Spectral power density calculations for pulsed Doppler

Range-gated pulsed Doppler can be used to make localized velocity measurements within a blood vessel. A spectral flow profile can be created by stepping a sufficiently small sample volume across the lumen, but no set of spectra will correspond directly to the true velocity profile. Spectral flow profiles are affected by a complex interplay between different sources of spectral broadening. In this study we developed a systematic theoretical method which allows spectral power density functions to be calculated under a very wide range of conditions, and used it to obtain simulated flow spectra. The model was formulated analytically. It is based on the weighted-volume approach and incorporates, through the concept of a spread function, the intrinsic spectral broadening associated with a focused transducer. It can be applied for arbitrary values of the spread parameter; for non-uniform beam profiles; with maximal (continuous wave-type) or minimal (pulse wave-type) range-gated sample volumes; and for beams that intersect the flow tube axis, or are off centre. Results are presented for a Gaussian beam and parabolic flow. Simulated spectral flow profiles are given which illustrate how a profile's appearance can be altered by the different sources of spectral broadening.     

Experimental study of the effects of pulsed Doppler sample volume size and position on the Doppler spectrum

With a pulsed Doppler system, the recorded Doppler spectrum is expected to vary depending upon the sample volume size relative to the diameter of the vessel, the position of the sample volume in the vessel and the velocity profile. In the in vitro experiments described in this paper, the velocity profile was kept constant by using steady parabolic flow in a flow model. As the Doppler sample volume size and position were changed, the maximum variations of quantitative measurements from the Doppler spectrum were determined. The maximum, mean and mode frequencies and spectral broadening index (SBI) were affected by the position of the sample volume but to a lesser degree by its length (1.5-5.0 mm) relative to the 9.5 mm beam path length across the tube. When the centre of the Doppler sample volume was moved within the central 25% of the tube, the maximum variations were as follows: maximum frequency 3-5%, mean frequency 8-9%, mode frequency 8-9% and SBI 16-18%, where the range indicates the effect of increasing the sample volume size. Based on these results obtained under steady flow conditions in vitro, it is concluded that quantification of pulsed Doppler spectra may be feasible if the sample volume is positioned within the central 25% of the vessel.     

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.     

Pulsed Doppler flow-line spectrum for focused transducers with apodized apertures.

The properties of the single flow-line Doppler spectrum using pulsed wave (PW) ultrasound is studied on the basis of previously developed spectral theory for transducers with apodized apertures. It has been shown previously that the spectral width of Doppler signals from a sample volume in low velocity-shear flow is independent of the sample volume depth but that is not true for the spectra from the individual streamlines. The work presented here on the Doppler flow-line spectrum shows that its width should be invariant with flow-line location, if the sample volume depth is fixed. At the same time, for a transducer operating in PW mode not only the Doppler spectral width depends on the sample volume depth, but also the modal Doppler frequency shift changes with flow-line displacement in the illuminating field except if the sample volume centre and the beam focus coincide. The variation of modal Doppler frequency shift is the more explicit manifestation of the effect of wavefront curvature increasing for lines and sounding depths distant from the focal point. The values of the Doppler shift and spectral bandwidth are reported taking account of beam diffraction and variations in its geometry due to focusing.     

Measurement of absolute flow velocity vector using dual-angle, delay-encoded Doppler optical coherence tomography

Single-beam laser Doppler measurements of flow velocity are only sensitive to the velocity component parallel to the optical axis. We describe a simple modification to a standard Doppler optical coherence tomography (OCT) system using a single sample beam that provides velocity information from multiple angles within the beam. By introducing a glass plate midway into the OCT beam path, the sample beam is divided into several components, each with a different group delay and each providing a separate interferogram with its own effective Doppler angle. By combining the Doppler shift measured in each of these component interferograms, the flow velocity vector is fully determined.     

A novel ultrasound instrument for investigation of arterial mechanics

The study of arterial mechanics concerns functional characteristics depending on wall elasticity and flow profile. Wall elasticity can be investigated through the estimation of parameters like the arterial distensibility, which is of high clinical interest because of its known correlation not only with the advanced atherosclerotic disease, but also with aging and major risk factors for cardiovascular disease. The flow velocity profile is also clinically relevant, because it modulates endothelial function and can be responsible for the development and distribution of atherosclerotic plaques. A clinically relevant variable extracted from the blood velocity profile is the wall shear rate (WSR), which represents the spatial velocity gradient near the vessel wall. This paper describes an integrated ultrasound system, capable of detecting both the velocity profile and the wall movements in human arteries. It basically consists of a PC add-on board including a single high-speed digital signal processor. This is dedicated to the analysis of echo-signals backscattered from 128 range cells located along the axis of the interrogating ultrasound (US) beam. Echoes generated from the walls (characterized by high amplitudes and low Doppler frequencies) and from red blood cells (characterized by low amplitudes and relatively high Doppler frequencies) are independently processed in real-time. Wall velocity is detected through the autocorrelation algorithm, while blood velocity is investigated through a complete spectral analysis of all signals backscattered by erythrocytes and WSR is extracted from the estimated velocity profile. Preliminary applications of the new system, including the simultaneous analysis of blood flow and arterial wall movement in healthy volunteers and in a diseased patient, are discussed, and first results are presented.     

