Role of models in understanding and interpreting clinical Doppler ultrasound

Mathematical and physical models are essential tools in both fundamental and clinically applied Doppler ultrasound research. In this paper we illustrate a variety of models and show how they can be used to understand and interpret clinical Doppler ultrasound signals, particularly from stenosed arteries. The physical models discussed include both steady and pulsatile flow systems, and also a flow visualization technique that can be used to interpret the Doppler signals at a fundamental hemodynamic level. The mathematical models deal with three different aspects of the Doppler signal: models that describe the mechanism of ultrasound scattering by blood, a model to stimulate the returned Doppler signal and a model that may be used to aid in the analysis of clinical recordings. Each of these models provides a more complete understanding of blood flow through normal and stenosed vessels and contributes to the interpretation of clinical Doppler signals.     

Detection of ophthalmic artery stenosis by least-mean squares backpropagation neural network

Doppler ultrasound is a noninvasive technique that allows the examination of the direction, velocity, and volume of blood flow. In this study, ophthalmic artery Doppler signals were obtained from 105 subjects, 48 of whom had suffered from ophthalmic artery stenosis. A least-mean squares backpropagation neural network was used to detect the presence or absence of ophthalmic artery stenosis. Spectral analysis of ophthalmic artery Doppler signals was done by the Welch method for determining the neural network inputs. The network was trained, cross validated and tested with subject records from the database. Performance indicators and statistical measures were used for evaluating the neural network. Ophthalmic artery Doppler signals were classified with the accuracy varying from 88.9% to 90.6%.     

Mathematical model of an arterial stenosis,allowing for tethering

Closed-form solutions are presented for approximate equations governing the pulsatile flow of blood through models of mild axisymmetric arterial stenosis, taking into account the effect of arterial distensibility. Results indicate the existence of back-flow regions and the phenomenon of flow-reversal in the cross-sections. The effects of pulsatility of flow and elasticity of vessel wall for arterial blood flow through stenosed vessels are determined.     

Photoacoustic and high-frequency power Doppler ultrasound biomicroscopy: a comparative study

Both photoacoustic imaging and power Doppler ultrasound are capable of producing images of the vasculature of living subjects, however, the contrast mechanisms of the two modalities are very different. We present a quantitative and objective comparison of the two methods using phantom data, highlighting relative merits and shortcomings. An imaging system for combined photoacoustic and high-frequency power Doppler ultrasound microscopy is presented. This system uses a swept-scan 25-MHz ultrasound transducer with confocal dark-field laser illumination optics. A pulse-sequencer enables ultrasonic and laser pulses to be interlaced so that photoacoustic and power Doppler ultrasound images can be coregistered. Experiments are performed on flow phantoms with various combinations of vessel size, flow velocity, and optical wavelength. For the task of blood volume detection, power Doppler is seen to be advantageous for large vessels and high flow speeds. For small vessels with low flow speeds, photoacoustic imaging is seen to be more effective than power Doppler at the detection of blood as quantified by receiver operating characteristic analysis. A combination of the two modes could provide improved estimates of fractional blood volume in comparison with either mode used alone.     

Effect of pulsatile swirling flow on stenosed arterial blood flow

The existence of swirling flow phenomena is frequently observed in arterial vessels, but information on the fluid-dynamic roles of swirling flow is still lacking. In this study, the effects of pulsatile swirling inlet flows with various swirling intensities on the flow field in a stenosis model are experimentally investigated using a particle image velocimetry velocity field measurement technique. A pulsatile pump provides cyclic pulsating inlet flow and spiral inserts with two different helical pitches (10D and 10/3D) induce swirling flow in the stenosed channel. Results show that the pulsatile swirling flow has various beneficial effects by reducing the negative wall shear stress, the oscillatory shear index, and the flow reverse coefficient at the post-stenosis channel. Temporal variations of vorticity fields show that the short propagation length of the jet flow and the early breakout of turbulent flow are initiated as the swirling flow disturbs the symmetric development of the shear layer. In addition, the overall energy dissipation rate of the flow is suppressed by the swirling component of the flow. The results will be helpful for elucidating the hemodynamic characteristics of atherosclerosis and discovering better diagnostic procedures and clinical treatments.     

