Entropy measures as indicators of connectivity paths in the human brain

We develop an analytical framework that benefits from a set of information theory variables to study brain activity under different stimuli. fMRI signals from different brain regions are treated as time series, and information production as well as pattern redundancy are measured using entropy density, effective measure complexity, and informational distance estimated by Lempel-Ziv complexity. The estimators assume neither linearity nor stationarity, so both linear and non-linear dynamics contribute to the measures. The framework requires no generative model, no design matrix, and no parameters fitted to the data; the fixed choices are the binarization threshold, the neighborhood size of the activation criterion, and the distance threshold of the connectivity graphs. The framework is applied to task-based fMRI data from the Human Connectome Project under motor, working memory, emotion recognition, and language tasks, as well as resting state. The complexity entropy map identifies regional engagement consistent with established task-relevant areas, providing a model-free indicator of activation. The Lempel-Ziv distance between region pairs is then used to construct distance matrices, dendrograms, and connectivity graphs that recover hierarchical and modular functional structure: active regions cluster by functional specialization, while non-active regions form a densely interconnected backbone shared across tasks. Since the analytical framework neither depends on prior knowledge nor assumes linearity, it is well suited for exploratory research and for the study of brain connectivity, where non-linear interactions occur across multiple functional levels.