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- Thread starter fa21212
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Hi @fa21212 -
Excellent question, as usual! What's going on here is that in general, the accuracy of Doppler imaging will be affected by the angle formed between the measuring beam and the velocity that is being measured. I'm attaching an image from a Next Step passage that deals with this topic in the context of police cars catching speeders.
In this setup, the measured speed (Vm) will equal the true speed (Vt) times cos(beta): Vm = Vt cos(beta). The accuracy of the measurement will be maximized when the angle β is small, making cos(beta) close to 1. That will also correspond to the maximum measured values. In other words, as beta increases, the measured velocity will become both smaller and less accurate.
This question is asking you to apply this same reasoning to the accuracy of ultrasound beams. Equation 2 is a way to calculate the velocity of the blood if you know theta, which is a different problem than what the question asks you to reason about. Here's a neat and short article that discusses some of these issues. That said, I definitely understand how this confusion could arise, and as usual, I will bring it to the FL team's attention for review.
Excellent question, as usual! What's going on here is that in general, the accuracy of Doppler imaging will be affected by the angle formed between the measuring beam and the velocity that is being measured. I'm attaching an image from a Next Step passage that deals with this topic in the context of police cars catching speeders.
In this setup, the measured speed (Vm) will equal the true speed (Vt) times cos(beta): Vm = Vt cos(beta). The accuracy of the measurement will be maximized when the angle β is small, making cos(beta) close to 1. That will also correspond to the maximum measured values. In other words, as beta increases, the measured velocity will become both smaller and less accurate.
This question is asking you to apply this same reasoning to the accuracy of ultrasound beams. Equation 2 is a way to calculate the velocity of the blood if you know theta, which is a different problem than what the question asks you to reason about. Here's a neat and short article that discusses some of these issues. That said, I definitely understand how this confusion could arise, and as usual, I will bring it to the FL team's attention for review.
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Hi @fa21212 -
If you google around for information on Doppler ultrasonography & the cosine error, you'll find plenty of sources with the same basic info -- I picked that one to share primarily because it was concise, clear, and didn't have much extraneous info, not because of any specific connection with the passage. But yes, I absolutely do see your point about clarifying the scope of the question. On a side note, not that I'm an expert in medical US imaging, but my impression is that it would be quite hard for the machine to automatically recognize & correct for the angle (not least because the direction of blood flow will vary in 3 dimensions depending on where you're holding the transducer), so manual angle correction remains part of why ultrasonography is a pretty operator-dependent technique.
If you google around for information on Doppler ultrasonography & the cosine error, you'll find plenty of sources with the same basic info -- I picked that one to share primarily because it was concise, clear, and didn't have much extraneous info, not because of any specific connection with the passage. But yes, I absolutely do see your point about clarifying the scope of the question. On a side note, not that I'm an expert in medical US imaging, but my impression is that it would be quite hard for the machine to automatically recognize & correct for the angle (not least because the direction of blood flow will vary in 3 dimensions depending on where you're holding the transducer), so manual angle correction remains part of why ultrasonography is a pretty operator-dependent technique.