How to Simulate magnitude of Mz in Gradient echo

Hi everyone,

I need to use Matlab to simulate the magnitude of Mz in gradient echo, through 256 RF excitations with flip angles of 10o, 30o, 50o, 70o, 90o, separately. When two tissues, gray matter (T1 = 1300 ms) and white matter (T1 = 900 ms), are imaged,

How can I plot their corresponding Mz versus number of RF excitations with TR of 90 ms?

Is there any suppored functions in Matlab to do that?

Great thanks

Answer 1

[Aditya]

Hi Peter,

I understand that you want to calculate and plot the magnitude of Mz (the longitudinal magnetization) in a gradient echo sequence with multiple RF excitations. You can use the Bloch equations for this. MATLAB does not have a built-in function specifically for simulating gradient echo sequences, but you can write a script to perform the simulation using the equations.

Here's a basic template that you can use:

% Define the parameters 
T1_gray = 1300; % T1 for gray matter in ms 
T1_white = 900; % T1 for white matter in ms 
TR = 90; % Repetition time in ms 
flip_angles = [10, 30, 50, 70, 90]; % Flip angles in degrees 
num_excitations = 256; % Number of RF excitations 

% Pre-allocate arrays for Mz 
Mz_gray = zeros(length(flip_angles), num_excitations); 
Mz_white = zeros(length(flip_angles), num_excitations); 

% Loop over each flip angle 
for i = 1:length(flip_angles) 
    alpha = flip_angles(i) * pi / 180; % Convert flip angle to radians 
    
    % Calculate Mz for each excitation for gray matter 
    for n = 1:num_excitations 
        Mz_gray(i, n) = % write the correct equation 
    end 
    
    % Calculate Mz for each excitation for white matter 
    for n = 1:num_excitations 
        Mz_white(i, n) = % write the correct equation 
    end 
    
    % Plot Mz for gray matter 
    figure; 
    plot(1:num_excitations, Mz_gray(i, :), 'b', 'DisplayName', 'Gray Matter'); 
    hold on; 
    
    % Plot Mz for white matter 
    plot(1:num_excitations, Mz_white(i, :), 'r', 'DisplayName', 'White Matter'); 
    
    % Customize the plot 
    title(['Mz vs. Number of RF Excitations (Flip Angle = ', num2str(flip_angles(i)), '°)']); 
    xlabel('Number of RF Excitations'); 
    ylabel('Mz'); 
    legend('show'); 
    hold off; 
end 

This script calculates the Mz values for both gray matter and white matter based on the provided equation. It then plots the results in separate figures for each flip angle, with the number of RF excitations on the x-axis and Mz on the y-axis.

Hope this helps!