I have a question based on application of the FFT. It has been 30 years since I worked with FFT’s so, please explain as if explaining to a neophyte as there are many cobwebs. I will explain the image as basically as I can since I do not know if anyone will have seen this type of medical image before.

The image below shows the Doppler spectrum produced by an FFT. The FFT bins correspond to velocity through the Doppler equation (note the scale to the right of the Doppler spectrum). There is now a “raging” debate in the medical field about the lighter envelope portion of the spectrum (red dotted line) that basically duplicates the darker envelope (modal velocity traced in light green) below the baseline. Some are arguing that this higher velocity (red envelope) is artifactual based on the FFT processing and some are arguing that this is the result of a hemodynamic situation which results in an increased velocity.

I want to discuss one more general point about Doppler FFT processing before I can really described the situation and pose the question. The Doppler signal is separated into an I and Q channel so as to detect flow direction (represented as flow signals above or below the baseline). I am well aware of the “mirroring” that can occur in the Doppler spectrum when some of the signal “crosstalks” between the I and Q channel. If there is not perfect separation between the two channels, we see the result as replication of the real signal “mirrored” across the baseline.

I will briefly describe the situation. This picture represents the imaging of a prosthetic mitral valve (top image with color) and a continuous wave Doppler, spectrum below. Continuous wave implies that the flow velocity is detected along the entire Doppler line (dotted white line down the center of reference image above spectrum). In this case, the valve has been replaced with a mechanical prosthetic valve with metal discs. A well understood artifact that occurs sometimes in ultrasound (and frequently with specular reflectors like metal which acts like a mirror to sound waves) is a reverberation artifact. In essence, the sound, instead of making a single path down and back from each part of the image, makes two or more paths (reverberates) between the strong reflectors. The result is that the specular reflectors (and of course every structure between the specular reflectors, is duplicated a second time (and possibly more times) below the location of the actual structure within the ultrasound image. The fact that this reverberation artifact is happening in this image is confirmed with other views I am not including.

So some people are theorizing that just as the image is being replicated, the Doppler shift is being replicated (this I completely believe since the sound beams used to detect Doppler shifts behave in the same manner as the sound beams used to create the 2D image). However, the velocity presented is related to the Doppler frequency shift, not if the shift is detected twice, so detecting the same Doppler shift again does not explain the increase in velocity shown. In other words, detecting the same frequency twice should result in energy in the same frequency bins, not higher order bins corresponding to higher frequencies( velocities). The question is whether it is possible that since the “same” shift is being replicated and detected twice instead of once can result in an explainable result in the FFT the produces signal in higher order FFT bins (the signal in the fainter envelope traced in red). In other words, is there a mathematical explanation (like there is for the “mirroring” artifact for this “double envelope” artifact?

For completeness: others are theorizing that this is not related to the FFT processing at all, but is the result of the vena contracta and complex flow acceleration that results from impingement of this flow on the septal wall. I will not go into more detail on this theory as this relates to fluid dynamics and I know this is a forum for answering questions about Fourier Transforms.