Physical principles of Doppler ultrasound

Chapter 11 Physical principles of Doppler ultrasound






THE DOPPLER PRINCIPLE


The Doppler principle is named after the mathematician and physicist Christian Johann Doppler who first described this effect in 1842 by studying light from stars. He demonstrated that the colored appearance of moving stars was caused by their motion relative to the earth. This relative motion resulted in either a red shift or blue shift in the light’s frequency. This shift in observed frequencies of waves from moving sources is known as the Doppler effect and applies to sound waves as well as light waves.




THE DOPPLER EFFECT APPLIED TO DIAGNOSTIC ULTRASOUND


The Doppler effect in diagnostic imaging can be used to study blood flow, for example, and provides the operator with three pieces of information to determine:





The transducer acts as both a transmitter and receiver of Doppler ultrasound. When using Doppler to investigate blood flow in the body, the returning backscattered echoes from blood are detected by the transducer. These backscattered signals (Fr) are then processed by the machine to detect any frequency shifts by comparing these signals to the transmitted Doppler signals (Ft). The frequency shift detected will depend on two factors, namely the magnitude and direction of blood flow (see Fig. 11.2).



Let us consider a simple arrangement as seen in Figure 11.3. The transducer transmits a Doppler signal with frequency Ft. The transmitted Doppler signal interrogates a blood vessel and the transducer receives the backscattered signals from the red blood cells within the vessel at a frequency Fr. The Doppler frequency shift (Fd) can be calculated by subtracting the transmitted signal Ft from the received signal Fr.



Blood flow moving towards the transducer produces positive Doppler shifted signals and conversely blood flow moving away from the transducer produces negative Doppler shifted signals. Figure 11.3 illustrates the change in the received backscattered signals and the resulting Doppler shifts for blood moving towards and away from the transducer.


In Figure 11.3a the relative direction of the blood flow with respect to the Doppler beam is towards the transducer. In this arrangement blood flow moving towards the transducer produces received signals (Fr) which have a higher frequency than the transmitted beam (Ft). The Doppler shifted signal (Fd) can be calculated by subtracting Ft from Fr and produces a positive Doppler shifted signal.


Conversely, Figure 11.3b illustrates blood flow which is moving away from the Doppler beam and the transducer. In this arrangement blood flow moving away from the transducer produces received signals (Fr) which have a lower frequency than the transmitted beam (Ft). This time the Doppler shifted frequencies (Fr − Ft) produces a negative Doppler shifted signal.


When there is no flow or movement detected then the transmitted frequency (Ft) is equal to the received frequency (Fr). Therefore Fr = Ft and Fd = Fr − Ft = 0, resulting in no Doppler shifted signals.


It is important to appreciate that the amplitude of the backscattered echoes from blood is much weaker than those from soft tissue and organ interfaces which are used to build up our B-mode anatomical images. The amplitude of the backscattered signal from blood can be smaller by a factor of between 100 and 1000. Therefore highly sensitive and sophisticated hardware and processing software is required to ensure that these signals can be detected and processed.



THE DOPPLER EQUATION


The Doppler equation shows the mathematical relationship between the detected Doppler shifted signal (Fd) and the blood flow velocity (V):



1 image



where:


Fd = Doppler shifted signal


Ft = transmitted Doppler frequency


c = the propagation speed of ultrasound in soft tissue (1540 ms−1)


V = velocity of the moving blood


θ = the angle between the Doppler ultrasound beam and the direction of blood flow


The number 2 is a constant indicating that the Doppler beam must travel to the moving target and then back to the transducer.


Equation 1: The Doppler equation.




Significance of the Doppler Angle (θ)


Ultrasound machines are able to calculate Doppler shifted frequencies over a wide range of angles and it is important that an operator understands the significance of the angle of insonation (θ) between the Doppler beam and the direction of blood flow in vessels. Figure 11.4 graphically shows how the Doppler shifted signal changes as the Doppler beam angle changes.



When the Doppler beam is pointing towards the direction of blood flow a positive Doppler shifted signal is observed, but once the Doppler beam is pointed away from the direction of blood flow a negative Doppler shifted signal is seen. The smaller the angle between the Doppler beam and blood vessel, the larger the Doppler shifted signal. Very small signals are produced as the Doppler beam angle approaches a 90° angle.


Table 11.1 shows the relationship between the angle of the Doppler beam (θ) and the value of cosθ. The value of cosθ varies with the angle from 0 to 1. When θ = 0°, cosθ = 1 and when θ = 90°, cosθ = 0.


Table 11.1 Variation of the value of cosθ over a range of angles of insonation. Maximum value of cosθ corresponds to a Doppler beam angle of 0°.
























ANGLE θ VALUE OF COSθ
0 1
30 0.87
45 0.71
60 0.5
75 0.26
90 0

For a constant flow velocity (V), the maximum value of cosθ and therefore the highest value of the Doppler shifted signal (Fd) is at an angle of 0°. This corresponds to a Doppler beam which is parallel with the vessel, which can rarely be achieved in practice.


Theoretically, when θ = 90° this means the blood flow is perpendicular to the Doppler beam, cosθ = 0 and no Doppler shifted signals will register.


In practice, when taking measurements of blood flow, a Doppler beam angle of between 30 and 60° is important to ensure reliable Doppler shifted signals. Avoid using angles greater than 60° and remember no Doppler shifted signals are generated at 90°.


Greater flow velocities and smaller angles produce larger Doppler shifted frequencies, but not stronger Doppler shift signals.




TYPES OF DOPPLER INSTRUMENTATION IN DIAGNOSTIC IMAGING


There are a number of types of Doppler instrumentation used in ultrasound which include:






Doppler techniques applied to diagnostic ultrasound can be characterized as either being non-imaging or imaging. Non-imaging techniques typically use small or handheld units, and use continuous wave (CW) Doppler. The main purpose of these simple CW units is to either identify and/or monitor blood flow. Two examples of clinical examinations include fetal heart monitors in obstetrics and peripheral blood flow assessment in vascular practice.


Imaging Doppler techniques such as color and spectral PW Doppler are always used with B-mode imaging where the gray scale anatomical image is used to identify blood vessels and areas for blood flow evaluation. These techniques require more sophisticated processing than CW devices.


Mar 10, 2016 | Posted by in ULTRASONOGRAPHY | Comments Off on Physical principles of Doppler ultrasound
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