Sound waves change in frequency as a result of relative expansion between the transmitter and receiver. This frequency shift is called the Doppler effect, named after the Viennese mathematician Christian Doppler (1803 to 1852), and is proportion also the velocity between the transmitter and receiver. In addition, the frequency shift is influenced by the direction of motion: the frequency increases as the transmitter and receiver approach each other and decreases as they move apart.In diagnostic ultrasound, the Doppler effect is used to measure blood flow velocity. In this application, when the emitted ultrasound beam strikes moving blood cells, the latter reflect the pulse with a specific Doppler shift frequency that depends on the velocity and direction of blood flow. The shift is detected by the transducer. The direction of blood flow relative to the transducer determines whether the returning chose have a higher or lower frequency and flow velocity determines the magnitude of the frequency shift. On the other hand, the Doppler frequency shift is proportion also the carrier frequency.
Blood flow is fastest in the center of the vessel and decreases toward the wall. The drawing illustrates the effect of theangle of incidence on the Doppler measurement. In the equation for calculating the Doppler shift, this angle is represented by the cosine function. The Doppler shift increases with the acuity of the angle (cosine of 90° = 0). (T transmitter, R receiver, F0 emitted frequency,Fr reflected frequency)
Fd = F0 – Fr = 2F0 · · cosc
Fd Doppler frequency shift, F0 emitted frequency, Fr reflected frequency, mean flow velocity of the reflecting red blood cells,c speed of sound in soft tissue (about 1,540 m/s),angle between ultrasound beam and direction of blood flow.
In the trans cutaneous measurement of blood flow by Doppler ultrasound, angle correction is necessary to calculate the flow velocity since the axis of the ultrasound beam is not in line with the longitudinal axis of the vessel or the direction of flow.The transformation with representation of the different velocity vectors is expressed mathematically as a cosine function of the angle between the sound beam and the blood vessel(cos ).Fd is proportional to the velocity of blood flow, cos , and the carrier frequency of the ultrasound beam.For angles of about 90°, the cosine function yields values around 0, at which there is no Doppler frequency shift, and the Doppler shift increases as the angle decreases (with maximum cos of 1 at = 0°). The blood flow velocity is calculated by solving the Doppler shift equation for V:
V = (F – F0) · c cos · 2F0
This formula allows one to calculate the blood flow velocity from the Doppler frequency shift occurring at a given transmit frequency and angle of incidence. The accuracy of velocity measurements increases with the acuity of the angle. Ideally,a small angle should be used (less than 60°) since larger angles will result in unacceptably high errors in the velocity estimate. At angles above 60°, even minor errors in determining the Doppler angle (which are unavoidable in the clinical setting, especially when curved vessels are scanned)unduly distort the velocity calculation. At angles around 90°, a Doppler shift is no longer detectable and the flow direction cannot be determined. This is reflected in the color duplex scan by the absence of color-coded flow signals although flow is present.
Blood flow is fastest in the center of the vessel and decreases toward the wall. The drawing illustrates the effect of theangle of incidence on the Doppler measurement. In the equation for calculating the Doppler shift, this angle is represented by the cosine function. The Doppler shift increases with the acuity of the angle (cosine of 90° = 0). (T transmitter, R receiver, F0 emitted frequency,Fr reflected frequency)
Fd = F0 – Fr = 2F0 · · cosc
Fd Doppler frequency shift, F0 emitted frequency, Fr reflected frequency, mean flow velocity of the reflecting red blood cells,c speed of sound in soft tissue (about 1,540 m/s),angle between ultrasound beam and direction of blood flow.
In the trans cutaneous measurement of blood flow by Doppler ultrasound, angle correction is necessary to calculate the flow velocity since the axis of the ultrasound beam is not in line with the longitudinal axis of the vessel or the direction of flow.The transformation with representation of the different velocity vectors is expressed mathematically as a cosine function of the angle between the sound beam and the blood vessel(cos ).Fd is proportional to the velocity of blood flow, cos , and the carrier frequency of the ultrasound beam.For angles of about 90°, the cosine function yields values around 0, at which there is no Doppler frequency shift, and the Doppler shift increases as the angle decreases (with maximum cos of 1 at = 0°). The blood flow velocity is calculated by solving the Doppler shift equation for V:
V = (F – F0) · c cos · 2F0
This formula allows one to calculate the blood flow velocity from the Doppler frequency shift occurring at a given transmit frequency and angle of incidence. The accuracy of velocity measurements increases with the acuity of the angle. Ideally,a small angle should be used (less than 60°) since larger angles will result in unacceptably high errors in the velocity estimate. At angles above 60°, even minor errors in determining the Doppler angle (which are unavoidable in the clinical setting, especially when curved vessels are scanned)unduly distort the velocity calculation. At angles around 90°, a Doppler shift is no longer detectable and the flow direction cannot be determined. This is reflected in the color duplex scan by the absence of color-coded flow signals although flow is present.
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