Dynamic Functional Connectivity Using Heat Kernel

Sliding and tapered sliding window methods are the most common approaches in computing dynamic correlations between brain regions. However, due to data acquisition and physiological artifacts in resting-state fMRI, the sidelobes of the window functions in spectral domain will cause high-frequency fluctuations in dynamic correlations. To address the problem, we propose to define the heat kernel, a generalization of the Gaussian kernel, on a circle continuously without boundary. The windowless dynamic correlations are then computed by the weighted cosine series expansion, where the weights are related by the heat kernel. The proposed method is applied to the study of dynamic interhemispheric connectivity in the human brain in identifying the state space more accurately than the existing window methods.