Use of multiple acoustic wave modes for assessment of long bones: model study

Recycled windshield glass as new material for producing ultrasonic phantoms of cortical bone-healing stages

The quantitative ultrasound technique was used to evaluate bone-mimicking phantoms; however, these phantoms do not mimic the intermediate stages of cortical bone healing. We propose using windshield glass as an original material to produce phantoms that mimic the characteristics of three different stages of cortical bone healing. This material was processed via a route that included breaking, grinding, compacting, drying, and sintering in four temperature groups: 625 °C, 645 °C, 657 °C, and 663 °C. The parameters evaluated were the ultrasonic longitudinal phase velocity (cL), corrected (αc) ultrasonic attenuation coefficient, and bulk density (ρs). The results showed that the mean values ofcL,αc,andρsvaried from 2, 398 to 4, 406 m·s^-1, 3 to 10 dB·cm^-1, and 1, 563 to 2, 089 kg·m^-3, respectively. The phantoms exhibited properties comparable with the three stages of cortical bone healing and can be employed in diagnostic and therapeutic studies using ultrasound.

Real-time acoustic sensing and artificial intelligence for error prevention in orthopedic surgery

In this work, we developed and validated a computer method capable of robustly detecting drill breakthrough events and show the potential of deep learning-based acoustic sensing for surgical error prevention. Bone drilling is an essential part of orthopedic surgery and has a high risk of injuring vital structures when over-drilling into adjacent soft tissue. We acquired a dataset consisting of structure-borne audio recordings of drill breakthrough sequences with custom piezo contact microphones in an experimental setup using six human cadaveric hip specimens. In the following step, we developed a deep learning-based method for the automated detection of drill breakthrough events in a fast and accurate fashion. We evaluated the proposed network regarding breakthrough detection sensitivity and latency. The best performing variant yields a sensitivity of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$93.64 \pm 2.42$$\end{document}93.64±2.42% for drill breakthrough detection in a total execution time of 139.29\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\hbox { ms}}$$\end{document}ms. The validation and performance evaluation of our solution demonstrates promising results for surgical error prevention by automated acoustic-based drill breakthrough detection in a realistic experiment while being multiple times faster than a surgeon’s reaction time. Furthermore, our proposed method represents an important step for the translation of acoustic-based breakthrough detection towards surgical use.

Ex Vivo Assessment of Cortical Bone Properties Using Low-Frequency Ultrasonic Guided Waves

The early diagnosis of osteoporosis through bone quality assessment is a major public health challenge. Research in axial transmission using ultrasonic guided waves has shown the method to be sensitive to the geometrical and mechanical properties of the cortical layer in long bones. However, because of the asymmetric nature of cortical bone, the introduction of a more elaborate numerical model than the analytical plate and cylinder models, as well as its inversion, continues to be challenging. The aim of this article is, therefore, to implement a bone-like geometry using semianalytical finite-element (SAFE) modeling to perform the inverse characterization of ex vivo radii at low frequencies (< 60 kHz). Five cadaveric radiuses were taken from donors aged between 53 and 88 and tested using a typical axial transmission configuration at the middle of the diaphysis. The dispersion curves of the propagating modes were measured experimentally and then systematically compared with the solutions obtained with the SAFE method. For each sample, four parameters were estimated using a parameter identification procedure: 1) the bulk density; 2) the thickness; 3) the outer diameter; and 4) a shape factor (SF). The results showed a moderate agreement between the predicted bulk density and the average voxel value calculated from X-ray computed tomography images. Furthermore, a good agreement was observed between the geometrical parameters (thickness, outer diameter, and SF) and the reference images.

Non-radiative healing assessment techniques for fractured long bones and osseointegrated implant

The paper provides an overview of the fracture healing process of long bones, a review of work that proposed appropriate physical parameters for the assessment of healing and highlights some recent work that reported on the development of non-radiative technique for healing assessment. An overview of the development and monitoring of osseointegration for trans-femoral osseointegrated implant is also presented. The state of healing of a fractured long bone and the stability of osseointegrated implants can be seen as engineering structural components where the mechanical properties are restored to facilitate their desired function. To this end, this paper describes non-radiative techniques that are useful for healing assessment and the stability assessment of osseointegrated implants. The achievement of non-radiative quantitative assessment methodologies to determine the state of healing of fractured long bones and to assess the stability of osseointegrated implant will shorten the patient's rehabilitation time, allowing earlier mobility and return to normal activities. Recent work on the development of assessment techniques supported by the Office of Naval Research as part of the Monitoring of Osseointegrated Implant Prosthesis program is highlighted.

Effect of intracortical bone properties on the phase velocity and cut-off frequency of low-frequency guided wave modes (20-85 kHz)

The assessment of intracortical bone properties is of interest since early-stage osteoporosis is associated with resorption in the endosteal region. However, understanding the interaction between ultrasonic guided waves and the cortical bone structure remains challenging. The purpose of this work is to investigate the effect of intracortical bone properties on the ultrasonic response obtained at low-frequency (<100 kHz) using an axial transmission configuration. The semi-analytical finite element method was used to simulate the propagation of guided waves in a waveguide with realistic geometry and material properties. An array of 20 receivers was used to calculate the phase velocity and cut-off frequency of the excited modes using the two-dimensional Fourier transform. The results show that the position of the emitter around the circumference of the bone is an important parameter to control since it can lead to variations of up to 10 dB in the amplitude of the transmitted modes. The cut-off frequency of the high order modes was, however, only slightly affected by the circumferential position of the emitter, and was sensitive mainly to the axial shear modulus. The phase velocity and cut-off frequency in the 20-85 kHz range are promising parameters for the assessment of intracortical properties.

