Application of the dual-frequency ultrasonometer for osteoporosis detection

Study of Ultrasonic Guided Wave Propagation in Bone Composite Structures for Revealing Osteoporosis Diagnostic Indicators

Tubular bones are layered waveguide structures composed of soft tissue, cortical and porous bone tissue, and bone marrow. Ultrasound diagnostics of such biocomposites are based on the guided wave excitation and registration by piezoelectric transducers applied to the waveguide surface. Meanwhile, the upper sublayers shield the diseased interior, creating difficulties in extracting information about its weakening from the surface signals. To overcome these difficulties, we exploit the advantages of the Green's matrix-based approach and adopt the methods and algorithms developed for the guided wave structural health monitoring of industrial composites. Based on the computer models implementing this approach and experimental measurements performed on bone phantoms, we analyze the feasibility of using different wave characteristics to detect hidden diagnostic signs of developing osteoporosis. It is shown that, despite the poor excitability of the most useful modes associated with the diseased inner layers, the use of the improved matrix pencil method combined with objective functions based on the Green's matrix allows for effective monitoring of changes in the elastic moduli of the deeper sublayers. We also note the sensitivity and monotonic dependence of the resonance response frequencies on the degradation of elastic properties, making them a promising indicator for osteoporosis diagnostics.

Automatic mode extraction of ultrasonic guided waves using synchrosqueezed wavelet transform

Multimodal and dispersive characteristics of ultrasonic guided waves (GWs) cause the wave-packet overlapping in time domain and frequency domain, which challenges the signal interpretation. In this study, we propose an automatic method for individual mode extraction. The inversible synchrosqueezed wavelet transform (SWT) is employed to obtain the high-resolution time-frequency representation (TFR) of the GW signal. Then, two image processing steps, i.e., watershed transform and region growing, are used to process the TFR distributions and extract the TFR trajectory of each individual component. After the TFR segmentation, the individual modes are reconstructed by using the inverse SWT. The algorithm performance is investigated by synthesized multimodal signals. The results show that the reconstructed individual modes are consistent with the original ones. The experimental results measured in a bovine tibia plate and a steel plate are further employed to testify the proposed algorithm. Results suggest that the presented study provides a robust tool for processing multimodal ultrasonic GW signals.

Sensitivity of low-frequency axial transmission acoustics to axially and azimuthally varying cortical thickness: A phantom-based study

Purpose

Cortical thickness (cTh) is one of the main factors determining a bone’s mechanical properties, and its quantification is therefore critical for understanding and monitoring bone pathologies such as osteoporosis. Axial quantitative acoustics (ax-QA) offers a non-radiative, non-invasive method to measure cTh. Even though previous works have ascertained ax-QA’s ability to measure azimuthally varying cTh, the effect of axially varying cTh remains unclear. Furthermore, previous experiments and theoretical predictions indicate that measurement of the fundamental flexural mode at low frequencies in the kHz range could increase sensitivity to cTh. However, due to the associated long wavelengths, the approximation of bone geometry as a tube could break down at such frequencies. The presented study therefore investigates a) the sensitivity of ax-QA measurements to cTh in the kHz-regime, b) the applicability of tube theory in this regime, and c) the effect of varying cTh along the long axis on the bone.

Materials and methods

Axial-transmission acoustic measurements were performed at 3kHz on 14 bone phantoms with a femur-like cross-section and a) axially varying cortical thickness or b) axially and azimuthally varying cortical thickness (cTh-range: 1.5mm-7.5mm). Experimental results were compared to theoretical predictions based on an exact elastic tube theory.

Results and discussion

Phase velocity measurements using low-frequency ax-QA exhibited a high sensitivity to local cTh less than 4mm, albeit with a complex, not yet understood pattern. Tube theory failed to predict the wave’s behavior in the kHz range, indicating that due to the corresponding long wavelengths the bone can no longer be approximated by a tube, thus requiring more faithful modelling of the bone geometry. The fact that results from both types of phantoms were similar (Pearson correlation coefficient: 0.94) further indicates that the slowly varying cTh along the bone’s long axis did not strongly affect wave propagation as measured by ax-QA measurements.

