Golay-encoded excitation for dual-frequency harmonic detection of ultrasonic contrast agents

Golay-encoded excitation in combination with the third harmonic (3f?) transmit phasing is examined for both signal-to-noise ratio (SNR) and contrast-to-tissue ratio (CTR) improvements in harmonic imaging of contrast microbubbles. To produce the cancellation pair of tissue harmonic signal in 3f? transmit phasing, the phase of the bit waveform is properly designed for both the fundamental and the 3f? transmit signals to provide the Golay encoding of the received harmonic responses. Results indicate that the proposed Golay excitation can effectively suppress the tissue harmonic amplitude to increase CTR. Meanwhile, the SNR of the contrast harmonic signal also improves because of the elongated waveform of Golay excitation. Nevertheless, the generation of marked range side-lobes of the bubble region would degrade the achievable SNR improvement and the image contrast, especially when the bit of Golay excitation increases. The range side-lobes could result from the nonlinear resonance of the microbubbles that interferes with the phase modulation of the Golay encoding.     

Design of chirp excitation waveform for dual-frequency harmonic contrast detection

Tissue background suppression is essential for harmonic detection of ultrasonic contrast microbubbles. To reduce the tissue harmonic amplitude for improvement of contrast-to-tissue ratio (CTR), the method of third harmonic (3f₀) transmit phasing uses an additional 3f₀ transmit signal to provide mutual cancellation between the frequency-sum component and the frequency-difference component of tissue harmonic signal. Chirp excitation can further improve the SNR in harmonic imaging without requiring an excessive transmit pressure and thus reduce potential bubble destruction. However, for effective suppression of tissue harmonic background in 3f₀ transmit phasing, the 3f₀ chirp waveform has to be carefully designed for the generation of spectrally matched cancellation pairs over the entire second harmonic band. In this study, we proposed a chirp waveform suitable for the method of 3f₀ transmit phasing, the different-bandwidth chirp signal (DBCS). With the DBCS waveform, the frequency-difference component of tissue harmonic signal becomes a chirp signal similar to its frequency-sum counterpart. Thus, the combination of the DBCS waveform with the 3f₀ transmit phasing can markedly suppress the tissue harmonic amplitude for CTR improvement together with effective SNR increase of contrast harmonic signal. Our results indicate that, as compared with the conventional Gaussian pulse, the DBCS waveform can provide 6-dB improvement of SNR in 3f₀ transmit phasing with a CTR increase of 3 dB. Nevertheless, the limitation of available transmit bandwidth and the frequency-dependent attenuation can degrade the performance of the DBCS waveform in tissue suppression. The design of the DBCS waveform is also applicable to other dual-frequency imaging techniques that rely on the harmonic generation at the difference frequency.     

Dual high-frequency difference excitation for contrast detection

Stimulating high-frequency nonlinear oscillations of ultrasound contrast agents is helpful to distinguish microbubbles from background tissues. Nevertheless, inefficiency of such oscillations from most commercially available contrast agents and intense attenuation of the resultant high-frequency harmonics limit microbubble detection with high-frequency ultrasound. To avoid this high-frequency nature, we devised and explored a dual-frequency difference excitation technique to induce efficiently low-frequency, rather than high-frequency, nonlinear scattering from microbubbles by using high-frequency ultrasound. The proposed excitation pulse is comprised of 2 high-frequency sinusoids with frequency difference subject to the microbubble resonance frequency. Its envelope, with frequency being the difference between the 2 frequencies, is used to stimulate nonlinear oscillation of microbubbles for the consonant low-frequency harmonic generation, whereas high-imaging resolution is retained because of narrow high-frequency transmit beams. Hydrophone measurements and phantom experiments of speckle-generating flow phantoms were performed to demonstrate the efficacy of the proposed technique. The results show that, especially when the envelope frequency is near the microbubbleiquests resonance frequency, the envelope of the proposed excitation pulse can induce significant nonlinear scattering from microbubbles, the induced nonlinear responses tend to increase with the pulse pressures, and up to 26 dB and 36 dB contrast-to-tissue ratios with second- and fourth-order nonlinear responses, respectively, can be obtained. Potential applications of this method include microbubble fragmentation and cavitation with high-frequency ultrasound.     

