PROBE/ SVQ parameters

Raw files

The combination and averaging of data into frames is the only processing performed on a “raw” data set.

The averaged, raw PROBE/SVQ data set is written to a standard raw file, e.g., the P06656.7 raw file, which is stored in the system directory /usr/g/mrraw. There are only 196 unique file names so the raw files should be moved or renamed if you wish to retain the raw data for further processing or long term reference. Data in raw PROBE/SVQ files are NOT processed before storage; the files contain the raw, unprocessed data.

Spectrum files

The image is a standard image with a spectrum plotted onto the image. A PROBE/SVQ image can be printed and archived like any other image. Note however, that the complex raw data are not stored in the PROBE/SVQ image file, the “spectrum” is simply drawn on the image, and is not recorded as a sequence of complex values suitable for further processing. Only a raw PROBE/SVQ file contains the information necessary for complete data analysis or processing. If the raw file has been stored, PROBE/SVQ spectra and quantitative information can be obtained by processing the raw file with off-line data processing software; e.g., SAGE - Version 7.0.

Reconstruction details

When a PROBE/SVQ data acquisition is complete, the raw data, comprised of water reference and water suppressed frames, reside in the system memory. The data acquisition process saves the raw data file to the system disk, and queues a PROBE/SVQ reconstruction processing job. The reconstruction process calculates the spectrum, calculates the quantitative information, and then creates and stores an image file that contains the spectrum and quantitative data.

In the standard operating mode, all steps of the PROBE/SVQ reconstruction are performed, including water subtraction and quantitative analysis of the data.

Signal processing: water referencing, water subtraction, phase correction

In order to display an artifact-free pure absorption spectrum, B₀ shifts, phase offsets, and frequency offsets must be removed. Since each of these errors is manifested as a phase error, we simply refer to this entire correction as a phase correction. Assuming that the B₀, phase, and frequency errors for the water suppressed and non-water suppressed signals are the same, we extract the phase of the water signal from the non-water suppressed signal, and use it to frequency correct, phase correct, and B₀ correct both the water suppressed and non-water suppressed signals. This technique of phase correction is known as water referencing.

Spectrum image creation

General algorithm

Temperature induced frequency correction

The NA residues, Cr, Ch, and mI resonances are defined relative to the frequency of the water resonance; however, the resonant frequency of water is temperature dependent. Since the primary application of PROBE/ SVQ is in the human brain, the locations of these resonances are specified relative to the water resonance at the nominal temperature 37°C.

Line broadening, width normalization, and shape transformation

Before curve fitting, the spectral line shape is manipulated to improve fitting by removing any errors associated with line width variations. There are three line shape manipulations in PROBE/SVQ: line broadening, line width normalization, and line shape transformation. Each of these manipulations can be performed by a separate, specific apodization, or, for processing speed, they can be combined into a single apodization step.

The major advantage of curve fitting, over simple direct peak height and width measurements, is that curve fitting effectively averages out noise. This improvement is bought at a cost of an increased number of fitting iterations, and decreased robustness of fitting as the spectrum becomes noisier. One can decrease the noise sensitivity of the curve fitting process by taking local averages, or, equivalently, by line broadening the spectrum before fitting. Broadened spectra are fit more quickly, and more robustly than nosier non-line broadened spectra.

One difficulty with fitting MR spectra is that the Lorentzian peaks have quite a broad base, causing peaks to overlap. By transforming a spectrum of wide Lorentzian shapes to a spectrum of narrower Gaussian shapes, the overlap of the Lorentzian peaks can be greatly decreased. This transformation is only strictly valid for spectra that are made of peaks that all have the same width and shape. If all of the peaks in a spectrum have the same width and shape, then de-apodization (dividing the signal by the apodization function rather than multiplying) by the apodization function associated with that line width and shape followed by reapodization by the apodization function associated with a second line width and shape will convert a spectrum made of a sum of peaks of the first width and shape to a spectrum made of a sum of peaks of the second width and shape. This is the method used in the PROBE/SVQ quantitative analysis to improve the curve fitting process.