Can low-frequency guided waves at the tibia paired with machine learning differentiate between healthy and osteopenic/osteoporotic subjects? A pilot study

PURPOSE

Axial transmission quantitative acoustics (ax-QA) has shown to be a promising tool for assessing bone health and properties in a safe, inexpensive, and portable manner. This study investigated the efficacy of low-frequency ax-QA measured at the tibia, paired with a support vector machine (SVM) approach for combining multiple acoustic indicators, to diagnose osteoporosis as defined by bone mineral density.

METHODS

This pilot study measured 41 female subjects using ax-QA (flexural mode, 3 kHz) at the tibia and using dual X-ray absorptiometry (DXA) at the lumbar spine, femoral neck, and distal radius. For each location, a threshold classifier and SVM were trained to differentiate between healthy and non-healthy subjects based on the phase velocity at different frequencies. Receiver Operating Characteristics and area under curve values (AUC) were used to assess the classifiers' performances for various thresholds and class-weights.

RESULTS

The SVM outperformed the threshold classifier for all three bone locations at low false positive rates. While differentiation between healthy and non-healthy bone states was poor for the spine (AUC: 0.56 ± 0.04), good to moderate performances were observed for the radius (AUC: 0.83 ± 0.03) and hip (AUC: 0.71 ± 0.04).

CONCLUSIONS

Low-frequency ax-QA has demonstrated potential for complementing DXA in screening for osteoporosis at the radius and hip. Through further addition of acoustic indicators ax-QA could provide a diagnostic alternative in third-world countries, and bring bone health screening and monitoring into the hands of clinicians and general health practitioners everywhere.

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.

Ultrasound tomography in bone mimicking phantoms: Simulations and experiments

Bone quality assessment for osteoporosis diagnosis is usually performed using dual energy X-ray absorptiometry or X-ray quantitative computed tomography. Recent research demonstrated that both methods are inaccurate in diagnosing osteoporosis since they rely only on the bone mineral density. The literature on bone quantitative ultrasound suggests that ultrasonic waves are sensitive to multiple significant bone parameters such as mechanical properties, the bone volume fraction, and the micro-architecture. Typical ultrasound tomography techniques are limited to image objects with a low speed of sound contrast relative to a background medium. In this study, the possibility of adapting a more advanced ultrasound inversion technique referred to as the hybrid algorithm for robust breast ultrasound tomography for velocity mapping of bone mimicking phantoms was examined. The cortical bone thickness and the cortical bone speed of sound, which are directly related to the bone elastic properties, are parameters strongly correlated with the overall bone quality. A finite element model and an experimental test bench were developed to adapt the hybrid algorithm for robust breast ultrasound tomography to bone quality assessment. Although artefacts were present in the images generated, the results obtained enabled discrimination of a healthy bone phantom over an osteoporotic bone phantom based on the cortical bone thickness and the average cortical bone velocity. The speed of sound inside the cortical region of the bone phantoms was underestimated by 9.38% for the osteoporotic phantom, and by 10.68% for the healthy phantom relative to the values supplied by the bone phantom manufacturer, but there was a difference of 3.97% between the two samples. The difference between the measured cortical bone thickness of the reconstructed image and the X-ray computed tomography images was on average 0.4 mm.

Towards assessing cortical bone porosity using low-frequency quantitative acoustics: A phantom-based study

PURPOSE

Cortical porosity is a key characteristic governing the structural properties and mechanical behaviour of bone, and its quantification is therefore critical for understanding and monitoring the development of various bone pathologies such as osteoporosis. Axial transmission quantitative acoustics has shown to be a promising technique for assessing bone health in a fast, non-invasive, and radiation-free manner. One major hurdle in bringing this approach to clinical application is the entanglement of the effects of individual characteristics (e.g. geometry, porosity, anisotropy etc.) on the measured wave propagation. In order to address this entanglement problem, we therefore propose a systematic bottom-up approach, in which only one bone property is varied, before addressing interaction effects. This work therefore investigated the sensitivity of low-frequency quantitative acoustics to changes in porosity as well as individual pore characteristics using specifically designed cortical bone phantoms.

