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Analytic Z-spectra water, CEST - cw

Here you find analytic solutions of the Bloch-McConnell equations describing Z-spectra. This is the R-model as published in Zaiss and Bachert (2013), NMR Biomed., 26: 507–518. doi: 10.1002/nbm.2887.

It is a very lean code to give you a tool illustrating the principal behaviour of a CEST effect and its interaction with the direct water saturation.

Dowload zipped Matlab implementations here or find the package on


The code


First the pool parameters are defined in the parameter struct P:

%pool system parameters
%water pool A
P.R1A=1/3;          % longitudinalrelaxation rate [s^-1]
P.R2A=2;            % transversal relaxation rate [s^-1]
P.dwA=0;            %deltaW_A in [ppm]
%CEST pool B
P.fB=0.001;         % proton fraction: [water protons]/[CEST agent protons]
P.kBA=200;          % exchange rate [s^-1]
P.dwB=1.9;          % (chemical shift) deltaW_B in [ppm} 
P.R2B=30;           % transversal relaxation rate [s^-1]

Now the CEST sequence parameters are defined

% sequence parameters
P.Zi=1;             % Z initial, in units of thermal M0, Hyperpol.: 10^4                  
P.FREQ=300;         % [MHz]  I use ppm and µT, therefore gamma=267.5153;
P.B1=2;             % [µT];             % pulse duration = saturation time [s]
P.xZspec= [-5:0.1:5]; % ppm

Now the function Z_cw(P) is called and plotted:

figure(32), plot(P.xZspec,Z_cw(P),'r-') ;   hold on;

function Z_cw(P)

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analytic_z-spectra-cw-2pool.txt · Last modified: 2021/10/11 13:22 (external edit)