Correlation functions and power spectra of Doppler response signals in ultrasonic medical applications

Ultrasound Doppler methods are widely used in clinical practice as prospective investigational tool to study the vascular system and soft biological tissues. Meanwhile, the most general relationship between the power Doppler spectra, spectral characteristics of the scattering fluctuations and the probing ultrasound field parameters for some clinical implementations are still unexplored. Based upon the continuum model of scattering inhomogeneities, a set of the closed-form expressions for the correlation functions and the spectra of Doppler response of soft tissues and blood have been derived. The influence of the correlation among inhomogeneities and the diffusion processes on the Doppler power spectra formed by stationary flows have been examined. Computer simulations of Doppler spectra were performed for different values of correlation radius and diffusion coefficient. With simulation results the effects of the correlation among inhomogeneities and the diffusion processes on the spectral width and mean frequency are established and discussed in respect to turbulent flows. Closed-form expressions for correlation functions and Doppler spectra for the vibrational sonoelastography technique for visualizing malignant tumors in tissues have been derived. Based on the peculiarities of the obtained Doppler spectra, it is shown that the differentiation of soft tissues with respect to the amplitude value of constrained oscillations is feasible. The expressions were derived for the cases of non-stationary accelerated blood movement. It has been found that the frequency dependence reveals solely at a finite time of observation and depends on the initial phase of the accelerated movement.     

改进的经验模态分解法分离超声多普勒血流与管壁信号

超声多普勒血流信号常包含管壁信号的干扰,准确分离二者对提高血流检测的精度具有重要作用。本文提出两种改进的经验模态分解(EMD)方法,先将含管壁信号的超声多普勒信号分解成多层本征模态函数(IMF),然后根据血流信号与管壁信号的不同特性,对既含管壁信号又含血流信号的IMF分量进行分离处理,最后将各层IMF分量中的管壁成分叠加得到管壁信号的估计,而血流信号可通过原信号减去估计的管壁信号而得到。将本方法用于计算机仿真信号和人体实测的超声多普勒信号,并与高通滤波器法、空间选择性降噪法和原EMD法进行比较,结果表明:本文提出的两种方法能在较大的管壁搏动速度范围内准确地分离血流信号和管壁信号,其平均相对误差比高通滤波器的结果降低了约52%和57%。可见,本文提出的两种方法有望用于血流信号与管壁信号的准确分离。      

Intensity fluctuations of ultrasonic scattering in a highly turbulent flow

Aspects of ultrasound intensity fluctuations backscattered from additive microstructures in a turbulent flow have been investigated theoretically and experimentally for the conditions of a small insonified volume, a high sound frequency and strong turbulence. These conditions are typically found in high resolution Doppler sonar applications. An easily applicable expression for the auto-correlation of scattering intensity fluctuations is obtained by introducing open-channel turbulence theory, a semi-empirical scalar spectrum (including a Batchelor spectrum) and a Gaussian window function. Experiments carried out in a laboratory-clear water, open-channel flow for different turbulence levels verify the underlying assumptions. A good agreement is found with the predictions made with the above-derived expression. The feasibility of extracting flow information from the backscattered intensity fluctuations is discussed.     

Doppler ultrasound technique for measuring capillary-speed flow velocities with strong stationary echoes.

Ultrasound Doppler is widely used for low measurement in both medicine and industry, having the advantages of being non-invasive and comparatively simple and therefore inexpensive. The technique has not however been used for capillary blood flow measurement, because of the relatively low velocities encountered and because of the presence of strong interfering signals from the encompassing tissue. An ultrasound Doppler system capable of measuring flow velocities of one millimetre per second in the presence of one thousand times stronger interfering signals is described, as well as test results using both thread and flow phantoms.     

车载激光多普勒测速仪参数估计的Cramer-Rao下限

考虑到加速度和高斯型包络对激光多普勒测速仪的影响,在引入加速度分量的基础上,研究了高斯包络型多普勒信号的参数估计.根据数理统计的理论,分析了多普勒圆频率及其一阶变化率估计方差的Cramer-Rao下限(CRLB),给出了参数估计方差的CRLB计算公式,并讨论了各参数带修正的功率谱估计.理论分析及仿真结果表明:参数估计方...     

