# Stejskal tanner analysis.m

Regression analysis using the Stejskal-Tanner (ST) equation.

## Syntax

stejskal_tanner_analysis(parameters)

## Description

This function can be used obtain the diffusion coefficient from the last square fitting of the Gaussian decay obtained upon the increase of the gradient amplitude in diffusion weighting NMR pulse sequences.

## Arguments

1) parameters.gradient.pattern - shape of the gradient that can be rectangular or sine bell with monopolar, bipolar or unbilanced-bipolar pattern

2) parameters.method - kind of analysis to perform that can be: 1. convergence and accuracy: to test effect of the number of points on the values of the diffusion coefficients 2. fitting: to perform a regression analysis to obtain the diffusion coefficient from theoretical diffusion decay 3. Comparison: to extract the diffusion coefficient from the experimental diffusion decay and comparison with theoretical decay

## Returns

The diffusion coefficient and fractional residual between theoretical diffusion decay and fit with the ST-equation.

## Notes

Spinach has periodic boundaries in spatial dimensions that make diffusion processes wrapping concentrations around decreasing the accuracy in the calculation of the diffusion coefficient. To improve the accuracy of the simulations, sufficient white space has to be added on both the sides of the initial state phantom, this would avoid self-interaction across the periodic boundary.

## See also

Dosy_oneshot.m, pfg_spin_echo.m, pfg_stim_echo.m, bpp_stim_echo.m and corresponding examples.

*Version 1.10, authors: Maria Grazia Concilio*