超音波多角度平面波延遲相乘加總(Delay-multiply-and-sum, DMAS)成像透過發射事件(Tx-DMAS)、接收通道(Rx-DMAS)或兩者(2D-DMAS)的信號相關性以抑制低相關性雜波，但其成像聲速是否正確對應傳播介質組織聲速(Speed of Sound, SOS)仍是維持影像品質的基本要求。目前已有許多利用接收通道信號或影像品質分析估計傳播介質組織平均聲速的方法但皆不是針對多角度平面波成像特性所開發的，因此在本研究的第一部分中，我們進一步擴展多角度平面波DMAS成像以量化信號相關性程度，並將其用於估計多角度平面波成像中的組織聲速。此外多角度平面波DMAS影像因強調信號相關性而會具有較明顯的斑點顆粒特徵，因此在本研究的第二部分中，我們也將探討多角度平面波DMAS影像用於斑點追蹤以改善血流流速估計的可行性。
在本論文第一部分中，我們將所得的多角度平面波DMAS影像與傳統同調性平面波複合(Coherent Plane-wave Compounding, CPWC)影像之間的像素值比定義為相位同調因子(Phase Coherent Factor, PCF)。當成像聲速(Cbeam)與實際組織聲速不匹配時，由於聚焦誤差增大使得信號相關性降低，並導致相位同調因子值減小。在計算多個成像聲速下的相位同調因子後，具有最大相位同調因子值的成像聲速即為最佳成像聲速(Copt)，最佳成像聲速也對應我們所估計的實際組織聲速。
PICMUS模擬數據結果指出，當接收孔徑變大且通道訊雜比變大時，最佳成像聲速估計結果將更加準確，在三種DMAS成像方法中，Tx-DMAS在較低通道訊雜比的情況下可以使用較小的接收孔徑提供具有最小偏誤及標準差的最佳成像聲速估計結果，此外，本研究提出的最佳成像聲速估計方法當多角度平面波DMAS成像的p值不小於2時表現將會趨於穩定。在PICMUS實驗數據中，我們所提出的相位同調因子方法所估計的最佳成像聲速確實具有最佳的圖像品質。而在Prodigy成像系統實驗數據中，透過Tx-DMAS所估計的最佳成像聲速為1426±6 m/s，透過2D-DMAS以及Rx-DMAS所估計的最佳成像聲速皆為1428±4 m/s，與使用單一元件探頭通過脈衝回波法測得的實際組織聲速(1427 m/s)非常接近，也與具有最小-6-dB橫向寬度的成像聲速以及具有最佳對比度的成像聲速誤差在10 m/s內。
在本論文第二部分中，我們結合最小方差向量都卜勒(Least-Squares Vector Doppler, VD)以及一維斑點追蹤(Speckle Tracking, ST)進行二維血流流速估計，該血流流速估計方法能夠改善VD橫向分量估計結果不準確以及二維ST計算量過大的缺點，其中ST將於斑點顆粒特徵明顯的多角度平面波DMAS影像上進行血流流速估計。
模擬結果可以發現對影像進行一維斑點追蹤估計血流流速橫向分量時，多角度平面波DMAS相較於傳統CPWC(亦即2D-DAS)的血流流速估計表現而言並沒有太大的幫助，舉例而言，雖然Tx-DMAS成像雖然在訊雜比不小於-15 dB的情況下可有較低的血流估計偏誤與標準差，但其改善程度皆不到於最高流速的1 %。至於2D-DMAS以及Rx-DMAS甚至在訊雜比大於0 dB的情況下反而有較高的血流估計偏誤與標準差，此外當DMAS成像p值變大時估計結果會更差。通過對多角度平面波DMAS影像進行一維斑點追蹤的效果不佳，因為DMAS波束成形技術本身特性會產生乘性雜訊使得血流散射子在影像間相似降低，斑點追蹤演算法容易算出錯誤的結果反而降低血流流速估計的準確度。

Ultrasound multi-angle plane-wave (PW) delay-multiply-and-sum (DMAS) imaging uses the signal coherence among transmit events (Tx-DMAS), receive channels (Rx-DMAS) or both (2D-DMAS) to suppress low-coherence clutters. However, whether the beamforming velocity (Cbeam) correctly corresponds to the sound velocity of the propagating medium is still a basic requirement for maintaining image quality. Various methods have been proposed to estimate the average tissue speed of sound (SOS) of propagating medium by using the received channel signal or the image quality analysis, but none of them are developed for the characteristics of multi-angle PW imaging. Therefore, in the first part of this study, we further extend the multi-angle PW DMAS imaging to quantify the level of signal coherence for estimating the tissue SOS in multi-angle PW imaging. In addition, multi-angle PW DMAS images will have more obvious speckle characteristics due to the emphasis on signal coherence. Therefore, in the second part of this study, we will also discuss the feasibility of multi-angle PW images for speckle tracking to improve the estimation of flow velocity of blood.
