Quantitative blood speed imaging with intravascular ultrasound

Previously, we presented a method of real-time arterial color flow imaging using an intravascular ultrasound (IVUS) imaging system, where real-time RF A-scans were processed with an FIR (finite-impulse response) filter bank to estimate relative blood speed. Although qualitative flow measurements are clinically valuable, realizing the full potential of blood flow imaging requires quantitative flow speed and volume measurements in real time. Unfortunately, the rate of RF echo-to-echo decorrelation is not directly related to scatterer speed in a side-looking IVUS system because the elevational extent of the imaging slice varies with range. Consequently, flow imaging methods using any type of decorrelation processing to estimate blood speed without accounting for spatial variation of the radiation pattern will have estimation errors that prohibit accurate comparison of speed estimates from different depths. The FIR filter bank approach measures the rate of change of the ultrasound signal by estimating the slow-time spectrum of RF echoes. A filter bank of M bandpass filters is applied in parallel to estimate M components of the slow-time DFT (discrete Fourier transform). The relationship between the slow-time spectrum, aperture diffraction pattern, and scatterer speed is derived for a simplified target. Because the ultimate goal of this work is to make quantitative speed measurements, we present a method to map slow time spectral characteristics to a quantitative estimate. Results of the speed estimator are shown for a simulated circumferential catheter array insonifying blood moving uniformly past the array (i.e., plug flow) and blood moving with a parabolic profile (i.e., laminar flow)     

Single-ensemble-based eigen-processing methods for color flow imaging--Part II. The matrix pencil estimator

Parametric spectral estimators can potentially be used to obtain flow estimates directly from raw slow-time ensembles whose clutter has not been suppressed. We present a new eigen-based parametric flow estimation method called the matrix pencil, whose principles are based on a matrix form under the same name. The presented method models the slow-time signal as a sum of dominant complex sinusoids in the slow-time ensemble, and it computes the principal Doppler frequencies by using a generalized eigen-value problem-formulation and matrix rank reduction principles. Both fixed rank (rank-one, rank-two) and adaptive-rank matrix pencil flow estimators are proposed, and their potential applicability to color flow signal processing is discussed. For the adaptive-rank estimator, the nominal rank was defined as the minimum eigen-structure rank that yields principal frequency estimates with a spread greater than a prescribed bandwidth. In our initial performance evaluation, the fixed-rank matrix pencil estimators were applied to raw color flow data (transmit frequency: 5 MHz; pulse repetition period: 0.175 ms; ensemble size: 14) acquired from a steady flow phantom (70 cm/s at centerline) that was surrounded by rigid-tissue-mimicking material. These fixed-rank estimators produced velocity maps that are well correlated with the theoretical flow profile (correlation coefficient: 0.964 to 0.975). To facilitate further evaluation, the matrix pencil estimators were applied to synthetic slow-time data (transmit frequency: 5 MHz; pulse repetition period: 1.0 ms; ensemble size: 10) modeling flow scenarios without and with tissue motion (up to 1 cm/s). The bias and root-mean-squared error of the estimators were computed as a function of blood-signal-to-noise ratio and blood velocity. The matrix pencil flow estimators showed that they are comparatively less biased than most of the existing frequency-based flow estimators like the lagone autocorrelator.     

Adaptive spectral doppler estimation

In this paper, 2 adaptive spectral estimation techniques are analyzed for spectral Doppler ultrasound. The purpose is to minimize the observation window needed to estimate the spectrogram to provide a better temporal resolution and gain more flexibility when designing the data acquisition sequence. The methods can also provide better quality of the estimated power spectral density (PSD) of the blood signal. Adaptive spectral estimation techniques are known to provide good spectral resolution and contrast even when the observation window is very short. The 2 adaptive techniques are tested and compared with the averaged periodogram (Welch's method). The blood power spectral capon (BPC) method is based on a standard minimum variance technique adapted to account for both averaging over slow-time and depth. The blood amplitude and phase estimation technique (BAPES) is based on finding a set of matched filters (one for each velocity component of interest) and filtering the blood process over slow-time and averaging over depth to find the PSD. The methods are tested using various experiments and simulations. First, controlled flow-rig experiments with steady laminar flow are carried out. Simulations in Field II for pulsating flow resembling the femoral artery are also analyzed. The simulations are followed by in vivo measurement on the common carotid artery. In all simulations and experiments it was concluded that the adaptive methods display superior performance for short observation windows compared with the averaged periodogram. Computational costs and implementation details are also discussed.     