A new kind of energy transfer from high frequency mode to low frequency mode in a composite laminated plate

This paper brings to light a new type of nonlinear resonant motion in a fiber-reinforced composite laminated rectangular thin plate, which is not reported in other literature. The investigated system is a simply supported symmetric cross-ply composite laminated rectangular thin plate subjected to parametric excitation whose frequency is near to the first-order natural frequency of the plate. This new phenomenon demonstrates that the responses of a low-order frequency mode can be excited by those of a high-order frequency mode. The high-order frequency is the first-order natural frequency of the test plate, and the low-order frequency here is lower than the first-order nature frequency. Experimental research works on the nonlinear vibrations of the composite laminated rectangular thin plate have been carried out for the first time. It is found from the experimental results that the nonlinear dynamic responses consist of four modes, whose frequencies include a lower frequency than the first-order natural frequency, 1/3 sub-harmonic, 2/3 sub-harmonic and the first-order natural frequencies. In this case, the amplitude of the mode for lower frequency is larger than those of modes for the aforementioned frequencies. Moreover, the theoretical job goes to analyze this new phenomenon. An analytical mode is given to explain the interactions between the first-order mode and the lower-frequency mode observed in the experiment. Based on Reddy’s third-order shear deformation plate theory, the nonlinear governing equations of motion are formulated for the test plate under parametric excitation. Galerkin’s method is utilized to discretize the partial differential governing equations of motion for the composite laminated rectangular thin plate to a two-degree-of-freedom nonlinear system. The results of numerical simulations qualitatively agree very well with the experimental results. In addition, the multi-pulse chaotic motions are also found in numerical simulations.     

A new imaging strategy using wideband transient response of ultrasound contrast agents

High-resolution clinical systems operating near 15 MHz are becoming more available; however, they lack sensitive harmonic imaging modes for ultrasound contrast agent (UCA) detection, primarily due to limited bandwidth. When an UCA is driven to nonlinear oscillation, a very wideband acoustic transient response is produced that extends beyond 15 MHz. We propose a novel strategy using two separate transducers at widely separated frequencies and arranged confocally to simultaneously excite and receive acoustic transients from UCAs. Experiments were performed to demonstrate that this new mode shows similar resolution, higher echo amplitudes, and greatly reduced attenuation compared to transmission at a higher frequency, and superior resolution compared to transmission and reception at a lower frequency. The proposed method is shown to resolve two 200 microm tubes with centers separated by 400 microm. Strong acoustic transients were detected for rarefaction-first 1-cycle pulses with peak-negative pressures above 300 kPa. The results of this work may lead to uses in flow and/or targeted imaging in applications requiring very high sensitivity to contrast agents.     

Designing waveforms for temporal encoding using a frequency sampling method

In this paper a method for designing waveforms for temporal encoding in medical ultrasound imaging is described. The method is based on least squares optimization and is used to design nonlinear frequency modulated signals for synthetic transmit aperture imaging. By using the proposed design method, the amplitude spectrum of the transmitted waveform can be optimized, such that most of the energy is transmitted where the transducer has large amplification. To test the design method, a waveform was designed for a BK8804 linear array transducer. The resulting nonlinear frequency modulated waveform was compared to a linear frequency modulated signal with amplitude tapering, previously used in clinical studies for synthetic transmit aperture imaging. The latter had a relatively flat spectrum which implied that the waveform tried to excite all frequencies including ones with low amplification. The proposed waveform, on the other hand, was designed so that only frequencies where the transducer had a large amplification were excited. Hereby, unnecessary heating of the transducer could be avoided and the signal-to-noise ratio could be increased. The experimental ultrasound scanner RASMUS was used to evaluate the method experimentally. Due to the careful waveform design optimized for the transducer at hand, a theoretic gain in signal-to-noise ratio of 4.9 dB compared to the reference excitation was found, even though the energy of the nonlinear frequency modulated signal was 71% of the energy of the reference signal. This was supported by a signal-to-noise ratio measurement and comparison in penetration depth, where an increase of 1 cm was found in favor for the proposed waveform. Axial and lateral resolutions at full-width half-maximum were compared in a water phantom at depths of 42, 62, 82, and 102 mm. The axial resolutions of the nonlinear frequency modulated signal were 0.62, 0.69, 0.60, and 0.60 mm, respectively. The corresponding axial resolutions for the reference waveform were 0.58, 0.65, 0.62, and 0.60 mm, respectively. The compression properties of the matched filter (mismatched filter for the linear frequency modulated signal) were tested for both waveforms in simulation with respect to the Doppler frequency shift occurring when probing moving objects. It was concluded that the Doppler effect of moving targets does not significantly degrade the filtered output. Finally, in vivo measurements are shown for both methods, wherein the common carotid artery on a 27-year-old healthy male was scanned.     