MATERIALS AND METHODS

14 bone phantoms were designed with varying pore size, axial-, and radial pore number, resulting in porosities (bone volume fraction) between 0% and 15%, similar to porosity values found in human cortical bone. All phantoms were manufactured using laser sintering, measured using axial-transmission acoustics and analysed using a full-wave approach. Experimental results were compared to theoretical predictions based on a modified Timoshenko theory.

RESULTS

A clear dependence of phase velocity on frequency and porosity produced by increasing pore size or radial pore number was demonstrated, with the velocity decreasing by between 2-5 m/s per percent of additional porosity, which corresponds to -0.5% to -1.0% of wave speed. While the change in phase velocity due to axial pore number was consistent with the results due to pore size and radial pore number, the relative uncertainties for the estimates were too high to draw any conclusions for this parameter.

CONCLUSIONS

This work has shown the capability of low-frequency quantitative acoustics to reflect changes in porosity and individual pore characteristics and demonstrated that additive manufacturing is an appropriate method that allows the influence of individual bone properties on the wave propagation to be systematically assessed. The results of this work opens perspectives for the efficient development of a multi-frequency, multi-mode approach to screen, diagnose, and monitor bone pathologies in individuals.

Reliability of Phase Velocity Measurements of Flexural Acoustic Waves in the Human Tibia In-Vivo

Purpose

Axial-transmission acoustics have shown to be a promising technique to measure individual bone properties and detect bone pathologies. With the ultimate goal being the in-vivo application of such systems, quantification of the key aspects governing the reliability is crucial to bring this method towards clinical use.

Materials and Methods

This work presents a systematic reliability study quantifying the sources of variability and their magnitudes of in-vivo measurements using axial-transmission acoustics. 42 healthy subjects were measured by an experienced operator twice per week, over a four-month period, resulting in over 150000 wave measurements. In a complementary study to assess the influence of different operators performing the measurements, 10 novice operators were trained, and each measured 5 subjects on a single occasion, using the same measurement protocol as in the first part of the study.

Results

The estimated standard error for the measurement protocol used to collect the study data was ∼ 17 m/s (∼ 4% of the grand mean) and the index of dependability, as a measure of reliability, was Φ = 0.81. It was shown that the method is suitable for multi-operator use and that the reliability can be improved efficiently by additional measurements with device repositioning, while additional measurements without repositioning cannot improve the reliability substantially. Phase velocity values were found to be significantly higher in males than in females (p < 10⁻⁵) and an intra-class correlation coefficient of r = 0.70 was found between the legs of each subject.

Conclusions

The high reliability of this non-invasive approach and its intrinsic sensitivity to mechanical properties opens perspectives for the rapid and inexpensive clinical assessment of bone pathologies, as well as for monitoring programmes without any radiation exposure for the patient.

Stimulation of osteoblast differentiation with guided ultrasound waves

Background

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

Methods

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

Results

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

Conclusion

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

Wave dispersion and attenuation on human femur tissue

Cortical bone is a highly heterogeneous material at the microscale and has one of the most complex structures among materials. Application of elastic wave techniques to this material is thus very challenging. In such media the initial excitation energy goes into the formation of elastic waves of different modes. Due to “dispersion”, these modes tend to separate according to the velocities of the frequency components. This work demonstrates elastic wave measurements on human femur specimens. The aim of the study is to measure parameters like wave velocity, dispersion and attenuation by using broadband acoustic emission sensors. First, four sensors were placed at small intervals on the surface of the bone to record the response after pencil lead break excitations. Next, the results were compared to measurements on a bulk steel block which does not exhibit heterogeneity at the same wave lengths. It can be concluded that the microstructure of the tissue imposes a dispersive behavior for frequencies below 1 MHz and care should be taken for interpretation of the signals. Of particular interest are waveform parameters like the duration, rise time and average frequency, since in the next stage of research the bone specimens will be fractured with concurrent monitoring of acoustic emission.