Decorrelation-based blood flow velocity estimation: effect of spread of flow velocity,linear flow velocity gradients,and parabolic flow

In recent years, a new method to measure transverse blood flow, based on the decorrelation of the radio frequency (RF) signals has been developed. In this paper, we investigated the influence of nonuniform flow on the velocity estimation. The decorrelation characteristics of transverse blood flow using an intravascular ultrasound (IVUS) array catheter are studied by means of computer modeling. Blood was simulated as a collection of randomly located point scatterers; moving this scattering medium transversally across the acoustical beam represented flow. First-order statistics were evaluated, and the signal-to-noise ratio from the signals were measured. The correlation coefficient method was used to present the results. Three velocity profiles were simulated: random spread of blood-flow velocity, linear blood-flow velocity gradient, and parabolic blood-flow. Radio frequency and envelope signals were used to calculate the decorrelation pattern. The results were compared to the mean decorrelation pattern for plug blood-flow. The RF signals decorrelation patterns were in good agreement with those obtained for plug blood flow. Envelope decorrelation patterns show a close agreement with the one for plug blood flow. For axial blood flow, there is a discrepancy between decorrelation patterns. The results presented here suggest that the decorrelation properties of an IVUS array catheter for measuring quantitative transverse blood flow probably will not be affected by different transverse blood-flow conditions     

Doppler angle and flow velocity estimations using the classic and transverse Doppler effects

Current clinical Doppler ultrasound systems could only measure the flow vector parallel to the ultrasound beam axis, and the knowledge of the Doppler angle (beam-to-flow angle) is needed to calculate the real flow velocity. Currently, the Doppler angle is determined visually by manually aligning a vessel axis marker along the blood vessel on the duplex scan image of the ultrasound. The application of this procedure is often limited by practical constraints; therefore, measurements are not reliable. In order to overcome this problem, the authors developed a simple Doppler angle and flow velocity estimation method using a combination of the classic and transverse Doppler effects. This method uses only a single focused annular array transducer to estimate the Doppler angle and the flow velocity. The authors have verified experimentally that this method is successful for measuring constant flow in a flow phantom between 45 degrees and 80 degrees Doppler angle. The standard deviation of the estimated Doppler angles is less than 4.5 degrees . This method could be implemented easily in medical Doppler ultrasound systems to automatically estimate the Doppler angle and the flow velocity.     

Estimating 2-D vector velocities using multidimensional spectrum analysis

Wilson (1991) presented an ultrasonic wideband estimator for axial blood flow velocity estimation through the use of the 2-D Fourier transform. It was shown how a single velocity component was concentrated along a line in the 2-D Fourier space, where the slope was given by the axial velocity. Later, it was shown that this approach could also be used for finding the lateral velocity component by also including a lateral sampling. A single velocity component would then be concentrated along a plane in the 3-D Fourier space, tilted according to the 2 velocity components. This paper presents 2 new velocity estimators for finding both the axial and lateral velocity components. The estimators essentially search for the plane in the 3- D Fourier space, where the integrated power spectrum is largest. The first uses the 3-D Fourier transform to find the power spectrum, while the second uses a minimum variance approach. Based on this plane, the axial and lateral velocity components are estimated. Several phantom measurements, for flow-to-depth angles of 60, 75, and 90 degrees, were performed. Multiple parallel lines were beamformed simultaneously, and 2 different receive apodization schemes were tried. The 2 estimators were then applied to the data. The axial velocity component was estimated with an average standard deviation below 2.8% of the peak velocity, while the average standard deviation of the lateral velocity estimates was between 2.0% and 16.4%. The 2 estimators were also tested on in vivo data from a transverse scan of the common carotid artery, showing the potential of the vector velocity estimation method under in vivo conditions.     

Single-ensemble-based eigen-processing methods for color flow imaging--Part I. The Hankel-SVD filter

