Application of the Mahalanobis Distance for Depicting the Neuroanatomical Variability within Autism Spectrum Disorders
Douglas C Dean III1, Nicholas Lange2, Brittany Travers1, Nagesh Adluru1, Do Tromp1, Daniel Destiche1, Abigail Freeman1, Danica Samsin1, Brandon Zielinski3, Molly Prigge3, P.T. Fletcher3, Jeffery Anderson3, Erin Bigler4, Janet Lainhart1, and Andrew Alexander1

1Waisman Center, University of Wisconsin-Madison, Madison, WI, United States, 2McLean Hospital, Boston, MA, United States, 3University of Utah, Salt Lake City, UT, United States, 4Brigham Young University, Provo, UT, United States

Synopsis

To date, the heterogeneity of neuroimaging findings has made it challenging to identify specific brain-related phenotypes within autism spectrum disorder (ASD). In particular, a quantitative index of individual deviation across a set of brain measurements may be informative for constructing distributions of brain variation and identifying individuals who may or may not have abnormal brain structure. To this end, we investigated the use of the Mahalanobis distance to characterize multidimensional brain measures in individuals with and without ASD and to demonstrate that patterns of brain features distinguishing individuals with ASD are multidimensional and likely encompass differing cortical and sub-cortical characteristics.

Target Audience

Researchers interested in autism spectrum disorders (ASD) and the use of diffusion tensor imaging (DTI) in understanding white matter changes in ASD.

Introduction

Brain imaging findings in children with autism spectrum disorder (ASD) suggest the disorder is complex and heterogeneous, making the interpretation of the underlying neurobiology of ASD challenging. Such heterogeneity may suggest that the neuroanatomy of ASD is not restricted to a single brain region or network, rather that differences are subtle and more widespread1. Thus, consideration of multivariate relationships of the brain may enable better characterization and discrimination of individuals with ASD. Distinguishing these multidimensional brain relationships at both the group and individual level are therefore critical as characterization may be informative for identifying ASD subgroups as well as understanding individual brain variation in ASD. Here, we propose that the Mahalanobis distance2, a multidimensional generalization of a standard score (i.e., z-score for univariate statistics), may provide an informative index of characterizing individual brain variation in ASD. The Mahalanobis distance is constructed as the distance from the typically developing control (TD) sample mean in multidimensional feature space weighted by the TD covariance. In this study we used longitudinal trajectories of structural and microstructural brain development to construct the individual Mahalanobis distances and compare the distributions of brain variability between ASD and TD individuals.

Methods

MRI Acquisition: Longitudinal data from 148 participants (92 ASD and 56 TD) between 3.1 and 34.5 years of age were used for this study. A total of 213 scans from ASD participants and 123 scans from TD individuals were acquired on a 3 Tesla Siemens Tim Trio scanner and consisted of structural T1-weighted (MP-RAGE) and diffusion tensor imaging (DTI) data. Diffusion weighted images were corrected for distortion and head motion and tensors were subsequently fit using the robust estimation algorithm (RESTORE3). Analysis: Volumetric measures from 16 brain regions were computed using FreeSurfer [version 5.14], following the steps for longitudinal processing5, while the mean FA were computed from 21 major white matter tracts6 and used in subsequent analyses. To construct the Mahalanobis distance metric, longitudinal trajectories were first separately modeled for TD and ASD groups using mixed effects modeling. Distances from the population-averaged TD trajectory were then computed and normalized by the covariance matrix of fit residuals, forming the Mahalanobis distance.

Results

Fig. 1 shows a visualization of the distributions of Mahalanobis distances calculated from the ASD and TD groups. Qualitatively, we notice a differential pattern between individuals with and without ASD. In particular, the ASD group’s distribution of Mahalanobis distances is shifted rightward, signifying larger multivariate brain deviation compared to the TD group. Comparing these distributions quantitatively, we find the mean of the ASD distribution (1.2125 [0.3792]) to be significantly larger (p<0.0001) than the mean of the TD distribution (0.4751 [0.2237]). Also of note, the standard deviation of the Mahalanobis distributions was found to be larger in the ASD group compared to the TD group, highlighting the heterogeneity across the ASD population.

