## Yi Zhang* , Jinkai Li* , Xin Liu* and Dong Chyuan Liu*## |

Flow (L/hr) | Measured flow (mL/s) | RMG | IWMF | MXF | |||
---|---|---|---|---|---|---|---|

Volume flow (mL/s) | Error (%) | Volume flow (mL/s) | Error (%) | Volume flow (mL/s) | Error (%) | ||

20 | 5.28 | 5.58 | 5.68 | 5.89 | 11.55 | 7.93 | 50.20 |

24 | 6.33 | 6.32 | 0.16 | 6.10 | 3.60 | 8.34 | 31.75 |

30 | 7.92 | 7.29 | 7.95 | 6.63 | 16.29 | 9.41 | 18.81 |

40 | 10.56 | 10.11 | 4.26 | 8.48 | 19.70 | 13.09 | 23.96 |

50 | 13.19 | 12.40 | 5.99 | 9.63 | 27.00 | 15.42 | 16.91 |

Mean error (%) | 4.81 | 15.65 | 28.33 |

Fig. 4 shows the experimental results of mean velocity estimation in the spectral profile images of six different SNR conditions. It is found that in the lower SNR spectral profile images, as shown in Fig. 4, the IWMV and MXV have larger errors. With the increase of noise, the mean velocity curves obtained by IWMV and MXV show serious jitter and it leads to inaccurate calculation of the mean velocity at the local details. Therefore, in the results from IWMV and MXV in Fig. 4, the mean velocity estimation is failing in the case of greater noise. In the same condition of low SNR, the proposed DIV algorithm works well.

where M is the actual number of estimated mean velocity points, N is the number of standard mean velocity points, is the scaling constant (usually 1/9), and d(i) is the distance between estimated mean velocity point and standard mean velocity.

Experiments on 10 sets of data are carried out to obtain the mean values and standard deviations of PFOM values under different noise conditions. We add the Gaussian white noise with a constant mean of 0 and variance of 0.01, 0.02, 0.03, 0.04, and 0.05, respectively, to each set of original data. Fig. 5 gives the results of PFOM mean for the three algorithms. The PFOM mean of DIV is significantly higher than the IWMV and MXV. The PFOM mean of DIV is closer to 1 and it shows that the mean velocity curve obtained by DIV is closer to the ideal curve drawn by the experienced clinician. Moreover, the line chart shows that the PFOM mean of the algorithm DIV is more stable and its jitter is smaller in the case of different noises.

Fairly low standard deviations of DIV algorithm in different noise conditions are found in Table 2. Less than 6% mean standard deviation by using DIV algorithm to estimate mean velocity is observed. Therefore, it is steady when Gaussian white noise is added with mean of 0 and variance range of 0.1–0.5, which indicates that the mean velocity estimated by DIV has very low sensitivity to SNR. Mean velocity estimated using DIV in vivo data can be observed to show better performance compared with IWMV and MXV at the same SNR level. These results point toward robust mean velocity estimation of DIV algorithm with low sensitivity to SNR. When the noise level is very high, the algorithm MXV fails completely and the PFOM mean of each set of data is very small, as shown in Fig. 5, so the standard deviation is very small. Therefore, there will be such a case that the standard deviation is small in Table 2.

In this paper a robust ultrasound blood volume flow estimation algorithm based on multigate (RMG) and an accurate double iterative algorithm for estimating the mean velocity (DIV) have been presented. Based on the multigate method, the velocity and volume flow of each sub sampling gate can be estimated, which provides clinicians with detail information on the local velocity distribution. Experiments to test the performance of the DIV algorithm were done for different SNR levels. Low errors in mean velocity estimation are observed. Mean standard deviation of the mean velocity estimation is 5.34% and is significantly low. The stability in PFOM calculation for different SNR levels suggest that the DIV algorithm is robust and with low sensitivity to SNR. The RMG algorithm is tested in a custom-designed experimental setup, Doppler phantom and imitation blood flow control system. Less than 5% mean error suggests that the RMG algorithm provides better performance compared with the existing volume flow estimation algorithms. Estimation of accurate blood volume flow in ultrasound Doppler blood flow spectrograms is of important guiding significance for monitoring cardiovascular diseases. Therefore, the stability and robustness of the proposed algorithm shows that it can be widely applied to real-time blood volume flow estimation in clinical practice, which can be useful in monitoring cardiovascular diseases. In summary, we are optimistic about the potential of this new approach to blood volume flow estimation for use in future medical instruments.

She received B.S. degree in College of Software Engineering from Sichuan University, Chengdu, China in 2017. Since September 2017, she is with the College of Computer Science from Sichuan University as a MS candidate. Her current research interests include medical image analysis and ultrasonic image processing.

He received B.S. and M.S. degrees in College of Software Engineering and College of Computer Science from Sichuan University in 2013 and 2016, respectively. He is now an engineer whose research interests include digital image processing and medical imaging in a company, Stork Healthcare Co., Ltd, Hi-Tech Zone, Chengdu, Sichuan, China. His research interests include digital image processing and medical imaging.

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