Integrated multimodal network approach to PET and MRI based on multidimensional persistent homology.

Finding underlying relationships among multiple imaging modalities in a coherent fashion is one of the challenging problems in multimodal analysis. In this study, we propose a novel approach based on multidimensional persistence. In the extension of the previous threshold-free method of persistent homology, we visualize and discriminate the topological change of integrated brain networks by varying not only threshold but also mixing ratio between two different imaging modalities. The multidimensional persistence is implemented by a new bimodal integration method called 1D projection. When the mixing ratio is predefined, it constructs an integrated edge weight matrix by projecting two different connectivity information onto the one dimensional shared space. We applied the proposed methods to PET and MRI data from 23 attention deficit hyperactivity disorder (ADHD) children, 21 autism spectrum disorder (ASD), and 10 pediatric control subjects. From the results, we found that the brain networks of ASD, ADHD children and controls differ, with ASD and ADHD showing asymmetrical changes of connected structures between metabolic and morphological connectivities. The difference of connected structure between ASD and the controls was mainly observed in the metabolic connectivity. However, ADHD showed the maximum difference when two connectivity information were integrated with the ratio 0.6. These results provide a multidimensional homological understanding of disease-related PET and MRI networks that disclose the network association with ASD and ADHD. Hum Brain Mapp 38:1387-1402, 2017.