In the first part of this paper, we defined the pixel value ratio between the obtained multi-angle PW DMAS image and the traditional coherent PW compounding (CPWC) image as the phase coherent factor (PCF). When the Cbeam mismatch the true SOS, the signal coherence of echo matrix decreases due to elevated focusing error and thus leads to reduced PCF value. After calculating the PCFs at various Cbeam, the Cbeam with the largest PCF value is the optimal beamforming velocity (Copt) which corresponds to the tissue SOS estimated in our method.
The results of the PICMUS simulation dataset indicates that, when the Rx aperture becomes larger and the channel signal-to-noise ratio (SNR) increases, the estimation of Copt will be more accurate. Among the three DMAS imaging methods, Tx-DMAS can use a smaller Rx aperture to provide a Copt estimation result with the smallest deviation and standard deviation, especially in the low channel SNR situation. In addition, the Copt estimation method proposed in this study will tend to stabilize when the p-value of DMAS imaging is not less than 2. In the PICMUS experimental dataset, the Copt estimated by our proposed method does have the best image quality. In the experimental dataset of Prodigy imaging system, the Copt estimated by Tx-DMAS is 1426±6 m/s, and the Copt estimated by Rx-DMAS and 2D-DMAS are 1426±6 m/s, all are very close to the actual tissue SOS (1427 m/s) measured by pulse-echo method using a single-element probe. The estimated Copt also correspond to the Cbeam with the minimal -6-dB lateral width (LW) and the maximal contrast (CR) within an error of 10 m/s.
In the second part of this paper, we combine the least-squares vector doppler (VD) and one-dimensional (1D) speckle tracking (ST) to estimate two-dimensional (2D) flow velocity of blood. This method can improve the disadvantages of inaccurate lateral component of estimation in VD method and lager computational complexity in 2D ST. And ST will perform on the multi-angle PW DMAS images which have obvious particle characteristics of speckle to estimate flow velocity of blood.
The simulation results indicate that when performing 1D ST on the image to estimate the lateral component of flow velocity of blood, the multi-angle PW DMAS imaging is not helpful compared to the traditional CPWC imaging (that is, 2D-DAS). For example, although Tx-DMAS imaging can have a lower flow estimation error and standard deviation when the flow channel SNR is not less than -15 dB, its improvement is less than 1% of the maximum flow velocity. As for 2D-DMAS and Rx-DMAS, even when the flow channel SNR is greater than 0 dB, they have higher flow estimation errors and standard deviations. In addition, the estimation results will be worse when the p-value of DMAS imaging becomes larger. The effect of performing 1D ST on multi-angle PW DMAS images is not good, because the characteristics of DMAS beamforming technique will produce multiplicative noises that reduce the similarity of blood flow scatterers between images. Thus, the ST algorithms tend to calculate wrong results and reduce the accuracy of the estimation of flow velocity of blood.

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