Analysis details

Summary

The software performs several types of analysis on uploaded fMRI data, checking for scanner instabilities, signal-to-noise and fluctuation levels. The first analysis is named after its original developer, Robert Weisskoff and is named here as Weiskoff Analysis. It involves signal detrending, coefficient of variation calculation, region of interest (ROI) scaling, and radius of decorrelation calculation to measure statistical independence loss. Additionally, advanced noise analyses are included, including signal image averaging, temporal fluctuation noise image calculation, signal to fluctuation noise ratio (SFNR) value determination, and static spatial noise measurement for signal-to-noise ratio (SNR) summary value assessment. These processes help in understanding and quantifying the quality of fMRI data by evaluating factors such as stability and noise levels.

This is based on the principles and methodologies outlined in the papers:

"Simple Measurement of Scanner Stability for Functional NMR Imaging of Activation in the Brain", Weisskoff (1996).
“FBIRN Stability phantom QA procedures”, G.H. Glover (2003-2005).
"Report on a Multicenter fMRI Quality Assurance Protocol", L. Friedman, G.H. Glover (2006). The protocol in this paper is known as the Glover stability QA protocol (GSQAP)

For avoidance of doubt, any methods used here will align with the GSQAP.

Weisskoff Analysis

The software will perform the Weisskoff Analysis on the uploaded data. The analysis assumes that scanner instabilities will impart some increase in the inter-voxel correlation, presumably because such instabilities will have some low-spatial-frequency characteristics. If there are no such instabilities (or spatial smoothing in the reconstruction; see below), then each voxel is (relatively) independent of its neighbours, and the coefficient of variation (CV, the standard deviation (SD) of a time-series divided by the mean of the time-series) for an ROI should scale inversely with the square root of the number of voxels in the ROI. This involves several steps:

Signal Detrending

Mean Over Time Calculation

The software will calculate the mean signal intensity over time for the specified region of interest (ROI). The software should consider the central ROI, found via a centre-of-mass calculation.

Polynomial Fit

The software will fit a second-order polynomial to the mean signal intensity over time. This can be represented by the equation:

where , , and are the coefficients of the polynomial.

Fit Line Calculation

The software will calculate the fit line for all time-points using the coefficients of the polynomial.

Detrending

The software will subtract the fit line from the signal intensity at each voxel (at the relevant time point) to detrend the data.

Coefficient of Variation Calculation

For each voxel in the fMRI data, the software will calculate the coefficient of variation (CV), which is the standard deviation of the mean ROI signal intensity over time divided by the mean signal intensity. This can be represented by the equation:

where is the coefficient of variation (CV) for an ROI of size , is the standard deviation of the signal intensity for mean ROI value of size, and is the mean signal intensity of the time-series for the ROI. In practice, as the nominal size of the ROI (N) increases, the reduction in CV plateaus and becomes independent of N. This occurs because system instabilities result in low-spatial-frequency image correlations, so that the statistical independence of the voxels is lost.

ROI Scaling

The software will then calculate the CV for different ROI sizes. The CV for an ROI will scale inversely with the square root of the number of voxels in the ROI (this is a general assumption regarding measurement uncertainty. If the samples are independent and identically distributed (i.i.d) random variables, this will hold true). This can be represented by the equation:

where is the square root of the number of voxels in ROI , where . This corresponds with the Central Limit Theorem.

Radius of Decorrelation Calculation

The software will calculate the radius of decorrelation (RDC), which is a measure of the size of the ROI at which statistical independence of the voxels is lost. This can be calculated as:

where is the maximum ROI size. In the GSQAP, this is 21, therefore we will use this value. It is worth noting that the theoretical (and maximum) value for RDC is :

Noise analyses

Signal Image

The signal image is the simple average, voxel by voxel, across the time-series.

Temporal Fluctuation Noise Image

To calculate the fluctuation noise image, the time-series, for each voxel, is detrended with a second-order polynomial. The fluctuation noise image is an image of the standard deviation (SD) of the residuals, voxel by voxel, after this detrending step.

Signal-to-Fluctuation-Noise Ratio (SFNR) Image and Summary SFNR Value

The signal image and the temporal fluctuation image are divided voxel by voxel to create the SFNR image. A 21x21 voxel ROI, placed in the centre of the image, is created. The average SFNR across these 441 voxels is the SFNR summary value.

Static Spatial Noise Image

The first step is to sum all the odd-numbered images (sumODD image) and separately sum all the even-numbered images (sumEVEN image). The difference between the sum of the odd images and the sum of the even images (DIFF = sumODD – sumEVEN) is taken as a raw measure of static spatial noise. If the images in the time-series exhibit no drift in amplitude or geometry, theDIFF image will display no structure from the phantom, and the variance in this image will be a measure of the intrinsic noise.

SNR Summary Value

The static spatial noise variance summary value is the variance of the static spatial noise (DIFF) image across a 21x21 voxel ROI centred on the image. The signal summary value is the average of the signal image across this same ROI. Then, SNR (signal summary value)/((variance summary value)/N time points).