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.

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.

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.

[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