超声动态向量血流成像的产品化实现

传统超声彩色多普勒成像测量的是血流沿超声传播方向上的速度分量,故无法得到垂直于超声传播方向的血流。向量血流成像是一种更加先进的超声血流成像技术。它不受角度限制,可以直接计算出血流速度的大小和方向。本文总结了现有多种超声向量血流成像技术的特点和发展情况,并从产品化实现的角度分析了各项技术的优缺点。从超声系统发射接收、血流成像、向量速度方向合成、显示等几个方面详述了迈瑞超声向量血流成像技术产品化实现过程中遇到的主要问题及解决方案。实验采用了中科院声学所研制的超声多普勒仿血流体模,通过向量血流成像和脉冲多普勒成像分别测量体模的仿血流速度。将向量血流成像直接计算出来的速度值与脉冲多普勒经过角度校正得到的速度进行对比。在不同条件下,经过多次测量,二者的平均相对误差均在10%以内。     

Doppler power spectrum from a Gaussian sample volume

A closed-form expression for the Doppler power spectrum due solely to the range of blood velocities passing through a Gaussian sample volume placed anywhere in a vessel under conditions of axisymmetric flow, uniform backscatter and negligible intrinsic spectral broadening has been derived. The formulation presented here allows the independent specification of the sample volume position and width, in the three dimensions, and enables simple estimations of spectral shape for pulsed wave Doppler systems. Simpler expressions were derived for the cases of symmetric sample volume projections onto the vessel cross-section and/or sample volumes centred in the vessel. Closed form expressions were derived for mean frequency and spectral width in the case of a symmetric sample volume projection centred in the vessel. The effects of sample volume size and position on the Doppler spectral width and mean frequency are shown for a range of velocity profiles.     

Acoustic characterization of a new trisacryl contrast agent. Part II: Flow phantom study and in vivo quantification

The biocompatible trisacryl particles (TMP) are made of a cross-linked acrylic copolymer. Their inherent acoustic properties, studied for a contrast agent application, have been previously demonstrated in a in vitro Couette device. To measure their acoustic behaviour under circulating blood conditions, the TMP backscatter enhancement was further evaluated on a home-made flow phantom at different TMP doses (0.12-15.6 mg/ml) suspended in aqueous and blood media, and in nude mice (aorta and B16 grafted melanoma). Integrated backscatter (IB) was measured by spectral analysis of the Doppler signals recorded from an ultrasound system (Aplio^®) combined with a 12-MHz probe. Doppler phantom experiments revealed a maximal IB of 17 ± 0.88 dB and 7.5 ± 0.7 dB in aqueous and blood media, respectively. IB measured on mice aorta, in pulsed Doppler mode, confirmed a constant maximal value of 7.29 ± 1.72 dB over the first minutes after injection of a 7.8 mg/ml TMP suspension. Following the injection, a 60% enhancement of intratumoral vascularization detection was observed in power Doppler mode. A preliminary histological study revealed inert presence of some TMP in lungs 8 and 16 days after injection.Doppler phantom experiments on whole blood allowed to anticipate the in vivo acoustic behaviour. Both protocols demonstrated TMP effectiveness in significantly increasing Doppler signal intensity and intratumoral vascularization detection. However, it was also shown that blood conditions seemed to shadow the TMP contrast effect, as compared to in vitro observations. These results encourage further investigations on the specific TMP targeting and on their bio-distribution in the different tissues.     

Ultrasonic pulsed Doppler transoesophageal measurement of aortic haemodynamics in humans.

Centreline blood velocity and exterior wall motion were measured in the descending aorta of humans using an oesophageal probe, a pulsed ultrasound Doppler velocity meter and an ultrasonic echo tracking system. The development of a method for easily measuring haemodynamics in the thoracic region using an oesophageal probe will provide an essentially non-invasive method for the assessment of cardiac function and the nature of blood vessels in that region. Detailed anatomical studies of the thorax were conducted by cross-sectioning of the thorax of a cadaver. Blood velocity waveforms were recorded from the descending aorta both during rest and exercise. In one volunteer, the peak centreline velocity increased from a resting value of approximately 30 cm s-1 to an exercise value of approximately 50 cm s-1. Vessel diameter waveforms similar to those for pressure were also recorded showing diameter changes of 1.8 mm. The accuracy and resolution of the technique would be improved by multicrystal probes and multigate ultrasonic flowmeters allowing for accurate calculation of the Doppler angle, imaging of vascular flow regions, and measurement of pulse wave velocity.     

Doppler ultrasound signals simulation from vessels with various stenosis degrees

As a non-invasive method, the Doppler ultrasound technique is used to detect the vessel stenosis. To search for characteristics of Doppler ultrasound signals sensitive to the stenosis, a computer simulation approach is proposed in this paper to generate Doppler ultrasound signals from vessels with various stenosis degrees. The blood flow velocity distribution in a stenosed vessel is firstly calculated using the transient finite element method (FEM). Then the power spectral density of Doppler signals is estimated using the overall-distribution nonparametric estimation method. Finally Doppler signals are generated using the cosine-superposed method. The proposed approach is proved to be useful for simulating Doppler ultrasound signals from vessels with various stenosis degrees. It is also shown that characteristics of Doppler ultrasound signals may be used to estimate the vessel's stenosis degree.     