High frequency coded imaging system with RF

Coded transmission is an approach to solve the inherent compromise between penetration and resolution required in ultrasound imaging. Our goal was to examine the applicability of the coded excitation to HF (20-35 MHz) ultrasound imaging. A novel real-time imaging system for research and evaluation of the coded transmission was developed. The digital programmable coder- digitizer module based on the field programmable gate array (FPGA) chip supports arbitrary waveform coded transmission and RF echo sampling up to 200 megasamples per second, as well as real-time streaming of digitized RF data via a high-speed USB interface to the PC. All RF and image data processing were implemented in the software. A novel balanced software architecture supports real-time processing and display at rates up to 30 frames/sec. The system was used to acquire quantitative data for sine burst and 16-bit Golay code excitation at 20 MHz fundamental frequency. SNR gain close to 14 dB was obtained. The example of the skin scan clearly shows the extended penetration and improved contrast when a 35-MHz Golay code is used. The system presented is a practical and low-cost implementation of a coded excitation technique in HF ultrasound imaging that can be used as a research tool as well as to be introduced into production.     

High-frequency, nonlinear flow imaging of microbubble contrast agents

It has been shown that nonlinear scattering can be stimulated from microbubble contrast agents at high-transmit frequencies (14-32 MHz). This work was extended to demonstrate the feasibility of nonlinear contrast imaging through modifications of existing ultrasound biomicroscopy linear B-scan imaging instrumentation. In this study, we describe the development and evaluation of prototype coherent flow imaging instrumentation for nonlinear microbubble imaging using transmit frequencies from 10 to 50 MHz. Phantom validation experiments were conducted to demonstrate color and power flow imaging using nonlinear 10 MHz (subharmonic) scattering induced by a 20 MHz transmit frequency. In vivo flow imaging of a rabbit ear microvessel was successfully performed. This work indicates the feasibility of performing flow imaging at high frequencies using nonlinear scattering from microbubbles.     

Wideband linear power amplifier for high-frequency ultrasonic coded excitation imaging

Linear power amplifiers are critical components in ultrasonic imaging systems that implement chirp-coded excitation. Bench-top commercial power amplifiers are usually used in academic laboratories for high-frequency ultrasound imaging, and the imaging performance depends greatly on these general-purpose instruments. To achieve a wide dynamic range, a power amplifier consisting of two stages is developed for chirp-coded ultrasound imaging applications through the implementation of custom-designed broadband 1:1 transformers and the optimization of feedback circuits. The amplifier has broad bandwidth (5 to 135 MHz), maintaining a linearity up to the 1-dB gain compression point (P1dB) of 41.5 dBm, allowing 16 dBm input power level at 60 MHz. The mean and the maximum values of output third-order intercept points (OIP3) are 51.8 and 53.5 dBm, respectively, between 20 and 110 MHz. With 12 dBm input power, the gain of the amplifier varies between 24 and 29 dB, offering a uniformity which would allow excitation of a 70-MHz single-element transducer with windowed chirp-coded bursts sweeping from 40 to 100 MHz. The performance in high-frequency ultrasound imaging is evaluated with a wire phantom. Echo signal-to-noise ratio (eSNR) of the designed amplifier is 7 dB better than a commercial amplifier, and spatial resolution is maintained.     