Pulsatile blood flow in a stenosed artery—a theoretical model

To understand the special flow conditions which may be produced by the presence of stenosis in arteries, an analytical solution is obtained for pulsatile laminar flow in an elliptic tube. Blood is approximated by a Newtonian model and the geometry of the stenosis is introduced by specifying the change in area of cross-section of the stenosed artery with axial distance. The results for velocity, pressure, shear stress and impedance are presented. These are compared with the steady flow results as well as with those of the flow in a stenosed tube of circular cross-section. The study indicates that the fluid dynamic characteristics of the flow are affected by the percentage of stenosis as well as the geometry of the stenosis. The frequency of oscillation is also found to influence shearing stress and the impedance.     

Pulse onset detection using neighbor pulse-based signal enhancement

Detecting onsets of cardiovascular pulse wave signals is an important prerequisite for successfully conducting various analysis tasks involving the concept of pulse wave velocity. However, pulse onsets are frequently influenced by inherent noise and artifacts in signals continuously acquired in a clinical environment. The present work proposed and validated a neighbor pulse-based signal enhancement algorithm for reducing error in the detected pulse onset locations from noise-contaminated pulsatile signals. Pulse onset was proposed to be detected using the first principal component extracted from three adjacent pulses. This algorithm was evaluated using test signals constructed by mixing arterial blood pressure, cerebral blood flow velocity and intracranial pressure pulses recorded from neurosurgical patients with white noise of various levels. The results showed that the proposed pulse enhancement algorithm improved (p<0.05) pulse onset detection according to all three different onset definitions and for all three types of pulsatile signals as compared to results without using the pulse enhancement. These results suggested that the proposed algorithm could help achieve robustness in pulse onset detection and facilitate pulse wave analysis using clinical recordings.     

彩色多普勒对移植肝脏的血流动力学监测

采用彩色多普勒超声对移植肝血流动力学进行监测，了解肝移植前后肝脏血流动力学变化。观察与推测血管吻合口的通畅程度，寻找与排除并发症的存在，进而判断移植肝成活度及预后，就本院近期6例同种原位肝移植术后的移植肝血流进行检测，观察动、静脉吻合口的通畅情况及门静脉与肝动脉血流动力学改善程序，6例移植肝脏周围未见液性及实性异常回声，肝内实质及管道回声与血流方向，速度正常，在24个吻合口中，5例门静脉吻合口通过，1例门静脉吻合口稍窄，局部血流速度稍快，12个腔静脉吻合口中11个吻合口通畅，1个下腔静脉肝下段吻合口稍窄，6个肝动脉吻合口以远的肝动脉血流速度，阻力指数正常，肝移植是解决门脉高压的根本办法，彩色多普勒超声是移植肝血流动力学变化无创检测最佳手段。     

Large-Eddy simulation of pulsatile blood flow

Large-Eddy simulation (LES) is performed to study pulsatile blood flow through a 3D model of arterial stenosis. The model is chosen as a simple channel with a biological type stenosis formed on the top wall. A sinusoidal non-additive type pulsation is assumed at the inlet of the model to generate time dependent oscillating flow in the channel and the Reynolds number of 1200, based on the channel height and the bulk velocity, is chosen in the simulations. We investigate in detail the transition-to-turbulent phenomena of the non-additive pulsatile blood flow downstream of the stenosis. Results show that the high level of flow recirculation associated with complex patterns of transient blood flow have a significant contribution to the generation of the turbulent fluctuations found in the post-stenosis region. The importance of using LES in modelling pulsatile blood flow is also assessed in the paper through the prediction of its sub-grid scale contributions. In addition, some important results of the flow physics are achieved from the simulations, these are presented in the paper in terms of blood flow velocity, pressure distribution, vortices, shear stress, turbulent fluctuations and energy spectra, along with their importance to the relevant medical pathophysiology.     

