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signal-to-noise ratio (SNR) chemical shift artefact (also the echo time, TE) Receiver Bandwidth affects receiver Bandwidth = 1 sampling time of echo © D M Higgins Dont get confused: receiver bandwidth is different from the transmit bandwidth, which refers to the RF excitation pulse used for slice selection in a pulse sequence. The receiver bandwidth is the range of frequencies used to sample the MR signal. Generally, if someone mentions bandwidth, especially if they say SNR in the same breath, they mean receiver bandwidth. Receiver bandwidth (rBW) is one of the parameters you can change on your scanner. We know that the signal-to-noise ratio (SNR) is proportional to 1/rBW but why this is so can be a bit confusing. Hopefully, this tutorial will help. The time it takes to sample the MR signal is related to the rBW. (This relationship refers to the sampling time. The actual number of samples taken is set with the matrix size.) This is a schematic MR signal or echo, just one of the many MR signals needed to create an MR image. It is one line of k- space. It takes a certain amount of time to read out / sample this signal. We do this with the frequency encoding (readout) gradient.
centre spatial frequency patient signals time sampling time of echo receiver Bandwidth = 1 sampling time of echo © D M Higgins
centre spatial frequency patients signals time receiver Bandwidth = 1 sampling time of echo sampling time of echo increase the receiver bandwidth This slide illustrates what happens to the signal in time, when the rBW is increased. You can see here why increasing rBW allows a shorter TE to be used. If the sampling time is reduced, the whole pulse sequence can be squashed up to use up the extra time gained. According to this relationship, the sampling time of one MR echo is reduced by increasing the bandwidth. Ok, so maybe you can accept that changing the rBW affects the time it takes to sample the signal. But why? Its because the way a change of bandwidth is implemented (all other things being equal) is by a change of gradient strength. Read on… © D M Higgins
patient frequency encoding gradient 0 frequency Increase the receiver bandwidth… …and the gradient gets steeper. A steeper gradient means that the rephasing it causes happens more quickly, and so the echo forms faster. I.e., the sampling time is reduced and the sampling rate is increased accordingly. body arm bandwidth © D M Higgins
amplitude frequency (kHz) arm body 1-D projection 0 32 Double the receiver bandwidth signal decrease? noise power spectrum Now lets consider what happens to the signal and the noise when the range of frequencies (rBW) used to encode the MR signal is increased. We know that the SNR in the image is reduced when the rBW is increased, so either the signal is going down, or the noise is going up, or both. If we take the central line of k-space and perform a 1-D Fourier transform (FT) on it, we get a 1-D projection of whatever was in the scanner. The FT has worked out how much signal goes into which column of pixels in the image. How the signal would be divided up into the rows is not known. Lets double the rBW and see what happens… What do you notice? Increasing the rBW has stretched out the range of frequencies used for each column of pixels. As we share out the protons to a wider range of frequencies, the amount of signal from the individual frequencies in the new range must reduce. This is why the signal amplitudes on this frequency graph go down. Notice also that the noise level for any one particular frequency does not change when the rBW is increased. Notice that the noise power spectrum (the noise levels over all the frequencies) is constant. BUT, also notice that the area each column occupies hasnt changed. (They may have reduced in height, but theyve also gotten wider.) This reflects the fact that we havent changed the pixel size. In other words, we have the same number of protons per-voxel as before. They are just resonating at more (and different) frequencies. This is important, because it tells us that although the signal amplitudes for the range of frequencies within any particular voxel have reduced, the total amount of signal per voxel is unchanged. When the rBW is increased, the same noise power but over a larger frequency range contaminates the signal from each voxel. Thus the total amount of noise included in each voxel is increased. Hopefully now it will be clear what textbooks mean when they say that increasing the rBW includes more noise. © D M Higgins the signal amplitudes decrease and change frequency the signal per voxel does not decrease the noise power per voxel is increased …so in the image, SNR decreases
chemical shift 1 rBW SNR 1 rBW Rule: as rBW changes, SNR, chemical shift artefact (and TE) do the opposite e.g. rBW SNR chemical shift artefact TE Dont like remembering equations? Use this handy rule: Notice that a trade-off exists here. We may want to reduce the chemical shift artefact in an image, or reduce the echo time (TE), but can we sacrifice SNR? These decisions are made by the operator. © D M Higgins
Fixing rBW: what do you change on the scanner? (receive) bandwidth frequency matrix chemical shift for your magnet e.g. ±16 kHz= 32 kHz e.g x 10 3 (Hz) 256 (pixels) 125 Hz / pixel 3.5 ppm 224 Hz 1.5T) = 1.8 pixels (receive) bandwidth frequency matrix chemical shift for your magnet in this example GE: rBW range (kHz) Philips: water-fat shift (pixels) Siemens: rBW-per-pixel (Hz/pixel) It depends on the manufacturer. E.g.: The relationship between these parameters is clearly shown when we work out the number of pixels of chemical shift artefact that will occur on our image: (this is what you change on a GE scanner) (this is what you change on a Siemens scanner) (this is what you change on a Philips scanner) © D M Higgins
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