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.

Osteoporosis detection in postmenopausal women using axial transmission multi-frequency bone ultrasonometer: clinical findings

The objective of this study was to evaluate if the Bone UltraSonic Scanner (BUSS) can detect osteoporosis in postmenopausal women. BUSS is an axial transmission multi-frequency ultrasonometer for acquisition of wave propagation profiles along the proximal anterior tibia. We derived 10 diagnostically significant BUSS parameters that were then compared with the DXA spine T-score, which was used in this study as the "gold standard" for the assessment of osteoporosis (T-score<-2.5). BUSS wave parameters were studied in 331 postmenopausal women examined by 9 trained operators at 3 clinical sites with use of 3 devices. The efficiency of each BUSS parameter in osteoporosis detection was assessed using a receiver operating characteristic curve analysis. Area under the curve (AUC) for each of 10 parameters ranged from 58.1% to 70.2%. Using these parameters a linear classifier was derived which provided at its output 83.0% AUC, 87.7% sensitivity and 63.2% specificity to DXA-identified osteoporosis. The results of this study confirm BUSS's capability to detect osteoporosis in postmenopausal women.

Ultrasound to assess bone quality

Bone quality is determined by a variety of compositional, micro- and ultrastructural properties of the mineralized tissue matrix. In contrast to X-ray-based methods, the interaction of acoustic waves with bone tissue carries information about elastic and structural properties of the tissue. Quantitative ultrasound (QUS) methods represent powerful alternatives to ionizing x-ray based assessment of fracture risk. New in vivo applicable methods permit measurements of fracture-relevant properties, [eg, cortical thickness and stiffness at fragile anatomic regions (eg, the distal radius and the proximal femur)]. Experimentally, resonance ultrasound spectroscopy and acoustic microscopy can be used to assess the mesoscale stiffness tensor and elastic maps of the tissue matrix at microscale resolution, respectively. QUS methods, thus, currently represent the most promising approach for noninvasive assessment of components of fragility beyond bone mass and bone microstructure providing prospects for improved assessment of fracture risk.

Measuring the wavenumber of guided modes in waveguides with linearly varying thickness

Measuring guided waves in cortical bone arouses a growing interest to assess skeletal status. In most studies, a model of waveguide is proposed to assist in the interpretation of the dispersion curves. In all the reported investigations, the bone is mimicked as a waveguide with a constant thickness, which only approximates the irregular geometry of cortical bone. In this study, guided mode propagation in cortical bone-mimicking wedged plates is investigated with the aim to document the influence on measured dispersion curves of a waveguide of varying thickness and to propose a method to overcome the measurement limitations induced by such thickness variations. The singular value decomposition-based signal processing method, previously introduced for the detection of guided modes in plates of constant thickness, is adapted to the case of waveguides of slowly linearly variable thickness. The modification consists in the compensation at each frequency of the wavenumber variations induced by the local variation in thickness. The modified method, tested on bone-mimicking wedged plates, allows an enhanced and more accurate detection of the wavenumbers. Moreover, the propagation in the directions of increasing and decreasing thickness along the waveguide is investigated.

Axial transmission method for long bone fracture evaluation by ultrasonic guided waves: simulation, phantom and in vitro experiments

