%
% 2017.01.30 Patrick Magrath & DBE@UCLA
%% HW01 Problem #2A
% Define some constants
dt=1e-6; % Time steps in seconds
dt_2 = 1e-10;
gamma=42.57e6; % Gyromagnetic ratio, [Hz/T]
B0=5.87e-6; % External magnetic field strength [T]
%PPM=3.0e-2; % Fat-Water shift was stated as 2.4ppm, but it is really 3.4ppm
N_Steps=1000; % Number of time steps
N_Steps_2 = 10000; % Number of time steps for B0
M0=[1 0 0]'; % Initial condition [A.U.]
t_max=dt*N_Steps; % Maximum time of simulation [s]
t_max_2 = dt_2*N_Steps_2; % For the B0 simulation
t=linspace(0,t_max,N_Steps); % Vector of time points [s]
t_2 = linspace(0,t_max_2,N_Steps_2); %For the second simulation
% Since we're just looking at precession with respect to a given
% field, we treat the B1 field as if it was the B0 field over the duration
% of the RF pulse.
M_H20=zeros(4,N_Steps); % Initialize the magnetization vectors
M_H20(:,1)=[M0; 0]; % Define the initial condition
M_part2(:,1) = [M0;0];
dB0_H20=PAM_B0_op(gamma,B0,dt); % Define the incremental precession
dB0_part2 = PAM_B0_op(gamma,3,dt_2);
% Simulate precession
for n=2:N_Steps
M_H20(:,n) = dB0_H20*M_H20(:,n-1);
end
for n=2:N_Steps_2
M_part2(:,n) = dB0_part2*M_part2(:,n-1);
end
M_part2(:,n) = dB0_part2*M_part2(:,n-1);
% Plot the results - Note F/W differences are hard to see on short time scales...
figure; hold;
plot(t,M_H20(1,:),'linewidth',2);
plot(t,M_H20(2,:),'linewidth',2);
%plot(t,M_H20(3,:),'linewidth',2);
xlabel('Time [s]');
ylabel('Magnetization [a.u.]');
legend('Mx B1 Field','My B1 Field');
title('Precession in the B1 Field')
set(gcf,'Color','w');
set(gca,'Color','w','XColor','k','YColor','k');
set(gca,'Color','w','XColor','k','YColor','k','LineWidth',1.25,'Fontsize',11,'Fontweight','bold');
set(get(gca,'Title'),'Color','k','FontSize',16);
set(get(gca,'Xlabel'),'FontSize',14,'fontweight','bold');
set(get(gca,'Ylabel'),'FontSize',14,'fontweight','bold');
grid('on')
print2desktop('/Users/pmagrath/desktop/','HW2_P2_B1')
figure; hold;
plot(t_2(1:1000),M_part2(1,1:1000),'linewidth',2);
plot(t_2(1:1000),M_part2(2,1:1000),'linewidth',2);
%plot(t,M_H20(3,:),'linewidth',2);
xlabel('Time [s]');
ylabel('Magnetization [a.u.]');
legend('Mx B0 Field','My B0 Field');
title('Precession in the B0 Field');
set(gcf,'Color','w');
set(gca,'Color','w','XColor','k','YColor','k');
set(gca,'Color','w','XColor','k','YColor','k','LineWidth',1.25,'Fontsize',11,'Fontweight','bold');
set(get(gca,'Title'),'Color','k','FontSize',16);
set(get(gca,'Xlabel'),'FontSize',14,'fontweight','bold');
set(get(gca,'Ylabel'),'FontSize',14,'fontweight','bold');
grid('on')
print2desktop('/Users/pmagrath/desktop/','HW2_P2_B0')