Signal Modelling
Multiexponential T2 Mapping
For multiexponential T2 mapping, the transverse magnetization (Mxy) acquired at different echo times (TE) can be modeled as a sum of exponential decays :
where each term of the summation represents the contribution of the ith tissue component to the overall transverse magnetization decay Collewet et al., 2022Dortch, 2020.
Figure 3.4 presents a single-voxel simulation of T2 relaxation curves of myelin water (MW) and intra/extracellular water (IEW) using mono-exponential T2 fitting, compared to a multi-exponential fitting for both MW and IEW. In this example, we see that using a multi-exponential model rather than mono-exponential for complex tissues like myelin enables more precise quantification of the T2 relaxation time within each voxel.
Figure 3.4:Comparison of mono-exponential and multi-exponential T2 fitting. This figure contrasts mono-exponential and multi-exponential fitting approaches for a single voxel containing myelin water (MW) and intra/extracellular water (IEW). The green and orange curves represent mono-exponential fittings for MW and IEW, respectively. The dotted purple curve illustrates the multi-exponential fitting, which combines both MW and IEW components.
Figure 3.7:Comparison of mono-exponential and multi-exponential T2 fitting. This figure contrasts mono-exponential and multi-exponential fitting approaches for a single voxel containing myelin water (MW) and intra/extracellular water (IEW). The green and orange curves represent mono-exponential fittings for MW and IEW, respectively. The dotted purple curve illustrates the multi-exponential fitting, which combines both MW and IEW components.
Click here to view the qMRLab (MATLAB/Octave) code that generated Figure 3.4.
%% Requirements
% qMRLab must be installed: git clone https://www.github.com/qMRLab/qMRLab.git
% The mooc chapter branch must be checked out: git checkout mooc-03-T2
% qMRLab must be added to the path inside the MATLAB session: startup
close all
clear all
Model = mwf
% Define initial MWF and T2 times of myelin water and intra- and extracellular water
x = struct;
x.MWF = 50;
x.T2MW = 20;
x.T2IEW = 120;
% Define echo times
params.TE = linspace(0, 300, 100);
% Set simulation options
Opt.SNR = 120;
Opt.T2Spectrumvariance_Myelin = 5;
Opt.T2Spectrumvariance_IEIntraExtracellularWater = 20;
% Run simulation
figure('Name','Single Voxel Curve Simulation');
FitResult = Model.Sim_Single_Voxel_Curve(x,Opt);
% T2 relaxation curves for myelin water and intra/extracellular water
% (using a mono-exponential curve)
signal_mono_MW = exp(-params.TE / FitResult.T2MW);
signal_mono_IEW = exp(-params.TE / FitResult.T2IEW);
% T2 relaxation curve for multi-expo model
signal_multi_MWF = (FitResult.MWF/100)*signal_mono_MW + (1 - FitResult.MWF/100)*signal_mono_IEW;
%% Export
TE = squeeze(params.TE)
save("multiexpo_T2_curves.mat", "signal_mono_MW", "signal_mono_IEW", "signal_multi_MWF", "TE", "FitResult", "params", "x", "Opt")- Collewet, G., Musse, M., El Hajj, C., & Moussaoui, S. (2022). Multi-exponential MRI T2 maps: A tool to classify and characterize fruit tissues. Magn. Reson. Imaging, 87, 119–132.
- Dortch, R. D. (2020). Quantitative T2 and T2* Mapping. In Advances in Magnetic Resonance Technology and Applications (pp. 47–64). Elsevier.