Relaxation and Kinetics Analysis
T1 Inversion Recovery and single-exponential T2 data can be analyzed. First order kinetics data for either reactant or product can be analyzed.
The data set being analyzed must contain multiple spectra, and must include a list of delay values. Up to a maximum of 64 delay values can be viewed or entered by typing D1. The analysis is performed on one peak at a time.
The first step in the process is to measure the area of the chosen peak for each spectrum in the series. The program will measure the integral of the displayed region for each spectrum, so it works best by zooming in very close to the peak. Good phasing and good baselines are important to minimize the error in the analysis.
Type GR (or choose Relaxation/kinetcis Analysis from the Tools menu), which measures the integrals. To display and fit the data, type DR (or choose Data Reduction data from the Relaxation/kinetcis Analysis option under the Tools menu). A plot of integral value vs. time for the chosen peak is displayed, but the curve that is initially shown is a first guess, not the result of fitting the data. By default, the data are assumed to be T1 relaxation, but this can be changed - type E or choose Edit Parameters from the Edit menu. Then type F (or choose Fit from the Edit menu) to perform a Simplex fit to the data.
A sample set of T1 data (13C spectra of sucrose, shown below) is available on the Acorn NMR web site, and is called Sucrose.t1.
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 or kinetics experiment. If a variable delay list was identified when the data file was imported, the values will be displayed. Otherwise, the user can enter them manually. Space is provided for up to 64 values.
These values are used in calculating relaxation times or rate constants.
GR -- Get Relaxation data
Used in calculating T1, T2 or a rate constant 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.
To use GR, the data must first be transformed, phased and baseline corrected. 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 >> Relaxation/kinetics menu). GR 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 relaxation (or kinetics) data can be displayed by typing DR (or choosing Display Relaxation data from the Tools>>Relaxation/kinetcis menu). The entire process is repeated for each peak of interest.
GR can take various arguments, used for setting parameters for the data analysis. Allowed arguments are:
T1IR - 2-parameter T1 fit
T13IR - 3-parameter T1 fit
T2S - T2 fit to single exponential
T2M - T2 fit to multiple exponentials (note that this has not yet been implemented)
K1I - first-order kinetics where peak increases over time (reaction product)
K1D- first-order kinetics where peak decreases over time (reactant)
height - use peak heights instead of peak areas
area - use peak areas (default)
help
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, or first order kinetics.
These steps must precede the DR command:
Typing DR (or choosing Data Reduction data from the Tools>>Relaxation/kinetcis 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 Edit menu. Choosing Edit Parameters brings up a dialog box which allows the user to select the fitting function. The choices are
Equations are shown below.
Also from this dialog box, the user can choose to use peak heights rather than integrals.
To perform a fit, type F or select Fit from the Edit menu. The curve determined by fitting the chosen equation to the data points is displayed, as are the values calculated in the fit process. If the integral for the largest peak in the series 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 clipboard by typing B or selecting Copy 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 a Note for display on the spectrum, or into an external text editor or spreadsheet.
The list of delay values used in the experiment can be displayed and edited by typing D1 from the base level or from within the DR subroutine by typing D.
Subcommands:
The equations used to fit relaxation and kinetics data are:
T13IR (3-parameter T1-Inversion Recovery)
y = A * { 1 - [ 1 + W * ( 1 - exp( -K/T ) ) ] * exp( -x/T ) }
where
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 ) }
where
ref: Levy et al, J.Magn.Reson., 11, 58 (1973).
T2 - Single exponential decay
y = A * exp( -x/T )
where
K1D - First order kinetics for the reaction A --> B, where the chosen peak decreases with time (reactant, A)
y = A0 * exp( -kt )
where
K1I - First order kinetics for the reaction A --> B, where the chosen peak increases with time (product, B)
y = A0 * [1-exp( -kt )]
where
Last updated: 12/19/07