Fatigue evaluation of long cortical bone using ultrasonic guided waves

Bone fatigue fracture is a progressive disease due to stress concentration. This study aims to evaluate the long bone fatigue damage using the ultrasonic guided waves. Two-dimensional finite-difference time-domain method was employed to simulate the ultrasonic guided wave propagation in the long bone under different elastic modulus. The experiment was conducted on a 3.8 mm-thick bovine bone plate. The phase velocities of two fundamental guided modes, A1 and S1, were measured by using the axial transmission technique. Simulation shows that the phase velocities of guided modes A1 and S1 decrease with the increasing of the fatigue damage. After 20,000 cycles of fatigue loading on the bone plate, the average phase velocities of A1 and S1 modes were 6.6% and 5.3% respectively, lower than those of the intact bone. The study suggests that ultrasonic guided waves can be potentially used to evaluate the fatigue damage in long bones.

Semi-analytical finite-element modeling approach for guided wave assessment of mechanical degradation in bones

Numerical models based on the Semi Analytical Finite-Element method are used to study the characteristics of guided wave modes supported by bone-like multi-layered tubular structures. The method is first validated using previous literature and experimental studies on phantoms mimicking healthy and osteoporotic conditions of cortical bone, and later used to study a trilayer marrow–bone–tissue system at varying mechanical degradation levels. The results show that bone condition strongly affects the modal properties of axially propagating guided waves and indicates that L(0,3) and F(1,6) are suitable modes for assessing the mechanical condition of the bone. The work here reports suitable modal selection and their dispersion properties which would the aid in development of a transduction mechanism for mechanical assessment of bones.

Characterization of a new ultrasound device designed for measuring cortical porosity at the human tibia: A phantom study

Quantitative ultrasound (QUS) measurements of trabecular bone are a useful tool for the assessment of osteoporotic fracture risk. However, cortical bone properties (e.g. porosity) have an impact on bone strength as well and thus current research is focused on QUS assessment of cortical bone properties. Simulation studies of ultrasound propagation through cortical bone indicate that anisotropy, calculated from the ratio of the velocities in axial and tangential directions, is correlated with porosity. However, this relationship is affected by error sources, specifically bone surface curvature and variability of probe positioning. With the aim of in vivo estimation of cortical porosity a new ultrasound device was developed, which sequentially measures velocities in 3 different directions (axial=0° and ±37.5°) using the axial transmission method. Measurements on planar porosity phantoms (0-25%) were performed to confirm the results of the afore mentioned simulation studies. Additionally, measurements on cylindrical phantoms without pores (min. radius=34mm for strongest curvature) were performed to estimate the influence of surface curvature on velocity measurements (the tibia bone surface is fairly flat but may show surface curvature in some patients). The velocities in the axial and ±37.5° directions were used to calculate an anisotropy index. The velocities measured on the porosity phantoms showed a decrease by -6.3±0.2m/s and -10.1±0.2m/s per percent increase in porosity in axial and ±37.5° directions, respectively. Surface curvature had an effect on the velocities measured in ±37.5° directions which could be minimized by a correction algorithm resulting in an error of 5m/s. The anisotropy index could be used to estimate porosity with an accuracy error of 1.5%. These results indicate that an estimation of porosity using velocity measurements in different directions might be feasible, even in bones with curved surface. These results obtained on phantom material indicate that the approach tested may be suited for porosity measurements on human tibia bone.

Physical constraints on the non-dimensional absorption coefficients of compressional and shear waves for viscoelastic cylinders

BACKGROUND

Normalized absorption coefficients for the longitudinal and shear waves in viscoelastic (polymer-type) materials, extracted from non-fictional experimental data showed anomalous effects, such as the generation of a negative radiation force (NRF) in plane progressive waves, negative energy absorption and extinction efficiencies and a scattering enhancement, not in agreement with energy conservation.

OBJECTIVE

The objective of this work is directed towards analyzing those anomalies from the standpoint of energy conservation. Physical conditions which demonstrate that the ratio of the normalized absorption coefficients cannot be of arbitrary value but depends on the ratio of the square of the compressional and shear wave speeds, are established and discussed.

METHOD

The necessary physical condition for the validity of the linear viscoelastic (VE) model for any passive (i.e. that does not generate energy) polymeric cylinder with an ultrasonic absorption of hysteresis-type submerged in a non-viscous fluid requires that the absorption efficiency be positive (Q_abs>0) since there are no active radiating sources inside the core material. This condition imposes restrictions on the values attributed to the normalized absorption coefficients for the compressional and shear-wave wavenumbers for each partial-wave mode n. The forbidden values produce anomalous/unphysical NRF, negative absorption and extinction efficiencies, as well as an enhancement of the scattering efficiency using plane progressive waves, not in agreement with energy conservation.

