Journal of Visualization

, Volume 9, Issue 1, pp 69–82 | Cite as

The flow velocity distribution from the doppler information on a plane in three-dimensional flow

  • Ohtsuki S. 
  • Tanaka M. 


In order to observe and estimate the flow of fluid in three-dimensional space, the pulsed Doppler method has been used widely. However, the velocity information acquired is only the velocity component in the beam direction of the wave even if an observation plane is formed by beam scanning. Accordingly, it is difficult to know the velocity distribution in the observation plane in tree-dimensional flow. In this paper, the new idea for processing the velocity distribution in the beam direction on an observation plane for transposing to flux distribution (flow function method) has been introduced. Further, the flow in an observation domain is divided into two kinds of flows, viz., the base flow which indicates the directivity of the flow in the observation domain and the vortex which is considered a two-dimensional flow. By applying the theory of a stream function to the two-dimensional flow, and by using the physical feature of a streamline to the base flow, the velocity component v which intersects perpendicularly to the beam direction is estimated. The flow velocity distribution in a scanning plane (observation plane) can be known from these two components of velocity, viz., beam direction componentu and perpendicular component to the beam directionv. The principle was explained by an example of the blood flow measurement in normal and abnormal heart chamber, by the ultrasonic Doppler method.


Pulsed Doppler technique Ultrasonic Doppler method Flow function C-mode flow Flow velocity distribution Stream function Streamline 


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  1. Namekawa, K., Kasai, C., Tsukamoto, M. and Koyano, A., Real time blood flow imaging system utilizing auto-correlation techniques, Ultrasound Med. Biol., Suppl., 2 (1983), 203.Google Scholar
  2. Ohtsuki, S., Okujima, M. and Tanaka, M., Blood flow mapping based on Doppler information. J. Ultrasound in Med. & Biol., (Abstr. of 31st AIUM Annual Conv.), 5 (1986), 86.Google Scholar
  3. Ohtsuki, S., Okujima, M. and Tanaka, M., A method of flow vector mapping deduced from Doppler information, J. Acoust. Soc. Jap., 43 (1987), 764–767 ( in Japanese).Google Scholar
  4. Ohtsuki, S.,Tanaka, M. and Okujima, M., The method for deducing the velocity distribution from two dimensional Doppler information. J. Flow Visual. Soc. Jap., 9 (1989), 269–272.Google Scholar
  5. Ohtsuki, S., Yamamoto, A., Tanaka, M. and Okujima, M., A method of flow vector mapping deduced Doppler data on sector scanned plane and its application, Automedica, 12 (1989), 41–52, Gordon Breach Science Pub. Inc., UK.Google Scholar
  6. Sasaki and Yoshi, K., Tornado and Hurricane — Need of accurate prediction and effective dissemination of information, J. Visual. Soc. Jap., 19 (1998), 187–192.Google Scholar
  7. Tanaka, M., Okujima, M., Ohtsuki, S., Terasawa, Y., Konno, K. and Ebina, T., Non-invasive measurement of the blood flow velocity and of velocity distribution in cardiac chambers and great vessels by a new Doppler flow meter system, White, D., & Brown, R. E., eds. Ultrasound in Medicine, 3B, (1977), 1263–1277, Engineering Aspect, Plenum Press, N.Y. & London.Google Scholar
  8. Tanaka, M., Yamamoto, A., Endo, M., Takahashi, K., Ohtsuki, S. and Okujima, M., Quantitative evaluation of flow character of the blood flow in heart chambers. J. Flow Visual. Soc. Jap., 9 (1989), 41–344.Google Scholar
  9. Tatehira, R., Visualization of meteorological phenomena by radar, J. Flow Visual. Soc. Jap., 7 (1987), 411–417.Google Scholar

Copyright information

© The Visualization Society of Japan 2006

Authors and Affiliations

  1. 1.Precision and Intelligence LaboratoryTokyo Institute of TechnologyYokohamaJapan
  2. 2.Cardiovascular CenterTohoku Employee’s Pension Welfare HospitalSendaiJapan

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