Victor F. Humphrey

Nonlinear propagation in ultrasonic fields : measurements, modelling and harmonic imaging

In high amplitude ultrasonic fields, such as those used in medical ultrasound, nonlinear propagation can result in waveform distortion and the generation of harmonics of the initial frequency. In the nearfield of a transducer this process is complicated by diffraction effects associated with the source. The results of a programme to study the nonlinear propagation in the fields of circular, focused and rectangular transducers are described, and comparisons made with numerical predictions obtained using a finite difference solution to the Khokhlov-Zabolotskaya-Kuznetsov (or KZK) equation. These results are extended to consider nonlinear propagation in tissue-like media and the implications for ultrasonic measurements and ultrasonic heating are discussed. The narrower beamwidths and reduced side-lobe levels of the harmonic beams are illustrated and the use of harmonics to form diagnostic images with improved resolution is described.

An experimental investigation of streaming in pulsed diagnostic ultrasound beams

Streaming is shown to occur in water in the focused beams produced by a number of medical pulse-echo devices. The use of hot film anemometry to measure the streaming velocity is described and velocities measured in water using commercial equipment are quoted. The highest velocities occur in pulsed Doppler mode with a maximum velocity of 14 cm s-1 being observed. An experimental set-up was used to investigate the parameters affecting streaming and it was found that the harmonic content of the pulse waveform had a major effect on the streaming velocity. The time taken for a stream to become established at the focus of the acoustic beams studied was typically approximately 0.5 s.

Evidence for ultrasonic finite‐amplitude distortion in muscle using medical equipment

Finite-amplitude distortion of ultrasonic waves from medical equipment has been observed to occur following transmission through calf muscle in human volunteers. Measurements were made using both dynamic pulse-echo imaging equipment and physiotherapy equipment. In both cases irradiation was carried out under operating conditions commonly used clinically. Pressure waveforms were measured at the skin surface using a broadband polyvinylidene difluoride membrane hydrophone. Using a pulsed, weakly focused 2.5-MHz beam with input peak pressure of 0.8 MPa and a pressure gain of 5.3 at the focus, the mean second harmonic peak magnitude (16 measurements) was 17 dB below the fundamental peak. A 1.1-MHz continuous wave therapy set with input peak pressure of 0.5 MPa showed mean second harmonic magnitude 23 dB below the fundamental.

Mechanisms of Pelvic Floor Muscle Function and the Effect on the Urethra during a Cough

BACKGROUND Current measurement tools have difficulty identifying the automatic physiologic processes maintaining continence, and many questions still remain about pelvic floor muscle (PFM) function during automatic events. OBJECTIVE To perform a feasibility study to characterise the displacement, velocity, and acceleration of the PFM and the urethra during a cough. DESIGN, SETTING, AND PARTICIPANTS A volunteer convenience sample of 23 continent women and 9 women with stress urinary incontinence (SUI) from the general community of San Francisco Bay Area was studied. MEASUREMENTS Methods included perineal ultrasound imaging, motion tracking of the urogenital structures, and digital vaginal examination. Statistical analysis used one-tailed unpaired student t tests, and Welchs correction was applied when variances were unequal. RESULTS AND LIMITATIONS The cough reflex activated the PFM of continent women to compress the urogenital structures towards the pubic symphysis, which was absent in women with SUI. The maximum accelerations that acted on the PFM during a cough were generally more similar than the velocities and displacements. The urethras of women with SUI were exposed to uncontrolled transverse acceleration and were displaced more than twice as far (p=0.0002), with almost twice the velocity (p=0.0015) of the urethras of continent women. Caution regarding the generalisability of this study is warranted due to the small number of women in the SUI group and the significant difference in parity between groups. CONCLUSIONS During a cough, normal PFM function produces timely compression of the pelvic floor and additional external support to the urethra, reducing displacement, velocity, and acceleration. In women with SUI, who have weaker urethral attachments, this shortening contraction does not occur; consequently, the urethras of women with SUI move further and faster for a longer duration.

The nonlinear pressure field of a plane circular piston: Theory and experiment

The measured nearfield pressure levels of a plane circular piston are compared with a numerical solution of the parabolic approximation to the nonlinear wave equation under conditions of high nonlinearity (100 kPa at the piston face). The solution allows for nonlinearity, diffraction, and absorption in continuous wave pressure fields. The measurements were made in water, using a transducer (38‐mm diameter) driven at 2.25 MHz and a 1‐mm‐diam membrane hydrophone. Comparisons are made along and across the acoustic axis for the amplitudes of the fundamental, second, and third harmonics and the phases of the second and third harmonics. Good agreement is shown between experiment and theory within the known limitations of both.

Distortion and high‐frequency generation due to nonlinear propagation of short ultrasonic pulses from a plane circular piston

A numerical finite‐difference model for the prediction of nonlinear propagation has been adapted to examine the high‐frequency components generated by short ultrasonic pulses. Comparisons are made in both the time and frequency domains between the model predictions and experimental measurements. The experimental measurements were obtained, in water, using a 1‐mm‐diam membrane hydrophone to sample the pressure field generated by a plane transducer (38 mm in diameter) that was driven by a diagnostic medical ultrasound system. The pulses generated were a few cycles long with a zero‐crossing frequency of about 2 MHz and a maximum peak positive pressure of about 300 kPa. It is shown that the theoretical model can be used to provide accurate predictions (typically better than 10%) both on and off the acoustic axis for pulsed pressure fields in water. An important factor in obtaining good agreement is the initial characterization of the transducer and pulse.

