Lorentzian line fitting to the Z-spectrum

This module fits Lorentzian lines to the Z-spectrum in order to aid quantification. Lorentzian ļ¬tting to CEST Z-spectra allows the derivation of information from several different exchange effects that would otherwise be convolved into a single asymmetry measurement. To perform Lorentzian fitting, select the Lorentzian Fitting tab:

Tab to perform Z-spectrum Lorentzian fitting

Set up the input section, then set:

  • The Lorentzian line specification file. This is a text file that you create using your favourite text editor, which determines the Lorentzians to fit. The text file consists of 3 columns of numbers. Each Lorentzian to be fitted occupies one line of the text file.

    • The first column is the frequency offset (relative to water, in ppm) of the Lorentzian central frequency. The central frequency is fixed and is not a fit variable.
    • The second column is the initial guess for the relative amplitude, and must be between 0 and 1. The relative amplitude is a fit variable.
    • The third column initial guess for the Lorentzian line-width (full-width at half-maximum [FWHM]). The FWHM is a fit variable, unless Check box to fix the FWHM, so that it is not a fit variable. is selected. If selected, the FWHM is fixed to the value set in this third column.

    Note: in addition to the Lorentzians specified in the Lorentzian line specification file, two other Lorentzians will automatically be fitted:

    • The first models direct water saturation. This has a fixed offset frequency of zero.
    • The second models MT effect. This has a fixed offset of -1 ppm, and the FWHM is limited between 10 and 100 ppm.

    Thus, you do not need to include the direct water saturation and MT effects in the Lorentzian specification file.

    Below is an example of a Lorentzian specification file which fits two Lorentzians. The first is at 4.2 ppm, and with initial guesses for the relative amplitude of 0.1, and FWHM of 0.25 ppm. The second is at 5.5 ppm, and with initial guesses for the relative amplitude of 0.05, and FWHM of 0.2 ppm.

          4.2 0.1 0.25
      5.5 0.05 0.20

  • S0 image. The Z-spectrum is normalised by dividing by the the image intensity with no saturation pulses applied. Supply an image acquired using the same pulse sequences as for Z-spectrum but without saturation pulses here:

    The image with no saturation pulses applied.

    This image must have the same dimensions as the Z-spectrum images, and with a number of slices matching that set in the input images section.

  • B0 map. This is a map of B0 inhomogeneity produced from the WASSR analysis to correct for field deviations.

    The image of B0 inhomogeneity.

    This image must have the same dimensions as the Z-spectrum images, and with a number of slices matching that set in the input images section.

When set up, press Button to perform the analysis to fit the Lorentzians pixel-by-pixel. When complete, a new image is created for each of the Lorentzians in the specification file, showing the integrated area under the Lorentzian. The image name will be taken from the input image (or first input image, in the case of multiple input images), with a suffix related to the Lorentzian frequency offset (e.g. "_4.2").

N.B. fitting will take some time, particularly if Lorentzian line-widths are included as fit variables.