The theory of correlation functions and power spectra of doppler response signals in ultrasonic medical applications
Keywords:
Doppler ultrasound, Doppler spectrum, Doppler blood flow, power Doppler ultrasound, vibroelastography, spectral width, spectral broadening, pulsatile flow, tissue motion
Abstract
Based upon the continuum model of scattering irregularities we have derived both a set of expressions for
the correlation functions and the spectra of Doppler response of soft tissues and blood flow-lines with an
allowance for different physical factors. The influence of the irregularity correlation radius magnitude and
the diffusion processes upon the spectra formed by stationary flows has been theoretically examined for
the Doppler technique for studying blood steams, which is widely used in cardiology. An increase in the
irregularity correlation radius and the accounting of their diffusion bring about an additional broadening
of the Doppler spectrum. The case of the non-stationary blood flow typical for the systolic cardiac phase
cycle has been examined and the condition for generating Doppler spectra are ascertained. We have
obtained analytical expressions for correlation functions and Doppler spectra for vibroelastography
technique to be used for diagnosing malignant tumors in soft tissues. In terms of the distinctive features of
the Doppler spectra thus obtained we have shown that it is possible to differentiate among the soft tissues
according to the magnitude of forced oscillations. The results obtained leads us to conclude that different
physical processes and characteristics of biological tissues affect the Doppler spectra and in this way are
indicative of improving the effectiveness of medical investigations.
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References
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31. А.Г.Свешников, А.Н.Тихонов. Теория функций комплексной переменной. – М.: Наука, 1967. – 304 с.
32. A. Erdelyi. Asymptotic Expansions. – New York: Dover Publications, 1956. – P. 39.
33. Justin J., Kitamura H. and Sigel B. Roles of hematocrit and fibrinogen in red cell aggregation determined by ultrasonic scattering properties // Ultrasound Med. & Biol. – 1995. – V. 21, N. 6. – P. 827-832.
34. Fontaine I., Bertrand M., and Cloutier G. A system-based approach to modeling the ultrasound signal backscattered by red blood cells // Biophysical Journal. – 1999. – V. 77. – P. 2387-2399.
35. Shung K.K., Cloutier G. and Lim C.C. The effect of hematocrit, shear rate, and turbulence on ultrasonic Doppler spectrum from blood // IEEE transactions in biomedical engineering. – 1992. – V. 39, N. 5. – P. 462-469.
36. W.S. Furneaux. Human Physiology. – New Delhi: B. Jain Publishers, 2004. – P. 119.
37. Meiselman H.J., Neu B., Rampling M.W. and Baskurt O.K. RBC aggregation: laboratory data and models // Indian Journal of Experimental Biology. – 2007, – V. 45. – P. 9-17.
38. J.-F. Stoltz, M. Singh, P. Riha. Hematorheology in practice. – Amsterdam: IOS Press, 1999. – 128 p.
39. Wu S.J., Shung K.K. and Brasseur J.G. In situ measurement of Doppler power vs. flow turbulence intensity in red cell suspensions // Ultrasound Med. Biol. – 1998. – V. 24. – P. 1009-1021.
40. Bascom J., Cobbold R.C., Routh H.F. and Johnston K.W. On the Doppler signal from steady flow asymmetrical stenosis model: effects of turbulence // Ultrasound Med. Biol. – 1993. – V. 19, N. 3. – P. 197-210.
41. Lifang Wang, Yufeng Zhang, Dingkang Wang, Nafeng Su, Chengyan Du. Simulation Model for Doppler Ultrasound Signals from Pulsatile Blood Flow in Stenosed Vessels // International Conference on BioMedical Engineering and Informatics, 2008. – V. 2. – P. 339-343.
42. Cloutier G., Allard L. and Durand L.G. Change in ultrasonic Doppler Backscattered Power downstream of concentric and eccentric stenosed under pulsatile flow // Ultrasound Med. Biol. – 1996. – V. 21. – P. 59-70.
43. Л.Д. Ландау, Е.М.Лифшиц. Гидродинамика. – М.: Наука, 1986. – 736с.
44. Foster F.K., Garbini J.L. and Jorgensen J.E. Hemodynamic turbulence measurements using ultrasound techniques // Proceedings of the 4th Annual New England Bioengineering Conference. – New Haven, May 7-8 1976, ed S Saha Pergamon Press, 1976, pp. 253-256.
2. J.C. Bamber, M. Tristam. Diagnostic Ultrasound // In Webb S. The Physics of Medical Imaging. – Bristol and Philadelphia: Adam Hilger, 1988. – P. 319-388.