Mode conversion occurs when the ultrasonic guided waves encounter fractures. The aim of this study was to investigate the feasibility of fracture assessment in long cortical bone using guided-mode conversion. Mode conversion behavior between the fundamental modes S0 and A0 was analyzed. The expressions proposed for modal velocity were used to identify the original and converted modes. Simulations and phantom experiments were performed using 1.0-mm-thick steel plates with a notch width of 0.5 mm and notch depths of 0.2, 0.4, 0.6 and 0.8 mm. Furthermore, in vitro experiments were carried out on nine ovine tibias with 1.0-mm-wide partial transverse gap break and cortical thickness varying from 2.10 to 3.88 mm. The study confirmed that mode conversion gradually becomes observable as fracture depth increases. Energy percentages of the converted modes correlated strongly with fracture depth, as illustrated by the frequency-sweeping experiments on steel phantoms (100-1100 kHz, r(2) = 0.97, p < 0.0069) and the fixed-frequency experiments on nine ovine tibias (250 kHz, r(2) = 0.97, p < 0.0056). The approaches described, including mode excitation, velocity expressions and energy percentage criteria, may also contribute to ultrasonic monitoring of long bone fracture healing.

Discrimination of fractures by low-frequency axial transmission ultrasound in postmenopausal females

SUMMARY

In this cross-sectional study, 95 postmenopausal women, with and without fracture history, were measured by low-frequency axial transmission ultrasound. The measured ultrasound velocity discriminated the fractured subjects from the nonfractured ones equally or better than peripheral quantitative computed tomography (pQCT) and dual energy x-ray absorptiometry (DXA). These results suggest that low-frequency ultrasound is suitable for bone fragility assessment.

INTRODUCTION

Quantitative low-frequency axial transmission ultrasound is a promising modality for assessing mineral density and geometrical properties of long bones such as radius and tibia. The aim of the current study was to evaluate the ability of low-frequency axial transmission ultrasound to discriminate fractures retrospectively in postmenopausal women.

METHODS

A cross-sectional study involved 95 female subjects aged 45-88 years, whose fracture information was gathered retrospectively. The fracture group was defined as subjects with one or more low-/moderate-energy fractures. The radius and tibial shaft were measured with a custom-made ultrasonometer to assess the velocity of the low-frequency first-arriving signal (V (LF)). Site-matched pQCT was used to measure volumetric cortical and subcortical bone mineral density (sBMD), and cortical thickness (CTh). Areal BMD (aBMD) was measured using DXA for the whole body (WB), lumbar spine, and hip.

RESULTS

The majority (19/32; 59 %) of the fractures were in the upper limb. V (LF) in the radius, but not in the tibia, discriminated fractures with an age- and BMI-adjusted odds ratio (OR) of 2.06 (95 % CI 1.21-3.50, p < 0.01). In the radius, CTh and cortical BMD (CBMD) significantly discriminated fractures, as did the total, cortical, and sBMD in the tibia (adjusted OR 1.35-2.15, p < 0.05). Sensitivity and specificity were similar among all the measurements (area under the receiver operating characteristic curve 0.74-0.81, p < 0.001).

CONCLUSIONS

Low-frequency axial transmission ultrasound in the radius was able to discriminate fractured subjects from the nonfractured ones. This suggests that low-frequency axial transmission ultrasound has the potential to assess bone fragility in postmenopausal women.

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

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

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.

Experimental and simulation results on the effect of cortical bone mineralization in ultrasound axial transmission measurements: a model for fracture healing ultrasound monitoring

Ultrasound axial transmission (UAT), a technique using propagation of ultrasound waves along the cortex of cortical bones, has been proposed as a diagnostic technique for the evaluation of fracture healing. Quantitative ultrasound parameters have been reported to be sensitive to callus changes during the regeneration process. The aim of this work was to identify the specific effect of cortical bone mineralization on UAT measurements by means of numerical simulations and experiments using a reverse fracture healing approach. A cortical bovine femur sample was used, in which a 3mm fracture gap was drilled. A 3mm thick cortical bone slice, extracted from another location in the bone sample, was submitted to a progressive demineralization process with EDTA during 12 days. UAT measurements and simulations using a 1MHz probe were performed with the demineralized slice placed into the fracture gap to mimic different stages of mineralization during the healing process. The calcium loss of the slice due to the EDTA treatment was recorded everyday, and its temporal evolution could be modeled by an exponential law. A 50MHz scanning acoustic microscopy was also used to assess the mineralization degree of the bone slice at the end of the intervention. These data were used in the numerical simulations to derive a model of the time evolution of bone slice mechanical properties. From both the experiments and the simulations, a significant and progressive increase in the time of flight (TOF; p<0.001) of the propagating waves measured by UAT was observed during the beginning of the demineralization process (first 4 days). Although the simulated TOF values were slightly larger than the experimental ones, they both exhibited a similar time-dependence, validating the simulation approach. Our results suggest that TOF measured in axial transmission is affected by local changes of speed of sound induced by changes in local mineralization. TOF may be an appropriate indicator to monitor callus maturation.

