Abstract
We introduce a novel method for the measurement of information level in fMRI (functional Magnetic Resonance Imaging) neural data sets, based on image subdivision in small polygons equipped with different entropic content. We show how this method, called maximal nucleus clustering (MNC), is a novel, fast and inexpensive image-analysis technique, independent from the standard blood-oxygen-level dependent signals. MNC facilitates the objective detection of hidden temporal patterns of entropy/information in zones of fMRI images generally not taken into account by the subjective standpoint of the observer. This approach befits the geometric character of fMRIs. The main purpose of this study is to provide a computable framework for fMRI that not only facilitates analyses, but also provides an easily decipherable visualization of structures. This framework commands attention because it is easily implemented using conventional software systems. In order to evaluate the potential applications of MNC, we looked for the presence of a fourth dimension's distinctive hallmarks in a temporal sequence of 2D images taken during spontaneous brain activity. Indeed, recent findings suggest that several brain activities, such as mind-wandering and memory retrieval, might take place in the functional space of a four dimensional hypersphere, which is a double donut-like structure undetectable in the usual three dimensions. We found that the Rényi entropy is higher in MNC areas than in the surrounding ones, and that these temporal patterns closely resemble the trajectories predicted by the possible presence of a hypersphere in the brain.
Highlights
In this paper, we introduce a novel technique of fMRI images analysis, called computational proximity method, i.e., nucleus clustering in Voronoï tessellations (Peters and Inan, 2016a)
We showed in the above paragraphs that in a Voronoï tessellation of an fMRI image, of particular interest is the presence of maximal nucleus clusters (MNC), i.e., clusters with the highest number of adjacent polygons
We have demonstrated that computational proximity in 2D fMRI images is able to reveal hidden temporal patterns of Rényi entropy, enabling us to detect functional information from morphological data
Summary
We introduce a novel technique of fMRI images analysis, called computational proximity method, i.e., nucleus clustering in Voronoï tessellations (Peters and Inan, 2016a). The images are subdivided in contiguous (without interstice or overlap) polygons, called the “Voronoï polygons.”. They yield a density map, called “tessellation,” that makes it possible to make an objective measurement of the polygon areas’ spatial distribution and helps to define “random,” “regular,” and Entropy in Brain fMRI Images “clustered” distributions (Duyckaerts and Godefroy, 2000; Edelsbrunner, 2014). In a Voronoï tessellation of an fMRI image, of particular interest is the presence of maximal nucleus clusters (MNC), i.e., zones with the highest number of adjacent polygons (Peters et al, 2016). MNC reveals regions of the brain, independent from blood-oxygen-level dependent (BOLD) signals, characterized by different gradient orientation and diverse functional dimensions (Saye and Sethian, 2011)
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