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Reconstructive interpolation for pulse wave estimation to improve local PWV measurement of carotid artery

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Abstract

Ultrasonic transit time (TT)-based local pulse wave velocity (PWV) measurement is defined as the distance between two beam positions on a segment of common carotid artery (CCA) divided by the TT in the pulse wave propagation. However, the arterial wall motions (AWMs) estimated from ultrasonic radio frequency (RF) signals with a limited number of frames using the motion tracking are typically discrete. In this work, we develop a method involving motion tracking combined with reconstructive interpolation (MTRI) to reduce the quantification errors in the estimated PWs, and thereby improve the accuracy of the TT-based local PWV measurement for CCA. For each beam position, normalized cross-correlation functions (NCCFs) between the reference (the first frame) and comparison (the remaining frames) RF signals are calculated. Thereafter, the reconstructive interpolation is performed in the neighborhood of the NCCFs’ peak to identify the interpolation-deduced peak locations, which are more exact than the original ones. According to which, the improved AWMs are obtained to calculate their TT along a segment of the CCA. Finally, the local PWV is measured by applying a linear regression fit to the time-distance result. In ultrasound simulations based on the pulse wave propagation models of young, middle-aged, and elderly groups, the MTRI method with different numbers of interpolated samples was used to estimate AWMs and local PWVs. Normalized root mean squared errors (NRMSEs) between the estimated and preset values of the AWMs and local PWVs were calculated and compared with ones without interpolation. The means of the NRMSEs for the AWMs and local PWVs based on the MTRI method with one interpolated sample decrease from 1.14% to 0.60% and 7.48% to 4.61%, respectively. Moreover, Bland-Altman analysis and coefficient of variation were used to validate the performance of the MTRI method based on the measured local PWVs of 30 healthy subjects. In conclusion, the reconstructive interpolation for the pulse wave estimation improves the accuracy and repeatability of the carotid local PWV measurement.

Graphical abstract

Ultrasonic transit time-based local pulse wave velocity (PWV) measurement is defined as the distance between two beam positions on a segment of common carotid artery (CCA) divided by the transit time of the pulse wave (PW). However, PWs estimated from ultrasonic radio frequency (RF) signals with a limited number of frames using the motion tracking are typically discontinuous. In this work, a method that involves motion tracking combined with reconstructive interpolation (MTRI) is proposed for PW estimation to improve local PWV measurement. For each beam position, normalized cross-correlation functions (NCCFs) between the reference (the first frame) and comparison (the remaining frames) RF signals are calculated. Thereafter, the reconstructive interpolation is performed in the neighborhood of the NCCFs’ peak to identify the interpolation-deduced peak locations, which are more exact than the original ones. According to which, the improved PWs are obtained to calculate their transit time along a segment of the CCA. Finally, the local PWV is measured by applying a linear regression fit to the time-distance result. In ultrasound simulations based on the PW propagation models of young, middle-aged, and elderly groups, the MTRI method with different numbers of interpolated samples was used to estimate PWs and local PWVs. Normalized root mean squared errors (NRMSEs) between the estimated and preset values of the PWs and local PWVs were calculated and compared with ones without interpolation. The means of the NRMSEs for the PWs and local PWVs based on the MTRI method with one interpolated sample decrease from 1.14% to 0.60% and 7.48% to 4.61%, respectively. Moreover, Bland-Altman analysis and coefficient of variation were used to validate the performance of the MTRI method based on the measured local PWVs of 30 healthy subjects. In conclusion, the MTRI method can improve the PW estimation and thus afford more accurate local PWV measurement.

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Abbreviations

AWM:

Arterial wall motion

CCA:

Common carotid artery

MTRI:

Motion tracking combined with reconstructive interpolation

MTWI:

Motion tracking without interpolation

NCCF:

Normalized cross-correlation function

NRMSE:

Normalized root mean squared error

PWV:

Pulse wave velocity

RF:

Radio frequency

TD:

Time delay

TFP:

Time fiduciary point

TT:

Transit time

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Acknowledgements

The work was supported by the National Natural Science Foundations of China (No. 62201495 and No.62261057) and the Guizhou Provincial Science and Technology Projects(Grant No. Qianke He Foundation-ZK [2021] General 300).

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Authors and Affiliations

  1. Department of Electronic Engineering, Information School, Yunnan University, Kunming, 650091, Yunnan, China

    Ouyang Gu, Bingbing He, Li Xiong, Yufeng Zhang & Xun Lang

  2. Department of Ultrasound, the Third Affiliated Hospital of Kunming Medical College, Kunming, 650118, China

    Zhiyao Li

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  1. Ouyang Gu
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Correspondence to Bingbing He.

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Gu, O., He, B., Xiong, L. et al. Reconstructive interpolation for pulse wave estimation to improve local PWV measurement of carotid artery. Med Biol Eng Comput 62, 1459–1473 (2024). https://doi.org/10.1007/s11517-023-03008-5

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