Petro Moilanen

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

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

Mode separation of Lamb waves based on dispersion compensation method.

Ultrasonic Lamb modes typically propagate as a combination of multiple dispersive wave packets. Frequency components of each mode distribute widely in time domain due to dispersion and it is very challenging to separate individual modes by traditional signal processing methods. In the present study, a method of dispersion compensation is proposed for the purpose of mode separation. This numerical method compensates, i.e., compresses, the individual dispersive waveforms into temporal pulses, which thereby become nearly un-overlapped in time and frequency and can thus be extracted individually by rectangular time windows. It was further illustrated that the dispersion compensation also provided a method for predicting the plate thickness. Finally, based on reversibility of the numerical compensation method, an artificial dispersion technique was used to restore the original waveform of each mode from the separated compensated pulse. Performances of the compensation separation techniques were evaluated by processing synthetic and experimental signals which consisted of multiple Lamb modes with high dispersion. Individual modes were extracted with good accordance with the original waveforms and theoretical predictions.

Ultrasonically determined thickness of long cortical bones: Three-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.

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.

Assessment of the Fundamental Flexural Guided Wave in Cortical Bone by an Ultrasonic Axial-Transmission Array Transducer

The fundamental flexural guided wave (FFGW), as modeled, for example, by the A0 Lamb mode, is a clinically useful indicator of cortical bone thickness. In the work described in this article, we tested so-called multiridge-based analysis, based on the crazy climber algorithm and short-time Fourier transform, for assessment of the FFGW component recorded by a clinical array transducer featuring a limited number of elements. Methods included numerical finite-element simulations and experiments in bone phantoms and human radius specimens (n = 41). The proposed approach enabled extraction of the FFGW component and determination of its group velocity. This group velocity was in good agreement with theoretical predictions and possessed reasonable sensitivity to cortical width (r(2) = 0.51, p < 0.001) in the in vitro experiments. It is expected that the proposed approach enables related clinical application. Further work is still needed to analyze in more detail the challenges related to the impact of the overlying soft tissue.

Phase-delayed laser diode array allows ultrasonic guided wave mode selection and tuning

Selecting and tuning modes are useful in ultrasonic guided wave non-destructive testing (NDT) since certain modes at various center frequencies are sensitive to specific types of defects. Ideally one should be able to select both the mode and the center frequency of the launched waves. We demonstrated that an affordable laser diode array can selectively launch either the S0 or A0 ultrasonic wave mode at a chosen center frequency into a polymer plate. A fiber-coupled diode array (4 elements) illuminated a 2 mm thick acrylic plate. A predetermined time delay matching the selected mode and frequency was employed between the output of the elements. The generated ultrasound was detected by a 215 kHz piezo receiver. Our results imply that this array permits non-contacting guided wave ultrasonic NDT. The solution is small, affordable, and robust in comparison to conventional pulsed lasers. In addition, it does not require experienced operators.

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.

Effects of a low-frequency sound wave therapy programme on functional capacity, blood circulation and bone metabolism in frail old men and women

Objective: To evaluate the effects of a low-frequency sound wave therapy programme on functional capacity, blood circulation and bone metabolism of the frail elderly. Design: Single-blind, randomized, controlled trial. Setting: Two senior service centres. Subjects: Forty-nine volunteers (14 males and 35 females) aged 62—93 years with up to 12 diagnosed diseases were allocated in either the intervention group (n = 30) or control group (n = 19). Intervention: The intervention group underwent sound wave therapy, 3—5 times a week for 30 minutes per session over a period of 6 months. The control group received no intervention. Main measurements: Blood pressure, functional capacity, mobility, bone density, biochemical markers, isometric muscle strength, balance, and skin surface temperature. Results: Compared with the control group, the intervention group’s mobility and the amount of self-reported kilometres walked per week increased by 3 km (P<0.05), while levels of cholesterol (4.97 (0.72) to 4.52 (0.65) mmol/L, P =0.019), low-density lipoprotein (2.82 (0.72) to 2.45 (0.61) mmol/L, P =0.022), bone markers of total osteocalcin (11.0 (6.5) to 10.3 (5.9) ng/mL, P =0.048)) and tartrate-resistant acid phosphatase isoform 5b (2.50 (1.0) to 2.41 (1.1) IU/L, P =0.021)) decreased. The average skin surface temperature was significantly higher during active sessions at the end of the intervention than in the beginning (P = 0.004). No change was found during placebo sessions. Conclusions: Low-frequency sound wave therapy may have the potential to promote well-being of frail elderly subjects via improved functional capacity, especially in subjects who are too frail to undertake exercise.

Contributions of individual muscles to the sagittal- and frontal-plane angular accelerations of the trunk in walking

This study was conducted to analyze the unimpaired control of the trunk during walking. Studying the unimpaired control of the trunk reveals characteristics of good control. These characteristics can be pursued in the rehabilitation of impaired control. Impaired control of the trunk during walking is associated with aging and many movement disorders. This is a concern as it is considered to increase fall risk. Muscles that contribute to the trunk control in normal walking may also contribute to it under perturbation circumstances, attempting to prevent an impending fall. Knowledge of such muscles can be used to rehabilitate impaired control of the trunk. Here, angular accelerations of the trunk induced by individual muscles, in the sagittal and frontal planes, were calculated using 3D muscle-driven simulations of seven young healthy subjects walking at free speed. Analysis of the simulations demonstrated that the abdominal and back muscles displayed large contributions throughout the gait cycle both in the sagittal and frontal planes. Proximal lower-limb muscles contributed more than distal muscles in the sagittal plane, while both proximal and distal muscles showed large contributions in the frontal plane. Along with the stance-limb muscles, the swing-limb muscles also exhibited considerable contribution. The gluteus medius was found to be an important individual frontal-plane control muscle; enhancing its function in pathologies could ameliorate gait by attenuating trunk sway. In addition, since gravity appreciably accelerated the trunk in the frontal plane, it may engender excessive trunk sway in pathologies.

Ultrasonic guided waves in bone

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