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

Investigation of bone fracture diagnosis system using transverse vibration response

In this study, a new diagnostic system is developed to easily identify bone fractures in non-medical environments. It is difficult to determine the extent of cracks, fractures, and the healing process inside humans owing to the differences among people and limitations of state-of-the-art medical devices. Thus, various medical techniques, such as X-ray, computed tomography, or fork tuning systems have been developed, and more advanced technologies are emerging in the medical engineering field. In hazardous circumstances, medical devices to detect bone fracture are not available or cannot be easily applied. Thus, there is a need for the rapid detection of bone fractures without medical devices. To this end, this study analyzes the transverse vibration responses of bones because bone fractures cause different mechanical vibration reactions. By comparing the transverse vibration responses of both healthy and fractured bones, the modal assurance criterion can be calculated and applied to detect the existence of bone fractures. The transverse vibration responses at low and high frequencies are different and exhibit different modal assurance criteria depending on whether or not they are abnormal. Then, the virtual spectrogram of the differences between the signals from non-fractured and fractured bones is calculated. With the help of the present criterion with transverse vibration data, this difference can be analyzed quantitatively and effectively. To validate the proposed system, experiments with artificial specimens, animal legs, and a cadaver are performed.

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.

Numerical evaluation of the backward propagating acoustic field in healing long bones

The propagation of ultrasound in healing long bones induces complex scattering phenomena due to the interaction of an ultrasonic wave with the composite nature of callus and osseous tissues. This work presents numerical simulations of ultrasonic propagation in healing long bones using the boundary element method aiming to provide insight into the complex scattering mechanisms and better comprehend the state of bone regeneration. Numerical models of healing long bones are established based on scanning acoustic microscopy images from successive postoperative weeks considering the effect of the nonhomogeneous callus structure. More specifically, the scattering amplitude and the acoustic pressure variation are calculated in the backward direction to investigate their potential to serve as quantitative and qualitative indicators for the monitoring of the bone healing process. The role of the excitation frequency is also examined considering frequencies in the range 0.2-1 MHz. The results indicate that the scattering amplitude decreases at later stages of healing compared to earlier stages of healing. Also, the acoustic pressure could provide supplementary qualitative information on the interaction of the scattered energy with bone and callus.

Transverse and Oblique Long Bone Fracture Evaluation by Low Order Ultrasonic Guided Waves: A Simulation Study

Ultrasonic guided waves have recently been used in fracture evaluation and fracture healing monitoring. An axial transmission technique has been used to quantify the impact of the gap breakage width and fracture angle on the amplitudes of low order guided wave modes S0 and A0 under a 100 kHz narrowband excitation. In our two dimensional finite-difference time-domain (2D-FDTD) simulation, the long bones are modeled as three layers with a soft tissue overlay and marrow underlay. The simulations of the transversely and obliquely fractured long bones show that the amplitudes of both S0 and A0 decrease as the gap breakage widens. Fixing the crack width, the increase of the fracture angle relative to the cross section perpendicular to the long axis enhances the amplitude of A0, while the amplitude of S0 shows a nonmonotonic trend with the decrease of the fracture angle. The amplitude ratio between the S0 and A0 modes is used to quantitatively evaluate the fracture width and angles. The study suggests that the low order guided wave modes S0 and A0 have potentials for transverse and oblique bone fracture evaluation and fracture healing monitoring.

Boundary element simulation of ultrasonic backscattering during the fracture healing process

Competent fracture healing monitoring and treatment requires an extensive knowledge of bone biology and microstructure. The use of non-invasive and non-radiating means for the monitoring of the bone healing process has gained significant interest in recent years. Ultrasound is considered as a modality which can contribute to the assessment of bone status during the healing process, as well as, enhance the rate of the tissues' ossification. This work presents boundary element simulations of ultrasound propagation in healing long bones to investigate the monitoring potential of backscattering parameters. The interaction of a plane wave at 100 kHz with the bone and the callus is examined by calculating the acoustic pressure and scattering amplitude in the backward direction. Callus is considered as a two-dimensional, non-homogeneous medium consisted of multiple layers with evolving material properties. It was shown that the backscattering parameters could potentially reflect the fracture healing progress.

