对于fmri的hrf血液动力学响应函数的一个很直观的解释-by 西南大学xulei教授

 

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clear all;clc;

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% haemodynamic response function: BOLD signal has stereotyped shape every

% time a stimulus hits it. We usually use the spm_hrf.m in SPM toolbox to

% produce HRF. Here, we use the 29 vector to represent HRF from 0 s to

% 28 s. In this simulation, we suppose TR=1 s.



HRF = [0 0.004 0.043 0.121 0.188 0.211 0.193 0.153 0.108 0.069 0.038 0.016 0.001 -0.009 -0.015 -0.018 -0.019 -0.018 -0.015 -0.013 -0.010 -0.008 -0.006 -0.004 -0.003 -0.002 -0.001 -0.001 -0.001];

% We will plot its shape with figure 1:

figure(1)

% here is the x-coordinates

t = [0:28];

plot(t,HRF,'d-');

grid on;

xlabel('Time (s)');

ylabel('fMRI respond');

title('haemodynamic response function (HRF)');

结果：

　　

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% Suppose that our scan for 120 s, we will have 120 point (because TR = 1

% s). If a stimulus onset at t=20 s, we can use a vector to represent this

% stimulation.

onset_1 = [zeros(1,19) 1 zeros(1,100)];

% i.e. the whole vector is maked with 19 zeros, a single 1, and then 100

% zeros. As we have the stimulus onset vector and HRF we can convolve them.

% In Matlab, the command to convolve two vectors is "conv":

conv_1 = conv(HRF,onset_1);

% Let's plot the result in figure 2 

figure(2);

% This figure will have 2 rows of subplots.

subplot(2,1,1);

% "Stem" is a good function for showing discrete events:

stem(onset_1);

grid on;

xlabel('Time (s)');

ylabel('Stimulus onset');

subplot(2,1,2);

plot(conv_1,'rx-');

grid on;

xlabel('Time (s)');

ylabel('fMRI signal');

结果：

　　

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% Usually, we have repeat a task many times in a run. If three stimulus 

% onsets at t=20, 50, 80 s, we also can use a vector to represent this

% stimulation.

onset_2 = [zeros(1,19) 1 zeros(1,29) 1 zeros(1,29) 1 zeros(1,20)];

% Here we use the conv again:

conv_2 = conv(HRF,onset_2);

% Let's plot the result in figure 3 

figure(3);

% This figure will have 2 rows of subplots.

subplot(2,1,1);

% "Stem" is a good function for showing discrete events:

stem(onset_2);

grid on;

xlabel('Time (s)');

ylabel('Stimulus onset');

subplot(2,1,2);

plot(conv_2,'rx-');

grid on;

xlabel('Time (s)');

ylabel('fMRI signal');

　结果：

　

 

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% Now let's think about the fast event design. In this condition, we will

% have many task during a short time. If three stimulus onsets at t=20, 25,

% 30 s:

onset_3 = [zeros(1,19) 1 zeros(1,4) 1 zeros(1,4) 1 zeros(1,70)];

conv_3 = conv(HRF,onset_3);

figure(4);

subplot(2,1,1);

stem(onset_3);

grid on;

xlabel('Time (s)');

ylabel('Stimulus onset');

subplot(2,1,2);

plot(conv_3,'rx-');

grid on;

xlabel('Time (s)');

ylabel('fMRI signal');

结果：

% The three events are so closed, the result signal is like a blocked

% design. Such as:

onset_4 = [zeros(1,19) ones(1,11) zeros(1,70)]*(3/11);

conv_4 = conv(HRF,onset_4);

figure(5);

subplot(2,1,1);

stem(onset_4);

grid on;

xlabel('Time (s)');

ylabel('Stimulus onset');

subplot(2,1,2);

plot(conv_4,'rx-');

% We will compare the result

hold on; % plot more than one time on a figure

plot(conv_3,'bx-');

grid on;

xlabel('Time (s)');

ylabel('fMRI signal');

结果：