‐6 mm soft tissue layer. The ratio of the acoustic wavelength to the soft tissue layer thickness defines the level of the soft tissue effect.

Ultrasonic guided waves in bone

Recent progress in quantitative ultrasound (QUS) has shown increasing interest towards measuring long bones by ultrasonic guided waves. This technology is widely used in the field of non‐destructive 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 relate to its mechanical properties at different length scales. As guided waves could yield diverse characterization of 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 problem. This paper discusses the promises and challenges related to bones characterization by ultrasonic guided waves.

Three-dimensional simulation of ultrasound propagation through trabecular bone structures measured by synchrotron microtomography

Three-dimensional numerical simulations of ultrasound transmission were performed through 31 trabecular bone samples measured by synchrotron microtomography. The synchrotron microtomography provided high resolution 3D mappings of bone structures, which were used as the input geometry in the simulation software developed in our laboratory. While absorption (i.e. the absorption of ultrasound through dissipative mechanisms) was not taken into account in the algorithm, the simulations reproduced major phenomena observed in real through-transmission experiments in trabecular bone. The simulated attenuation (i.e. the decrease of the transmitted ultrasonic energy) varies linearly with frequency in the MHz frequency range. Both the speed of sound (SOS) and the slope of the normalized frequency-dependent attenuation (nBUA) increase with the bone volume fraction. Twenty-five out of the thirty-one samples exhibited negative velocity dispersion. One sample was rotated to align the main orientation of the trabecular structure with the direction of ultrasonic propagation, leading to the observation of a fast and a slow wave. Coupling numerical simulation with real bone architecture therefore provides a powerful tool to investigate the physics of ultrasound propagation in trabecular structures. As an illustration, comparison between results obtained on bone modelled either as a fluid or a solid structure suggested the major role of mode conversion of the incident acoustic wave to shear waves in bone to explain the large contribution of scattering to the overall attenuation.

Nonconventional approaches to ultrasonic assessment of skeletal system

Conventional bone ultrasonometry is based on the transmission mode measurement of the linear acoustic parameters of bone (speed of sound and broadband attenuation). It is a well-established technique specifically for osteoporosis diagnostics though it is highly limited in its applications. It cannot be used for the assessment of the hip bone which is the most important area in characterization of the skeletal system and can hardly be used in pediatric applications, particularly in neonatology, for the assessment of newborns and premature and low-birth-weight infants skeletal systems, which became especially vital during the last few decades. There are several new ideas on acoustic assessment of the skeletal sites hardly accessible by the conventional bone ultrasonometry and on principles of the acoustic characterization of bone quality, fracture risk evaluation, and monitoring of therapeutic interventions. New approaches are based on the use of the ultrasound radiation pressure for the remote generation of acoustic waves in bones, on the use of various modes of guided acoustic waves having a propagation speed dependent on both the elasticity modulus and the bone thickness, on the use of geometrical dispersion of sound velocity for bone characterization, and the use of principles of nonlinear acoustic spectroscopy for remote bone testing. [Work supported by NIH.]

Guided ultrasonic waves in long bones: modelling, experiment and in vivo application

Existing ultrasound devices for assessing the human tibia are based on detecting the first arriving signal, corresponding to a wave propagating at, or close to, the bulk longitudinal velocity in bone. However, human long bones are effectively irregular hollow tubes and should theoretically support the propagation of more complex guided modes similar to Lamb waves in plates. Guided waves are attractive because they propagate throughout the bone thickness and can potentially yield more information on bone material properties and architecture. In this study, Lamb wave theory and numerical simulations of wave propagation were used to gain insights into the expected behaviour of guided waves in bone. Experimental measurements in acrylic plates, using a prototype low-frequency axial pulse transmission device, confirmed the presence of two distinct propagating waves: the first arriving wave propagating at, or close to, the longitudinal velocity, and a slower second wave whose behaviour was consistent with the lowest order Lamb antisymmetrical (A0) mode. In a pilot study of healthy and osteoporotic subjects, the velocity of the second wave differed significantly between the two groups, whereas the first arriving wave velocity did not, suggesting the former to be a more sensitive indicator of osteoporosis. We conclude that guided wave measurements may offer an enhanced approach to the ultrasonic characterization of long bones.

Theoretical study of temperature elevation at muscle/bone interface during ultrasound hyperthermia.

This paper examines the distributions of the SAR (specific absorption rate) ratio and temperature elevation when an ultrasound beam propagates through the interface of muscle and bone. This interface is regarded as a flat boundary to partition the energy of the ultrasound beam, and the analytical solution of temperature distribution is based on the steady-state bio-heat transfer equation. The parameters considered are the incident angle of ultrasound beam, the ultrasound frequency, the acoustic attenuation coefficients of refracted longitudinal and shear waves in bone, and the blood perfusion in muscle. The results show that the peak of the SAR ratio is always at the interface of muscle and bone, while the peak of temperature is located in the bone region beyond the interface. A muscle with lower perfusion or a bone with higher acoustic attenuation results in the shifting of the temperature peak closer to the interface. It is more difficult to heat a higher perfused muscle in front of a bone using a lower frequency ultrasound since the temperature elevation for bone relative to muscle is greater.