Adaptive transverse blood velocity estimation in medical ultrasound: A simulation study
Introduction
In the blood circular system, the pulsatile flow profile is observed in the arteries. Reportedly, for investigation of the health of different components of the cardiovascular system, as the diameter of the basal arteries does not face remarkable change during the blood flow cycle, the flow can be considered to be directly proportional to the velocity [1], [2]. Currently, in order to attain information for complex flow visualization and to investigate the hemodynamics in the human body, various techniques of vector velocity estimation using ultrasound, which reveals both magnitude and direction of the blood velocity, are employed in clinical use [3], [4].
A frequently used clinical examination routine for estimating the blood velocity distribution at a specific depth is to estimate the power spectral density (PSD) of the sampled signal, which is traditionally conducted using periodogram or modified averaged periodogram, known as Welch’s method [5]. Moreover, for the navigation of the region of interest (ROI) by the operator, a B-mode image of the tissue is required, which is generated among velocity estimation procedure at interleaved transmission sequences. Routinely, about 40% of all transmissions should be allocated to B-mode imaging for an adequate updating frequency of the B-mode images. Furthermore, in case the remaining portion of emissions could be employed in the examination of two different regions of the vessel simultaneously, an opportunity to monitoring the blood velocity before and after stenosis would be prepared for the medical doctor [6]. In addition, obviously, the employment of a large number of transmissions in the estimation of the spectrogram leads to the reduction of temporal resolution and, thus loss in tracking the details in the rapid acceleration phases of the cardiac cycle. Therefore, it is necessary to develop improved techniques capable of estimating the blood spectral density from a small number of samples.
To overcome the drawbacks of traditional averaged periodogram technique, such as high leakage or low resolution in low observation durations, the data-adaptive techniques in the matched filter-bank framework such as blood amplitude and phase estimation technique (BAPES) [7], [8], or blood power spectral capon (BPC) estimation approaches led to satisfactory results [3], [6], [7], [9]. Also, it is shown that by utilizing adaptive spectral estimators, improvement of measuring blood velocities corrupted by clutter filters is possible [10]. In [11], the authors evaluated the quantitative spectral analysis of blood velocities for conventional color flow imaging (CFI) with limited ensemble sizes (8–16) using the data-adaptive Capon spectral estimator. By investigating the spectral broadening at different scenarios of velocities and beam to flow angles, it is shown that despite the dependency on CFI frame rate and beam-to-flow angle, the results attained by adaptive spectral estimators admit an improved precision in estimations. Additionally, some efficient methods are established to deal with computational load and complexity in adaptive medical ultrasound imaging [12], [13], [14], that can be adapted to adaptive blood velocity estimation issue, either. Adaptive techniques drastically reduce the number of required observations in addition to the increment of the PSD resolution and elimination of the artifacts compared to the techniques based on conventional methods [7]. Apart from the PSD qualities and emission numbers required for either conventional or adaptive methods for spectrogram inference, the unexceptional drawback is that no velocity is reported at a 90° angle between the blood velocity vector and the ultrasound beam [15]. The ability to determine the velocity distribution is due to the axial oscillation introduced by the emitted pulse. The pivotal generating mechanism is, thus, the axial oscillation in the conventional acoustic field that modulates the signal along with the scatterer movement through the range gate. If the recorded signal is sampled at this depth, the resulted slow-time signal will have a center frequency directly dependent on the axial blood velocity [1], [2]. In other respects, the measured frequency is proportional to the projection of the motion vector onto the ultrasound beam direction which features a band symmetric around the frequency of zero at 90° beam to flow angle, and therefore, the spectrum correction procedure is not possible at this angle [15]. Some researchers are pointing at this issue, such as [16], which compares the two methods of speckle tracking (ST) and vector Doppler (VD) in the estimation of flow velocity with a complex pattern. As an overall, the VD was the superior axial velocity estimator, whereas ST was the better lateral estimator. However, considering some practical limitations of the VD, the research concluded that ST might provide a more consistent and practical approach to 2-D velocity estimation in complex flow patterns. In another work, the capability of the plane wave excitation (PWE) method was discussed in the estimation of both the axial and transverse components of the flow velocity, and validation was made by the magnetic resonance (MR) scanning [4]. From another point of view, to directly estimate the velocity components transverse to the beam, a signal should be generated with an oscillation across the beam in addition to the initial axial oscillations. This desire is fulfilled in the transverse oscillation (TO) method. The transverse oscillation approach, already approved by FDA [17], was developed by Jensen and Munk [18] and tested in vivo by several works [4], [15], [19], [20], [21]. A similar method was proposed by Anderson [22] (spatial quadrature).