RESULTS

Based on the partial wave series expansion method in cylindrical coordinates, numerical results for the radiation force, extinction, absorption and scattering energy efficiencies assuming plane progressive wave incidence are performed for three VE polymer cylinders immersed in a non-viscous host liquid (i.e. water) with particular emphasis on the shear-wave absorption coefficient, the dimensionless size parameter ka (where k is the wavenumber and a is the radius of the cylinder) and the partial-wave mode number n. Physical and mathematical conditions are established for the non-dimensional absorption coefficients of the longitudinal and shear waves for a cylinder (i.e. the 2D case) in terms of the sound velocities in the VE material. The physical condition for the spherical 3D case is also noted.

CONCLUSION

For passive materials, the physical conditions must be always satisfied to allow accurate computations of the acoustic radiation force, torque, and energy absorption, extinction and scattering efficiencies for VE cylinders having a hysteresis type of absorption (such as polymers and plastics), and submerged in a non-viscous fluid. The physical conditions must be always satisfied regardless of the shape of the incident field. They also serve to validate and verify experimental data for VE materials and test the accuracy of related numerical computations.

In Vivo Characterization of Cortical Bone Using Guided Waves Measured by Axial Transmission

Cortical bone loss is not fully assessed by the current X-ray methods, and there is an unmet need in identifying women at risk of osteoporotic fracture, who should receive a treatment. The last decade has seen the emergence of the ultrasound (US) axial transmission (AT) techniques to assess a cortical bone. Recent AT techniques exploit the multimode waveguide response of the long bones such as the radius. A recent ex vivo study by our group evidenced that a multimode AT approach can yield simultaneous estimates of cortical thickness (Ct.Th) and stiffness. The aim of this paper is to move one step forward to evaluate the feasibility of measuring multimode guided waves (GW) in vivo and to infer from it cortical thickness. Measurements were taken on the forearm of 14 healthy subjects with the goal to test the accuracy of the estimated thickness using the bidirectional AT method implemented on a dedicated 1-MHz linear US array. This setup allows determining in vivo the dispersion curves of GW transmitted in the cortical layer of the radius. An inverse procedure based on the comparison between the measured and modeled dispersion curves predicted by a 2-D transverse isotropic free plate waveguide model allowed an estimation of cortical thickness, despite the presence of soft tissue. The Ct.Th values were validated by comparison with the site-matched estimates derived from X-ray high-resolution peripheral quantitative computed tomography. Results showed a significant correlation between both measurements ( r² = 0.7 , , and [Formula: see text] mm). This pilot study demonstrates the potential of bidirectional AT for the in vivo assessment of cortical thickness, a bone strength-related factor.

Combined estimation of thickness and velocities using ultrasound guided waves: a pioneering study on in vitro cortical bone samples

This paper reports for the first time on inverse estimation of several bone properties from guided-wave measurements in human bone samples. Previously, related approaches have focused on ultrasonic estimation of a single bone property at a time. The method is based on two steps: the multi-Lamb mode response is analyzed using the singular value decomposition signal processing method recently introduced in the field, then an identification procedure is run to find thickness and anisotropic elastic properties of the considered specimen. Prior to the measurements on bone, the method is validated on cortical bone-mimicking phantoms. The repeatability and the trueness of the estimated parameters on bone-mimicking phantoms were found around a few percent. Estimation of cortical thickness on bone samples was in good agreement with cortical thickness derived from high-resolution peripheral quantitative computed tomography data analysis of the samples.

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.

Multi-frequency axial transmission bone ultrasonometer

The last decade has seen a surge in the development of axial transmission QUS (Quantitative UltraSound) technologies for the assessment of long bones using various modes of acoustic waves. The condition of cortical bones and the development of osteoporosis are determined by numerous mechanical, micro-structural, and geometrical or macro-structural bone properties like hardness, porosity and cortical thickness. Such complex manifestations of osteoporosis require the evaluation of multiple parameters with different sensitivities to the various properties of bone that are affected by the disease. This objective may be achieved by using a multi-frequency ultrasonic examination The ratio of the acoustic wavelength to the cortical thickness can be changed by varying the frequency of the ultrasonic pulse propagating through the long bone that results in the change in composition of the induced wave comprised of a set of numerous modes of guided, longitudinal, and surface acoustic waves. The multi-frequency axial transmission QUS method developed at Artann Laboratories (Trenton, NJ) is implemented in the Bone Ultrasonic Scanner (BUSS). In the current version of the BUSS, a train of ultrasonic pulses with 60, 100, 400, 800, and 1200 kHz frequencies is used. The developed technology was tested on a variety of bone phantoms simulating normal, osteopenic, and osteoporotic bones. The results of this study confirm the feasibility of the multi-frequency approach for the assessment of the processes leading to osteoporosis.

A study on Rayleigh wave dispersion in bone according to Mindlin's Form II gradient elasticity

The classical elasticity cannot effectively describe bone's mechanical behavior since only homogeneous media and local stresses are assumed. Additionally, it cannot predict the dispersive nature of the Rayleigh wave which has been reported in experimental studies and was also demonstrated in a previous computational study by adopting Mindlin's Form II gradient elasticity. In this work Mindlin's theory is employed to analytically determine the dispersion of Rayleigh waves in a strain gradient elastic half-space. An isotropic semi-infinite space is considered with properties equal to those of bone and dynamic behavior suffering from microstructural effects. Microstructural effects are considered by incorporating four intrinsic parameters in the stress analysis. The results are presented in the form of group and phase velocity dispersion curves and compared with existing computational results and semi-analytical curves calculated for a simpler case of Rayleigh waves in dipolar gradient elastic half-spaces. Comparisons are also performed with the velocity of the first-order antisymmetric mode propagating in a dipolar plate so as to observe the Rayleigh asymptotic behavior. It is shown that Mindlin's Form II gradient elasticity can effectively describe the dispersive nature of Rayleigh waves. This study could be regarded as a step toward the ultrasonic characterization of bone.

