Study of Fourier-Based Velocimetry

Jean Martial Mari

Imperial College London, South Kensington Campus, London, UK.

DOI: 10.4236/oja.2013.33A005                

Abstract

Standard phase-domain pulsed Doppler techniques used in Colour Flow Mapping such as spectral Doppler or autocorrelation are monochromatic, focused on the analysis of the centre transmit frequency. As such all the algorithms using those approaches are limited: in terms of spatial Doppler resolution because of the long pulses typically used for transmission, in terms of frame rate because of the necessity to perform many Doppler lines repetitions and additional B-mode imaging transmissions, and in terms of accuracy which depends on the stability of the Doppler signal at the frequency considered. A velocimetry technique is presented which estimates the shifts between successive Doppler line segments using the phase information provided by the Fourier transform. Such an approach allows extraction of more information from the backscattered signal through the averaging of results from multiple frequencies inside the bandwidth, as well as the transmission of wide band-high resolution-pulses. The technique is tested on Doppler signals acquired with a research scanner in a straight latex pipe perfused with water and cellulose scatterers, and on an ultrasound contrast agent solution. The results are compared with the velocity estimates provided by standard spectral Doppler and autocorrelation methods. Results show that the proposed technique performs better than both other approaches, especially when few Doppler lines are processed. The technique is also shown to be compatible with contrast Doppler imaging. The proposed approach enables high frame rate, high resolution Doppler.

Keywords

Doppler; Fourier; Ultrasonic Imaging; Wideband; High Speed

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	C. G. Caro, J. M. Fitzgerald and R. C. Schroter, “Atheroma and Arterial Wall Shear—Observation, Correlation and Proposal of A Shear Dependent Mass Transfer Mechanism for Altherogenesis,” Proceedings of the Royal Society, Vol. 177, No. 1046, 1971, pp. 109-133
[2]	T. Yamamoto, Y. Ogasawara, A. Kimura, et al., “Blood Velocity Profiles in the Human Renal Artery by Doppler Ultrasound and Their Relationship to Atherosclerosis. Arteriosclerosis,” Thrombosis & Vascular Biology, Vol. 16, No. 1, 1996, pp. 172-177. doi:10.1161/01.ATV.16.1.172
[3]	K. Ferrara and G. DeAngelis, “Color Flow Mapping,” Ultrasound in Medicine and Biology, Vol. 23, No. 3, 1997, pp. 321-345. doi:10.1016/S0301-5629(96)00216-5
[4]	S. K. Alam and K. J. Parker, “Implementation Issues in Ultrasonic Flow Imaging,” Ultrasound in Medicine & Biology, Vol. 29, No. 4, 2003, pp. 517-528. doi:10.1016/S0301-5629(02)00704-4
[5]	J. A. Jensen, “Algorithms for estimating velocities using ultrasound,” Ultrasonics, Vol. 38, No. 1-8, 2000, pp. 358-362. doi:10.1016/S0041-624X(99)00127-4
[6]	P. Atkinson and J. P. Woodcock, “Doppler Ultrasound and Its Use in Clinical Measurement,” Academic Press Inc., London, 1982.
[7]	C. Kasai, K. Namekawa, A. Koyano and R. Omoto, “Real-Time Two-Dimensional Blood Flow Imaging Using an Autocorrelation Technique,” IEEE Transactions on Sonics and Ultrasonics, Vol. 32, No.3, 1985, pp. 458- 464.
[8]	L. N. Bohs, B. J. Geiman, M. E. Anderson, S. C. Gebhart and G. E. Trahey, “Speckle Tracking for Multidimensional Flow Estimation”, Ultrasonics, Vol. 38, No. 1-8, 2000, pp. 369-375. doi:10.1016/S0041-624X(99)00182-1
[9]	L. S. Wilson, “Description of broad-band pulsed Doppler ultrasound processing using the two-dimensional Fourier transform,” Ultrasonic Imaging, Vol. 13, No. 4, 1991, pp. 301-315.
[10]	J. A. Jensen, “Implementation of Ultrasound Time Domain Cross-Correlation Blood Velocity Estimators,” IEEE Transactions on Biomedical Engineering, Vol. 40, No. 5, 1993, pp. 468-474.
[11]	P. M. Embree and W. D. O’Brien, “The Accurate Ultrasonic Measurement of the Volume Flow of Blood by Time Domain Correlation,” Proceedings Ultrasonics Symposium, San Francisco, 16-18 October 1985, pp. 963-966.
[12]	P. J. Brands, A. P. G. Hoeks, L. A. F. Ledoux, R. S. Reneman, “A Radio Frequency Domain Complex Cross- Correlation Model to Estimate Blood Flow Velocity and Tissue Motion by Means of Ultrasound,” Ultrasound in Medicine & Biology, Vol. 23, No. 6, 1997, pp. 911-920. doi:10.1016/S0301-5629(97)00021-5
[13]	R. Cobbold, “Foundations of Biomedical ultrasound,” Oxford University Press, Oxford, 2007.
[14]	R. Eriksson, H. W. Persson, S. O. Dymling and K. Lindstrom, “Blood Perfusion Measurement with Multifrequency Doppler Ultrasound,” Ultrasound in Medicine & Biology, Vol. 21, No. 1, 1995, pp. 49-57. doi:10.1016/0301-5629(94)00087-5
[15]	J. M. Mari, O. BouMatar, T. Blu, M. Unser and C. Cachard, “A bulk modulus dependent linear model for acoustical imaging,” Journal of the Acoustical Society of America, Vol. 125, No. 4, 2009, pp. 2413-2419. doi:10.1121/1.3087427
[16]	E. Brigham, “The Fast Fourier Transform and Its Applications,” Prentice Hall, Englewood Cliffs, 1988.
[17]	D. W. Rickey, P. A. Picot, D. A. Christopher and A. Fenster, “A Wall-Less Vessel Phantom for Doppler Ultra- sound Studies,” Ultrasound in Medicine & Biology, Vol. 21, No. 9. 1995, p. 176. doi:10.1016/0301-5629(95)00044-5
[18]	A. D. A. Christopher, P. N. Burns, J. Armstrong and F. Stuart Foster, “A High-Frequency Continuous-Wave Doppler Ultrasound System for the Detection of Blood Flow in the Microcirculation,” Ultrasound in Medicine & Biology, Vol. 22, No. 9, 1996, pp.1191-1203. doi:10.1016/S0301-5629(96)00153-6
[19]	J. Tu, J. Guan, Y. Qiu and T. Matula, “Estimating the Shell Parameters of SonoVue Microbubbles Using Light Scattering,” Journal of the Acoustical Society of America, Vol. 126, No. 6, pp. 2954-2962. doi:10.1121/1.3242346??
[20]	C. J. Harvey, J. M. Pilcher, R. J. Eckersley, M. J. Blomley and D. O. Cosgrove, “Advances in Ultrasound,” Clinical Radiology, Vol. 57, No. 3, 2002, pp. 157-177.
[21]	Loupas, et al., “An Axial Velocity Estimator for Ultrasound Blood Flow Imaging,” IEEE TUFFC, Vol. 42, No. 4, 1995, pp. 911-920.
[22]	K. W. Ferrara, V. R. Algazi and J. Liu, “The Effect of Frequency Dependent Scattering and Attenuation on the Estimation of Blood Velocity Using Ultrasound,” IEEE TUFFC, Vol. 39, No. 6, 1992, pp. 754-767. doi:10.1109/58.165561