### Abstract

Original language | English |
---|---|

Journal | I E E E Transactions on Ultrasonics, Ferroelectrics and Frequency Control |

Volume | 51 |

Issue number | 1 |

Pages (from-to) | 80-92 |

ISSN | 0885-3010 |

DOIs | |

Publication status | Published - 2004 |

### Bibliographical note

Copyright: 2004 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE### Cite this

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*I E E E Transactions on Ultrasonics, Ferroelectrics and Frequency Control*, vol. 51, no. 1, pp. 80-92. https://doi.org/10.1109/TUFFC.2004.1268470

**Maximum Likelihood Blood Velocity Estimator Incorporating Properties of Flow Physics.** / Schlaikjer, Malene; Jensen, Jørgen Arendt.

Research output: Contribution to journal › Journal article › Research › peer-review

TY - JOUR

T1 - Maximum Likelihood Blood Velocity Estimator Incorporating Properties of Flow Physics

AU - Schlaikjer, Malene

AU - Jensen, Jørgen Arendt

N1 - Copyright: 2004 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE

PY - 2004

Y1 - 2004

N2 - The aspect of correlation among the blood velocities in time and space has not received much attention in previous blood velocity estimators. The theory of fluid mechanics predicts this property of the blood flow. Additionally, most estimators based on a cross-correlation analysis are limited on the maximum velocity detectable. This is due to the occurrence of multiple peaks in the cross-correlation function. In this study a new estimator (CMLE), which is based on correlation (C) properties inherited from fluid flow and maximum likelihood estimation (MLE), is derived and evaluated an a set of simulated and in vivo data from the carotid artery. The estimator is meant for two-dimensional (2-D) color flow imaging. The resulting mathematical relation for the estimator consists of two terms. The first term performs a cross-correlation analysis on the signal segment in the radio frequency (RF)-data under investigation. The flow physic properties are exploited in the second term, as the range of velocity values investigated in the cross-correlation analysis are compared to the velocity estimates in the temporal and spatial neighborhood of the signal segment under investigation. The new estimator has been compared to the cross-correlation (CC) estimator and the previously developed maximum likelihood estimator (MLE). The results show that the CMLE can handle a larger velocity search range and is capable of estimating even low velocity levels from tissue motion. The CC and the MLE produce incorrect velocity estimates due to the multiple peaks, when the velocity search range is increased above the maximum detectable velocity. The root-mean square error (RMS) on the velocity estimates for the simulated data is on the order of 7 cm/s (14%) for the CMLE, and it is comparable to the RMS for the CC and the MLE. When the velocity search range is set to twice the limit of the CC and the MLE, the number of incorrect velocity estimates are 0, 19.1, and 7.2% for the CMLE, CC, and MLE, respectively. The ability to handle a larger search range and estimating low velocity levels was confirmed on in vivo data.

AB - The aspect of correlation among the blood velocities in time and space has not received much attention in previous blood velocity estimators. The theory of fluid mechanics predicts this property of the blood flow. Additionally, most estimators based on a cross-correlation analysis are limited on the maximum velocity detectable. This is due to the occurrence of multiple peaks in the cross-correlation function. In this study a new estimator (CMLE), which is based on correlation (C) properties inherited from fluid flow and maximum likelihood estimation (MLE), is derived and evaluated an a set of simulated and in vivo data from the carotid artery. The estimator is meant for two-dimensional (2-D) color flow imaging. The resulting mathematical relation for the estimator consists of two terms. The first term performs a cross-correlation analysis on the signal segment in the radio frequency (RF)-data under investigation. The flow physic properties are exploited in the second term, as the range of velocity values investigated in the cross-correlation analysis are compared to the velocity estimates in the temporal and spatial neighborhood of the signal segment under investigation. The new estimator has been compared to the cross-correlation (CC) estimator and the previously developed maximum likelihood estimator (MLE). The results show that the CMLE can handle a larger velocity search range and is capable of estimating even low velocity levels from tissue motion. The CC and the MLE produce incorrect velocity estimates due to the multiple peaks, when the velocity search range is increased above the maximum detectable velocity. The root-mean square error (RMS) on the velocity estimates for the simulated data is on the order of 7 cm/s (14%) for the CMLE, and it is comparable to the RMS for the CC and the MLE. When the velocity search range is set to twice the limit of the CC and the MLE, the number of incorrect velocity estimates are 0, 19.1, and 7.2% for the CMLE, CC, and MLE, respectively. The ability to handle a larger search range and estimating low velocity levels was confirmed on in vivo data.

U2 - 10.1109/TUFFC.2004.1268470

DO - 10.1109/TUFFC.2004.1268470

M3 - Journal article

VL - 51

SP - 80

EP - 92

JO - I E E E Transactions on Ultrasonics, Ferroelectrics and Frequency Control

JF - I E E E Transactions on Ultrasonics, Ferroelectrics and Frequency Control

SN - 0885-3010

IS - 1

ER -