Photo-acoustic excitation and optical detection of fundamental flexural guided wave in coated bone phantoms

Photo-acoustic (PA) imaging was combined with skeletal quantitative ultrasound (QUS) for assessment of human long bones. This approach permitted low-frequency excitation and detection of ultrasound so as to efficiently receive the thickness-sensitive fundamental flexural guided wave (FFGW) through a coating of soft tissue. The method was tested on seven axisymmetric bone phantoms, whose 1- to 5-mm wall thickness and 16-mm diameter mimicked those of the human radius. Phantoms were made of a composite material and coated with a 2.5- to 7.5-mm layer of soft material that mimicked soft tissue. Ultrasound was excited with a pulsed Nd:YAG laser at 1064-nm wavelength and received on the same side of the coated phantom with a heterodyne interferometer. The FFGW was detected at 30-kHz frequency. Fitting the FFGW phase velocity by the FLC(1,1) tube mode provided an accurate (9.5 ± 4.0%) wall thickness estimate. Ultrasonic in vivo characterization of cortical bone thickness may thus become possible.

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.

Modeling elastic waves in coupled media: Estimate of soft tissue influence and application to quantitative ultrasound

The effect of medium coupling on propagation of elastic waves is a general concern in a variety of engineering and bio-medical applications. Although some theories and analytical models are available for describing waves in multi-layered engineering structures, they do not focus on canvassing ultrasonic waves in human bones with coupled soft tissues, where the considerable differences in acoustic impedance between bone and soft tissue may pose a challenge in using these models (the soft tissues having an acoustic impedance around 80% less than that of a typical bone). Without proper treatment of this coupling effect, the precision of quantitative ultrasound (QUS) for clinical bone assessment can be compromised. The coupling effect of mimicked soft tissues on the first-arriving signal (FAS) and second-arriving signal (SAS) in a series of synthesized soft-tissue-bone phantoms was investigated experimentally and calibrated quantitatively. Understanding of the underlying mechanism of the coupling effect was supplemented by a dedicated finite element analysis. As revealed, the medium coupling impacts influence on different wave modes to different degrees: for FAS and SAS, the most significant changes take place when the soft tissues are initially introduced, and the decrease in signal peak energy continues with increase in the thickness or elastic modulus of the soft tissues, but the changes in propagation velocity fluctuate within 5% regardless of further increase in the thickness or elastic modulus of the soft tissues. As an application, the calibrated effects were employed to enhance the precision of SAS-based QUS when used for predicting the simulated healing status of a mimicked bone fracture, to find prediction of healing progress of bone fracture based on changes in velocity of the FAS or the SAS is inaccurate without taking into account the effect of soft tissue coupling, entailing appropriate compensation for the coupling effect.

Noncontact ultrasound imaging applied to cortical bone phantoms

PURPOSE

The purpose of this paper was to take the first steps toward applying noncontact ultrasound (NCU) to the tasks of monitoring osteoporosis and quantitative ultrasound imaging (QUS) of cortical bone. The authors also focused on the advantages of NCU, such as its lack of reliance on a technologist to apply transducers and a layer of acoustical coupling gel, the ability of the transducers to operate autonomously as specified by preprogrammed software, and the likely reduction in statistical and systematic errors associated with the variability in the pressure applied by the clinician to the transmitting transducer that NCU might provide. The authors also undertook this study in order to find additional applications of NCU beyond its past limited usage in assessing the severity of third degree burns.

METHODS

A noncontact ultrasound imaging system using a pair of specially designed broadband, 1.5 MHz noncontact piezoelectric transducers and cortical bone phantoms, were used to determine bone mineral density (BMD), speed of sound (SOS), integrated response (IR), and ultrasonic transmittance. Air gaps of greater than 3 cm, two transmission and two reflection paths, and a digital signal processor were also used in the collection of data from phantoms of nominal mass densities that varied from 1.17 to 2.25 g/cm(3) and in bone mineral density from 0 to 1.7 g/cm(3).

RESULTS

Good correlations between known BMD and measured SOS, IR, and transmittance were obtained for all 17 phantoms, and methods for quantifying and minimizing sources of systematic errors were outlined. The BMD of the phantom sets extended through most of the in vivo range found in cortical bone. A total of 16-20 repeated measurements of the SOS, thickness, and IR for the phantom set that were conducted over a period of several months showed a small variation in the range of measurements of ±1%-2%. These NCU data were shown to be in agreement with similar results using contact ultrasound to be within 1%-2%. Transmittance images of cortical bone phantoms showed differences in the nominal overall BMD values of the phantoms that were large enough to be distinguished by a visual examination. A list of possible sources of errors in quantitative NCU was also included in this study.

CONCLUSIONS

The results of this paper suggest that NCU might find additional applications in medical imaging, beyond its original and only previous usage in assessing third degree burns. The fact that the authors' phantom measurements using conventional, gel coupled ultrasound are in agreement with those obtained with NCU demonstrates that in spite of large additional levels of attenuation of up to 150 dB and new error sources, NCU could have comparable levels of accuracy to those of conventional quantitative ultrasound, while providing the medical and patient comfort-related advantages of not involving direct contact.

