Stochastic brain dynamics exhibits differential regional distribution and maturation-related changes.

Functional magnetic resonance imaging (fMRI) is a powerful non-invasive method for studying brain function by analyzing blood oxygenation level-dependent (BOLD) signals. These signals arise from intricate interplays of deterministic and stochastic biological elements. Quantifying the stochastic part is challenging due to its reliance on assumptions about the deterministic segment. We present a methodological framework to estimate intrinsic stochastic brain dynamics in fMRI data without assuming deterministic dynamics. Our approach utilizes Approximate Entropy and its behavior in noisy series to identify and characterize dynamical noise in unobservable fMRI dynamics. Applied to extensive fMRI datasets (645 Cam-CAN, 1086 Human Connectome Project subjects), we explore lifelong maturation of intrinsic brain noise. Findings indicate 10% to 60% of fMRI signal power is due to intrinsic stochastic brain elements, varying by age. These components demonstrate a physiological role of neural noise which shows a distinct distributions across brain regions and increase linearly during maturation.

Physiological Noise: Definition, Estimation, and Characterization in Complex Biomedical Signals.

BACKGROUND: Nonlinear physiological systems exhibit complex dynamics driven by intrinsic dynamical noise. In cases where there is no specific knowledge or assumption about system dynamics, such as in physiological systems, it is not possible to formally estimate noise. AIM: We introduce a formal method to estimate the power of dynamical noise, referred to as physiological noise, in a closed form, without specific knowledge of the system dynamics. METHODOLOGY: Assuming that noise can be modeled as a sequence of independent, identically distributed (IID) random variables on a probability space, we demonstrate that physiological noise can be estimated through a nonlinear entropy profile. We estimated noise from synthetic maps that included autoregressive, logistic, and Pomeau-Manneville systems under various conditions. Noise estimation is performed on 70 heart rate variability series from healthy and pathological subjects, and 32 electroencephalographic (EEG) healthy series. RESULTS: Our results showed that the proposed model-free method can discern different noise levels without any prior knowledge of the system dynamics. Physiological noise accounts for around 11% of the overall power observed in EEG signals and approximately 32% to 65% of the power related to heartbeat dynamics. Cardiovascular noise increases in pathological conditions compared to healthy dynamics, and cortical brain noise increases during mental arithmetic computations over the prefrontal and occipital regions. Brain noise is differently distributed across cortical regions. CONCLUSION: Physiological noise is very part neurobiological dynamics and can be measured using the proposed framework in any biomedical series.

Characterization of Physiological Noise in Complex Cardiovascular Variability Series.

The cardiovascular system can be analyzed using spectral, nonlinear, and complexity metrics. Nevertheless, dynamical noise may significantly impact these quantifiers. To our knowledge, there has been no attempt to quantify the intrinsic cardiovascular system noise driving heartbeat dynamics. To this end, this study presents a novel, model-free framework to define and quantify physiological noise using nonlinear Approximate Entropy profile. The framework was tested using analytical noisy series and then applied to real Heart Rate Variability (HRV) series gathered from a publicly-available dataset of recordings from 19 young and 19 elderly subjects watching the movie "Fantasia". Results suggest that physiological noise may account for over 15% of cardiovascular dynamics and is influenced by aging, with decreased cardiac noise in the elderly compared to the young subjects. Our findings indicate that physiological noise is a crucial factor in characterizing cardiovascular dynamics, and current spectral, nonlinear, and complexity assessments should take into account underlying dynamical noise estimates.

Multiscale partition-based Kolmogorov-Sinai Entropy: a preliminary HRV study on Heart Failure vs. Atrial Fibrillation.

Several approaches for estimating complexity in physiological time series at various time scales have recently been developed, with a special focus on heart rate variability (HRV) series. While numerous multiscale complexity quantifiers have been investigated, a multiscale Kolmogorov-Sinai (K-S) entropy for the characterization of cardiovascular dynamics still has to be properly assessed. In this pilot study, we investigate the Algorithmic Information Content, which is calculated using an effective compression algorithm, to quantify multiscale partition- based K-S entropy on experimental HRV series. Data were gathered from publicly available datasets comprising long-term, unstructured recordings from 10 healthy subjects, as well as 10 patients with congestive heart failure (CHF) and 10 patients with atrial fibrillation. Results show that multiple time scales and domain partitions statistically discern healthy vs. pathological cardiovascular dynamics. We conclude that the proposed multiscale partition-based K-S entropy may constitute a viable tool for the complexity assessment of cardiovascular variability series.

A Multiscale Partition-Based Kolmogorov-Sinai Entropy for the Complexity Assessment of Heartbeat Dynamics.

BACKGROUND: Several methods have been proposed to estimate complexity in physiological time series observed at different time scales, with a particular focus on heart rate variability (HRV) series. In this frame, while several complexity quantifiers defined in the multiscale domain have already been investigated, the effectiveness of a multiscale Kolmogorov-Sinai (K-S) entropy has not been evaluated yet for the characterization of heartbeat dynamics. METHODS: The use of the algorithmic information content, which is estimated through an effective compression algorithm, is investigated to quantify multiscale partition-based K-S entropy on publicly available experimental HRV series gathered from young and elderly subjects undergoing a visual elicitation task (Fantasia). Moreover, publicly available HRV series gathered from healthy subjects, as well as patients with atrial fibrillation and congestive heart failure in unstructured conditions have been analyzed as well. RESULTS: Elderly people are associated with a lower HRV complexity and a more predictable cardiovascular dynamics, with significantly lower partition-based K-S entropy than the young adults. Major differences between these groups occur at partitions greater than six. In case of partition cardinality greater than 5, patients with congestive heart failure show a minimal predictability, while atrial fibrillation shows a higher variability, and hence complexity, which is actually reduced by the time coarse-graining procedure. CONCLUSIONS: The proposed multiscale partition-based K-S entropy is a viable tool to investigate complex cardiovascular dynamics in different physiopathological states.

Quantifying partition-based Kolmogorov-Sinai Entropy on Heart Rate Variability: a young vs. elderly study.

In the last decades, a considerable effort has been devoted to quantify complexity in physiological time series, with a particular focus on heart rate variability (HRV). To this end, exemplary quantifiers including Approximate Entropy and Sample Entropy have successfully been applied by leveraging on statistical approximation and further parametrization through the definition of tolerance and embedding dimension, among others. In this study, we investigate the use of the Algorithmic Information Content, which is estimated through an effective compression algorithm, to quantify partition-based Kolmogorov-Sinai (K-S) entropy on HRV series. We test such a K-S estimate on real data gathered from the Fantasia database, aiming to discern young vs. elderly complex dynamics. Experimental results show that elderly people are associated with a lower HRV complexity and a more predictable behavior, with significantly lower partition-based K-S entropy than the young adults. We conclude that partition-based K-S entropy may effectively be used to investigate pathological conditions in the cardiovascular system, complementing state-of-the-art methods for complexity assessment.