Sample entropy and regularity dimension in complexity analysis of cortical surface structure in early Alzheimer's disease and aging

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• A practical model was constructed for calculating SampEn and regularity dimension.
• We applied this model for the first time to quantify brain structural complexity.
• An increase of cortical surface structure complexity was detected in early AD.
• An increasing structural irregularity with aging was observed.
• The model may be used to construct a useful biomarker of AD and cognitive decline.

We apply for the first time the sample entropy (SampEn) and regularity dimension model for measuring signal complexity to quantify the structural complexity of the brain on MRI. The concept of the regularity dimension is based on the theory of chaos for studying nonlinear dynamical systems, where power laws and entropy measure are adopted to develop the regularity dimension for modeling a mathematical relationship between the frequencies with which information about signal regularity changes in various scales. The sample entropy and regularity dimension of MRI-based brain structural complexity are computed for early Alzheimer's disease (AD) elder adults and age and gender-matched non-demented controls, as well as for a wide range of ages from young people to elder adults. A significantly higher global cortical structure complexity is detected in AD individuals (p < 0.001). The increase of SampEn and the regularity dimension are also found to be accompanied with aging which might indicate an age-related exacerbation of cortical structural irregularity. The provided model can be potentially used as an imaging bio-marker for early prediction of AD and age-related cognitive decline.