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;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 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：

　　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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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 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： 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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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% 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：

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% 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：

本文转自二郎三郎博客园博客，原文链接：http://www.cnblogs.com/haore147/p/3633515.html，如需转载请自行联系原作者

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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