Because of their adaptability to the slow-time signal contents, eigen-based filters have shown potential in improving the flow detection performance of color flow images. This paper proposes a new eigen-based filter called the Hankel-SVD filter that is intended to process each slowtime ensemble individually. The new filter is derived using the notion of principal Hankel component analysis, and it achieves clutter suppression by retaining only the principal components whose order is greater than the clutter eigen-space dimension estimated from a frequency based analysis algorithm. To assess its efficacy, the Hankel-SVD filter was first applied to synthetic slow-time data (ensemble size: 10) simulated from two different sets of flow parameters that model: 1) arterial imaging (blood velocity: 0 to 38.5 cm/s, tissue motion: up to 2 mm/s, transmit frequency: 5 MHz, pulse repetition period: 0.4 ms) and 2) deep vessel imaging (blood velocity: 0 to 19.2 cm/s, tissue motion: up to 2 cm/s, transmit frequency: 2 MHz, pulse repetition period: 2.0 ms). In the simulation analysis, the post-filter clutter-to- blood signal ratio (CBR) was computed as a function of blood velocity. Results show that for the same effective stopband size (50 Hz), the Hankel-SVD filter has a narrower transition region in the post-filter CBR curve than that of another type of adaptive filter called the clutter-downmixing filter. The practical efficacy of the proposed filter was tested by application to in vivo color flow data obtained from the human carotid arteries (transmit frequency: 4 MHz, pulse repetition period: 0.333 ms, ensemble size: 10). The resulting power images show that the Hankel-SVD filter can better distinguish between blood and moving-tissue regions (about 9 dB separation in power) than the clutter-downmixing filter and a fixed-rank multi ensemble-based eigen-filter (which showed a 2 to 3 dB separation).     

Rotating Inclined Cylinder and the Effect of the Tilt Angle on Vortices

We study numerically some possible vortex configurations in a rotating cylinder that is tilted with respect to the rotation axis and where different numbers of vortices can be present at given rotation velocity. In a long cylinder at small tilt angles the vortices tend to align along the cylinder axis and not along the rotation axis. We also show that the axial flow along the cylinder axis, caused by the tilt, will result in the Ostermeier-Glaberson instability above some critical tilt angle. When the vortices become unstable the final state often appears to be a dynamical steady state, which may contain turbulent regions where new vortices are constantly created. These new vortices push other vortices in regions with laminar flow towards the top and bottom ends of the cylinder where they finally annihilate. Experimentally the inclined cylinder could be a convenient environment to create long lasting turbulence with a polarization which can be adjusted with the tilt angle.     

Quantitative volume flow estimation using velocity profiles

The direct measurement of the velocity profile of blood flowing in a vessel yields a volume flow estimate that is more accurate than single-point Doppler ultrasound. A volume flow estimate is made by assuming a circularly symmetric velocity field and integrating the velocity profile measured along a diameter. The many velocity measurements made contribute to higher precision in the integrated velocity estimate. Also, the velocity profile furnishes the functional diameter of the vessel at many points through the cardiac cycle. This algorithm, as implemented on the Philips CVI system, was tested theoretically by numerical modelling, and experimentally with a flow simulator. The effect of beamwidth, vessel size, and measurement position misalignment on the volume flow estimate were studied. Experimental and theoretical results agreed well and showed that the flow estimation algorithm can produce precise and accurate volume flow estimates. The flow estimate is sensitive to the flow angle and is inaccurate by 5% per degree error in the angle. Beamwidths of 1.0 to 1.5 mm are a good match to axial resolution and yield accurate volume flow estimates in vessels over 2 mm in diameter. Larger beamwidths give lower volume flow estimates, but are not as sensitive to misalignment     

PIV血流场显示测速技术

通过分析多普勒测速技术与粒子图像测速技术的区别,从一个新角度把PIV全流场测速技术应用于血液流场的研究中。用激光片光源照亮血流粒子场,再计算确定实验系统光学参数,以获得最佳流场图片。对流场分析常用的互相关算法进行改进,辅以曲面拟合和误差修正,获得了亚像素级的全流场速度的大小和方向,并进一步计算出血流场的涡量分布和剪切率分布。为了验证改进的算法,对日本视频协会提供的PIV-STD序列标准图像进行仿真计算和误差分析,与原算法相比其速度矢量图的误差降低了2个百分点,流场速度值的平均误差小于±1%。该结果表明文中建立的方法是有效的,并可推广用于其它的流场分析。     

Measuring distribution of the ellipsoid of birefringence through the thickness of optical disk substrates

We have measured the birefringence of polycarbonate optical disk substrates, using ellipsometry. For a more comprehensive characterization, the probe beam was incident upon substrates in a wide range of polar angles and from different azimuths relative to track direction (?). Our measurements show that the ellipsoid of birefringence is tilted in the plane of radial (r) and normal (z) directions. The tilt angle varies through thickness, with a maximum value of approximately 10°. For beams passing through the substrate in the ?-z plane and at large incident angles, this tilt causes significant conversion (up to 100%) between p- and s-polarized components. Distributions of other parameters, such as the values of in-plane and vertical birefringence, are obtained simultaneously in the measurements.     