Analysis of intrinsic stability criteria for isotropic third-order Green elastic and compressible neo-Hookean solids

Internal stability of isotropic nonlinear elastic materials under homogeneous deformation is studied. Results provide new insight into various intrinsic stability measures, first proposed elsewhere, for generic nonlinear elastic solids. Three intrinsic stability criteria involving three different tangent elastic stiffness matrices are considered, corresponding to respective increments in strain measures conjugate to thermodynamic tension, first Piola–Kirchhoff stress, and Cauchy stress. Primary deformation paths of interest include spherical (i.e., isotropic) deformation, uniaxial strain, and simple shear; unstable modes are not constrained to remain along primary deformation paths. Effects of choices of second- and third-order elastic constants on intrinsic stability are systematically studied for physically realistic ranges of constants. For most cases investigated here, internal stability according to strain increments conjugate to Cauchy stress is found to be the most stringent criterion. When third-order constants vanish, internal stability under large compression tends to decrease as Poisson’s ratio increases. When third-order constants are nonzero, a negative (positive) pressure derivative of the shear modulus often promotes unstable modes in compression (tension). For large shear deformation, larger magnitudes of third-order constants tend to result in more unstable behavior, regardless of the sign of the pressure derivative of the shear modulus. A compressible neo-Hookean model is generally much more intrinsically stable than second- and third-order elastic models when Poisson’s ratio is non-negative.     

Parametric array technique for microbubble excitation

This study investigates the use of an acoustic parametric array as a means for microbubble excitation. The excitation wave is generated during propagation in a nonlinear medium of two high-frequency carrier waves, whereby the frequency of the excitation wave is the difference frequency of the carrier waves. Carrier waves of around 10 and 25 MHz are used to generate low-frequency waves between 0.5 and 3.5 MHz at amplitudes in the range of 25 to 80 kPa in water. We demonstrate with high-speed camera observations that it is possible to induce microbubble oscillations with the low frequency signal arising from the nonlinear propagation process. As an application, we determined the resonance frequency of Definity contrast agent microbubbles with radius ranging from 1.5 to 5 μm by sweeping the difference frequency in the range from 0.5 to 3.5 MHz.     

Contact force identification using the subharmonic resonance of a contact-mode atomic force microscopy

We propose a step-by-step experimental procedure for characterization of the nonlinear contact stiffness on surfaces using contact-mode atomic force microscopy. Our approach directly estimates the first-, second-, and third-order coefficients of the contact stiffness. It neither uses nor requires the underlying assumptions of the Hertzian contact theory. We use a primary resonance excitation of the probe to estimate the linear coefficient of the contact stiffness. We use the method of multiple scales to obtain closed-form expressions approximating the response of the probe to a subharmonic resonance excitation of order one-half. We utilize these expressions and higher-order spectral measurements to independently estimate the quadratic and cubic coefficients of the contact stiffness.     

Aluminum for nonlinear plasmonics: resonance-driven polarized luminescence of Al, Ag, and Au nanoantennas

Resonant optical antennas are ideal for nanoscale nonlinear optical interactions due to their inherent strong local field enhancement. Indeed second- and third-order nonlinear response of gold nanoparticles has been reported. Here we compare the on- and off-resonance properties of aluminum, silver, and gold nanoantennas, by measuring two-photon photoluminescence. Remarkably, aluminum shows 2 orders of magnitude higher luminescence efficiency than silver or gold. Moreover, in striking contrast to gold, the aluminum emission largely preserves the linear incident polarization. Finally, we show the systematic resonance control of two-photon excitation and luminescence polarization by tuning the antenna width and length independently. Our findings point to aluminum as a promising metal for nonlinear plasmonics.     

Performance evaluation of dual-frequency driving plate ultrasonic motor based on an analytical model

An analytical model is presented to explain the effects of dual-frequency drive on the plate ultrasonic motor in this paper. The experimental prototype is a plate ultrasonic motor using single-phase asymmetric excitation, which can work under a single vibration or multiple vibration modes. Based on the linear superposition of vibrations with two different excitation frequencies, an analytical model is established using the classic Coulomb friction model, and the non-load rotation speed and maximum stall torque are deduced. Moreover, some crucial parameters such as preload and dead-zone in dual-frequency superposition model are identified or modified automatically by searching for the maximum correlation coefficient between simulation and experimental data using single-frequency drive. It is found that simulation and experiment results agree well when no excitation frequency component is at resonance.     