光谱法测量等离子体离子温度和旋转速度

分析多普勒展宽和多普勒频移的区别，讨论了弦积分的线形分布和高斯分布的差异，利用光谱多道分析仪测量了碳227．1nm谱线的线形分布，通过选点拟合得出辐射粒子的离子温度和旋转速度径向分布。     

Semi-empirical bone model for determination of trabecular structure properties from backscattered ultrasound

A novel semi-empirical scattering model of trabecular bone facilitating its characterization and allowing optimization of the interrogating pulse-echo transducer performance was developed. The model accounts for spatial density distribution of the trabeculae and includes measurement conditions such as pressure–time waveform of the probing ultrasound wave, the emitted field structure, and the transfer function and limited bandwidth of the acoustic source operating in pulse-echo mode. These measurement conditions are of importance as they modify the scattered echoes, which in turn are linked to the micro-architecture of the bone. The bone was modeled by a random distribution of long and thin cylindrical scatterers having randomly varying diameters and mechanical properties, and oriented perpendicularly to the ultrasound beam axis. To mimic clinically encountered conditions the relevant empirical data obtained at 1 MHz were input to the model. The data included pulse-echo source pressure field distribution in the focal zone and the above mentioned transfer function. With these data the model allowed frequency dependent backscattering coefficient of the simulated bone structure and its statistical properties to be determined. The results obtained indicated that the computer simulation is of particular relevance in studying scattering properties of the cancellous bone and holds promise as a tool to determine the relationship between the physical dimensions and shape of the scatterers and for monitoring of osteoporosis. The results of simulations also indicated that the new bone model proposed is well suited to mimic clinically relevant conditions. In contrast to the existing bone models, which usually assume scatterers to be randomly distributed as infinitely long identical cylinders with a cross-section much smaller than the probing ultrasound wave, the new model includes two populations of scatterers having different physical dimensions and also allows the mechanical properties of the scatterers to be varied.     

Scatterer size estimation in pulse-echo ultrasound using focused sources: theoretical approximations and simulation analysis

The speckle in ultrasound images has long been thought to contain information related to the tissue microstructure. Many different investigators have analyzed the frequency characteristics of the backscattered signals to estimate the scatterer acoustic concentration and size. Previous work has been mostly restricted to unfocused or weakly focused ultrasound sources, thus limiting its implementation with diagnostically relevant fields. Herein, we derive equations capable of estimating the size of a scatterer for any reasonably focused source provided that the velocity potential field in the focal region can be approximated as a three-dimensional Gaussian beam, scatterers are a sufficient distance from the source, and the field is approximately constant across the scatterer. The calculations show that, when estimating the scatterer size, correcting for focusing requires a generalized attenuation-compensation function that includes both attenuation and focusing along the beam axis. The Gaussian approximation is validated by comparing the ideal velocity potential field for three spherically focused sources with f-numbers of 1, 2, and 4 to the Gaussian approximation for frequencies from 2 to 14 MHz. The theoretical derivations are evaluated by simulating the backscatter by using spherically focused sources (f-numbers of 1, 2, and 4) adjacent to attenuating media (0.05 to 1 dB/cm/MHz) that contain scatterers with Gaussian impedance distributions. The generalized attenuation-compensation function yielded results accurate to 7.2% while the traditional attenuation-compensation functions that neglected focusing had errors as high as 103%.     

Principal-component-analysis-based estimation of blood flow velocities using optical coherence tomography intensity signals

The intensity signal in optical coherence tomography contains information about the translational velocity of scatterers, and can be used to quantify blood flow. We apply principal component analysis to efficiently extract this information. We also study use of nonuniform temporal sampling of the intensity signal to increase the range of quantifiable flow velocities. We demonstrate this technique in simulation, phantom and in vivo blood flow measurements, and highlight its potential to enable three-dimensional wide-field mapping of blood flow using OCT.     

Temperature dependent ultrasonic characterization of biological media

Quantitative ultrasound (QUS) is an imaging technique that can be used to quantify tissue microstructure giving rise to scattered ultrasound. Other ultrasonic properties, e.g., sound speed and attenuation, of tissues have been estimated versus temperature elevation and found to have a dependence with temperature. Therefore, it is hypothesized that QUS parameters may be sensitive to changes in tissue microstructure due to temperature elevation. Ultrasonic backscatter experiments were performed on tissue-mimicking phantoms and freshly excised rabbit and beef liver samples. The phantoms were made of agar and contained either mouse mammary carcinoma cells (4T1) or chinese hamster ovary cells (CHO) as scatterers. All scatterers were uniformly distributed spatially at random throughout the phantoms. All the samples were scanned using a 20-MHz single-element f/3 transducer. Quantitative ultrasound parameters were estimated from the samples versus increases in temperature from 37 °C to 50 °C in 1 °C increments. Two QUS parameters were estimated from the backscatter coefficient [effective scatterer diameter (ESD) and effective acoustic concentration (EAC)] using a spherical Gaussian scattering model. Significant increases in ESD and decreases in EAC of 20%-40% were observed in the samples over the range of temperatures examined. The results of this study indicate that QUS parameters are sensitive to changes in temperature.     