Discussion

Previous studies have consistently indicated both gross and microstructural brain differences in ASD compared to typical development7,8. While univariate measures provide informative insight to specific brain regions and biological mechanisms implicated in ASD, consideration of the multivariate relationships of the brain may enable better characterization and discrimination of individuals with ASD. In this work, we used mixed effects modeling and the Mahalanobis distance to characterize patterns of multivariate brain measures in ASD and TD. Our results suggest that that the distribution of Mahalanobis distances in ASD individuals is larger and more variable compared to TD individuals. These results additionally suggest that the Mahalanobis distance of differing image modalities may be valuable for distinguishing individuals with and without ASD as well as identifying possible subgroups of autism.

Conclusion

In this work, we have sought to examine the application of the Mahalanobis distance, to assess multivariate brain measures of ASD and TD brain development. Our results suggest that this measure may provide an informative metric for characterizing and distinguishing the multivariate patterns of brain development between ASD and TD individuals. Moreover, our results raise additional questions in regards to whether specific brain regions or image modalities are particularly sensitive to observed ASD brain differences.

Acknowledgements

We sincerely thank the children, adolescents, and adults with autism, the individuals with typical development, and all the families who participated in this study. This work was supported by the National Institute of Mental Health [RO1 MH080826 to JEL, ALA, NL, EDB; RO1 MH084795 to JEL, PTF, NL; RO1 MH097464 to JEL, ML, NL, ALA; K08 MH100609 to BAZ, and KO8 MH092697 to JSA], the Eunice Kennedy Shriver National Institute of Child Health and Human Development [T32 HD007489 to DCD, BGT, and P30 HD003352 to the Waisman Center], the Poelman Foundation [to EDB], the Primary Children’s Foundation [Early Career Development Award to BAZ], and the Hartwell Foundation [Postdoctoral Fellowship Award to BGT]. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institute of Mental Health, the National Institute of Child Health & Development, or the National Institutes of Health. We thank Zhan Xu, Anne M. Bartosic, Annahir Cariello, Celeste Knoles, Sam Doran, and Kristine McLaughlin for their contributions to this project.

References

[1] Ecker et al. Describing the brain in autism in five dimensions-magnetic resonance imaging-assisted diagnosis of autism spectrum disorder using a multiparameter classification approach. J. Neurosci. 2010; 30:10612–10623. [2] Mahalanobis. On the generalised distance in statistics. In: Proceedings National Institute of Science, India, 1936; Vol 2, No 1. [3] Chang et al. RESTORE: robust estimation of tensors by outlier rejection. MRM 2005 53:1088–1095. [4] Fischl, B. et al. Automatically parcellating the human cerebral cortex. Cerebral Cortex, 2004; 14: 11–22. [5] Reuter, M. et al. Within-subject template estimation for unbiased longitudinal image analysis. Neuroimage, 2012; 61:1402–1418. [6] Mazziotta J. et al. A four-dimensional probabilistic atlas of the human brain. J. Am. Med. Inform. Assoc. 2001;8:401–430. [7] Lange et al. Longitudinal Volumetric Brain Changes in Autism Spectrum Disorder Ages 6–35 Years. Autism Res 2015; 8: 82–93. [8] Travers et al. Diffusion tensor imaging in autism spectrum disorder: a review. Autism Research. 2012; 5: 289–313.

Figures

Figure 1: Distribution of calculated Mahalanobis distance measures for ASD (red) and TD (blue) individuals. The ASD distribution is shifted rightward, signifying larger Mahalanobis distances that suggest aberrant brain development compared to TD individuals.



Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
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