Flow through a stenosed artery subject to periodic body acceleration

Hjman bodies may occasionally be subjected to high external accelerations. The response of the vascular system under such situations has recently been the subject of several theoretical and experimental studies. However, little work appears to have so far been carried out on the analysis of blood flow in stenosed artery in the presence of body accelerations. In the paper we present a model of blood flow in a partially occluded tube subject to both the pulsatile pressure gradient due to the normal heart action and the periodic body acceleration. Closed-form solutions have been obtained for the instantaneous rate of flow and for the distributions of flow velocity, acceleration and shear stress over the stenosed length. Computational results corresponding to a stenosed carotid artery are presented and discussed.     

Detection of low-grade arterial stenosis using an automatic minimum-flow-velocity tracking system (MVTS) as an adjunct to pulsed ultrasonic Doppler vessel imaging

A microprocessor-controlled system for detecting minor flow disturbances in blood vessels is described. The system is composed of a multigated pulsed Doppler ultrasonic velocimeter (MAVIS) and an 8085 microprocessor acting as an interface for a signal processing system and/or a storage system. A minimum-particle-velocity method is used to extract. Doppler signals from selected sites as near as possible to the vessel wall. These Doppler signals can be monitored constantly during any vessel scanning procedure revealing flow abnormalities caused by stenoses of as little as 15 per centarea reduction. The performance of the microprocessor-controlled system was assessed using signals generated electronically. For thein vitro assessment of the system as a whole a test rig which generates pulsatile flow through nonsymmetric stenoses varying from 15 to 30 per cent area reduction was used. The study shows the development of disturbed flow not only downstream, but also upstream of the stenosis. The results show the capability of this method in discriminating flow disturbances caused by minor stenoses. Preliminaryin vivo assessment was carried out in patients with suspected carotid artery disease and the results have indicated how this method can be used to localise the exact position where flow disturbance is occurring.     

超声多普勒血流和管壁搏动信号的分离研究

目的针对超声多普勒血流检测中,传统的高通滤波法在滤除管壁搏动信号的同时也会滤除低频血流信号的问题,本研究提出一种以心电信号（electrocardiography,ECG）作为参考信号的自适应滤波的方法消除管壁干扰。方法包括两方面：其一,采用心电信号作为参考信号对超声多普勒信号进行自适应滤波;其二,采用多级自适应滤波并选择不同的参考信号的滤波方案。分别使用上述方法和高通滤波法对仿真的超声多普勒信号进行处理,并将结果进行比较。结果与传统的高通滤波法相比,该方法在有效抑制管壁搏动信号的同时保留一部分低频血流信号成分。结论该方法能较准确地提取出完整的血流超声多普勒信号,具有一定的临床应用价值。     

超声多普勒血流信号的小波特征提取及分类

利用小波变换对超声多普勒血流信号的最大频率曲线进行多尺度分析， 并从时间－尺度图上提取出模极大值的变化曲线。将这种方法应用到颈动脉血流的分析中，发现：该曲线对于脑血管床正常和异常的病例具有不同的形态。通过对该曲线进行多项式拟合，并将拟合的系数作为非线性变换单元组成的前馈网络（BP网络）的输入进行分类，临床试用效果良好，表明该方法为临床诊断脑血管疾病提供了一个新的依据。     

Physical characteristics and mathematical modelling of the pulsed ultrasonic flowmeter