3. Hoskins P.R. and McDicken W.N. Colour ultrasound imaging of blood flow and tissue motion // The British journal of radiology. – 1997. – V. 70. – P. 878-890.
4. Pulkovski N., Schenk P., Maffiuletti N.A. and Mannion A.F. Tissue Doppler imaging for detecting onset of muscle activity // Muscle Nerve. – 2008. – V. 37. – P. 638-649.
5. Wells P.N.T. Ultrasonic colour flow imaging // Phys. Med. Biol. – 1994. – V. 39. – P. 2113-2145.
6. Wells P.N.T. Doppler study of the vascular system (review) // European Journal of Ultrasound. – 1998. – V. 7, N. 1. – P. 3-8.
7. Gao L., Alam S.K., Lerner R.M. and Parker K.J. Sonoelasticity imaging: theory and experimental verification // J.Acoust. Soc. Am. – 1995. – V. 97. – P. 3875-3886.
8. Gao L., Parker K.J., Lerner R.M. and Levinson S.F. Imaging of the elastic properties of tissue – a review // Ultrasound Med. Biol. – 1996. – V.22. – P. 959-977.
9. Ophir J., Alam S.K., Garra B.S., Kallel F., Konofagou E., Krouscop T.A., Merritt C.R.B., Righetti R., Souchon R., Srinivasan S. and Varghese T. Elastography: imaging the elastic properties of soft tissues with ultrasound (review article) // J. Med. Ultrasonics. – 2003. – V. 29. – P. 155-171.
10. Barannik E.A. Influence of diffraction divergence and beam width on the Doppler signal spectrum // Sov. Phys. Acoust. – 1992. – V. 38, N 2. – P.127-131.
11. Barannik E. A. The Doppler signal spectrum bandwidth at pulse radiation mode // Acoustical Physics. – 1993. – V. 39, N 5.– P.496-498.
12. Barannik E. A. The effect of ultrasound wave focusing on the mean-square width of the Doppler spectrum // Acoustical Physics. – 1994. – V. 40, N 2. – P.188-190.
13. Barannik E. A. Optimum resolution of pulsed Doppler systems // Acoustical Physics. – 1997. – V. 43, N 4. – P.453-457.
14. Barannik E.A. Pulsed Doppler flow-line spectrum for focused transducers with apodized apertures // Ultrasonics. – 2001. – V. 39, N 2. – P.311-317.
15. Bastos C.A.C., Fish P.J., Steel R. and Vaz F. Doppler power spectrum from a Gaussian sample volume // Ultrasonics. – 2000. – V. 37, N. 4. – P. 623-632.
16. Tompson R.S. and Aldis G.K. Flow spectra from power density calculations for pulsed Doppler // Ultrasonics. – 2002. – V. 40, N. 1-8. – P. 835-841.
17. Censor D. et al Theory of ultrasound Doppler spectra velocimetry for arbitrary beam and flow configurations // IEEE Trans. on Biomed. Eng. – 1988. – V. 35, N. 9. – P. 740-751.
18. Guidi G., Newhouse V.L. and Tortoli P. Doppler spectrum shape analysis based on the summation of flow-line spectra // IEEE Trans. Ultrason. Ferroelec. Freq. Contr. – 1995. – V. 42, N. 5. – P. 907-915.
19. Newhouse V. L. and Reid J. Invariance of the Doppler bandwidth with flow displacement in the illuminating field // J. Acoust. Soc. Amer. – 1991. – V. 90, N. 5. – P. 2595-2601.
20. E.O. Attinger. Pulsatile Blood Flow. – New York: McGraw-Hill Book Company, 1964. – P. 30-32, 433-439.
21. Wu S.J. and Shung K.K. Cyclic Variation of Doppler Power from whole blood under pulsatile flow // Ultrasound Med. Biol. – 1996. – V. 22, N. 7 – P. 883-894.
22. Bamber J.C., Barbone P.E., Bush N.L., Cosgrove D.O., Doyley M.M., Fuechsel F.G., Meaney P.M., Miller N.R., Shiina T. and Tranquant F. Progress in freehand Elastography of the breast // IEICE Trans on Information and Systems. – V. 85-D(1). – 2002. – P. 5-14.
23. Parker J.K., Huang S.R., Musulin R.A., and Lerner R.M. Tissue response to mechanical vibrations for "sonoelasticity imaging" // Ultrasound Med. Biol. – 1990. – V. 16, N. 3. – P. 241-246.
24. Krouskop Т.А., Dougherty D.R. and Levinson S.F. A pulsed Doppler ultrasonic system for making noninvasive measurements of the mechanical properties of soft tissues // J. Rehabil. Res. and Dev. – 1987. – V. 24, N. 2. – P. 1-8.