Lateral blood flow velocity estimation based on ultrasound speckle size change with scan velocity

Conventional (Doppler-based) blood flow velocity measurement methods using ultrasound are capable of resolving the axial component (i.e., that aligned with the ultrasound propagation direction) of the blood flow velocity vector. However, these methods are incapable of detecting blood flow in the direction normal to the ultrasound beam. In addition, these methods require repeated pulse-echo interrogation at the same spatial location. A new method has been introduced which estimates the lateral component of blood flow within a single image frame using the observation that the speckle pattern corresponding to blood reflectors (typically red blood cells) stretches (i.e., is smeared) if the blood is moving in the same direction as the electronically-controlled transducer line selection in a 2-D image. The situation is analogous to the observed distortion of a subject photographed with a moving camera. The results of previous research showed a linear relationship between the stretch factor (increase in lateral speckle size) and blood flow velocity. However, errors exist in the estimation when used to measure blood flow velocity. In this paper, the relationship between speckle size and blood flow velocity is investigated further with both simulated flow data and measurements from a blood flow phantom. It can be seen that: 1) when the blood flow velocity is much greater than the scan velocity (spatial rate of A-line acquisition), the velocity will be significantly underestimated because of speckle decorrelation caused by quick blood movement out of the ultrasound beam; 2) modeled flow gradients increase the average estimation error from a range between 1.4% and 4.4%, to a range between 4.4% and 6.8%; and 3) estimation performance in a blood flow phantom with both flow gradients and random motion of scatterers increases the average estimation error to between 6.1% and 7.8%. Initial attempts at a multiple-scan strategy for estimating flow by a least-squares model suggest the possibility of increased accuracy using multiple scan velocities.     

A new time-domain narrowband velocity estimation technique for Doppler ultrasound flow imaging. I. Theory

A significant improvement in blood velocity estimation accuracy can be achieved by simultaneously processing both temporal and spatial information obtained from a sample volume. Use of the spatial information becomes especially important when the temporal resolution is limited. By using a two-dimensional sequence of spatially sampled Doppler signal "snapshots" an improved estimate of the Doppler correlation matrix can be formed. Processing Doppler data in this fashion addresses the range-velocity spread nature of the distributed red blood cell target, leading to a significant reduction in spectral speckle. Principal component spectral analysis of the "snapshot" correlation matrix is shown to lead to a new and robust Doppler mode frequency estimator. By processing only the dominant subspace of the Doppler correlation matrix, the Cramer-Rao bounds on the estimation error of target velocity is significantly reduced in comparison to traditional narrowband blood velocity estimation methods and achieves almost the same local accuracy as a wideband estimator. A time-domain solution is given for the velocity estimate using the root-MUSIC algorithm, which makes the new estimator attractive for real-time implementation.     

Three-dimensional vector flow estimation using two transducers andspectral width

Current ultrasonic blood flow measurement systems estimate only that component of flow which is parallel to the incident ultrasound beam. This is done by relating the mean backscattered frequency shift to the axial velocity component through the classical Doppler equation. A number of ultrasonic techniques for estimating the two-dimensional (2D) blood velocity vector have been published, both Doppler and non-Doppler. Several three-dimensional (3D) blood velocity vector techniques have also been proposed, all of which require a multiplicity of transducers or lines of sight. Here a technique is described for estimating the total velocity vector, using only two transducers. This is achieved by measuring not only the frequency shifts but also the bandwidths of the backscattered spectra, making use of the fact that the bandwidth of a Doppler spectrum has been shown to be proportional to the velocity component normal to the sound beam. Partial experimental verification of the proposed vector flow estimation scheme is demonstrated by using a constant velocity thread phantom     

Hydroxyl tagging velocimetry in a supersonic flow over a cavity

Hydroxyl tagging velocimetry (HTV) measurements of velocity were made in a Mach 2 (M 2) flow with a wall cavity. In the HTV method, ArF excimer laser (193 nm) beams pass through a humid gas and dissociate H2O into H + OH to form a tagging grid of OH molecules. In this study, a 7 x 7 grid of hydroxyl (OH) molecules is tracked by planar laser-induced fluorescence. The grid motion over a fixed time delay yields about 50 velocity vectors of the two-dimensional flow in the plane of the laser sheets. Velocity precision is limited by the error in finding the crossing location of the OH lines written by the excimer tag laser. With a signal-to-noise ratio of about 10 for the OH lines, the determination of the crossing location is expected to be accurate within +/- 0.1 pixels. Velocity precision within the freestream, where the turbulence is low, is consistent with this error. Instantaneous, single-shot measurements of two-dimensional flow patterns were made in the nonreacting M 2 flow with a wall cavity under low- and high-pressure conditions. The single-shot profiles were analyzed to yield mean and rms velocity profiles in the M 2 nonreacting flow.     

