UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS

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2024-11-23 12:05
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Conference: Bucharest University Faculty of Physics 2008 Meeting


Section: Electricity and Biophysics


Title:
The Fractal Brain


Authors:
Radu Mutihac


Affiliation:
Universitatea din Bucuresti, Facultatea de Fizica


E-mail


Keywords:


Abstract:
Brain analysis methods, which reveal statistical regularities in data associated with brain function, can be dichotomized in: (i) hypothesis-driven (confirmatory) and (ii) data-driven (exploratory) analysis. In statistical inference, the expected changes in brain activity are specified as regressors within a multiple linear regression framework and the estimated regression coefficients are tested against a null hypothesis. The voxelwise test statistics form summary images (maps) that are representations of the spatial distribution of functional activity induced by some experimental paradigms. Contrarily, exploratory analysis makes no reference to prior knowledge of data structure and provides models whose characteristics are solely determined by statistical properties of data. Multiresolution analysis falls somewhat in between since the key features of signals are identified and analyzed with resolutions matched to their scales and subsequently assessed for statistical significance. The approach is optimal in that of detecting transient events and adapting to local or nonstationary features in data within decomposition scales. Fractals define a class of objects with the characteristic property of self-similarity (or self-affinity), meaning that the statistics describing the structure in time or space of a fractal process remain the same as the process is measured over a range of different scales (or scale invariant). Fractals are complex, patterned, statistically self-similar or self-affine, scaling or scale-invariant structures with non-integer dimensions, generated by simple iterative rules widespread in real and synthetic systems. A wavelet is fractal and so a natural choice of basis for analysis of fractal data. Wavelet methods are particularly adequate in brain imaging data analysis due to broadly fractal properties exhibited by the brain in space and time. Hence wavelets are advocated more than just another basis for functional brain imaging data processing revealing activity patterns based on multiresolution analysis.