Using the gradient of human cortical bone properties to determine age-related bone changes via ultrasonic guided waves

Bone fragility depends not only on bone mass but also on bone quality (structure and material). To accurately evaluate fracture risk or propose therapeutic treatment, clinicians need a criterion, which reflects the determinants of bone strength: geometry, structure and material. In human long bone, the changes due to aging, accentuated by osteoporosis are often revealed through the trabecularization of cortical bone, i.e., increased porosity of endosteal bone inducing a thinning of the cortex. Consequently, the intracortical porosity gradient corresponding to the spatial variation in porosity across the cortical thickness is representative of loss of mass, changes in geometry (thinning) and variations in structure (porosity). This article examines the gradient of material properties and its age-related evolution as a relevant parameter to assess bone geometry, structure and material. By applying a homogenization process, cortical bone can be considered as an anisotropic functionally graded material with variations in material properties. A semi-analytical method based on the sextic Stroh formalism is proposed to solve the wave equation in an anisotropic functionally graded waveguide for two geometries, a plate and a tube, without using a multilayered model to represent the structure. This method provides an analytical solution called the matricant and explicitly expressed under the Peano series expansion form. Our findings indicate that ultrasonic guided waves are sensitive to the age-related evolution of realistic gradients in human bone properties across the cortical thickness and have their place in a multimodal clinical protocol.

Three-dimensional printing (3DP) of neonatal head phantom for ultrasound: thermocouple embedding and simulation of bone

A neonatal head phantom, comprising of an ellipsoidal geometry and including a circular aperture for simulating the fontanel was designed and fabricated, in order to allow an objective assessment of thermal rise in tissues during trans-cranial ultrasonic scanning of pre-term neonates. The precise position of a series of thermocouples was determined on the basis of finite-element analysis, which identified crucial target points for the thermal monitoring within the phantom geometry. Three-Dimensional Printing (3DP) was employed for the manufacture of the skull phantom, which was subsequently filled with dedicated brain-mimic material. A novel 3DP material combination was found to be able to mimic the acoustic properties of neonatal skull bone. Similarly, variations of a standard recipe for tissue mimic were examined, until one was found to mimic the brain of an infant. A specific strategy was successfully pursued to embed a thermocouple within the 3DP skull phantom during the manufacturing process. An in-process machine vision system was used to assess the correct position of the deposited thermocouple inside the fabricated skull phantom. An external silicone-made skin-like covering completed the phantom and was manufactured through a Direct Rapid Tooling (DRT) technique.

Comparative examination of human proximal tibiae in vitro by ultrasonic guided waves and pQCT

The velocity of ultrasonic guided waves in long bones is dependent upon two determinants of bone strength: the cortical thickness and the material properties. In this study, six human proximal tibiae in vitro were examined to test the efficacy of an ultrasonic method based on guided waves. Peripheral quantitative computed tomography (pQCT) was used as the comparative reference modality. The guided wave velocity (c(F)) was derived from two-dimensional (2-D) spatial-temporal waveform profiles formed by multiple ultrasonic signals acquired along the bones at 100 kHz frequency and passed wavelet processing. The ultrasonic profiles from the examined bones were ranged according to pQCT measurements of cortical thickness (CTh), and cortical bone mineral density (CBMD). Strong correlations between c(F) and CTh (r(S) = 0.83, p < 0.0001) and CBMD (r(S) = 0.88, p < 0.0001) resulted. The study confirmed a potential for guided waves to assess atrophic changes of the proximal tibia.

A numerical study on the propagation of Rayleigh and guided waves in cortical bone according to Mindlin's Form II gradient elastic theory

Cortical bone is a multiscale heterogeneous natural material characterized by microstructural effects. Thus guided waves propagating in cortical bone undergo dispersion due to both material microstructure and bone geometry. However, above 0.8 MHz, ultrasound propagates rather as a dispersive surface Rayleigh wave than a dispersive guided wave because at those frequencies, the corresponding wavelengths are smaller than the thickness of cortical bone. Classical elasticity, although it has been largely used for wave propagation modeling in bones, is not able to support dispersion in bulk and Rayleigh waves. This is possible with the use of Mindlin's Form-II gradient elastic theory, which introduces in its equation of motion intrinsic parameters that correlate microstructure with the macrostructure. In this work, the boundary element method in conjunction with the reassigned smoothed pseudo Wigner-Ville transform are employed for the numerical determination of time-frequency diagrams corresponding to the dispersion curves of Rayleigh and guided waves propagating in a cortical bone. A composite material model for the determination of the internal length scale parameters imposed by Mindlin's elastic theory is exploited. The obtained results demonstrate the dispersive nature of Rayleigh wave propagating along the complex structure of bone as well as how microstructure affects guided waves.

Low-frequency axial ultrasound velocity correlates with bone mineral density and cortical thickness in the radius and tibia in pre- and postmenopausal women

Axial transmission velocity of a low-frequency first arriving signal (V (LF)) was assessed in the radius and tibia of 254 females, and compared to site-matched pQCT measurements. V (LF) best correlated with cortical BMD, but significantly also with subcortical BMD and cortical thickness. Correlations were strongest for the radius in postmenopausal females.