Computational Study of the Effect of Cortical Porosity on Ultrasound Wave Propagation in Healthy and Osteoporotic Long Bones

Computational studies on the evaluation of bone status in cases of pathologies have gained significant interest in recent years. This work presents a parametric and systematic numerical study on ultrasound propagation in cortical bone models to investigate the effect of changes in cortical porosity and the occurrence of large basic multicellular units, simply called non-refilled resorption lacunae (RL), on the velocity of the first arriving signal (FAS). Two-dimensional geometries of cortical bone are established for various microstructural models mimicking normal and pathological tissue states. Emphasis is given on the detection of RL formation which may provoke the thinning of the cortical cortex and the increase of porosity at a later stage of the disease. The central excitation frequencies 0.5 and 1 MHz are examined. The proposed configuration consists of one point source and multiple successive receivers in order to calculate the FAS velocity in small propagation paths (local velocity) and derive a variation profile along the cortical surface. It was shown that: (a) the local FAS velocity can capture porosity changes including the occurrence of RL with different number, size and depth of formation; and (b) the excitation frequency 0.5 MHz is more sensitive for the assessment of cortical microstructure.

Computational modeling of ultrasonic backscattering to evaluate fracture healing

Fracture healing is a complex, regenerative procedure including several phases of recovery as the original mechanical and geometrical features of bone are gradually restored. Ultrasonic evaluation of bone pathologies such as osteoporosis and fracture healing has recently gained significant interest due to the non-invasive and non-radiating nature of the method. In this study, we present numerical simulations of ultrasonic backscattering in simple, two dimensional geometries of healing long bones to investigate the monitoring capacity of the acoustic pressure in the backward direction. The fracture process was modeled as a 7-stage procedure and the results were compared to the acoustic pressure derived for the case of intact bone. A 100 kHz plane wave was used as the excitation frequency and multiple receivers were placed at a distance of 20 mm from the cortical cortex. It was found that the acoustic pressure profile is gradually restored at the final healing stages approaching the values of intact bone.

Ultrasound propagation in cortical bone: Axial transmission and backscattering simulations

Cortical bone is a heterogeneous, composite medium with a porosity from 5-10%. The characterization of cortical bone using ultrasonic techniques is a complicated procedure especially in numerical studies as several assumptions must be made to describe the concentration and size of pores. This study presents numerical simulations of ultrasound propagation in two-dimensional numerical models of cortical bone to investigate the effect of porosity on: a) the propagation of the first arriving signal (FAS) velocity using the axial transmission method, and b) the displacement and scattering amplitude in the backward direction. The excitation frequency 1 MHz was used and different receiving positions were examined to provide a variation profile of the examined parameters along cortical bone. Cortical porosity was simulated using ellipsoid scatterers and the concentrations of 0-10% were examined. The results indicate that the backscattering method is more appropriate for the evaluation of cortical porosity in comparison to the axial transmission method.

Computational study of the influence of callus porosity on ultrasound propagation in healing bones

In the process of fracture healing, several phases of recovery are observed as the mechanical stability, continuity and normal load carrying capacity are gradually restored. The ultrasonic monitoring and discrimination of different healing stages is a complex process due to the significant microstructure and porous nature of osseous and callus tissues. In this study, we investigate the influence of the callus pores' size and concentration on ultrasound propagation in a long bone at a late healing stage. Different excitation frequencies are applied in the range of 300 kHz-1 MHz. A 2D geometry is developed and axial transmission calculations are performed based on a Finite Element Method. The velocity of the first arriving signal (FAS) and the propagation of guided waves are used as the estimated parameters. It was shown that the FAS velocity can reflect callus porosity changes, while the propagation of guided waves is sensitive to pores' distribution for higher frequencies.

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.

Quantification of guided mode propagation in fractured long bones

Guided modes propagation in intact, fractured and healing long bone has drawn significant research interests. However, mode quantifications for the direct comparison are still necessary to address. The aim of the study is to analyze the mode interaction with a notch-fracture in the long bone and find quantitative ultrasound parameters sensitive to depth and width variation of the fracture. We analyzed the impacts of the partially and completely diaphyseal osteotomy on fundamental guided modes propagation using the two-dimension finite-difference time-domain (2D-FDTD) simulations. The long bones were built as three layer models by a cortical plate embedded between overlying soft tissue and inner-coated marrow. Narrowband low-frequency sinusoids (100 kHz) were employed to only excite two fundamental guided modes. The mode amplitude variations were investigated as functions of the gap-breakage width and depth. It is found that the transverse fractures have strong influences on the anti-symmetric mode A0 transmission and reflection, whereas amplitudes of the symmetric mode S0 are not sensitive to the fracture degree. The quantitative results consistently indicate that reflection energy and transmission coefficients of the S0 and A0 modes can be used to quantify the mode interaction in the fractured long bone and further to evaluate long bone fracture status. Future study is needed to investigate the physical experiments on realistic fractured long bone and to insure that the proposed ultrasound parameters can be used to quantitatively evaluate the long bone fracture in clinical application.

