The exponential curve models

A number of different models are supported in this analysis. These include the two parameter exponential decay to zero, the inversion recovery experiment, and the saturation recovery experiment. These can be selected using the relax_fit.select_model user function.

The default is the two parameter exponential decay whereby the magnetisation starts at I0 and decays to zero. It has the parameters { Rx, I0}. The formula of this function is

I(t) = I0e-Rx⋅t, (5.1)

where I(t) is the peak intensity at any time point t, I0 is the initial intensity, and Rx is the relaxation rate (either the R1 or R2).

In the inversion recovery experiment, the magnetisation starts at a negative value at - I0 and relaxes to a positive I value. This curve consists of three parameters { Rx, I0, I}. The formula is

I(t) = I - I0e-Rx⋅t. (5.2)

In the saturation recovery experiment, the magnetisation starts at zero and relaxes to a positive I value. The model consists of the two parameters { Rx, I} and has the formula

I(t) = I$\displaystyle \left(\vphantom{ 1 - e^{-\mathrm{R}_x \cdot t} }\right.$1 - e-Rx⋅t$\displaystyle \left.\vphantom{ 1 - e^{-\mathrm{R}_x \cdot t} }\right)$. (5.3)

The relax user manual (PDF), created 2016-10-28.