A pulsed ultrasonic Doppler flowmeter for detailed measurements of velocity profiles in man is described. The device projects a beam of ultrasound in bursts of 0·4 μs duration, at 5 MHz, into the flow; the back-scattered signals are processed to produce a signal corresponding to the mean velocity over a small region of the flowing stream. The size and shape of this ‘sample volume’ determines the flowmeter sensitivity and accuracy. The velocity profile obtained from this instrument can be shown to be a weighted average of the ultrasonic intensity and the flowfield velocity over the sample volume, and is mathematically described by a convolution integral. A method of probing the ultrasonic beam and describing its characteristics in mathematical terms was developed. Using this model with a system whose velocity profile is parabolic, the pulsed ultrasonic Doppler-flowmeter output could be predicted via the convolution integral. Theoretical flowmeter-output curves were generated from the mathematical model by a digital-computer simulation and verified through experimental profiles in steady laminar flow. The modelling technique is sufficiently general for flowmeter output to be predicted for any general flow-velocity profile in steady or pulsetile flow.     

Development and feasibility study of a two-dimensional ultrasonic-measurement-integrated blood flow analysis system for hemodynamics in carotid arteries

Prevention and early detection of atherosclerosis are critical for protection against subsequent circulatory disease. In this study, an automated two-dimensional ultrasonic-measurement-integrated (2D-UMI) blood flow analysis system for clinical diagnosis was developed, and the feasibility of the system for hemodynamic analysis in a carotid artery was revealed. The system automatically generated a 2D computational domain based on ultrasound color Doppler imaging and performed a UMI simulation of blood flow field to visualize hemodynamics in the domain. In the UMI simulation, compensation of errors was applied by adding feedback signals proportional to the differences between Doppler velocities by measurement and computation while automatically estimating the cross-sectional average inflow velocity. The necessity of adjustment of the feedback gain was examined by analyzing blood flow in five carotid arteries: three healthy, one sclerosed, and one stenosed. The same feedback gain was generally applicable for the 2D-UMI simulation in all carotid arteries, depending on target variables. Thus, the present system was shown to be versatile in the sense that the parameter is patient independent. Moreover, the possibility of a new diagnostic method based on the hemodynamic information obtained by the 2D-UMI simulation, such as a waveform of the cross-sectional average inflow velocity and wall shear stress distributions, was suggested.     

Modelling of flow and wall behaviour in a mildly stenosed tube

In the present computational analysis, pulsatile flow and vessel wall behaviour in a simplified model of a stenosed vessel were investigated. Geometry of a 45% axisymmetrically stenosed (by area) cylindrical tube and a sinusoidal inflow waveform were simulated, with the fluid being assumed to be incompressible and Newtonian. The vessel wall was treated as a thick-walled, incompressible and isotropic material with uniform mechanical properties across the normal as well as the constricted segment. The study of fluid flow and wall motion was initially carried out separately using two commercial codes CFX4.2 and ABAQUS7 respectively. Their combined effects and interactions were later investigated through an iteratively coupled algorithm. Model validations on the rigid-wall fluid and static no-flow solid models were satisfactory, with Root Mean Square deviations of around 7% in centreline axial velocity between the prediction and measurement values for the rigid wall stenosis model, and 5% in circumferential stress for a cylindrical tube model under static loading when compared with the analytical solution. Results on velocity profiles, wall shear stress, intramural strain and stress for the rigid and compliant cases were all presented. Comparison between the rigid and compliant models revealed that, the flow separation layer distal to the stenosis was thicker and longer, and wall shear stress was slightly lower in the compliant model by less than 7.2%. Results obtained from the static wall model (with uniform pressure loading) and coupled fluid/wall interaction modelling of pulsatile flow showed qualitatively similar wall strain and stress patterns but considerable differences in magnitude. The radial and axial stresses were reduced by 31 and 8%, while the circumferential stress was increased by 13% due to the presence of pulsatile flow. Under the flow and structural conditions investigated, the effects of wall compliance were small, and did not change the flow and solid behaviours qualitatively in this case.     

Non-linear analysis of the arterial pulsatile flow: assessment of a model allowing a non-invasive ultrasonic functional exploration.

