Quantifying Similarity of Dynamic Brain Networks: Two Novel Indices for Structural Change and Temporal Evolution

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Abstract
Brain functional connectivity evolves dynamically during brain development, aging, illness, and cognitive activities. Traditional methods rely on static network snapshots, which do not capture the dynamics of the brain. We propose two new indices: Dynamic Network Similarity (DNS) to measure both temporal and structural dynamic similarity and Dynamic Network Evolution Similarity (DNES) to specifically measure the temporal evolution of dynamic networks. Performance was tested using simulated dynamic networks controlled by four variables (Δφ, λ, α, and β) concerning evolution variations in phase, relative amplitude, noise power, and the span of connectivity strength, respectively. Furthermore, real-world fMRI data from 25 stroke patients pre/post transcranial direct current stimulation (tDCS) rehabilitation were used to test the indices. Patients were randomly sub-grouped into tDCS1 and tDCS2. DNS and DNES thus compared those who received the same therapy (ST: tDCS1 versus tDCS2) and those who received different therapies (DT: tDCS1 versus sham-tDCS). The results showed that DNS was sensitive to all dynamic features, and DNES was primarily sensitive to Δφ and λ. Both indices were able to detect overall difference and capture significantly higher similarity in the ST groups than in the DT groups. Briefly, DNS and DNES appear to be effective tools for studying dynamically evolving brain networks, and may serve as alternatives to traditional static methods. They are particularly useful for analyzing longitudinal neuroimaging data in contexts such as neurodevelopment, aging, and recovery from illness.

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