Compared to the traditional TO-based vector velocity estimation techniques, which result in the estimation of the mean transverse and axial velocities at a specific location, by the transverse spectral velocity estimation, the evolution of the transverse spectrum in time at an addressed spatial location is attained. The drawback of zero velocity measurement in lateral motion of blood particles has been enhanced using TO-based spectrograms which result in reliable transverse PSD estimation for fully transverse flow, and an almost acceptable result for beam to flow angles up to 15–20° [23]. However, the conventional TO periodogram in transverse velocity estimation suffers from poor spectral resolution when the observation window length is limited. This constraints the system operation in case of B-mode image updating. Also, an iterative approach (TO-BIAA) was developed to reduce the number of emissions and also decrease the artifacts and spectral broadening [24]. Nevertheless, the results of TO-BIAA degrade for propagation angles less than 75°.
In this article, the goal is to reduce the number of emissions required for transverse PSD estimation in a double oscillating TO field, as well as increase the PSD quality. Two adaptive techniques are proposed for the measurement of the transverse velocity distribution with low amount of observed data. Firstly, the superior performance of the minimum variance spectral estimator is exploited in the TO field (TO-MV) to satisfactorily discriminate the desired fully transverse signal from noise and interference. Moreover, to further eliminate the contribution of the undesired components originated from noise and non-ideal complex quadrature TO pair, the eigen-structure of the data covariance matrix is utilized. The weight vector of the TO- eigenspace-based MV (TO-EIBMV) is found by projecting the MV weights, calculated upon TO field complex signals, onto the desired signal subspace constructed from eigen-structure of the covariance matrix. TO-EIBMV technique exhibits a pronounced performance despite a reduced number of emissions.
The performance of the methods is evaluated using Field II [1], [2], [25], Release 3.20, Jorgen Arendt Jensen, Technical University of Denmark, Lyngby, Denmark) on pulsatile blood flow data as an approximation for the femoral artery flow. The proposed methods are compared to the results attained by averaged periodogram applied to the initial fourth-order PSD estimator developed in [23]. The simulations indicate that the proposed adaptive methods offer a pronounced performance gain with lower relative standard deviation (RSD) and bias relative to the peak velocity in the vessel (RB), despite the lower number of observations and in the presence of beam to flow angle deviations. Moreover, a better crossectional profile estimation is attained by adaptive techniques.
The first section, being the general background, contains theory and formulation for the TO field in transverse velocity estimation. Furthermore, the conventional transverse PSD estimation technique based on the fourth-order estimator and averaged periodogram is given. In section three, which is related to the proposed methods, the formulation of the proposed TO-MV and TO-EIBMV methods are described at distinct subsections. Then, the simulation setups and required data processing for TO field consideration are exhibited in section four. Section five includes the attained results for pulsatile flow estimation, relevant discussions for various scenarios, and implementation concerns, and finally, a conclusion is given.
Section snippets
Background
In this section, initially, the theory for the estimation of the transverse velocity based on the TO method is described. Moreover, the formulation for adaptation of averaged periodogram to the conventional transverse PSD estimation approach [23], as well as two proposed adaptive techniques of TO-MV and TO-EIBMV, are presented.
Proposed methods
In this section, the proposed adaptive methods for direct estimation of the transverse velocity distribution of the blood are discussed. Initially, the superior performance of the minimum variance spectral estimator is exploited to obtain the transverse spectrogram from the slow-time signal received from the flow crossing a transversely oscillating field (TO-MV). Then, to achieve a better estimation, the proposed estimator is modified according to the eigen-space characteristics of the
Simulation setups
In this section, the simulation setup is presented. The flow modeling and transducer parameters, as well as the generation of TO fields along with required preprocessing, are described in distinct subsections.
Simulation results and discussion
In this section, two different adaptive transverse spectral estimation methods of TO-MV and the modified version (TO-EIBMV) are evaluated using Field II simulation tool, and the outcomes are compared to the averaged periodogram technique applied to the processed fourth-order signal attained from the double oscillating acoustic field (TO-AP). Different lengths of N = [48163264128] slow-time samples are considered for the observation window to investigate the reliability of the techniques
Conclusion
In this paper, firstly, we have proposed a novel data-adaptive direct transverse blood velocity spectral estimator, which exhibits a promising performance even in short observation window lengths. Furthermore, by considering the eigenspace separation of the observed data, the performance of the proposed estimator has been enhanced. The transversal modulation in the ultrasound field is applied to attain slow time signals sensitive to the transverse velocity of blood flow. Initially, the
Declaration of Competing Interest
There is no conflict of interest.
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A nonlinear beamforming for enhanced spatiotemporal sensitivity in high frame rate ultrasound flow imaging
2022, Computers in Biology and MedicineCitation Excerpt :However, it has been reported that the deep learning models could provide better results by incorporating temporal information of the microbubbles [45]. Towards improving the temporal resolution, a minimum variance based adaptive velocity estimation technique has been recently reported in [46], but with higher computational complexity. However, the efforts towards employing nonlinear beamformers of lower computational complexity (than minimum variance) like delay multiply and sum (DMAS) technique for flow imaging is limited.