25. Huang S.R., Lerner R.M., Parker K.J. On estimating the amplitude of harmonic vibration from the Doppler spectrum of reflected signals // J. Acoust. Soc. Am. – 1990. – V. 88, N. 6. – P. 2702-2712.
26. Huang S.R., Lerner R.M., and Parker K.J. Time domain Doppler estimators of the amplitude of vibrating targets // J. Acoust. Soc. Am. – 1992. – V. 91, N. 2. – P. 965-974.
27. Л.Д. Ландау, Е.М. Лифшиц. Электродинамика сплошных сред. – М.: Наука, 1982. – 621с.
28. Hill C.R. and Bamber J.C. Methology for Clinical Investigation // In C.R. Hill et al. Physical principles of medical ultrasonic (2nd edition). – Hoboken: John Wiley & Sons, 2004. – P. 303-335.
29. Sarvazyan A.P., Rudenko O.V., Swanson S.D., Fowlkes J.B., and Emelianov S.Y. Shear wave elasticity imaging: a new ultrasonic technology of medical diagnostics // Ultrasound Med. Biol. – 1998. – V. 24. – P. 1419-1435.
30. D. Brandwood. Fourier Transforms in Radar and Signal Processing. – Boston, London: Artech House, 2003. – P. 26.
31. А.Г.Свешников, А.Н.Тихонов. Теория функций комплексной переменной. – М.: Наука, 1967. – 304 с.
32. A. Erdelyi. Asymptotic Expansions. – New York: Dover Publications, 1956. – P. 39.
33. Justin J., Kitamura H. and Sigel B. Roles of hematocrit and fibrinogen in red cell aggregation determined by ultrasonic scattering properties // Ultrasound Med. & Biol. – 1995. – V. 21, N. 6. – P. 827-832.
34. Fontaine I., Bertrand M., and Cloutier G. A system-based approach to modeling the ultrasound signal backscattered by red blood cells // Biophysical Journal. – 1999. – V. 77. – P. 2387-2399.
35. Shung K.K., Cloutier G. and Lim C.C. The effect of hematocrit, shear rate, and turbulence on ultrasonic Doppler spectrum from blood // IEEE transactions in biomedical engineering. – 1992. – V. 39, N. 5. – P. 462-469.
36. W.S. Furneaux. Human Physiology. – New Delhi: B. Jain Publishers, 2004. – P. 119.
37. Meiselman H.J., Neu B., Rampling M.W. and Baskurt O.K. RBC aggregation: laboratory data and models // Indian Journal of Experimental Biology. – 2007, – V. 45. – P. 9-17.
38. J.-F. Stoltz, M. Singh, P. Riha. Hematorheology in practice. – Amsterdam: IOS Press, 1999. – 128 p.
39. Wu S.J., Shung K.K. and Brasseur J.G. In situ measurement of Doppler power vs. flow turbulence intensity in red cell suspensions // Ultrasound Med. Biol. – 1998. – V. 24. – P. 1009-1021.
40. Bascom J., Cobbold R.C., Routh H.F. and Johnston K.W. On the Doppler signal from steady flow asymmetrical stenosis model: effects of turbulence // Ultrasound Med. Biol. – 1993. – V. 19, N. 3. – P. 197-210.
41. Lifang Wang, Yufeng Zhang, Dingkang Wang, Nafeng Su, Chengyan Du. Simulation Model for Doppler Ultrasound Signals from Pulsatile Blood Flow in Stenosed Vessels // International Conference on BioMedical Engineering and Informatics, 2008. – V. 2. – P. 339-343.
42. Cloutier G., Allard L. and Durand L.G. Change in ultrasonic Doppler Backscattered Power downstream of concentric and eccentric stenosed under pulsatile flow // Ultrasound Med. Biol. – 1996. – V. 21. – P. 59-70.
43. Л.Д. Ландау, Е.М.Лифшиц. Гидродинамика. – М.: Наука, 1986. – 736с.
44. Foster F.K., Garbini J.L. and Jorgensen J.E. Hemodynamic turbulence measurements using ultrasound techniques // Proceedings of the 4th Annual New England Bioengineering Conference. – New Haven, May 7-8 1976, ed S Saha Pergamon Press, 1976, pp. 253-256.
Cited
How to Cite
Skresanova, I. V., & Barannik, E. A. (1). The theory of correlation functions and power spectra of doppler response signals in ultrasonic medical applications. Biophysical Bulletin, 2(25). Retrieved from https://periodicals.karazin.ua/biophysvisnyk/article/view/2769
Section
Medical physics
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