Cancellous bone analysis with modified least squares Prony's method and chirp filter: phantom experiments and simulation

The presence of two longitudinal waves in porous media is predicted by Biot's theory and has been confirmed experimentally in cancellous bone. When cancellous bone samples are interrogated in through-transmission, these two waves can overlap in time. Previously, the Modified Least-Squares Prony's (MLSP) method was validated for estimation of amplitudes, attenuation coefficients, and phase velocities of fast and slow waves, but tended to overestimate phase velocities by up to about 5%. In the present paper, a pre-processing chirp filter to mitigate the phase velocity bias is derived. The MLSP/chirp filter (MLSPCF) method was tested for decomposition of a 500 kHz-center-frequency signal containing two overlapping components: one passing through a low-density-polyethylene plate (fast wave) and another passing through a cancellous-bone-mimicking phantom material (slow wave). The chirp filter reduced phase velocity bias from 100 m/s (5.1%) to 69 m/s (3.5%) (fast wave) and from 29 m/s (1.9%) to 10 m/s (0.7%) (slow wave). Similar improvements were found for 1) measurements in polycarbonate (fast wave) and a cancellous-bone-mimicking phantom (slow wave), and 2) a simulation based on parameters mimicking bovine cancellous bone. The MLSPCF method did not offer consistent improvement in estimates of attenuation coefficient or amplitude.

Guided wave phase velocity measurement using multi-emitter and multi-receiver arrays in the axial transmission configuration

This paper is devoted to a method of extraction of guided waves phase velocities from experimental signals. Measurements are performed using an axial transmission device consisting of a linear arrangement of emitters and receivers placed on the surface of the inspected specimen. The technique takes benefit of using both multiple emitters and receivers and is validated on a reference wave guide. The guided mode phase velocities are obtained using a projection in the singular vectors basis. The singular vectors are determined by the singular values decomposition (SVD) of the response matrix between the two arrays in the frequency domain. This technique enables to recover accurately guided wave phase velocity dispersion curves. The SVD based approach was designed to overcome limitations of spatio-temporal Fourier transform for receiver array of limited spatial extent as in the case of clinical assessment of cortical bone in axial transmission.

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.

Frequency dependence of average phase shift from human calcaneus in vitro

If dispersion in a medium is weak and approximately linear with frequency (over the experimental band of frequencies), then it can be shown that the constant term in a polynomial representation of phase shift as a function of frequency can produce errors in measurements of phase-velocity differences in through-transmission, substitution experiments. A method for suppressing the effects of the constant phase shift in the context of the single-wave-model was tested on measurements from 30 cancellous human calcaneus samples in vitro. Without adjustment for constant phase shifts, the estimated phase velocity at 500 kHz was 1516+/-6 m/s (mean+/-standard error), and the estimated dispersion was -24+/-4 m/s MHz (mean+/-standard error). With adjustment for constant phase shifts, the estimated mean velocity decreased by 4-9 m/s, and the estimated magnitude of mean dispersion decreased by 50%-100%. The average correlation coefficient between the measured attenuation coefficient and frequency was 0.997+/-0.0026 (mean+/-standard deviation), suggesting that the signal for each sample was dominated by one wave. A single-wave, linearly dispersive model conformed to measured complex transfer functions from the 30 cancellous-bone samples with an average root-mean-square error of 1.9%+/-1.0%.

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.