Characterising brain network topologies: A dynamic analysis approach using heat kernels

Network theory provides a principled abstraction of the human brain: reducing a complex system into a simpler representation from which to investigate brain organisation. Recent advancement in the neuroimaging field is towards representing brain connectivity as a dynamic process in order to gain a deeper understanding of how the brain is organised for information transport. In this paper we propose a network modelling approach based on the heat kernel to capture the process of heat diffusion in complex networks. By applying the heat kernel to structural brain networks, we define new features which quantify change in heat propagation. Identifying suitable features which can classify networks between cohorts is useful towards understanding the effect of disease on brain architecture. We demonstrate the discriminative power of heat kernel features in both synthetic and clinical preterm data. By generating an extensive range of synthetic networks with varying density and randomisation, we investigate heat diffusion in relation to changes in network topology. We demonstrate that our proposed features provide a metric of network efficiency and may be indicative of organisational principles commonly associated with, for example, small-world architecture. In addition, we show the potential of these features to characterise and classify between network topologies. We further demonstrate our methodology in a clinical setting by applying it to a large cohort of preterm babies scanned at term equivalent age from which diffusion networks were computed. We show that our heat kernel features are able to successfully predict motor function measured at two years of age (sensitivity, specificity, F-score, accuracy = 75.0, 82.5, 78.6, and 82.3%, respectively).