The Doppler effect in NMR spectroscopy

An NMR sample may be subject to motions, such as those due to sample spinning or to liquid flow. Is the spectrum of such a sample affected by the Doppler effect? The question arises because, instrumental dimensions being much shorter than the wavelength, it is the near-field of the precessing magnetic moment which couples to the receiver coil, rather than the radiated far-field. We expand the near-field into plane propagating waves. For each such wave there is another one with the same amplitude, propagating in the opposite direction. The Doppler shifts are therefore equal and opposite. In the model case of a small fluid sample moving with constant velocity, this leads to a distribution of Doppler shifts which is symmetrical with respect to the unshifted frequency: there is no net spectral shift. We examine the possibility of observing the Doppler distribution in this case. We also consider the case of thermal motion of a gas. We draw attention to the resolved Doppler splitting of molecular rotational transitions in a supersonic burst as observed in a microwave resonator. We also mention briefly the Doppler effect in molecular beam spectroscopy.     

红外扫描和频振动光谱系统的激光线宽与光谱分辨率

本文报道了一个简化的利用可见光和红外光带宽来计算和频光谱分辨率的公式. 公式显示和频振动光谱的Voigt线宽可以通过振动模式的均匀线宽(洛伦兹线宽)、非均匀线宽(高斯线宽)、红外光与可见光的高斯线宽计算获得. 利用本实验室新搭建的频率分辨及偏振分辨的皮秒和频光谱系统验证了该公式的准确性. 实验结果显示,本激光系统获取的红外光的高斯线宽为1.5 cm^-1. 本激光系统的光谱分辨率约为4.6 cm^-1,结果与胆固醇单层膜光谱获取的光谱分辨率(3.5~5 cm^-1)基本一致.     

Doppler optical coherence tomography in cardiovascular applications

The study of flow dynamics in complex geometry vessels is highly important in various biomedical applications where the knowledge of the mechanic interactions between the moving fluid and the housing media plays a key role for the determination of the parameters of interest, including the effect of blood flow on the possible rupture of atherosclerotic plaques. Doppler Optical Coherence Tomography (DOCT), as a functional extension of Optical Coherence Tomography (OCT), is an optic, non-contact, noninvasive technique able to achieve detailed analysis of the flow/vessel interactions. It allows simultaneous high resolution imaging (∼10 μm typical) of the morphology and composition of the vessel and determination of the flow velocity distribution along the measured cross-section. We applied DOCT system to image high-resolution one-dimensional and multi-dimensional velocity distribution profiles of Newtonian and non-Newtonian fluids flowing in vessels with complex geometry, including Y-shaped and T-shaped vessels, vessels with aneurism, bifurcated vessels with deployed stent and scaffolds. The phantoms were built to mimic typical shapes of human blood vessels, enabling preliminary analysis of the interaction between flow dynamics and the (complex) geometry of the vessels and also to map the related velocity profiles at several inlet volume flow rates. Feasibility studies for quantitative observation of the turbulence of flows arising within the complex geometry vessels are discussed. In addition, DOCT technique was also applied for monitoring cerebral mouse blood flow in vivo. Two-dimensional DOCT images of complex flow velocity profiles in blood vessel phantoms and in vivo sub-cranial mouse blood flow velocities distributions are presented.     

MR imaging of model fluid velocity profiles

A projection MR technique for imaging the velocity profiles of moving fluids has been applied to various steady flow models designed to simulate a variety of flow conditions. From such profiles can be readily deduced peak velocities, volume flow rates, information concerning the degree of flow development, features such as flow separation, and estimates shear stresses at the vessel wall.     

Velocity magnitude estimation with linear arrays using Doppler bandwidth

The dependence of pulsed wave Doppler bandwidth on parameters typical of linear transducer arrays used in commercial Duplex and color flow mapping systems is investigated experimentally. For a single flow line it is observed that this bandwidth generally depends not only on the scatterer velocity and the beam-to-flow angle, but also on the flow line range and orientation. This is due to the fact that in Duplex and color flow systems the transducer is differently focused in the scan and elevation planes and its aperture and focal lengths are often made to vary, depending on the distance of the flow line from the transducer. It is however experimentally demonstrated that, at points where the ultrasound beamwidths in the scan and elevation planes are both comparable to the sample volume length, the Doppler bandwidth is independent of the beam-to-flow angle. It is also shown that this invariance can be extended to other ranges by appropriately modifying the array aperture. Finally, as an application of this independence, the flow-line velocity magnitude in these beam regions is estimated with better than 5% uncertainty through a simple bandwidth measurement.     

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.     

