Using space-filling curves and fractals to reveal spatial and temporal patterns in neuroimaging data

Area of Science:

• Neuroimaging
• Fractal Analysis
• Data Science

Background:

• Neuroimaging techniques like MRI and fMRI generate multidimensional data with complex spatial and temporal correlations.
• Existing methods for analyzing correlations in one-dimensional data are often inadequate for multidimensional neuroimaging datasets.
• Analyzing these correlations is crucial for medical diagnosis, cognitive neuroscience, and brain decoding.

Purpose of the Study:

• To introduce a novel method, Fractal Space-Curve Analysis (FSCA), for characterizing spatial and temporal correlations in multidimensional neuroimaging data.
• To demonstrate the robustness and applicability of FSCA using both simulated and real-world neuroimaging datasets.
• To explore FSCA's potential for identifying disease markers and understanding brain dynamics.

Main Methods:

• FSCA combines Space-Filling Curve (SFC) mapping for dimensionality reduction with fractal Detrended Fluctuation Analysis.
• Feasibility studies were conducted on artificial data (fractional Brownian motion, Cantor sets, Gaussian processes) with known fractal characteristics.
• The method was applied to real-world Magnetic Resonance Imaging (MRI) and functional MRI (fMRI) scans, comparing Hilbert SFC with a data-driven alternative.

Main Results:

• FSCA, particularly with Hilbert curves, is computationally efficient, robust to boundary effects, and resistant to data sub-sampling.
• The method accurately quantifies and distinguishes correlations in stationary and dynamic 2D images.
• In Alzheimer's MRI data, disease progression correlated with a decrease in the Hurst exponent. In fMRI, exponent changes distinguished experimental phases during a breath-holding task.

Conclusions:

• FSCA provides a robust framework for fractal characterization of spatial and temporal correlations in multidimensional neuroimaging data.
• The method's minimal assumptions allow for generalization to higher dimensions and application in diverse scientific fields.
• FSCA is valuable for analyzing fMRI experiments, detecting neurodegeneration markers, and gaining insights into brain dynamics during tasks.