Grela Jacek, Drogosz Zbigniew, Janarek Jakub, Ochab Jeremi K, Cifre Ignacio, Gudowska-Nowak Ewa, Nowak Maciej A, Oświęcimka Paweł, Chialvo Dante R
Institute of Theoretical Physics, Jagiellonian University, 30-348 Kraków, Poland.
Mark Kac Center for Complex Systems Research, Jagiellonian University, 30-348 Kraków, Poland.
J Neural Eng. 2025 Jan 27;22(1). doi: 10.1088/1741-2552/ada705.
. Magnetic resonance imaging (MRI), functional MRI (fMRI) and other neuroimaging techniques are routinely used in medical diagnosis, cognitive neuroscience or recently in brain decoding. They produce three- or four-dimensional scans reflecting the geometry of brain tissue or activity, which is highly correlated temporally and spatially. While there exist numerous theoretically guided methods for analyzing correlations in one-dimensional data, they often cannot be readily generalized to the multidimensional geometrically embedded setting.. We present a novel method, Fractal Space-Curve Analysis (FSCA), which combines Space-Filling Curve (SFC) mapping for dimensionality reduction with fractal Detrended Fluctuation Analysis. We conduct extensive feasibility studies on diverse, artificially generated data with known fractal characteristics: the fractional Brownian motion, Cantor sets, and Gaussian processes. We compare the suitability of dimensionality reduction via Hilbert SFC and a data-driven alternative. FSCA is then successfully applied to real-world MRI and fMRI scans.. The method utilizing Hilbert curves is optimized for computational efficiency, proven robust against boundary effects typical in experimental data analysis, and resistant to data sub-sampling. It is able to correctly quantify and discern correlations in both stationary and dynamic two-dimensional images. In MRI Alzheimer's dataset, patients reveal a progression of the disease associated with a systematic decrease of the Hurst exponent. In fMRI recording of breath-holding task, the change in the exponent allows distinguishing different experimental phases.. This study introduces a robust method for fractal characterization of spatial and temporal correlations in many types of multidimensional neuroimaging data. Very few assumptions allow it to be generalized to more dimensions than typical for neuroimaging and utilized in other scientific fields. The method can be particularly useful in analyzing fMRI experiments to compute markers of pathological conditions resulting from neurodegeneration. We also showcase its potential for providing insights into brain dynamics in task-related experiments.
磁共振成像（MRI）、功能磁共振成像（fMRI）和其他神经成像技术常用于医学诊断、认知神经科学，最近还用于脑解码。它们生成反映脑组织几何结构或活动的三维或四维扫描图像，这些图像在时间和空间上高度相关。虽然存在许多理论指导的方法来分析一维数据中的相关性，但它们往往不能轻易推广到多维几何嵌入的情况。我们提出了一种新方法，分形空间曲线分析（FSCA），它将用于降维的空间填充曲线（SFC）映射与分形去趋势波动分析相结合。我们对具有已知分形特征的各种人工生成数据进行了广泛的可行性研究：分数布朗运动、康托集和高斯过程。我们比较了通过希尔伯特SFC进行降维和数据驱动替代方法的适用性。然后，FSCA成功应用于实际的MRI和fMRI扫描。利用希尔伯特曲线的方法针对计算效率进行了优化，经证明对实验数据分析中典型的边界效应具有鲁棒性，并且对数据子采样具有抗性。它能够正确量化和辨别静态和动态二维图像中的相关性。在MRI阿尔茨海默病数据集中，患者显示出疾病的进展与赫斯特指数的系统性下降相关。在屏气任务的fMRI记录中，指数的变化允许区分不同的实验阶段。本研究介绍了一种用于对多种类型的多维神经成像数据中的时空相关性进行分形表征的鲁棒方法。极少的假设使其能够推广到比神经成像通常更多的维度，并应用于其他科学领域。该方法在分析fMRI实验以计算神经退行性变导致的病理状况标志物方面可能特别有用。我们还展示了它在为与任务相关的实验中的脑动力学提供见解方面的潜力。
