Consideration of generated beam angles increases the accuracy of ultrasonic displacement measurements
Chikayoshi Sumi, Yuuki Takanashi, Kento Ichimaru
Department of Information and Communication Sciences, Faculty of Science and Technology, Sophia University, Tokyo, Japan
Abstract: The development of practical ultrasonic (US) tissue displacement measurement methods increases the number of available and useful applications of displacement/strain measurements that can be made (eg, various blood flow measurements and measurements of tissue motion in organs such as the heart, liver, and so forth). Previously developed lateral modulation (LM) methods with a multidimensional autocorrelation method (MAM) or multidimensional Doppler method (MDM) and a steering angle method (ASTA) with lateral Doppler method produced accurate displacement vector and lateral displacement measurements, respectively. Such measurements cannot be obtained using only a conventional Doppler technique. Another new method has also been reported, using multiple crossed beams (MCBs) to obtain high-accuracy displacement vector measurements; that is, a displacement vector is synthesized using accurately measured axial displacements with previously developed multidimensional displacement measurement methods, including the one-dimensional autocorrelation method (1D AM) with a multidimensional moving average (MA), together with conventional rotation processing of global echo data or a coordinate system (ie, a global echo rotation referred to as r method) by the negative value of the steering angles used in beamforming. However, in real-world applications, directivities of transmission and reception apertures, scattering, reflection, and attenuation affect the direction and properties of US beams used for conventional axial displacement measurements employing beamforming methods such as a conventional nonsteered, steered, or secta beam, and they also affect ASTA and MCB methods. In this report, to improve accuracy in the measurements of an arbitrary directional displacement and a displacement vector using any beamforming methods, a spatial resolution in a beam angle (BA) is generated. For instance, for a two-dimensional (2D) Cartesian coordinate system, this is obtained by calculating the arctangent of the ratio of the axial and lateral instantaneous frequencies or the first moments of local spectra. On the basis of the 1D AM with a multidimensional MA, the local displacement in the beam direction is accurately measured by dividing the local instantaneous phase change by the instantaneous frequency calculated in the beam direction, and an arbitrary directional displacement can be measured (axial, lateral, radial, and so forth), which is done with or without a rotation of local echo data. These are respectively referred to as BA and BAr (BA + local rotation) methods or, specifically, as the 1D AMBA (1D AM + BA) and the 1D AMBAr (1D AM + BAr). Also, it is theoretically shown that the 1D AM with MCB but no echo rotation (ie, 1D AMBA with MCB) is equivalent to the most accurate MAM with LM, and that the 1D AMBA with ASTA can also provide a lateral Doppler measurement. Through agar phantom experiments, in addition to steered spherical focusing beams for both transmission and reception, measurement accuracies with all of the new methods are also evaluated for rapid scanning beamforming such as using one or plural, steered or nonsteered plane wave transmissions, and steered or nonsteered spherical focusing beam receptions. For comparisons with the 1D AMBA and the 1D AMBAr, the spectra frequency division method (SFDM) used in the MAM is also used instead of the 1D AM. All for the measurements of an axial displacement with axial compression and nonsteering, a lateral displacement with lateral compression and ASTA and a 2D displacement vector with lateral compression and MCBs, BA methods based on the 1D AM and SFDM approaches achieve more accurate measurements with significantly fewer calculations than the corresponding BAr or r methods (ie, real time). BA methods do not yield dead region data in a region of interest and they do not yield any measurement errors because of an approximate interpolation of echo data or of measured motion/deformation data. However, the measurement accuracies of one-directional displacements are significantly lower than those of displacement vectors, because of the practical three-dimensional deformation or motion (eg, about a half standard deviation of the lateral displacement measurement). In terms of required processing, the MAM or the MDM with LM is better than methods with MCB (ie, real time). The proper combination of the SFDM with LM or ASTA will yield more accurate measurements in a trade-off with increasing the number of calculations.
Keywords: beam direction, beam angle (BA), axial displacement, lateral displacement, displacement vector, lateral modulation (LM), a steering angle (ASTA), multiple crossed beams (MCBs), multidimensional or one-dimensional autocorrelation method (MAM or 1DAM), multidirectional moving-average (MA), spectra frequency division method (SFDM)
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