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Relaxation analysis



Relaxation and kinetics analysis

Analysis of relaxation and kinetics data are similar in that both involve changes in peak integrals as a function of time.  The same procedures apply to both, up to the point of choosing which function should be used to fit the data.  Parts of the discussion below refer to T1 analysis, but apply equally well to T2 or kinetics data.

See illustrated tutorial showing analysis of T1 data.

Relaxation and Kinetics Data

For a T1 or T2 relaxation experiment, or for first-order kinetics, NUTS provides the capability of plotting the integral value of a chosen peak as a function of time, and also calculates T1 or T2 or the rate constant. The time values are saved in a variable delay list and can be viewed and/or edited by typing D1. Be sure the time values are correctly entered in this list before attempting to calculate relaxation times or rate constants. If the list is edited, type UH to update the file header and save the corrected values.

First, use Zoom to display just the peak of interest. Exit the Zoom subroutine and type GR (or choose Get Relaxation data from the Tools menu). This command measures the integral of the chosen region for each spectrum in the data set. Next type DR (or choose Data Reduction data from the Tools menu). NUTS displays a plot of integral value vs. time for the chosen peak. By default, Nuts assumes the data are T1 data, but this can be changed from the Fit menu. The curve displayed is a first guess, not a fit to the data. An exponential can be fit to the data by typing O. The resulting curve is displayed and the calculated T1value printed on the screen. Note that good phasing and flat blaselines are necessary to get good integration and therefore, a good T1recovery curve. The phasing and baseline of individual slices in a 2D data set can be corrected and the corrected slice saved back into the 2D data set with the S2 command.

For details of the T1 calculation, see DR.

A sample set of T1 data (13C spectra of sucrose) is available on the Acorn NMR web site, and is called Sucrose.t1.

As an alternative to the automated approach, in which NUTS automatically integrates the peak for all time values, it is possible to create a table of time vs. amplitude values, saved as a file, and then fit these values to the T1 equation. See description of RR command for details.

D1 — Time values for arrayed experiment

Opens a dialog box for display and entry of a list of time values (in sec) used in an arrayed experiment, such as a T1 experiment. If NUTS can identify a list of variable delay values in the data header, it will place the values in this list. Otherwise, the user can enter them manually. After entering a list of values, close the dialog box and type UH to update the file header, saving the list. Space is provided for up to 64 values.

These values are used in calculating T1 . In the event that one or more spectra in a T1 data set are corrupted, and the user would like to eliminate those values from the T1 calculation, the corresponding delay value can simply be set to a negative number. NUTS will ignore the corresponding spectra for its calculation, although the values are still displayed on the plot, in a different color.

GR — Get Relaxation data

Used in calculating T1 or T2 or reaction rate from a series of spectra. This command integrates the chosen region for each file in the data set and creates a list of time and area values which will be fit to a T1 equation. (The user does not have the ability to edit this list, but as an alternative, can create his/her own list of values saved as a file. To use this file to calculate T1 instead of the automated approach, use the RR command to read in the Relaxation data file.)

To use GR, the data must first be transformed, phased and saved as slices in a 2D data set. The user first selects a peak using Zoom to expand the spectrum so that only the peak of interest is displayed. Exit the Zoom subroutine using Enter. Type GR (or choose Get Relaxation data from the Tools menu). NUTS measures the integral of the displayed region for each spectrum in the data set. Note that the baseline and phasing in the expanded region must be good in order to obtain a realistic value for the integral. The baseline may need to be corrected for each spectrum in the data set and the corrected spectra saved. The simplest way to do this would be to execute a link such as the following, having already expanded the spectrum to display the region of interest:


Be sure that the slice number (SL) is set to one before executing the link, so that the process is performed on the whole data set. The BF command removes DC and tilt for the currently displayed expanded region. The SC command saves the corrected data. A different name must be supplied for the corrected data set. See help on each command for more information.

To correct phasing or baseline of just single slices within the data set, make the changes and save the corrected slice with the S2 command, which saves the entire data set with only the currently displayed slice being changed.

The T1 data can be displayed by typing DR (or choosing Display Relaxation data from the Tools menu). The entire process is repeated for each peak of interest.

DR — Data Reduction

Plots integral vs. time for relaxation data on a chosen peak. The data can be fit using a choice of functions for T1 or T2 relaxation.

Three steps must precede the DR command:

  1. The data must first be processed and saved as a 2D file (see Example).
  2. A peak is selected by using Zoom to expand the spectrum so that only the chosen peak is displayed.
  3. The GR command must be executed, which measures the integral of that peak in each of the spectra. (Alternatively, peak heights can be used; see below.) The GR command is also available from the Tools menu.

As an alternative, the data to be fit can be read in from a file consisting of time, amplitude data points. See Read Relaxation data file (RR) for details.

Typing DR (or choosing Data Reduction data from the Tools menu) displays a plot of integral vs. time with each data point represented by a small square. An initial guess at an exponential curve is displayed, but this does NOT represent a fit to the data.

By default, the data are assumed to be T1 data, and a 3-parameter fit is used. The fitting function can be changed from the Fit menu. Choosing Fit Function brings up a dialog box which allows the user to select the fitting function. The choices are

T1 Inversion Recovery
T1 Inversion Recovery fitting 3 parameters (default)
First-order kinetics, for either reactant or product

Equations are shown below.

Also from this dialog box, the user can choose to use peak heights rather than integrals. Peak height can be chosen with or without interpolation. If this option is changed, it is necessary to exit the DR routine and re-execute GR to make the new measurement.

