The continuous configuration model (CCM) (https://doi.org/10.1002/mrm.29101) constitutes a representation of arbitrary magnetic resonance imaging (MRI) sequences and tissues, which allows for a rigorous and transparent treatment of signal localization by selective excitation and/or spatial encoding.
The configuration model toolkit (CoMoTk), specifically the Matlab class CoMo, implements the CCM
for Bloch-Torrey and Bloch-McConnell equations.
The examples/ folder contains all scripts needed to reproduce the results from the article and
the associated supporting information.
Just add the matlab/ folder with subdirectories to your Matlab path.
Important: A Matlab version of R2016b or later is required, since implicit expansion is used a lot.
The following example should give a first impression of how to work with the toolkit.
Further information is provided in the documented code and the scripts in the examples/ folder cover typical application
scenarios. To fully benefit from the toolkit, it is indispensable to take a closer look at the linked article though.
% Example: sample FID of SSFP during transient phase
% sequence and tissue parameters
TR = 1; % repetition time [ms]
TE = 0.1; % echo time [ms]
flip_angle = pi / 2; % flip angle [rad]
phase = 0; % phase [rad]
T1 = 100; % longitudinal relaxation time [ms]
T2 = 10; % transverse relaxation time [ms]
D = 0; % we neglect diffusion in this example
% initialize class
cm = CoMo;
% set tissue parameters
cm.R1 = 1 / T1; % longitudinal relaxation rate [1/ms]
cm.R2 = 1 / T2; % transverse relaxation rate [1/ms]
cm.D = D; % diffusion constant [um^2/ms]
% crusher gradient moment
p_c = 1;
p_crusher = [ p_c; 0; 0 ]; % since we neglect diffusion,
% it only matters that it is nonzero
% discretization of configuration space
% (ideally the greatest common divisor of all time intervals and/or gradient moments)
cm.d_tau = TE;
cm.d_p = p_crusher;
% set RF pulse parameters
rf.FlipAngle = flip_angle; % flip angle [rad]
rf.Phase = phase; % phase [rad]
% set time interval from RF pulse to echo
te.tau = TE; % duration
% set time interval from echo to RF pulse (includes crusher)
crusher.tau = TR - TE; % duration
crusher.p = p_crusher; % zero-order gradient moment
% desired number of samples
n_TR = 100;
% allocate space for results
m_xy = zeros( n_TR, 1 );
% execute sequence loop
for i = 1 : n_TR
cm.RF( rf ); % RF pulse
cm.time( te ); % time to echo
% only magnetization pathways with no dephasing by crushers contribute to the FID signal.
% this corresponds to cm.p == [ O; O; O ], as explained in the article, linked above.
% to avoid possible rounding problems, we replace the condition by a more robust one.
fid = [];
fid.b_n = cm.occ & ( max( abs( cm.p ), [], 1 ) < 0.1 * p_c ); % cm.occ denotes occupied configurations
res = cm.sum( fid ); % extract FID
m_xy( i ) = res.xy; % store transverse component
cm.time( crusher ); % time to next RF pulse (includes crusher gradient)
end
% done
CoMoTk constitutes a proof-of-concept implementation of the CCM. Its numerical performance is limited, as it only supports single-core computation. For serious projects consider porting it to a parallel architecture, since the time-consuming part of the CCM iterations will benefit from it.
To supplement the submission of the background article about the CCM, a packaged, citable version of CoMoTk has been created:
Please use the issue tracker or write an email to [email protected].
Reporting bugs: Most helpful are small example scripts, which generate the error.