All PROBE/SVQ numerical analysis is based on peak amplitude, but by normalizing the line widths of the peaks, the analysis effectively measures areas and ratios of areas. The algorithm first determines the line width of the creatine peak. Since the peaks are assumed to be Lorentzian, a line broadening/narrowing is performed by exponential apodization. The actual line width of the creatine peak is measured. This line width is subtracted from a nominal line width of 1.0 Hz, and an exponential apodization with this calculated width is performed. This transforms a Lorentzian peak with a given line width to a Lorentzian peak with line width of 1.0 Hz.

To summarize, the following apodization scheme is used to reduce noise, reduce homogeneity sensitivity, and reduce line overlap. The apodization is applied before curve fitting the peaks in either the water reference or water suppressed spectrum.

• The line widths of the peaks are normalized to the width of the creatine peak.
• A (partial) Lorentzian to Gaussian transformation is performed.
• The line width normalization and the first part of the line shape transformation are combined into a single exponential apodization. The second half of the line shape transformation is performed by a Gaussian apodization.
• Line shape transformation depends upon all of the peaks having the same width and shape. This is not the case for proton spectra. However, deviation of line width relative to the final line width and shape is sufficiently small that for PROBE/SVQ the benefits outweigh the minor errors. Another drawback is that it has the counter intuitive effect of causing the measured noise level to vary with the line width of the reference species.

Frequency transformation and interpolation

Frequency transformation along with interpolation or decimation is performed. Spectra are interpolated or decimated to a standard frequency resolution of 0.01 per point before fitting.

Baseline correction

The baseline correction is a simple linear correction based on an average over two 300 Hz wide regions, one on each side of the spectrum. The baseline correction is subtracted from the data before fitting the data.

Curve fitting

PROBE/SVQ uses a simplified version of a Marquardt fitting program (for more information see the freqfit routine in the SAGE v7.0 software package). The simplifications and assumptions are:

• Only fits to the real channel are performed
• Each chemical species has a single peak
• Only one peak is fit at a time
• The fitting process only adjusts parameters for each region (species), it does not determine the global parameters of the entire spectrum
• There is only rudimentary control of free/non-free parameters

The data, model, and partial derivatives are all fully complex, and, while full complex channel fitting is implemented, it is not used. The first version of PROBE/SVQ did use full complex fitting with fitting of the phase parameter. This was removed because in the case of standard PROBE/SVQ data sets:

• The water reference phase is more accurate than the phase calculated by the fitting process
• The peaks overlap too strongly in the imaginary channel to fit single peaks
• The SNR advantage of fitting both real and imaginary channels is obtained by Fourier interpolation by a factor of two (i.e., the first zero filling)

Quantitative analysis failure modes

There are two quantitative analysis failure modes:

• the curve fitting process fails to fit a peak in one or more of the designated regions of the spectrum
• a peak exists in the region but either the SNR, or the goodness of the fit of the peak fails to meet the minimum standards set for PROBE/SVQ spectra

If the curve fitting procedure fails to find a peak in a designated region of the spectrum, or if the center frequency of a detected peak is outside of the region, the process reports that the fit has failed. Specifically, a "-void-"entry is displayed for the missing peak values. For example, if a phantom is scanned at room temperature, the frequencies of the metabolite peaks will be out of their designated (relative to the temperature dependent water resonant frequency) regions and “-void-“will be reported for all metabolite values.

If the quantitative analysis routine finds and fits a peak in a region, a failure is reported if the SNR of the peak is less than 5 to 1, and/or the goodness of fit of the peak is less than 4. SNR is the usual signal-to-noise ratio; the noise is estimated by taking the average RMS value over two regions of data (see below, Estimation of the Noise Level). The goodness of fit is a ratio of the power of the peak (over the fitting region) versus the power of the residue. The power of the peak is taken to be the lesser of the power of the data over the region, and the power of the curve fit data over the region. If neither criteria is met, a failure is reported and “-NotDet-“(for Not Detected) is displayed for the peak values.

Analysis of the metabolite reference peak

This portion of the procedure determines the temperature-induced shift of the frequencies of the metabolites relative to water, and the homogeneity of the sample. Creatine is used as the reference resonance. The spectral region containing the reference resonance is fit using a Marquardt-Levenberg least squares minimization to determine the temperature-induced shift of its frequency relative to water, and the effective homogeneity of the sample. This frequency is compared with the nominal resonant frequency of the reference, and the global frequency fit parameter is adjusted accordingly. The peak is re-fit to obtain an accurate frequency and line width. Again, the fit frequency is compared with the nominal resonant frequency of the reference, and the global frequency fit parameter is adjusted accordingly.