Sonic bands, bandgaps, and defect states in layered structures—Theory and experiment

The propagation of sound through a one‐dimensional periodic array of water and perspex plates is studied theoretically and experimentally. It is shown that the passbands and stop bands of a scatterer with a finite number of layers correspond to the bands and bandgaps of an infinite ‘‘sonic bandgap crystal.’’ The transmission coefficient of various finite structures is computed and measured as a function of frequency. The analogy with the electronic bandstructure of crystals, and the photonic bandstructure of macroscopic periodic dielectric structures, is found to be a close one. It is shown that the position and width of passbands can easily be engineered. Results are included for a finite ‘‘crystal’’ with a vacancy defect, in which a narrow passband appears in each of the stop bands.

Ultrasonic propagation in cortical bone mimics

Understanding the velocity and attenuation characteristics of ultrasonic waves in cortical bone and bone mimics is important for studies of osteoporosis and fractures. Three complementary approaches have been used to help understand the ultrasound propagation in cortical bone and bone mimics immersed in water, which is used to simulate the surrounding tissue in vivo. The approaches used were Lamb wave propagation analysis, experimental measurement and two-dimensional (2D) finite difference modelling. First, the water loading effects on the free plate Lamb modes in acrylic and human cortical bone plates were examined. This theoretical study revealed that both the S0 and S1 mode velocity curves are significantly changed in acrylic: mode jumping occurs between the S0 and S1 dispersion curves. However, in human cortical bone plates, only the S1 mode curve is significantly altered by water loading, with the S0 mode exhibiting a small deviation from the unloaded curve. The Lamb wave theory predictions for velocity and attenuation were then tested experimentally on acrylic plates using an axial transmission technique. Finally, 2D finite difference numerical simulations of the experimental measurements were performed. The predictions from Lamb wave theory do not correspond to the measured and simulated first arrival signal (FAS) velocity and attenuation results for acrylic and human cortical bone plates obtained using the axial transmission technique, except in very thin plates.

Empirical angle-dependent Biot and MBA models for acoustic anisotropy in cancellous bone

The Biot and the modified Biot-Attenborough (MBA) models have been found useful to understand ultrasonic wave propagation in cancellous bone. However, neither of the models, as previously applied to cancellous bone, allows for the angular dependence of acoustic properties with direction. The present study aims to account for the acoustic anisotropy in cancellous bone, by introducing empirical angle-dependent input parameters, as defined for a highly oriented structure, into the Biot and the MBA models. The anisotropy of the angle-dependent Biot model is attributed to the variation in the elastic moduli of the skeletal frame with respect to the trabecular alignment. The angle-dependent MBA model employs a simple empirical way of using the parametric fit for the fast and the slow wave speeds. The angle-dependent models were used to predict both the fast and slow wave velocities as a function of propagation angle with respect to the trabecular alignment of cancellous bone. The predictions were compared with those of the Schoenberg model for anisotropy in cancellous bone and in vitro experimental measurements from the literature. The angle-dependent models successfully predicted the angular dependence of phase velocity of the fast wave with direction. The root-mean-square errors of the measured versus predicted fast wave velocities were 79.2 m s(-1) (angle-dependent Biot model) and 36.1 m s(-1) (angle-dependent MBA model). They also predicted the fact that the slow wave is nearly independent of propagation angle for angles about 50 degrees , but consistently underestimated the slow wave velocity with the root-mean-square errors of 187.2 m s(-1) (angle-dependent Biot model) and 240.8 m s(-1) (angle-dependent MBA model). The study indicates that the angle-dependent models reasonably replicate the acoustic anisotropy in cancellous bone.

Ultrasound mimics the effect of mechanical loading on bone formation in vivo on rat ulnae.

While the effect of ultrasound as an extreme example of low-magnitude high-frequency stimulation has been explored in the response of bone to injury, little is known about its effect on normal bone. This experiment was designed to test the hypothesis that ultrasound exerts a similar influence on bone as mechanical stimulation at a physiological level. Three groups of female Wistar rats were anaesthetised (6 per group). In one group, the left ulna was loaded cyclically in vivo 40 times, repeated on a further 5 occasions on alternate days. In a second group, transcutaneous low-intensity pulsed ultrasound stimulation was applied to the left ulnae for the same duration as the period of loading. In a third group, loading and ultrasound stimulation were applied concurrently. The right ulna served as non-loaded control in each animal. At the end of the experiment after 14 days, both ulnae were removed. Induced bone formation was assessed by measuring the proportion of medial periosteal bone surface with double label (dLS/BS, %) and by calculation of mineral apposition rate (MAR) from the inter-label distance. All three treatments induced a significant periosteal response, increasing dLS/BS values from <10% in control limbs to >80% in treated limbs. Increases in MAR of experimental ulnae versus contralateral control ulnae were 2.9 (+/-0.9), 8.6 (+/-2.4) and 8.7 microm (+/-3.2) for the ultrasound only, ultrasound and load, and load only groups, respectively. The effects of loading plus ultrasound were not significantly different from ultrasound alone. These data suggest that ultrasound is able to induce changes in bone that share at least some features with mechanical loading.