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\begin{document}


\title{\bf 2D Voxel-based Morphometry Shows Less White Matter Concentration in Autism}
\author{Moo K. Chung$^{1,2,3}$, Kim D.
Dalton$^3$, Andrew L. Alexander$^{3,4,5}$,
Richard J. Davidson$^{3,4,6}$\\
\small $^1$Department of Statistics, $^2$Department of
Biostatistics and Medical Informatics, $^3$Keck Laboratory for
Functional Brain Imaging and Behavior\\
\small $^4$Department of Psychiatry, $^5$Department of Medical
Physics, $^6$Department of Psychology\\
University of Wisconsin-Madison, Madison, WI 53706 USA}
%$\tt{mchung@stat.wisc.edu}$}
\date{\small June 14, 2004}
 \maketitle \thispagestyle{empty}


\begin{multicols}{3}
\section*{Introduction}
Autism is a neurodevelopmental disorder with the abnormal
reduction in anterior, midbody and posterior part of the corpus
callosum (CC) \cite{Brambilla}. We applied 2D version of the
voxel-based morphometry (VBM) in quantifying the dynamic pattern
of the CC and show less white matter concentration in the high
functioning autistic (HFA) group at the genu and spleninum
removing the effect of age using the general linear model (GLM).
Further it is shown that the less white matter concentration is
due to hypoplasia rather than atrophy.
\begin{figure}
\centering
\includegraphics[width=160mm]{VBMflowchart.eps}
\caption{Data analysis flow.\label{fig:VBMflowchart}}
\end{figure}
\section*{Methods}
Gender and handedness affect the corpus callosum anatomy
\cite{Harden} so 16 HFA (age $16.1 \pm 4.5$) and 12 control
subjects (age $17.1 \pm 2.8$) used in this study are right-handed
males. Diagnoses were confirmed with the Autism Diagnostic
Interview-Revised (ADI-R) or clinical interview administered by a
certified psychologist. T1-weighted MRI data were collected on a
3T GE scanner. The 2D version of VBM was performed on the
midsagittal images based on SPM'99 \cite{Ashburner}. Based on
Gaussian mixture model, CCs are segmented automatically. The
advantage of VBM is hat it avoids artificial Witelson partition
\cite{Witelson}. Afterwards, 2D-Gaussian smoothing with 12mm FWHM
was performed on the resulting white matter density (Figure
\ref{fig:atlas}).
\begin{figure}
\centering
\includegraphics[width=185mm]{CCatlas.eps}
\caption{Left: white matter segmentation using SPM'99. Middle: 2D
Gaussian kernel smoothing of the white matter segmentation with
$12$ pixel wide FWHM.\label{fig:atlas}}
\end{figure}

\begin{figure}
\centering
\renewcommand{\baselinestretch}{1}
\includegraphics[width=185mm]{CCmean.eps}
\caption{\label{fig:CCmean} The sample mean of the white matter
density of the autistic group, the control group and their
difference respectively. We are interested in determining if this
difference is statistically significant.}
\end{figure}



Linear growth model of white matter density over age was fitted in
the least-squares fashion for each group to show different
dynamical pattern of white matter concentration change. To remove
the effect of age and corpus callosum size difference, the
following general linear model (GLM) was used:  $${\tt density} =
\lambda_1 + \lambda_2 \tt{age} +\lambda_3 \tt{area}+
\beta\tt{group}\label{eq:GLM02}$$ where the dummy variable ${\tt
group}$ is $1$ for autism and $0$ for control and ${\tt area}$ is
the relative total corpus callosum area. Then we are interested in
testing if there is any group difference, i.e. $H_0:\beta =0$.
Afterwards, the multiple comparison problem is solved thresholding
$F$-random field \cite{Worsley}.


\begin{figure}
\centering
\includegraphics[width=180mm]{HBM2004vbm01.eps}
\caption{Linear regression of the white matter density on age.
Linear growth model is fitted for each group separately. $P$-value
map measures the fit of linear regression. \label{fig:regression}}
\end{figure}

\begin{figure}
\centering
\includegraphics[width=180mm]{HBM2004vbm02.eps}
\caption{The simple linear fit correlating the white matter
density to age at the genu (a), midbody (b) and the splenium (c).
Red color is the autism group and blue color is the control group.
\label{fig:curvature}}
\end{figure}

\section*{Results}
Simple linear growth model shows that the white matter increase of
2.5$\%$ per year in the genu of the autistic group is
statistically significant. Although the autistic group exhibits
less white matter concentration at the early age in the genu, the
concentration seems to catch up with the normal subjects at the
rate of 2.5$\%$ per year. On the other hand both autistic and
control subjects exhibit increasing white matter in the selenium
over the years but there seems to be a gap of about 14$\%$ less
white matter in the autistic (Figure. 5-C). To test the hypothesis
of less white matter in the HFA removing the age effect, GLM was
used. The statistical significance for the genu and the rostrum
region is $P$-value $< 0.16$ (corrected) while the selenium is
$P$-value $< 0.097$ (corrected) (Figure 6). The orbital frontal
cortex projects through the rostrum while occipital and inferior
temporal cortex projects through the splenium. Since the white
matter density can be taken as an index for inter-hemispheric
connectivity, our results suggest impaired connectivity in
prefrontal and especially in temporal and occipital regions. The
detailed analysis result can be found in \cite{Chung}.

\begin{figure}
\centering
\includegraphics[width=180mm]{CCgroupeffect.eps}
\caption{$F$-map showing the statistically significant white
matter density difference (a) after controlling for age only and
(b) after controlling for both age and total corpus callosum area.
\label{fig:groupeffect}}
\end{figure}
\section*{Acknowledgements}
This work was funded by NIMH U54 MH066398-1A1 and by a NARSAD
Distinguished Investigator Award to RJD.
\begin{thebibliography}{10}
\small
\bibitem{Ashburner}
Ashburner, J., Friston, K.J. 2000. Voxel-based morphometry-the
method, {\em NeuroImage.} {\bf 11}:805-821.
\bibitem{Brambilla} Brambilla, P., Hardan, A., di Nemi, S. U., Perez, J., Soares, J.C., Barale, F. 2003.
Brain anatomy and development in autism: review of structural MRI
studies, {\em Brain Research Bulletin}, {\bf 61}:557-569.
\bibitem{Chung} Chung, M.K., Dalton, K.M., Alexander, A.L., Davidson,
R.J. 2004. Less white matter concentration in autism: 2D
voxel-based morphometry. {\em NeuroImage}, in press.

\bibitem{Harden} Hardan, A.Y., Minshew, N.J., Keshavan, M.S. 2000. Corpus
callosum size in autism. {\em Neurology} {\bf 55}:1033-1036.

%\bibitem{Hoffmann} Hoffmann, T.J., Chung, M.K., Dalton, K.M., Alexander,
%A.L., Wahba, G., Davidson, R.J. 2004. Subpixel curvature
%estimation of the corpus callosum via splines and its application
%to autism, HBM2004. See abstract number

\bibitem{Witelson} Witelson, S.F. 1989. Hand and sex differences in the isthmus and
genu of the human corpus callosum. {\em Brain}. {\bf 112}:799-835.


\bibitem{Worsley} Worsley, K.J., Marrett, S., Neelin, P., Vandal, A.C.,
Friston, K.J., and Evans, A.C. 1996. A unified statistical
approach for determining significant signals in images of cerebral
activation. {\em Human Brain Mapping} {\bf 4}:58-73.

\end{thebibliography}

\end{multicols}
\end{document}
