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Z-spectrum - water, CEST, MT - cw

Here you find analytic solutions of the Bloch-McConnell equations describing Z-spectra. This R-model is based on the article Zaiss et al. A combined analytical solution for chemical exchange saturation transfer and semi-solid magnetization transfer, (2014), NMR Biomed. doi: 10.1002/nbm.3237.

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. It is actually the same source code as for the Solution for 2-pools under cw irradiation. Just the BATCh file is adjusted.

Dowload zipped Matlab implementations here or find the package on



For the 3-pool-simulation the 2-pool code must only be extended by the following fields in the struct P.

    % % semi-solid MT pool 'c'
    P.fC=0.139;               % proton fraction of the semi-solid pool (WM-like)
    P.kCA=23;                 % exchange rate [s^-1]
    P.dwC=-2;                 % deltaW_B in [ppm} (chemical shift)
    P.R2C=1/(9.1*10^-6);      % transversal relaxation rate 1/T2 of pool c [s^-1]
    P.R1C=1;                  % longitudinal relaxation rate 1/T1 of pool c [s^-1]
    P.MT_lineshape='Lorentzian';            % semi-solid Lineshape

To see the full width of the MT the frequency axis must be extended.

% sequence parameters
P.xZspec= [-150:0.1:150]; % ppm

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

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

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analytic_z-spectra-cw-3pool.txt · Last modified: 2021/10/11 13:22 (external edit)