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.

Ultrasound imaging of long bone fractures and healing with the split-step fourier imaging method

We applied the split-step Fourier imaging method to back-propagate the ultrasound zero-offset wavefields acquired on the bone surface to the sources of scatterers, which are the reflecting interfaces. The method required, as an input, an estimated slowness (reciprocal of half the velocity) model to map the time-dependent sonogram to the depth image, which provides the geometric properties of the interfaces. The slowness was approximated by a depth-dependent term and a first-order spatially varying perturbation. Simulated data sets were used to validate the method. The reconstructed images show proper mapping of the interfaces and the fracture, and a reasonable cortical thickness measurement with 8.3% error. The images also illustrate clearly the bone fracture healing process of a 1-mm-wide 45° inclined crack with different in-filled tissue velocities for various healing stages. Reconstruction of a fractured bone plate using data from an in vitro experiment is also presented. This study suggests that the proposed imaging method has good potential in quantification of bone fractures and monitoring of the fracture healing process.

Computed radiographic and ultrasonic evaluation of bone regeneration during tibial distraction osteogenesis in rabbits

Computed radiography (CR) and a combined ultrasound (US) approach involving two-dimensional (2-D) and three-dimensional (3-D) ultrasonography with ultrasonometry were employed to evaluate their respective efficacies in monitoring bone regeneration during rabbit tibial distraction osteogenesis (DO). Results demonstrated that 2-D and 3-D ultrasonography depicted bone callus growth changes during distraction while CR could not. Evaluation of callus speed of sound, acoustic reflection and attenuation showed significant linear changes over time during early DO stage (p < 0.05). However, surrogate measure of callus density by CR only showed such significant linear changes during consolidation (p < 0.05). Also, callus speed of sound and acoustic reflection during early DO stage showed strong predictions to the bone mineral density and microstructural properties (adjusted-R(2) = 0.43-0.67) of consolidated bone callus measured at the treatment end-point by microcomputed tomography. Findings of the present study indicated a preferred use of the combined US approach over CR in the early monitoring of bone regeneration during DO treatment.

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.

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.

Ultrasonic airborne insertion loss measurements at normal incidence (L)

Transmission loss and insertion loss measurements of building materials at audible frequencies are commonly made using plane wave tubes or as a panel between reverberant rooms. These measurements provide information for noise isolation control in architectural acoustics and in product development. Airborne ultrasonic sound transmission through common building materials has not been fully explored. Technologies and products that utilize ultrasonic frequencies are becoming increasingly more common, hence the need to conduct such measurements. This letter presents preliminary measurements of the ultrasonic insertion loss levels for common building materials over a frequency range of 28-90 kHz using continuous-wave excitation.

Computational evaluation of the compositional factors in fracture healing affecting ultrasound axial transmission measurements

This work aimed at computationally evaluating the compositional factors in fracture healing affecting ultrasound axial transmission (UAT), using four numerical daily-changing healing models, representing more realistic clinical conditions. Using two-dimensional (2-D) simulations, a 1-MHz source and a receiver were positioned parallel to the bone surface to detect the first arriving signal (FAS). The time-of-flight of the FAS (TOF(FAS)) was found to be sensitive only to superficial modifications in the propagation path. It was also shown that callus mature bone better explained alone the variation in TOF(FAS) (R(2) >or= 0.70, p < 0.001). Better TOF(FAS) predictions are obtained when using the callus composition inside cortical fracture gap (R(2) = 0.98, p < 0.01). Callus composition could not well explain the changes in energy attenuation. These results suggest that UAT may be an important clinical tool for fracture healing assessment, identifying callus degree of mineralization and possible consolidation delays and nonunions.

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.

Monitoring the mechanical properties of healing bone

Fracture healing is normally assessed through an interpretation of radiographs, clinical evaluation, including pain on weight bearing, and a manual assessment of the mobility of the fracture. These assessments are subjective and their accuracy in determining when a fracture has healed has been questioned. Viewed in mechanical terms, fracture healing represents a steady increase in strength and stiffness of a broken bone and it is only when these values are sufficiently high to support unrestricted weight bearing that a fracture can be said to be healed. Information on the rate of increase of the mechanical properties of a healing bone is therefore valuable in determining both the rate at which a fracture will heal and in helping to define an objective and measurable endpoint of healing. A number of techniques have been developed to quantify bone healing in mechanical terms and these are described and discussed in detail. Clinical studies, in which measurements of fracture stiffness have been used to identify a quantifiable end point of healing, compare different treatment methods, predictably determine whether a fracture will heal, and identify factors which most influence healing, are reviewed and discussed.