The Fractal Geometry of Alzheimer’s disease Toward Better Cognitive Assessment

Human 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 analyse the complexity of structural and functional patterns of the human brain. The fractal dimension (FD) of the human brain quantifies the inherent complexity. Evidences strongly suggest that fractal properties of a biologic system might be related to entropy and metabolism. In several pathologies of the brain such as Alzheimer’s, Epilepsy and Stroke, fractal dimension (FD) is altered. FD in combination with other features is emerging as a powerful diagnostic approach at the hands of a clinician. Alzheimer disease (AD) is a progressive neurodegenerative disease that destroys memory and cognitive skills. Aging is the biggest risk factor for AD. The central quest of research on AD is to identify the steps in its pathogenesis that, if inhibited, would slow or prevent the disease. All AD patients develop neuritic plaques in brain areas subserving memory and cognition. These plaques consist of extracellular masses of Aβ filaments intimately associated with dystrophic dendrites and axons, activated microglia, and reactive astrocytes. In 1983, Benoit Mandelbrot, the founder of fractal geometry, presented the amazing world of fractals to the world. Fractals are infinitely complex objects which are self similar in different scales. In this study we are focused to understand the changes in fractal properties (FD) of human brain as a whole in glioma during the states of AD. A 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. From FD analysis, we noticed that the fractal dimension increases with aging the AD, i.e. the complexity and self similarity of brain structure increases. 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. 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. As 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.