多普勒展宽和多普勒频移在光谱分析中的应用

分析了多普勒展宽和多普勒频移区别，讨论了高斯拟合和弦积分线形分布的差异。利用多道光学分析仪（OSMA）测量HT-6M托卡马克限制器前Hα线形分布，通过高斯拟合由多普勒展宽和多普勒频移分别得出等离子温度和粒子入射速度。     

基于车载通信标准街道场景的电磁散射信道模型

针对室外无线信道视距(line of sight,LOS)/非视距(non-line of sight,NLOS)传输环境下的车到车(vehicular-to-vehicular,V2V)通信系统,本文提出了一种基于标准街道散射的统计信道模型,其移动发射机(mobile transmitter,MT)与移动接收机(mobile receiver,MR)处于运动状态,街道两旁分布的散射体固定.由几何模型出发又引入了一种随机的参考信道模型,其散射体有无穷多个,均以平行于街道两侧的散射条纹形式均匀分布在三维(three dimensional,3D)空间的一个二维(two dimensional,2D)矩形内部.在室外街道通信环境下,模型推导了散射信道中发射角(angle of departure,AOD)以及到达角(angle of arrival,AOA)的概率密度函数(probability density functions,PDFs)解析式;研究了多普勒功率谱密度(power spectral density,PSD)及其时间自相关函数(autocorrelation function,ACF);分析了模型多普勒参数以及街道散射体等因素对V2V通信系统性能的影响.与城市、农村的测量信道对比分析,表明本模型仿真的统计特性符合理论与实际,拓宽了室外V2V无线通信信道建模的研究.为评估室外V2V通信系统的传输特性、仿真无线通信系统提供了有力的研究工具.     

New Insights into Uniformly Accelerated Detector in a Quantum Field

We obtained an exact solution for a uniformly accelerated Unruh–DeWitt detector interacting with a massless scalar field in (3 + 1) dimensions which enables us to study the entire evolution of the total system, from the initial transient to late-time steady state. We find that the conventional transition probability of the detector from its initial ground state to excited states, as derived from time-dependent perturbation theory over an infinitely long duration of interaction, is valid only in the transient stage and is invalid for cases with proper acceleration smaller than the damping constant. We also found that, unlike in (1 + 1)D results, the (3 + 1)D uniformly accelerated Unruh– DeWitt detector in a steady state does emit a positive radiated power of quantum nature at late-times, but it is not connected to the thermal radiance experienced by the detector in the Unruh effect proper.     

Contrast enhanced vascular three-dimensional ultrasound imaging

In other imaging modalities three-dimensional (3D) data displays are well established; not so in ultrasound. Due to the real-time requirements of ultrasound the time available to compute 3D displays is limited, particularly when flow data is acquired with Doppler techniques. Consequently, it is only recently that improvements in computer processing power have resulted in useful vascular 3D ultrasound scans. Many manufacturers have now implemented free-hand 3D power Doppler capabilities on their scanners. However, to obtain flow signals from smaller vessels associated e.g., with tumor neovascularity, may very well require the introduction of a microbubble based ultrasound contrast agent into the blood stream. Given the up to 30 dB enhancement of Doppler signals produced by the contrast microbubbles quite spectacular vascular 3D images are feasible. Moreover, new contrast imaging techniques, such as harmonic imaging, have now permitted 3D vascular information to be acquired and displayed in grayscale with the associated improvement in resolution. In this paper we will review different aspects of contrast enhanced vascular 3D ultrasound imaging including implementation, contrast specific techniques and in vivo imaging.     

A wavelet space based approach for Doppler ultrasound blood signals separation

In medical Doppler ultrasound systems, a high-pass filter which is usually employed to filter wall clutter components, will remove the information of the low velocity blood flow. To extract intact Doppler ultrasound blood signals, a novel approach is proposed based on the spatially selective noise filtration. The wall signals are firstly estimated by the spatially selective noise filtration from wavelet spatial correlation property. Then the wall clutters are exactly obtained by a wavelet threshold de-noising technique which eliminates the residual blood flow signals. Finally the intact blood flow signals are achieved by subtracting the wall signals from the mixed signals. This approach is applied to both computer simulated and in vivo carotid Doppler ultrasound signals. The experiment results show that the wavelet space based approach can exactly extract the blood flow signals, and achieve about 45% lower results in the mean absolute error than that of the high-pass filtering. This approach is expected to be an effective method to remove the wall clutters in Doppler ultrasound systems.