INTRODUCTION

Ultrasonic low-frequency (LF; 0.2-0.4 MHz) axial transmission, based on the first arriving signal (FAS), provides enhanced sensitivity to thickness and endosteal properties of cortical wall of the radius and tibia compared to using higher frequencies (e.g., 1 MHz). This improved sensitivity of the LF approach has not yet been clearly confirmed by an in vivo study on adult subjects. The aims of the present study were to evaluate the extent to which LF measurements reflect cortical thickness and bone mineral density, and to assess whether an individual LF measurement can provide a useful estimate for these bone properties.

METHODS

Velocity of the LF FAS (V (LF)) was assessed in the radius and tibia shaft by a new ultrasonometer (CV(RMS) = 0.5%) in a cross-sectional study involving 159 premenopausal (20-58 years) and 95 postmenopausal females (45-88 years). Site-matched volumetric total bone mineral density (BMD), cortical bone mineral density (CBMD), subcortical bone mineral density (ScBMD) and cortical thickness (CTh) were assessed using pQCT.

RESULTS

For the postmenopausal females, V (LF) correlated best with CBMD in the radius (R = 0.850, p < 0.001), but significantly also with ScBMD and CTh (R = 0.759 and R = 0.761, respectively; p < 0.001). Similar trends but weaker correlations were observed for the tibia and for the premenopausal women.

CONCLUSIONS

The LF assessment, with an optimal excitation frequency, thus provided good prediction of both cortical thickness and subcortical bone material properties. These results suggest that the LF approach does indeed have enhanced sensitivity for detecting osteoporotic changes that occur deep in the endosteal bone.

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.

A review of tissue substitutes for ultrasound imaging

The characterization and calibration of ultrasound imaging systems requires tissue-mimicking phantoms with known acoustic properties, dimensions and internal features. Tissue phantoms are available commercially for a range of medical applications. However, commercial phantoms may not be suitable in ultrasound system design or for evaluation of novel imaging techniques. It is often desirable to have the ability to tailor acoustic properties and phantom configurations for specific applications. A multitude of tissue-mimicking materials and phantoms are described in the literature that have been created using a variety of materials and preparation techniques and that have modeled a range of biological systems. This paper reviews ultrasound tissue-mimicking materials and phantom fabrication techniques that have been developed over the past four decades, and describes the benefits and disadvantages of the processes. Both soft tissue and hard tissue substitutes are explored.

Diversity of biomedical applications of acoustic radiation force

This manuscript is a summary of the paper presented at the ICU'2009 on biomedical applications of acoustic radiation force with emphasis on emerging applications in microfluidics, biotechnology, biosensors and assessment of the skeletal system. In this brief overview of current and projected applications of radiation force, no detailed description of the experiments illustrating particular applications are given as this would result in a far different and longer paper. Various mechanisms of acoustic radiation force generations and their biomedical applications are considered. These mechanisms include: (a) change in the density of energy of the propagating wave due to absorption and scattering; (b) spatial variations of energy density in standing acoustic waves; (c) reflection from inclusions, walls or other interfaces; and (d) spatial variations in propagation velocity. The widest area of biomedical applications of radiation force is related to medical diagnostics, to assessing viscoelastic properties of biological tissues and fluids, and specifically to elasticity imaging. Another actively explored area is related to manipulation of biological cells and particles in standing ultrasonic wave fields. There are several poorly explored areas of potential biomedical applications of ultrasound radiation force. A promising area of biomedical application of ultrasound radiation force is stirring and mixing of microvolumes of liquids in microfluidics and in various biotechnological application where diffusion rate is the main factor limiting the efficiency of the process of interest. A new technique, called "swept frequency method", based on the use of radiation force in the standing acoustic wave for microstirring of liquids is described. The potential applications of the ultrasound radiation force for assessment of skeletal system, where conventional bone ultrasonometry are inapplicable are considered.

Analysis of the most energetic late arrival in axially transmitted signals in cortical bone

Axial transmission techniques are particularly suitable for the ultrasonic assessment of cortical bone. The generic term "axial transmission technique" indicates a measurement configuration in which emitters and receivers are placed on the same side of the skeletal site, along the bone axis. Whereas axially transmitted signals are composed of several contributions, only the first arriving signal was shown to be a robust indicator of bone status, because its velocity discriminates osteoporotic from healthy patients in clinical studies. Later arrivals may provide additional bone indicators enhancing diagnostic value, but the precise determination of their velocities is challenging. In this paper, we focus on the most energetic contribution and we applied a singular-value decomposition-based extraction method not yet employed in the domain of bone assessment with the aim of determining the velocity of this contribution. Signals acquired in vitro on human radii, together with academic models, were used to reveal the relationship between the velocity of the most energetic component and bone properties. The velocity of the most energetic component is highly correlated to cortical layer thickness in the in vitro database (R(2)= 0.6, P < 10(-5) compared with R(2)= 0.20, P < 10-(2) for the first arriving signal), consistent with a flexural type of wave on regular tubes or plates. Conclusions are in agreement with published papers based on other axial transmission and signal processing approaches.

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.