Quantitative analysis of the metabolites

The signal intensities of five individual chemical species, and the ratios of these intensities to the creatine signal intensity are determined by the PROBE/SVQ quantitative analysis process using the steps noted in this section.

First, the temperature-induced shift of the frequencies of the metabolites relative to water, and the homogeneity of the sample are determined (see above, Analysis of the metabolite reference peak). The peak is re-fit to obtain an accurate frequency and line width. Again, the fit frequency is compared with the nominal creatine resonant frequency, and the global frequency fit parameter is adjusted accordingly. If the curve fitting in this step fails and the creatine line width can not be calculated, a default line width of 3.0 Hz is used as the line width of the reference.

Next, the line widths of the peaks are normalized, and the line shapes are transformed from a (approximately) Lorentzian to a Gaussian shape by:

• an exponential de-apodization of the width of the creatine peak minus 1.0 Hz
• the application of a 4.0 Hz Gaussian apodization

As previously noted, these line shape transformations require that all of the lines have the same width and shape. This is not the case for proton spectra. However, the deviations of line width and shape are sufficiently small that, for PROBE/SVQ spectra, the benefits outweigh the minor errors.

After these line shape manipulations, the time domain data is transformed to the frequency domain with an appropriate interpolation (a single zero filling) such that the spectral resolution is 0.01 ppm per point.

The peak in each of the designated regions of the frequency domain data set is fit using a Marquardt curve fitting routine. Since the line widths of the peaks have been normalized, the area of each peak is proportional to the amplitude of the fit. The amplitudes (determined by fitting) for each peak are:

• reported as “Mach. #”, the machine number (a signal intensity)
• divided by the amplitude (determined by fitting) of the creatine reference peak. The result is reported as the metabolite ratio

In the case of the reference peak, “-ref-“is displayed rather than 1.0. As detailed previously, if the fitting to a peak in a region is successful but the measured SNR or calculated goodness of fit parameters were considered not significant, “-NotDet-“is displayed. If the fitting of a peak was not successful, “-void-“is displayed.

Estimation of the noise level

The noise level is estimated by computing the RMS noise values over two 4.7 ppm wide regions of the spectrum (the range of frequencies [9.0 ppm, 13.7 ppm] and [-1.0 ppm, -5.7 ppm]), and taking the greater of the two levels. The SNR of creatine (the reference species) is calculated as the ratio of the creatine (reference) amplitude to the noise, and is displayed as the SNR. Note that the reported SNR is NOT the SNR of the displayed spectrum which has undergone minimal processing relative to the spectrum produced by the quantitative analysis procedure.

Quantitative analysis of the water resonance

The intensity of the water signal in the non-water suppressed spectrum is determined in a similar manner. The global frequency fit parameter is reset to zero as water is the frequency reference, and requires no frequency correction. The same apodization that was applied to the water suppressed signal is applied to the water signal. Next, the line width of the water peak is normalized, and the line shape is transformed from a Lorentzian shape to a Gaussian shape by:

• an exponential de-apodization of the water peak to 1 Hz
• the application of a 4.0 Hz Gaussian apodization

After these line shape manipulations, the time domain data is transformed to the frequency domain with an appropriate interpolation (a single zero filling) such that the spectral resolution is 0.01 ppm per point.

The peak is fit using Marquardt curve fitting and, as was the case for the metabolite peaks, the line width has been normalized, and the area of the peak is proportional to the amplitude of the fit. This value is:

• reported as the “Mach. #” (signal intensity) of water
• divided by the amplitude (determined by fitting) of the creatine reference peak. The result is reported as the metabolite ratio for water

If the fit of the water peak is successful but the measured SNR or calculated goodness of fit parameters were considered not significant, “-NotDet-“is displayed. If the fitting of a peak was not successful, “-void-“is displayed.

Storing the values calculated by the quantitative analysis process

The signal intensities (reported as Mach. # when displayed), and the ratios of the signal intensities to the intensity of the creatine reference signal determined by the analysis process are stored in the image header. The values stored in the header are either positive, indicating a successful data analysis, or negative, indicating an exceptional value or a failure mode.