In recent years, there has been growing interest in studying the complexity of resting-state functional magnetic resonance imaging (rs-fMRI) brain signals. As one of the most commonly used complexity methods, entropy measures have been used to quantitatively characterize abnormal brain activity in aged individuals and patients with psychopathic and neurological disorders, and most studies have analyzed brain signals from a single channel. The widely used entropy methods include approximate entropy (AE), sample entropy (SE), permutation entropy (PE), and fuzzy entropy (FE). However, the test-retest reliability of different entropy methods remains to be explored. In this study, we investigated the distribution and test-retest reliability of four entropy measures and a new entropy algorithm we proposed, permutation fuzzy entropy (PFE), in three independent data sets at three levels, i.e., based on voxels, brain regions, and functional networks. Our results showed that analyzing fMRI signals with entropy showed strong tissue sensitivity. The highest reliability was achieved with PFE, and PE and FE were superior to AE and SE at all three levels. The percentage of nodes with good to excellent reliability in PFE, PE, FE, SE and AE was 94.31%, 52.65%, 18.56%, 11.36% and 0.76%, respectively. PFE and PE showed fair to good reliability in the visual network, auditory network, default-mode network, etc. In conclusion, characterizing brain entropy may provide an informative tool to assess the complexity of brain functions. Our results suggested that PFE and PE had better reliability and reflected more topological information related to normal and disordered functioning of the human brain.

The human brain is a complex system of interconnected brain regions that form functional networks with differing roles in cognition and behavior. However, the trajectories of these functional networks across development are unclear and designing a metric to track the complex trajectory of these characteristics throughout the lifespan is challenging. Here, permutation entropy (PE) was used to examine age‐related variations in functional magnetic resonance imaging (fMRI) in healthy subjects aged 6–85 from global, network, and nodal perspectives. The global PE followed an inverted U‐shaped trajectory that peaked at approximately age 40. The trajectory of the motor and somatosensory functional network was more consistent with a linear model and increased with age; other functional networks showed inverted U‐shaped trajectories that peaked between 25 and 52 years of age. All nodes showed inverted U‐shaped trajectories. Using cluster analysis, the peak ages of nodes were grouped into three clusters (at 24, 38, and 51 years). Overall, we characterized four aging trajectories: networks with a linear increase, early peak age, intermediate peak age, and older peak age. These findings suggest possible complexity in trajectories at critical age points regarding changes in related functional brain networks.

Drug-resistant epilepsy is frequent, persistent, and brings a heavy economic burden to patients and their families. Traditional epilepsy detection methods ignore the causal relationship of seizures and focus on a single time or spatial dimension, and the effect varies greatly in different patients. Therefore, it is necessary to research accurate automatic detection technology of epilepsy in different patients. We propose a causal-spatio-temporal graph attention network (CSTGAT), which uses transfer entropy (TE) to construct a causal graph between multiple channels, combining graph attention network (GAT) and bi-directional long short-term memory (BiLSTM) to capture temporal dynamic correlation and spatial topological structure information. The accuracy, specificity, and sensitivity of the SWEZ dataset were 97.24%, 97.92%, and 98.11%. The accuracy of the private dataset reached 98.55%. The effectiveness of each module was proven through ablation experiments and the impact of different network construction methods was compared. The experimental results indicate that the causal relationship network constructed by TE could accurately capture the information flow of epileptic seizures, and GAT and BiLSTM could capture spatiotemporal dynamic correlations. This model accurately captures causal relationships and spatiotemporal correlations on two datasets, and it overcomes the variability of epileptic seizures in different patients, which may contribute to clinical surgical planning.

To assess the short-term day-to-day reproducibility of 24-hour intraocular pressure (IOP) curves in various respects in untreated primary open-angle glaucoma (POAG) and ocular hypertension (OHT) patients. 47 subjects with POAG and 34 subjects with OHT underwent IOP measurements every 2 hours in both eyes for consecutive 48 hours by a non-contact tonometer (NCT). IOP values at each time point were recorded. Mean IOP, peak IOP, time difference of peak IOP between two days and IOP fluctuation were also calculated. Intraclass correlation coefficients (ICCs) and Bland-Altman plots were used to evaluate reproducibility. ICCs of the entire IOP values for a complete 24-hour curve were 0.577 and 0.561 in POAG and OHT patients, respectively. ICCs of IOP values at different time points ranged from 0.384 (10am) to 0.686 (4am) in POAG patients and from 0.347 (6am) to 0.760 (4am) in OHT patients. ICCs of mean IOP, peak IOP and IOP fluctuation were respectively 0.832, 0.704, 0.367 in POAG patients and 0.867, 0.816 0.633 in OHT patients. Only 37.23% and 35.29% of the peak IOP time points appeared within the time difference of 2 hours in POAG and OHT patients, respectively, while 53.19% and 48.53% appeared within 4 hours in POAG and OHT patients, respectively. A 24-hour IOP curve in a single day is not highly reproducible in short-term and has limited use for evaluating individual IOP condition. Mean IOP and peak IOP for a 24-hour IOP curve are useful parameters in clinical follow-up, while IOP value at a certain time point, IOP fluctuation and peak IOP time point should be interpreted with caution.

Entropy serves as an effective nonlinear dynamic indicator of time series complexity. A number of multivariate entropy methods exist and are effectively used in signal analysis. However, existing multivariate entropy methods are limited in capturing cross-channel and within-channel information. To address these limitations and represent a wide range of scale information, we propose multivariate multiscale variations dispersion entropy (mvMVDE). Moreover, to reduce the loss of signal information of mvMVDE, we develop multivariate multiscale variations fuzzy dispersion entropy (mvMVFDE) based on fuzzy membership functions. Experiments with simulated signals indicate that the proposed methods can better detect nonlinear dynamic changes in signals and exhibit reduced sensitivity to parameters, signal length, and noise, yielding more stable outcomes than mvMSE and mvMDE. Furthermore, real-world experiments on electroencephalogram (EEG) signals show that mvMVDE and mvMVFDE demonstrate a notable advantage in discerning the distinct dynamics of multichannel signals, and the accuracy of mvMVDE and mvMVFDE is higher than that of the popular mvMSE and mvMDE. In this study, we propose two valuable signal detection methods, each with its own performance advantages: the mvMVDE is fast, while the mvMVFDE has high accuracy.

Alzheimer’s disease (AD) is a degenerative brain disease, and the condition is difficult to assess. In the past, numerous brain dynamics models have made remarkable contributions to neuroscience and the brain from the microcosmic to the macroscopic scale. Recently, large-scale brain dynamics models have been developed based on dual-driven multimodal neuroimaging data and neurodynamics theory. These models bridge the gap between anatomical structure and functional dynamics and have played an important role in assisting the understanding of the brain mechanism. Large-scale brain dynamics have been widely used to explain how macroscale neuroimaging biomarkers emerge from potential neuronal population level disturbances associated with AD. In this review, we describe this emerging approach to studying AD that utilizes a biophysically large-scale brain dynamics model. In particular, we focus on the application of the model to AD and discuss important directions for the future development and analysis of AD models. This will facilitate the development of virtual brain models in the field of AD diagnosis and treatment and add new opportunities for advancing clinical neuroscience.