Heat Kernels with Functional Connectomes Reveal Atypical Energy Transport in Peripheral Subnetworks in Autism

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11848)


Autism is increasing in prevalence and is a neurodevelopmental disorder characterised by impairments in communication skills and social behaviour. Connectomes enable a systems-level representation of the brain with recent interests in understanding the distributed nature of higher order cognitive function using modules or subnetworks. By dividing the connectome according to a central component of the brain critical for its function (it’s hub), we investigate network organisation in autism from hub through to peripheral subnetworks. We complement this analysis by extracting features of energy transport computed from heat kernels fitted with increasing time steps. This heat kernel framework is advantageous as it can capture the energy transported in all direct and indirect pathways between pair-wise regions over ’time’, with features that have correspondence to small-world properties. We apply our framework to resting-state functional MRI connectomes from a large, publically available autism dataset, ABIDE. We show that energy propagating through the brain over time are different between subnetworks, and that heat kernel features significantly differ between autism and controls. Furthermore, the hub was functionally preserved and similar to controls, however, increasing statistical significance between groups was found in increasingly peripheral subnetworks. Our results support the increasing opinion of non-hub regions playing an important role in functional organisation. This work shows that analysing autism by subnetworks with the heat kernel reflects the atypical activations in peripheral regions as alterations in energy dispersion and may provide useful features towards understanding the distributed impact of this disorder on the functional connectome.


Connectome Functional network Heat kernel Diffusion equation Subnetworks Hubs Autism 



This project has received funding from the American Heart Association and Children’s Heart Foundation Postdoctoral Fellowship, 19POST34380005 (AWC) and the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 753896 (MDS).


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Stroke Division and Massachusetts General Hospital, J. Philip Kistler Stroke Research CenterHarvard Medical SchoolBostonUSA
  2. 2.Department of Population Health SciencesGerman Centre for Neurodegenerative Diseases (DZNE)BonnGermany
  3. 3.Fetal-Neonatal Neuroimaging and Developmental Science Center, Boston Children’s Hospital, Harvard Medical SchoolBostonUSA

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