To perform a fit, type O or select Optimize from the Fit menu. NUTS displays the curve determined by fitting the chosen equation to the data points, and also displays the values calculated in the fit process. A sample plot is shown below. If the integral for the longest delay value is set to 100, the integrals will be given as a percentage; otherwise, it is in the absolute integral units internal to the program. The plot can be printed by typing P or selecting Print from the File menu. The whole process is repeated for each peak of interest.

A table of time and integral values can be placed into the Windows clipboard by typing T or selecting Data to Clipboard from the Edit menu. The integral values will be listed as relative values if the integral has been assigned a value; otherwise it is given in the absolute units internal to the program. This table can then be pasted into the Notepad or other document. Like any other text in the clipboard, this can also be displayed on the screen by toggling on clipboard display by typing S or selecting Show Clipboard from the Edit menu (equivalent to the CB command).

The list of delay values used in the experiment can be displayed and edited by typing D1 from the NUTS base level or from within the DR subroutine by typing D or selecting Edit Time Data from the Edit menu. NUTS attempts to identify this list of values in the data header of the source data. If this attempt was unsuccessful, the user can simply enter the values. Executing a UH command (Update Header) saves the list in the header of the 2D data set. In the event that the user wishes to eliminate one or more spectra from the T1 calculation, this can be done simply by changing the corresponding value in the D1 list to a negative number, in which case NUTS ignores that point in the fit.

The equations used to fit the data are:

T13IR (3-parameter T1-Inversion Recovery)

y = A * { 1 – [ 1 + W * ( 1 – exp( -K/T ) ) ] * exp( -x/T ) }


T = T1 relaxation time
A = peak integral at time x >> T
K = total time between scans in the 180-t-90 sequence (equal to acquisition time plus relaxation delay time)
x = delay time t in the 180-t-90 pulse sequence
W = -(integral at time x=0 / A)

The parameter W is determined in the fitting process, as inversion in this experiment is not always perfect. This gives better results than assuming that the integral at time x=0 is simply the negative of the integral for infinitely long x.

ref: G.Levy and I.Peat, J.Magn.Reson., 18, 500 (1978).

T1IR (Inversion Recovery)

y = A * { 1 – [ 2 – exp( -K/T ) ] * exp( -x/T ) }


T = T1 relaxation time
A = peak integral at time x >> T
K = total time between scans in the 180-t-90 sequence (equal to acquisition time plus relaxation delay time)
x = delay time t in the 180-t-90 pulse sequence

ref: Levy et al, J.Magn.Reson., 11, 58 (1973).


y = A * exp( -x/T )


T = T2 relaxation time
A = peak integral at time x >> T
x = delay time t in the pulse sequence

1st-Order Kinetics – for reactant (integral decreases with time)

y = A * exp( -kx )


k = reaction rate (in units of 1/sec)
A = peak integral at time zero
x = reaction time

1st-Order Kinetics – for reaction product (integral increases with time)

y = A* {1 –  exp( -kx ) }


k = reaction rate (in units of 1/sec)
A = peak integral at time zero
x = reaction time


D Display/edit list of time values
F Choose fitting function
K Peak pick method: integrals, peak heights or interpolated peak heights
O Optimize fit to data points
P Print
S Show contents of clipboard on screen (must execute T first)
T Copy table of time and integral values to the clipboard
X Expand x-scale. Allows expansion to see details of early time points.
Ctrl-C Copy screen to clipboard for pasting into other applications
Enter Exit program

T1-Inversion Recovery plot of Integral vs time

RR — Read Relaxation data file

Reads in a file containing time and amplitude values to be fit to the T1 equation. This is an alternative to the Get Relaxation data (GR) command, which automatically measures integrals of the selected region for each file in the data set. After reading in a file with RR, the fit is performed with the Data Reduction (DR) command. These commands are also available from the Tools menu.

The format of the relaxation data file must be as follows:

Relaxation Data
time1 value1
time2 value2
time n value n

The file can be created with any text editor and must be saved before it can be read into NUTS. Extra spaces are ignored, as is any line beginning with a semi-colon, allowing comments to be inserted to identify the source of the data. The first line must be Relaxation Data and the last line must be END.

N.B. Be sure to read a spectrum into NUTS before executing RR and DR. This serves to initialize the display parameters. If RR and DR are executed immediately after the NUTS program is started, erroneous display and calculation result.

Converting a series of 1D data to pseudo-2D data 

To use the automated relaxation data processing capability, the original 1D data files must have sequential file extensions to allow NUTS to process them using either a Link or a macro. Most of the useful tools for displaying and analyzing a series of 1D files require that they first be converted to a 2D data set.

This can be done as a 2-step process or all at once. For the 2-step process, execute a Link such as:


This imports each FID, does an FT and phases the spectra, then saves them as a series of 1D spectra. NUTS will prompt for a file name for the spectra. Remember to set LB and phasing on one of the files before executing this Link. The IN command increments the file extension and loops back to the first command in the link. It will continue until it fails to find the next file. The spectra can then be converted to a 2D data set with a link such as:


The SC command creates a 2D file.

To process the FIDs and save them as a 2D file all in one step, execute a link such as


NUTS will prompt for the file name of the first file of the original data and the file name to save the data to, which will be a 2D file.

Note that the above Links are not appropriate for processing in the Arrayed Mode.  In Arrayed Mode, each command (such as FT) is applied simultaneously to all slices, so the sequence of commands is executed one time, and there is no IN command.

Use GA to read in the first slice of the 2D file, making it the current data set. The data can now be plotted as a stacked plot with SP or slices can be viewed with VW. This process is useful for any series of 1D files, such as kinetics data.


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Last updated: 1/27/08.