Ultrasonic measurements and modelling of blood flow in large vessels allows non-invasive evaluation of clinically interesting hemodynamic variables. To this aim, a non-linear mathematical model for the pulsatile arterial flow is proposed using the approximation of "local flow" theory. The model requires only measurements of instantaneous radius and centre-line blood velocity, and the knowledge of the tube distensibility to calculate blood velocity profiles, pressure gradient and wall shear stress. Evaluation of the proposed model using experimental data obtained from the literature proved that it can provide reliable results. In addition, as shown by assessing significance of various non-linear terms, results did not significantly change when a linear pressure-radius relationship was used instead of a non-linear relationship. Also, the model was found to be moderately sensitive to arterial tapering. Thus, the proposed model is suitable for a non-invasive clinical arterial exploration since it only requires three measurements which can be easily and precisely obtained in vivo using ultrasonic methods: the instantaneous radius, the centre-line velocity and the mean pulse wave velocity, this last variable characterizing the tube distensibility when assuming a linear pressure-radius relationship.     

Doppler ultrasound wall removal based on the spatial correlation of wavelet coefficients

In medical Doppler ultrasound systems, a high-pass filter is commonly used to reject echoes from the vessel wall. However, this leads to the loss of the information from the low velocity blood flow. Here a spatially selective noise filtration algorithm cooperating with a threshold denoising based on wavelets coefficients is applied to estimate the wall clutter. Then the blood flow signal is extracted by subtracting the wall clutter from the mixed signal. Experiments on computer simulated signals with various clutter-to-blood power ratios indicate that this method achieves a lower mean relative error of spectrum than the high-pass filtering and other two previously published separation methods based on the recursive principle component analysis and the irregular sampling and iterative reconstruction, respectively. The method also performs well when applied to in vivo carotid signals. All results suggest that this approach can be implemented as a clutter rejection filter in Doppler ultrasound instruments.     

Differential effects of sleep stage on coronary hemodynamic function during stenosis

We have demonstrated in a previous study that in the normal heart REM sleep induces surges in heart rate and coronary blood flow which are abolished by bilateral stellectomy. To study the effects of sleep in the stenosed coronary circulation, dogs were instrumented with Doppler flow probes and hydraulic occluders around the left circumflex coronary artery to measure coronary blood flow and to produce a 60% flow reduction. Catheters were placed in the aorta to measure mean arterial blood pressure. Electrodes were implanted via the frontal sinus to identify sleep stages. In the absence of stenosis, mean blood pressure was 95 +/- 3 mmHg, HR was 111 +/- 4 bpm, and coronary blood flow was 33 +/- 2 ml/min. During stenosis, REM induced episodic increases in heart rate which were accompanied by 38% decreases in coronary blood flow. We conclude that in the stenosed coronary circulation, REM sleep produces episodic sinus tachycardia and coronary blood flow reduction.     

Digital densitometric determination of relative coronary flow distributions

In clinical cardiology, stenosis in a coronary artery is measured on the basis of visual assessment. The reading of coronary arteriograms leads, however, to large inter- and intra-observer variability. Image analysis and computer assistance result in a more consistent assessment, but this approach is mainly based upon static geometric parameters, such as diameter reduction of a segment of the stenosed artery. A more functional, physiological measurement is thus desirable. This can be realised by measuring the difference between the normal coronary blood flow and the increased flow under hyperaemic conditions, yielding the so-called coronary flow reserve (CFR). In clinical practice, however, this method is difficult and time-consuming. A less demanding approach is reported, in which relative flow distributions are determined densitometrically from digital angiograms acquired under basal and hyperaemic conditions. The proposition is that, if the relative flow distribution in hyperaemic state differs from that during rest, the functional severity of a stenosis downstream from the bifurcation can be indicated. The new approach is validated by comparing the results of a theoretical model for steady flow with a flow phantom experiment for steady and pulsatile flow. The obtained flow ratios correlate very well, both in steady and pulsatile flow, with correlation coefficients exceeding 0.95.