What’s Your (Doppler) Angle?

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Korbin Haycock
Korbin Haycock
VExUS. Echocardiography in resuscitation. Likes to Doppler stuff.

The Pre-brief

If you don’t already know, I’ll tell you something fundamentally important to critical care and hemodynamics.  Doppler is magic. Magic, not in the sense of unicorns, or even worse, the latest pseudoscientific fad pushed on daytime TV or Instagram, but magic in the sense of a wonderful and powerful tool to help discern what is wrong with our sickest patients and find insight into how we might use this tool to help them.

Using Doppler when applied to echocardiography (and many other applications as well that I’ll hopefully address in the future) tells us information about flow, pressures of the various compartments of the cardiovascular system, compliance and elastance of those systems, performance of the ventricles, interactions between the heart and the vessels it is coupled with, intravascular volume status, chronicity of the derangement, and predictions about how our interventions will help our patients.  But before we understand how Doppler can do these things for us, we must understand the basics.  

No matter what form of the various applications of Doppler we use, the fundamental concept involves the principle that frequency shifts between the transmitted and received signals translate to the velocities of the objects we are measuring.  This “Doppler shift” and its relation to the velocity of tissue (whether that tissue be blood or heart muscle or something else) has been described by Christian Doppler in the early 19th century by the equation:

Here C is the speed of sound in tissue (1540 m/sec), Fr is the frequency of the signals received by the ultrasound probe, and Ft is the frequency of the sound waves transmitted from the probe.

This relationship between transmitted and received sound wave frequencies and the velocity of the measured tissue has several clinical implications and uses that help us at the bedside.  

First of all, when the velocity of blood is measured over time, we can know how far blood has traveled over that time period because the rate multiplied by time equals distance (Rate * TIme = Distance). This is the principle of the velocity-time integral that we use as one way to determine the cardiac output using the LVOT VTI method (as will be covered with my pal Segun in an upcoming post on cardiac output and echocardiography).  This principle has additional applications with regard to perfusing blood flow, inference of peripheral vascular resistance, and other things as well, which is another topic(s) for another time.  

Secondly, the modified Bernoulli equation allows us to convert velocities of blood across various chambers of cardiovascular structures into pressure gradients by squaring the velocities and multiplying them by 4:

In this way, we can estimate the various pressures and also differential pressures between structures. This has multiple implications with regard to hemodynamics, including heart or vessel chamber pressures, filling pressures of those chambers, and in addition, also implies elastance and compliance of the said chambers.  To fully understand some of these relationships, it may require the Doppler interrogation of heart muscle velocities in conjunction with blood velocities, but again, this is for another post.

Finally, I will mention that there are a few Doppler applications where the Doppler angle is not relevant, such as acceleration times or flow times which nonetheless give us some very valuable hemodynamic information and only reinforces the magic of the tool that is Doppler.

But to turn back to the topic of this post. The equation given to us by Christian Doppler shows us that the conversion of the Doppler shifts to velocities depends on the angle of insonation of our Doppler beam relative to the actual direction of flow of the tissue we are measuring.  This comes down to simple trigonometry, specifically the cosine of the triangle we create with the error of our angle of insonation to the actual direction of flow.  In the figure below, I’ve created a triangle showing the actual direction of flow compared to the beam of ultrasound waves we are sending out and measuring the Doppler shift from.

Here is how this triangle would look superimposed over the left ventricular outflow tract if we were to want to find out what the cardiac output is.  Note that the angle is not quite right, so we will underestimate the flow a little bit in this example:

Any difference in the direction of actual movement from our beam direction will create an angle that will translate to a virtual triangle from which we can apply an error in measurement dictated by the laws of trigonometry.  This error in angle of insonation will result in an underestimation of the Doppler shifts that translates directly to an underestimation in velocities.  In other words, if we underestimate the Doppler shift because we measured the Doppler angle 60 degrees off the actual direction of movement of the tissue, the cosine of the angle of 60 degrees tells us that we will underestimate the velocity of the tissue by 50%.  See this table of cosines below:

By pure arbitrary convention, in echocardiography, we have decided to draw the line in the angle of insonation error to no more than 20 degrees relative to the angle of the actual flow of blood or movement of tissue we are measuring.  This will equate to about less than 6% error of underestimation of actual velocities.  Not too bad, but something to consider and understand when using Doppler for clinical applications. 

The Debrief

  1. Doppler principles enable us to convert measured Doppler shifts into velocities.
  2. These velocities can be taken at face values to convert to flow (with some simple math) or used in other applications, or also used to convert to estimates of pressure differentials between compartments (much more on this in future posts).
  3. Angle of measurement errors relative to actual flow or tissue movement direction by the clinician result in underestimation of actual velocities and can thus lead to errors in clinical decision making.   

References

  1. Gill RW. Measurement of blood flow by ultrasound: accuracy and sources of error. Ultrasound Med Biol. 1985 Jul-Aug;11(4):625-41. doi: 10.1016/0301-5629(85)90035-3. PMID: 2931884.

  2. Ranke C, Hendrickx P, Roth U, Brassel F, Creutzig A, Alexander K. Color and conventional image-directed Doppler ultrasonography: accuracy and sources of error in quantitative blood flow measurements. J Clin Ultrasound. 1992 Mar-Apr;20(3):187-93. doi: 10.1002/jcu.1870200305. PMID: 1313832.

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