Correlation of tibial low-frequency ultrasound velocity with femoral radiographic measurements and BMD in elderly women

The ultrasonic axial transmission technique has been proposed as a method for cortical bone characterization. Using a low enough center frequency, Lamb modes can be excited in long bones. Lamb waves propagate throughout the cortical bone layer, which makes them appealing for characterizing bone material and geometrical properties. In the present study, a prototype low-frequency quantitative ultrasonic axial transmission device was used on elderly women (n = 132) to investigate the relationships between upper femur geometry and bone mineral density (BMD) and tibial speed of sound. Ultrasonic velocities (V) were recorded using a two-directional measurement set-up on the midtibia and compared with dual-energy X-ray absorptiometry measurements and plain radiographs of the hip. Statistically significant, but weak, correlations were found between V and femoral shaft cortex thickness measured from radiographs (r = 0.20-0.26). V also correlated significantly with various BMD and bone mineral content parameters (r = 0.20-0.35). Femoral BMD and geometry were found to be significant independent predictors of V (R(2) = 0.07-0.16, p < 0.01). This study showed that femoral geometry and BMD affect significantly the axial ultrasound velocity measured at the tibia. In addition, the results confirmed, for the first time, a relationship between tibial ultrasound velocity and cortical bone thickness at the proximal femur.

In vivo performance evaluation of bi-directional ultrasonic axial transmission for cortical bone assessment

Our objective was to assess a new quantitative ultrasound device suitable for the measurement of speed of sound in radius. The so-called "bidirectional" technique allows an accurate estimation of velocity based on a compensation for soft tissue effects implemented directly inside the probe. Velocity measurements at 1 MHz of the first arriving signal were performed at the one third distal radius in 358 enrolled women. The average velocity by age decade increases to a peak velocity of 4043 m/s in the class 30-39 y (n = 19) and decreases thereafter. Fracture discrimination was investigated on the subset of the population for which dual-energy x-ray absorptiometry measurement was available, in addition to first arriving signal velocity measurements. The study group consisted of 122 postmenopausal women without history of fracture (group NF) and 44 postmenopausal patients (group F) with osteoporotic fractures (hip, spine, Colles fracture). When adjusted for age and bone mass index, the odds ratio (OR) for fracture prediction by ultrasound velocity, was 1.81 (1.21; 2.70) and OR associated to neck femur BMD was 2.07 (1.31-3.29). For the full model including age and body mass index as cofactors, the area under the receiver operating characteristic curve was 0.77, either for ultrasound velocity or neck femur bone mineral density. Despite the small population and the variety of fractures in the fracture group, our data indicate that the velocity of the first arriving signal measured by bidirectional technique discriminates patients with osteoporotic fracture from controls.

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.

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.

Application of the dual-frequency ultrasonometer for osteoporosis detection

The paper presents results of a clinical validation study of Bone UltraSonic Scanner (BUSS), a novel dual-frequency axial transmission ultrasonometer, developed by Artann Laboratories. Assessment of bone conditions is based on evaluating relative changes of the axial profiles of ultrasonic characteristics in long bones and utilizes bulk and guided acoustic waves. The objective of this study was to determine the ability of BUSS to discriminate osteoporosis development stages. A total of 93 menopausal and post-menopausal women divided into five groups from normal to advanced osteoporosis according to their DXA hip t-score were enrolled in the study. The 2D waveform profiles at low (0.1 MHz) and high (1 MHz) frequencies were obtained by scanning 15 cm along the proximal tibia. A multi-parametric linear classifier based on a set of the parameters derived from 2D acoustic waveform profiles has been developed. The efficiency of this classifier in differentiating osteoporosis from a normal sample was assessed using a receiver operating characteristic (ROC) curve analysis. Based on the ROC analysis, BUSS demonstrated 76% sensitivity and 70% specificity to DXA-identified osteoporosis. The area under the ROC curve, which is a measure of how well a parameter can distinguish between the two diagnostic groups (diseased/normal) was 79.3%. The study confirmed BUSS's capability to discriminate between stages of bone atrophy and in particular to distinguish early changes induced by osteoporosis.

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.

Topography of acoustical properties of long bones: from biomechanical studies to bone health assessment

The article presents a retrospective view on the assessment of long bones condition using topographical patterns of the acoustic properties. The application of ultrasonic point-contact transducers with exponential waveguides on a short acoustic base for detailed measurements in human long bones by the surface transmission was initiated during the 1980s in Latvia. The guided wave velocity was mapped on the surface of the long bones and the topographical patterns reflected the biomechanical peculiarities. Axial velocity profiles obtained in vivo by measurements along the medial surface of tibia varied due to aging, hypokinesia, and physical training. The method has been advanced at Artann Laboratories (West Trenton, NJ) by the introduction of multifrequency data acquisition and axial scanning. The model studies carried out on synthetic phantoms and in bone specimens confirmed the potential to evaluate separately changes of the bone material properties and of the cortical thickness by multifrequency acoustic measurements at the 0.1 to 1 MHz band. The bone ultrasonic scanner (BUSS) is an axial mode ultrasonometer developed to depict the acoustic profile of bone that will detect the onset of bone atrophy as a spatial process. Clinical trials demonstrated a high sensitivity of BUSS to osteoporosis and the capability to assess early stage of osteopenia.

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.

