Global Scaling: Copied

Cambridge Group (link)

Global image signal

An important step in this analysis will be adjusting the data for the effect of global image signal. By global image signal, I mean the overall magnitude of all the VVs in an image. A large part of the variation of VVs between scans is explained by the overall amount of signal in the scan from which the VV has come. In the case of PET, the amount of signal in the scan is dictated by the amount of radioactivity that has reached the head, and this in turn is influenced by several factors, including the speed of blood circulation from the arm to the heart, and the amount of radioactivity injected. Thus, for a scan where a large amount of radioactivity has reached the head, all the VVs in the brain are likely to be higher than for the equivalent voxel from a scan where less radioactivity is present. SPM attempts to estimate this global signal by using a Thresholded Mean Voxel Value (TMVV). To calculate the TMVV, it does a two-pass mean of the values in the image. First it takes all the numbers that make up the image, and calculates the average of all these numbers. For the first scan in the example dataset, this mean is 0.0038. It then divides this mean value by 8, to give a threshold, on the basis that any voxel with a value this low is likely to be outside the brain. It then calculates the mean of all the VVs that are greater than this threshold. For our first scan, the threshold is 0.0038/8, 415717 of the 510340 voxels in the scan are above this threshold, and the mean of these 415717 values is 0.0046. The code for these calculations is in http://imaging.mrc-cbu.cam.ac.uk/scripts/statstalk.m. Below is a graph of the VVs from the (-20 -42 34) voxel, plotted against the TMVV for the scan from which the voxel came:

As you can see from the figure, higher TMVV values for the scan are associated with higher voxel values in our voxel of interest. For the reasons we discussed above, this is not very surprising, and indeed, the same relationship hold true right across the brain; so that the global signal / TMVV for a scan is a strong predictor of the values for the voxels from that scan. The factors that influence this overall level of signal, which we enumerated above, are usually unrelated to our experimental design; we will therefore need to try and remove this effect if we wish to see the smaller effects that our experiment has caused in our data. One simple way of doing this is to divide each VV by the TMVV for the scan from which it comes. The new VVs are therefore ratios of the value for this voxel to the overall average VV for the scan, where this average is calculated across all the voxels in the brain. For the example voxel, the value for the first scan was 0.053, and the TMVV was 0.046. The new VV, after proportional scaling, is 0.053/0.046 = 1.15.

Grand mean scaling

Grand mean scaling is another common manipulation to the voxel data before it goes into the analysis. Grand mean scaling is used to try and scale the VVs to give them a more readily comprehensible interpretation. For example, the VVs for our chosen voxel are in more or less arbitrary units, given to us by the PET scanner. As you can see from the figure above, for our example voxel the values range from about 0.0045 to 0.0054. The range of these values has no interesting physiological interpretation, so that can be helpful to mutliply the values by a scalefactor so that the units are easier to interpret. The choice of this scalefactor is in itself rather arbitrary. In activation PET studies, it is often assumed that the average blood flow across the whole brain, and across all the scans in the analysis, will have been about 50 mls of blood / 100 mls of brain tissue /min, which is a physiologically plausible value. We can adjust our arbitrary units by multiplying by a scale factor that makes the average of all the TMVVs (one per scan) to be equal to 50. This means that the units for the VVs will be something near to a guessed blood flow value, although this guess is extremely approximate. In our case, we have already proportionally scaled our images, so, by definition, the TMVV of all our scans is 1, and the mean of these values is also one. So to GM scale our VVs, we merely multiply them all by 50. In this simple case, with one subject, where all the scans are being scaled by the same factor, the GM scaling has no effect on the statistics; it only changes the units of the data.