Characterizing an Image Intensifier in a Full-Field Range Imaging System

We are developing a high precision full-field range imaging system. An integral component in this system is an image intensifier, which is modulated at frequencies up to 100 MHz. The range measurement precision is dictated by the image intensifier performance, in particular, the achievable modulation frequency, modulation depth, and waveform shape. By characterizing the image intensifier response, undesirable effects can be observed and quantified with regards to the consequence on the resulting range measurements, and the optimal operating conditions can be selected to minimize these disturbances.      

A multifunctional, reconfigurable pulse generator for high-frequency ultrasound imaging

High-frequency (>20 MHz) ultrasound (HFUS) imaging systems have made it possible to image small structures with fine spatial resolution. They find a variety of biomedical applications in dermatology, ophthalmology, intravascular imaging, and small-animal imaging. One critical technical challenge of HFUS is to generate high-voltage, high-frequency pulsed signals to effectively excite the transducer for a high SNR. This paper presents the development of a multifunctional, reconfigurable pulse generator for HFUS imaging. The pulse generator can produce a high-voltage unipolar pulse, a bipolar pulse, or arbitrary pulses for B-mode imaging, Doppler measurement, and modulated excitation imaging. The characteristics of the pulses, such as timing, waveform, and frequency are reconfigurable by a high-speed field-programmable gate array (FPGA). Customized software was developed to interface with the FPGA through a USB connector for pulse selection, and easy, flexible, real-time pulse management. The hardware was implemented in a compact, printed circuit board (PCB)-based scheme using state-of-the-art electronics for costeffectiveness and fully digital control. Testing results show that the unipolar pulse can reach over 165 Vpp with a 6-dB bandwidth of 70 MHz, and the bipolar pulse and arbitrary pulses can reach 150 and 60 Vpp with central frequencies of 60 and 120 MHz, respectively.     

Comparison of pulse subtraction Doppler and pulse inversion Doppler

In this paper, a new Doppler technique based on pulse subtraction imaging (PSD) is described and compared with pulse inversion Doppler (PID). Combining a nonlinear contrast agent imaging technique with a Doppler process provides a tool for detecting motion of both contrast agents and tissues. This has potential in targeted imaging in which attached microbubbles need to be separated from moving ones and surrounding tissues. The results from both simulation and experiment show that PSD is able to differentiate bubble motion from tissue motion. For Doppler processing conducted at the fundamental frequency, the contrast-to-tissue ratio (CTR) in PSD was 3.3 (±0.4) times higher on average than PID at a mechanical index (MI) of 0.1. At the harmonic frequency, PID was shown to have a 3.1 (±0.4) times higher CTR than PSD. Overall, taken in their optimum processing conditions, PID has a CTR up to 1.9 (±0.4) times higher than PSD. The CTRs for both techniques have also been shown to increase with increasing MI. However, for the same axial Doppler resolution. PSD also allows less energy to be transmitted into the medium, which makes it less disruptive. The relative performances of PSD and PID in terms of the bandwidth of the imaging system are also discussed.     

Effects of frequency and bandwidth on diagnostic information transfer in ultrasonic B-mode imaging

