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analytic_z-spectra-cw-2pool [2020/06/15 11:53] (current)
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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<sub>1ρ</sub>-model as published in **Zaiss and Bachert (2013), NMR Biomed., 26: 507–518. [[http://onlinelibrary.wiley.com/doi/10.1002/nbm.2887/abstract|doi: 10.1002/nbm.2887]]**. {{ :z_cw_b1.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. 
 + 
 +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>bSv7H7lUnTg?640x480|Tutorial: 2 minutes for 2 pools}}
 +
 +
 +===== The code ======
 +=== BATCH_Z_cw ===
 +
 +First the pool parameters are defined in the parameter struct P:
 +<code matlab>
 +
 +%% SETUP 
 +%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]
 +
 +</code>
 +Now the CEST sequence parameters are defined
 +<code matlab>
 +% 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]
 +P.tp=5;             % pulse duration = saturation time [s]
 +P.xZspec= [-5:0.1:5]; % 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>
 +
 +=== function Z_cw(P) ===
 +
 +{{ :logo_dkfz.png?direct&180|powered by DKFZ}}
  
analytic_z-spectra-cw-2pool.txt · Last modified: 2020/06/15 11:53 (external edit)