Instrumentation for in vivo ultrasonic characterization of bone strength

Although it has been more than 20 years since the first recorded use of a quantitative ultrasound (QUS) technology to predict bone fragility, the field has not yet reached its maturity. QUS has the potential to predict fracture risk in several clinical circumstances and has the advantages of being nonionizing, inexpensive, portable, highly acceptable to patients, and repeatable. However, the wide dissemination of QUS in clinical practice is still limited and suffering from the absence of clinical consensus on how to integrate QUS technologies in bone densitometry armamentarium. Several critical issues need to be addressed to develop the role of QUS within rheumatology. These include issues of technologies adapted to measure the central skeleton, data acquisition, and signal processing procedures to reveal bone properties beyond bone mineral quantity and elucidation of the complex interaction between ultrasound and bone structure. This article reviews the state-of-the art in technological developments applied to assess bone strength in vivo. We describe generic measurement and signal processing methods implemented in clinical ultrasound devices, the devices and their practical use, and performance measures. The article also points out the present limitations, especially those related to the absence of standardization, and the lack of comprehensive theoretical models. We conclude with suggestions of future lines and trends in technology challenges and research areas such as new acquisition modes, advanced signal processing techniques, and modelization.

Singular value decomposition-based wave extraction in axial transmission: application to cortical bone ultrasonic characterization

A singular value decomposition-based extraction algorithm is designed in order to recover the group velocity of an energetic contribution measured with an axial transmission device developed previously for cortical bone assessment. Its performance is evaluated on synthetic data mimicking in vivo signals, and it is compared with classical methods.

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.

Effect of porosity on effective diagonal stiffness coefficients (cii) and elastic anisotropy of cortical bone at 1 MHz: a finite-difference time domain study

Finite-difference time domain (FDTD) numerical simulations coupled to real experimental data were used to investigate the propagation of 1 MHz pure bulk wave propagation through models of cortical bone microstructures. Bone microstructures were reconstructed from three-dimensional high resolution synchrotron radiation microcomputed tomography (SR-muCT) data sets. Because the bone matrix elastic properties were incompletely documented, several assumptions were made. Four built-in bone matrix models characterized by four different anisotropy ratios but the same Poisson's ratios were tested. Combining them with the reconstructed microstructures in the FDTD computations, effective stiffness coefficients were derived from simulated bulk-wave velocity measurements. For all the models, all the effective compression and shear bulk wave velocities were found to decrease when porosity increases. However, the trend was weaker in the axial direction compared to the transverse directions, contributing to the increase of the effective anisotropy. On the other hand, it was shown that the initial Poisson's ratio value may substantially affect the variations of the effective stiffness coefficients. The present study can be used to elaborate sophisticated macroscopic computational bone models incorporating realistic CT-based macroscopic bone structures and effective elastic properties derived from muCT-based FDTD simulations including the cortical porosity effect.

Ultrasonically determined thickness of long cortical bones: two-dimensional simulations of in vitro experiments

Previously it has been demonstrated that cortical bone thickness can be estimated from ultrasonic guided-wave measurements, in an axial transmission configuration, together with an appropriate analytical model. This study considers the impact of bone thickness variation within the measurement region on the ultrasonically determined thickness (UTh). To this end, wave velocities and UTh were determined from experiments and from time-domain finite-difference simulations of wave propagation, both performed on a set of ten human radius specimens (29 measurement sites). A two-dimensional numerical bone model was developed with tunable material properties and individualized geometry based on x-ray computed-tomography reconstructions of human radius. Cortical thickness (CTh) was determined from the latter. UTh data for simulations were indeed in a excellent accordance (root-mean-square error was 0.26 mm; r2=0.94, p<0.001) with average CTh within the measurement region. These results indicate that despite variations in cortical thickness along the propagation path, the measured phase velocity can be satisfactorily modeled by a simple analytical model (the A(0) plate mode in this case). Most of the variability (up to 85% when sites were carefully matched) observed in the in vitro ultrasound data was explained through simulations by variability in the cortical thickness alone.

Three-dimensional finite element modeling of guided ultrasound wave propagation in intact and healing long bones

The use of guided waves has recently drawn significant interest in the ultrasonic characterization of bone aiming at supplementing the information provided by traditional velocity measurements. This work presents a three-dimensional finite element study of guided wave propagation in intact and healing bones. A model of the fracture callus was constructed and the healing course was simulated as a three-stage process. The dispersion of guided modes generated by a broadband 1-MHz excitation was represented in the time-frequency domain. Wave propagation in the intact bone model was first investigated and comparisons were then made with a simplified geometry using analytical dispersion curves of the tube modes. Then, the effect of callus consolidation on the propagation characteristics was examined. It was shown that the dispersion of guided waves was significantly influenced by the irregularity and anisotropy of the bone. Also, guided waves were sensitive to material and geometrical changes that take place during healing. Conversely, when the first-arriving signal at the receiver corresponded to a nondispersive lateral wave, its propagation velocity was almost unaffected by the elastic symmetry and geometry of the bone and also could not characterize the callus tissue throughout its thickness. In conclusion, guided waves can enhance the capabilities of ultrasonic evaluation.

[Quantitative ultrasound]

Methods of quantitative ultrasound (QUS) can be used to obtain knowledge about bone fragility. Comprehensive study results exist showing the power of QUS for the estimation of osteoporotic fracture risk. Nevertheless, the variety of technologies, devices, and variables as well as different degrees of validation of the single devices have to be taken into account. Using methods to simulate ultrasound propagation, the complex interaction between ultrasound and bone could be understood and the propagation could be visualized. Preceding widespread clinical use, it has to be clarified if patients with low QUS values will profit from therapy, as it has been shown for DXA. Moreover, the introduction of quality assurance measures is essential. The user should know the limitations of the methods and be able to interpret the results correctly. Applied in an adequate manner QUS methods could then, due to lower costs and absence of ionizing radiation, become important players in osteoporosis management.

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.