Highlight detection and removal from spectral image

We present a constrained spectral unmixing method to remove highlight from a single spectral image. In the constrained spectral unmixing method, the constraints have been imposed so that all the fractions of diffuse and highlight reflection sum up to 1 and are positive. As a result, the spectra of the diffuse image are always positive. The spectral power distribution (SPD) of the light source has been used as the pure highlight spectrum. The pure diffuse spectrum of the measured spectrum has been chosen from the set of diffuse spectra. The pure diffuse spectrum has a minimum angle among the angles calculated between spectra from a set of diffuse spectra and the measured spectrum projected onto the subspace orthogonal to the SPD of the light source. The set of diffuse spectra has been collected by an automated target generation program from the diffuse part in the image. Constrained energy minimization in a finite impulse response linear filter has been used to detect the highlight and diffuse parts in the image. Results by constrained spectral unmixing have been compared with results by the orthogonal subspace projection (OSP) method [Proceedings of International Conference on Pattern Recognition (2006), pp. 812-815] and probabilistic principal component analysis (PPCA) [Proceedings of the 4th WSEAS International Conference on Signal Processing, Robotics and Automation (2005), paper 15]. Constrained spectral unmixing outperforms OSP and PPCA in the visual assessment of the diffuse results. The highlight removal method by constrained spectral unmixing is suitable for spectral images.     

Analysis of velocity estimation error for a multidimensional Doppler ultrasound system

The error characteristics of a single-transducer (one dimensional), dual-transducer (two-dimensional), and triple-transducer (three-dimensional) system for velocity estimation are examined. A velocity vector is completely characterized by the magnitude and the directional angles. For a single-transducer case, the velocity magnitude alone can be estimated. The variation in the directional angles for a single-transducer case cannot be accounted for in the estimation process, thus resulting in large errors. For a dual transducer, both the velocity magnitude and the angle on the x-y plane can be estimated. The use of an extra transducer provides added flexibility in the estimation process. Variation in one of the directional angles is accounted for in the estimation process, thus resulting in smaller error than the single-transducer case. For a triple-transducer case, if the normal angles between the three transducer axes are known, then the complete velocity vector with all the directional angles can be estimated.     

Linear astigmatism of confocal off-axis reflective imaging systems and its elimination

Linear astigmatism of a confocal off-axis reflective imaging system when the object plane is tilted and located at a finite distance from the imaging system is derived. We show that linear astigmatism can be eliminated by proper configuration of the parent mirror axes in confocal off-axis two-mirror systems. The tilt angle of the image plane is also derived. The developed theory is verified by ray-tracing analysis of an example system.     

Ultrasound three-dimensional velocity measurements by featuretracking

This article describes a new angle-independent method suitable for three-dimensional (3-D) blood flow velocity measurement that tracks features of the ultrasonic speckle produced by a pulse echo system. In this method, a feature is identified and followed over time to detect motion. Other blood flow velocity measurement methods typically estimate velocity using one- (1-D) or two-dimensional (2-D) spatial and time information. Speckle decorrelation due to motion in the elevation dimension may hinder this estimate of the true 3-D blood flow velocity vector. Feature tracking is a 3-D method with the ability to measure the true blood velocity vector rather than a projection onto a line or plane. Off-line experiments using a tissue phantom and a real-time volumetric ultrasound imaging system have shown that the local maximum detected value of the speckle signal may be identified and tracked for measuring velocities typical of human blood flow. The limitations of feature tracking, including the uncertainty of the peak location and the duration of the local maxima are discussed. An analysis of the expected error using this method is given     

Experimental study of the phenomenon of 1 x N spectral switch due to diffraction of partially coherent light

Spectral properties of a class of partially coherent light with spectral profiles of varying bandwidths are studied on diffraction by a circular aperture in the far zone for different diffractive angles, i.e., for on-axis and off-axis points on the observation plane. It is found that the spectrum of the light in the far zone is different from that at the aperture plane. This change in the spectrum is termed spectral shift, which is found to be different at different diffractive angles. The spectral shift for a fixed diffactive angle shows a gradual change. However, for a critical value of the coherence at the aperture plane, the spectral shift shows a rapid transition, termed spectral switch. For different diffractive angles the coherence that causes the spectral switch also differs. Therefore the phenomenon of 1 x N spectral switch (consisting of one input port and N output ports) is studied experimentally.