Transmitted pressure pulses in ultrasonic B-mode imaging systems are commonly characterized by their center frequency and bandwidth. Both parameters are associated with tradeoffs in spatial resolution and signal-to-noise in ultrasonic system design, with no general understanding of where they are optimal when applied to specific clinical exams. We use the ideal observer and simple psychophysical studies with human observers to evaluate the efficiency of information transfer in B-mode imaging as a function of the transmitted pulse center frequency and fractional bandwidth. Our approach uses a statistical model of backscatter relevant to breast imaging, and a 2-D model of pulse propagation based on Rayleigh-Sommerfeld diffraction theory. The statistics of the backscattered signal are combined in an ideal observer calculation that quantifies the task-relevant information contained in the radio-frequency (RF) signal after delay-and-sum beamforming. This is followed by a psychophysical evaluation of observer performance on B-mode envelope-detected images in three simple tasks. This experimental design allows us to track the flow of diagnostic information through RF acquisition and subsequent reading of the envelope image. In a low-contrast detection task and a high-contrast boundary discrimination task, optimal efficiency for human observers is observed at the highest center frequencies tested (15 MHz) and at moderate bandwidth (40%). For detection of scattering material in a high-contrast hypoechoic lesion, optimal efficiency was observed at lower center frequencies (5 MHz) and higher bandwidth (80%). The ideal observer analysis shows that this task dependence does not arise in the acquisition stage, where efficiency is maximized at 15 MHz with bandwidths of 60% or greater, but rather in the subsequent processing and reading of the envelope image. In addition, at higher frequencies more information is lost in the processing and reading than in the acquisition of reflected signals.     

High frequency nonlinear B-scan imaging of microbubble contrast agents

It was previously shown that it is possible to produce nonlinear scattering from microbubble contrast agents using transmit frequencies in the 14-32 MHz range, suggesting the possibility of performing high-frequency, nonlinear microbubble imaging. In this study, we describe the development of nonlinear microbubble B-scan imaging instrumentation capable of operating at transmit center frequencies between 10 and 50 MHz. The system underwent validation experiments using transmit frequencies of 20 and 30 MHz. Agent characterization experiments demonstrate the presence of nonlinear scattering for the conditions used in this study. Using wall-less vessel phantoms, nonlinear B-scan imaging is performed using energy in one of the subharmonic, ultraharmonic, and second harmonic frequency regions for transmit frequencies of 20 and 30 MHz. Both subharmonic and ultraharmonic imaging modes achieved suppression of tissue signals to below the noise floor while achieving contrast to noise ratios of up to 26 and 17 dB, respectively. The performance of second harmonic imaging was compromised by nonlinear propagation and offered no significant contrast improvement over fundamental mode imaging. In vivo experiments using the subharmonic of a 20 MHz transmit pulse show the successful detection of microvessels in the rabbit ear and in the mouse heart. The results of this study demonstrate the feasibility of nonlinear microbubble imaging at high frequencies     

Arbitrary waveform coded excitation using bipolar square wave pulsers in medical ultrasound

This paper presents a new coded excitation scheme that efficiently synthesizes codes for arbitrary waveforms using a bipolar square wave pulser. In a coded excitation system, pulse compression is performed to restore the axial resolution. In order to maintain low range sidelobes, the system needs to transmit signals that have smooth spectra. However, such a transmitter requires the generation of arbitrary waveforms and, therefore, is more expensive. In other words, a trade-off is necessary between the compression performance and the transmitter cost. Here we propose a method that preserves the low-cost advantage of a bipolar pulser while achieving approximately the same compression performance as an arbitrary waveform generator. The key idea of the proposed method is the conversion of a nonbinary code (i.e., requiring an arbitrary waveform generator) with good compression performance into a binary code (i.e., requiring only a bipolar pulser) by code translation and code tuning. The code translation is implemented by sending the nonbinary code into a virtual one-bit, sigma-delta modulator, and the code tuning involves minimizing the root-mean-square error between the resultant binary code and the original nonbinary code by sequential and iterative tuning while taking the transducer response into account. Tukey-windowed chirps are known to have good compression performance. Such chirps of different durations (16, 20, and 24 micros), all with a taper ratio of 0.15, a center frequency of 2.5 MHz, and an equivalent bandwidth of 1.5 MHz, were converted into binary Tukey-windowed chirps that were compared with pseudochirps (i.e., direct binary approximations of the original chirp) over the same spectral band. The bit rate was 40 MHz. Simulation results show that the use of binary Tukey-windowed chirps can reduce the code duration by 20.6% or the peak sidelobe level by 6 dB compared to the commonly used pseudochirps. Experimental results obtained under the same settings were in agreement with the simulations. Our results demonstrate that arbitrary waveform coded excitation can be realized using bipolar square wave pulsers for applications in medical ultrasound.