The Fractal Geometry of Alzheimer’s disease

Abstract

AbstractBackgroundHuman brain is the most dynamic and varied system of the body. The brain is composed of neuron and glia. But how do they interact to generate emergent properties like memory, learning, emotion and sleep is little understood. Many such complex systems that exist in non‐linear dynamics are characterized by the fractal nature. The fractal dimension (FD) is a quantitative parameter that has been extensively used to analyze the complexity of structural and functional patterns of the human brain. The fractal dimension (FD) of the human brain quantifies the inherent complexity.MethodA non‐linear analysis called the Fractal Dimension (FD) has been performed to quantify the fractal complexity of AD. Our primary goal is to investigate FD to assess whether it can discriminate between different states of AD. We perform multi‐fractal analysis to discover whether AD and its states belong to class of multi‐fractal object for which a large number of scaling exponents are required to characterize their scaling structures. We plot the multi‐fractal spectra of the fMRI images to compare the width of the scaling exponent for each spectrum.ResultFrom FD analysis, we noticed that the fractal dimension increases with aging the AD, i.e. the complexity and self similarity of brain structure increases. According to our analysis, we have a wide range of exponents for AD fMRI images, which indicates different states of Alzheimer’s disease have multi‐fractal structure.ConclusionAs a result, fractal geometry can be considered as a computational framework to characterize different stages of AD and with further analysis, it can be used as a diagnostic tool to fight against Alzheimer’s disease.