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correspondence: chikayoshi Sumi Department of Information and communication Sciences, Faculty of Science and Technology, Sophia University, 7-1, Kioi cho, chiyoda Ku, Tokyo 102-8554, Japan Tel +81-3-3238-3415 Fax +81-3-3238-3321 email c-sumi@sophia.ac.jp Abstract: A number of ultrasonic displacement/velocity measurement methods have been extensively developed for measurements of blood flow, tissue motion, and strain. Lateral modulation (LM) methods have also been reported using steered, crossed beams, and these methods permit measurements of displacement vectors. In this report, a new beam steering method for the transmission and reception of ultrasound is proposed, which can enable measurements of lateral displacements and of arbitrary displacement vectors with a very high degree of accuracy. Because this beam steering method uses only a steering angle, this method is referred to as ASTA. With ASTA, the number of available methods to obtain a displacement vector measurement is limited to previously developed block-matching methods, such as the multidimensional cross-spectrum phase gradient method, and the multidimensional autocorrelation method (MAM) and the multidimensional Doppler method (MDM) using a block-matching method (the methods using block matching are referred to as MAMb and MDMb, respectively). Being dependent on the measurement method, only a lateral displacement measurement can be made even if the methods are multidimensional, ie, previously developed MAM and MDM using a moving average and a mirror setting of the obtained steered beams, and one-dimensional (1D), such as an autocorrelation method. Considerations of beamforming schemes using LM and ASTA show that the simple ASTA beamforming method increases capabilities for real-time measurements and requires a small physical aperture when compared with LM. For lateral displacement measurements (eg, blood flow in a carotid artery), a lateral coordinate must correspond to the direction of the target’s lateral motion, and the steering angle used is as large as possible to increase the measurement accuracy of a lateral displacement. However, for displacement vector measurements to describe complex tissue motions (eg, cardiac motion), if the axial coordinate corresponds to the depth direction in the target tissue, an ideal steering angle will be 45°. A two-dimensional echo simulation shows that for the block-matching methods, LM yields more accurate displacement vector measurements than ASTA, whereas with MAM and MDM using a moving average and a mirror setting and 1D methods, ASTA yields more accurate lateral displacement measurements than LM. The block-matching method requires fewer calculations than the moving average method; however, a lower degree of accuracy is obtained. As with LM, multidimensional measurement methods yield more accurate measurements with ASTA than the corresponding 1D measurement methods. Summarizing, for displacement vector measurements or lateral displacement measurements using the multidimensional measurement methods, the ranking of the degree of measurement accuracy and stability is ASTA with a mirror setting . LM with a moving average . LM with block matching . ASTA with block matching. Because every tissue has its own motion (heart, liver, etc) and occasionally obstacles, such as bones, interfere with the measurements, the target tissue will determine the selection of the proper beamforming method with a choice between LM and ASTA. As for use with LM previously clarified, an appropriate displacement measurement method should also be selected for use with ASTA according to the echo signal-to-noise ratio, a required spatial resolution and a required calculation speed. ASTA, together with LM, can potentially enable the utilization of new aspects of displacement measurements.

Utilization of an ultrasound beam steering angle for measurements of tissue displacement vector and lateral displacement