Fluctuations in neurofibrillary tangle density in Alzheimer’s disease revealed by Fourier (spectral) analysis

Significant densities of neurofibrillary tangles (NFT) often occur in regions of the cerebral cortex and hippocampus in cases of Alzheimer’s disease (AD). To investigate the spatial fluctuations of NFT in these regions, variations in the density of Gallyas-stained NFT were recorded in ‘transects’ of contiguous sample fields aligned parallel with the tissue boundary. Fourier (spectral) analysis was used to analyse the fluctuations in density of NFT and to interpret them in relation to the underlying neuroanatomy. The Fourier analysis suggested that NFT exhibited complex sinusoidal fluctuations in density in the cerebral cortex and hippocampus in AD. The fluctuations occurred at different scales, the most common pattern being a small-scale sinusoidal fluctuation repeating every 500-1000 mm and a larger-scale pattern repeating at distances greater than 1000 mm. These fluctuations in density may reflect the association of NFT with the modular structure of the cortex and hippocampus. Fourier analysis may be a useful statistical method for studying the patterns of NFT and other abundant cellular inclusions in neurodegenerative disease.