===== Z-spectrum -  water, CEST, MT - cw=====



Here you find analytic solutions of the Bloch-McConnell equations describing Z-spectra.
This R<sub>1ρ</sub>-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.** [[http://onlinelibrary.wiley.com/doi/10.1002/nbm.3237/full|doi: 10.1002/nbm.3237]].
{{ :z_cw_b1_mt.png?nolink&300|}}

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  [[Analytic Z-spectra-cw-2pool|Solution for 2-pools under cw irradiation]]. Just the BATCh file is adjusted.
 
Dowload zipped Matlab implementations [[https://github.com/cest-sources/Z-cw/archive/master.zip|here]] or find the package on [[https://github.com/cest-sources/Z-cw|github.com/cest-sources/Z-cw]]


====== Tutorial======


{{youtube>G0wFnHCogGw?640x480|Tutorial: 2 minutes for 3 pools}}


===== BATCH_Z_cw_3pool =====

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

    % % 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

</code>

To see the full width of the MT the frequency axis must be extended.
<code matlab>
% sequence parameters
P.xZspec= [-150:0.1:150]; % ppm
</code>

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

<code matlab>
figure(32), plot(P.xZspec,Z_cw(P),'r-') ;   hold on;
</code>

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