Imaging and quantifying transverse flow velocity with the Doppler bandwidth in a phase-resolved functional optical coherence tomography

The Doppler bandwidth extracted from the standard deviation of the frequency shift in phase-resolved functional optical coherence tomography (F-OCT) was used to image the velocity component that is transverse to the optical probing beam. It was found that above a certain threshold level the Doppler bandwidth is a linear function of flow velocity and that the effective numerical aperture of the optical objective in the sample arm determines the slope of this dependence. The Doppler bandwidth permits accurate measurement of flow velocity without the need for precise determination of flow direction when the Doppler flow angle is within +/-15 degrees perpendicular to the probing beam. Such an approach extends the dynamic range of flow velocity measurements obtained with the phase-resolved F-OCT.     

纳米流体的激光自混频功率谱密度研究

纳米流体运动特性和颗粒参数的测量对纳米流体换热效率的研究具有重要意义。本文将激光自混频技术应用于纳米流体测量中,给出了自混频信号功率谱密度函数的表达式并实验研究其变化规律。研究结果表明,功率谱密度展宽具有佛克脱函数的形式。激光垂直入射流动样品池时,功率谱密度得到展宽,展宽程度随着定向流速的增大或束腰半径的减小而增大。激光倾斜入射流动样品池时,功率谱密度在展宽的同时还伴随多普勒峰移,其位置随着定向流速的增大或散射矢量与定向流速之夹角的减小而迁移至高频。     

Effect of frequency dependent processes on pulsed Doppler sample volume

The change in the frequency spectrum of ultrasound pulses as a result of frequency dependent attenuation and scatter is known to alter the spectrum of Doppler signals from blood flow parallel to the beam axis. It is shown here that the change in pulse shape accompanying this pulse spectrum change as a result of these processes, together with the velocity dispersion accompanying frequency dependent attenuation and linked to it by the Kramers-Kronig relations, will change the pulsed Doppler sample volume shape and position.     

The flow velocity distribution from the doppler information on a plane in three-dimensional flow

In order to observe and estimate the flow of fluid in three-dimensional space, the pulsed Doppler method has been used widely. However, the velocity information acquired is only the velocity component in the beam direction of the wave even if an observation plane is formed by beam scanning. Accordingly, it is difficult to know the velocity distribution in the observation plane in tree-dimensional flow. In this paper, the new idea for processing the velocity distribution in the beam direction on an observation plane for transposing to flux distribution (flow function method) has been introduced. Further, the flow in an observation domain is divided into two kinds of flows, viz., the base flow which indicates the directivity of the flow in the observation domain and the vortex which is considered a two-dimensional flow. By applying the theory of a stream function to the two-dimensional flow, and by using the physical feature of a streamline to the base flow, the velocity component v which intersects perpendicularly to the beam direction is estimated. The flow velocity distribution in a scanning plane (observation plane) can be known from these two components of velocity, viz., beam direction componentu and perpendicular component to the beam directionv. The principle was explained by an example of the blood flow measurement in normal and abnormal heart chamber, by the ultrasonic Doppler method.     

High resolution nuclear magnetic resonance spectroscopy in liquids and gases at pressures up to 2500 bar: I. High pressure NMR spectrometer and experimental technique

This article is the first in a series of four papers, which deal with the effect of hydrostatic pressure on the high resolution proton magnetic resonance spectra of methane, ethylene, methanol and ethanol. The present paper describes the spectrometer in which high resolution spectra can be recorded at pressures up to 2500 bar. The most essential part of the spectrometer is a beryllium copper high pressure vessel in which the sample can be rotated under pressure. The positions of the spectral lines are referred to an external reference of benzene, contained in a sealed glass capillary. Frequency modulation of the transmitter is used in the measurement of the line positions. The paper describes how the apparatus can also be used for the measurement of the density dependence of the diamagnetic volume susceptibility.     

Doppler-based lateral motion tracking for optical coherence tomography

Nonuniform lateral scanning of the probe beam in optical coherence tomography produces imaging artifacts and leads to a morphologically inaccurate representation of the sample. Here, we demonstrate a solution to this problem, which is based on the Doppler shift carried by the complex-valued depth-resolved scattering amplitude. Furthermore, we demonstrate the feasibility of Doppler flow velocity measurements in underlying flow channels while laterally scanning the imaging probe over large surfaces with arbitrary and varying velocity. Finally, we performed centimeters-long hand-held B-mode imaging of skin in vivo.     

Pulsatile flow measurement in hydraulic systems using a laser velocimeter

Servo valves find their major application in high performance hydraulic control systems where the accurate control of position, velocity and load is essential. Because of this, it is important to determine the dynamic characteristics of the servo valve (i.e. flow rate as a function of input command signal) more precisely.Previous techniques for this evaluation depended on monitoring spool position using linear transducers, since flow measurement techniques capable of following fast transients and oscillating (or pulsating) flows were not easily applied. The introduction of the laser Doppler anemometer changes this. Steady state flow measurement, using the dual beam scatter system, is now common but since it needs a spectrum analyser to measure the Doppler frequency it is not suitable for unsteady flow. Since hydraulic systems are relatively particle free, the Doppler signals are dreceived intermittently. Because of this, a signal processing system has been developed which measures the period of one or more oscillations in the frequency burst caused by a scattering particle passing through the control volume.Using this technique steady and unsteady laminar flow profiles have been measured in order to assess its effectiveness in the performance testing of hydraulic servo systems.