Corpus Callosum White Matter Density Data and General
Linear Models (GLM)
Chung, M.K., Dalton, K.M., Alexander,
A.L., Davidson, R.J. 2004. Less
white matter concentration in autism: 2D voxel-based
morphometry. NeuroImage 23:242-251
Abstract
Autism is a neurodevelopmental disorder affecting behavioral
and social cognition, but there is little understanding about
the link between the functional deficit and its underlying
neuroanatomy. We applied a 2D version of voxel-based morphometry
(VBM) in differentiating the white matter concentration of the
corpus callosum for the group of 16 high functioning autistic
and 12 normal subjects. Using the white matter density as an
index for neural connectivity, autism is shown to exhibit less
white matter concentration in the region of the genu, rostrum,
and splenium removing the effect of age based on the general
linear model (GLM) framework. Further, it is shown that the less
white matter concentration in the corpus callosum in autism is
due to hypoplasia rather than atrophy.
PDF
Dataset
The imaging
data set used in the paper consists of the 2D midsagittal
section of the gray matter density value for 16 high functioning
autistic and 12 normal subjects. The data set is stored as text
file in brainimaging.waisman.wisc.edu/~chung/BIA/download/matlab.v1/CCdensity/.
To read the data set, run chapter03-GLM.m
line by line.
General Linear Model
(GLM) MATLAB function
GLM.m
The detailed documentation for this function is here.
This function combines the example below into a single function
call. The two-sample t-test and equivalent F-test result testing
the equality of 1:25 and 26:50 is given by done by
y=[1:50]'
Z=[]
X=[ones(25,1) ; zeros(25,1)]
stat=GLM(y,Z,X)
General Linear Model (GLM) Example
The following MATLAB (tested
under version 6.1) codes will remove the effect of age
in two sample group comparison. It will construct F
statistic at a given voxel. I did not write it as a
single function since people may need to modify the
codes to suit their applications.
% n.sample1 =
sample size for sample 1
% n.sample2 = sample size for sample 2
% age.sample1 = age for sample 1; column vector
% age.sample2 = age for sample 2; column vector
% obs1 = observation for sample 1
% obs2 = observation for sample 2
% group = 0 if sample 1 or 1 if sample 2
%total sample size
n = n.sample1 + n.sample2;
% combined age data. this should give a single column
vector.
age=[age.sample1; age.sample2];
% combined observations. this should give a single
column vector.
obs = [obs1; obs2];
% fitting null model of no group difference
% H_0: group = lambda1 + lambda2 * age
const=ones(n,1)
%design matrix
X=[const,age]
%estimate lambda's
lambda=zeros(2,1);
lambda=pinv(X)*obs;
%sum of squared errors of null model. denominator for F
stat
SSE0 = sum((obs - (X*lambda)).^2);
% fitting an alternate model of group difference
% H_0: group = lambda1 + lambda2 * age + \lambda3 *
group
% group = binary indexing for groups
% 0 if sample 1 or 1 if sample 2
group = [zeros(n.sample1,1);ones(n.sample2,1)];
lambda=zeros(3,1);
X=[const,age,group]
lambda=pinv(X)*obs;
% sum of squared errors of alternate model. numerator
for F stat
SSE1 = sum((obs - (X*lambda)).^2);
% F statistic = equvalent to ANOVA F statistic output
F=(SSE0-SSE1)/(SSE0/(n-1-2))
Documentation
The
following paper used above MATLAB code and contains detailed
explanation.
[1] Chung, M.K. 2013. Statistical and
Computational Methods in Brain Image Analysis. Chapman &
Hall/CRC. DATA/MATLAB
[2]
Chung, M.K.,
Robbins,S., Dalton, K.M., Davidson, Alexander, A.L., R.J.,
Evans, A.C. 2005. Cortical thickness
analysis in autism via heat kernel smoothing. NeuroImage 25:1256-1265
[3] Chung,
M.K., Dalton, K.M., Alexander, A.L., Davidson, R.J.
2004. Less
white matter concentration in autism: 2D Voxel-Based
Morphometry. NeuroImage 23:242-251.
Last update 02/25/2005; 04/08/2013;
09/27/2014