We present an approach, framed in information theory, to assess nonlinear causality between the subsystems of a whole stochastic or deterministic dynamical system. The approach follows a sequential ...procedure for nonuniform embedding of multivariate time series, whereby embedding vectors are built progressively on the basis of a minimization criterion applied to the entropy of the present state of the system conditioned to its past states. A corrected conditional entropy estimator compensating for the biasing effect of single points in the quantized hyperspace is used to guarantee the existence of a minimum entropy rate at which to terminate the procedure. The causal coupling is detected according to the Granger notion of predictability improvement, and is quantified in terms of information transfer. We apply the approach to simulations of deterministic and stochastic systems, showing its superiority over standard uniform embedding. Effects of quantization, data length, and noise contamination are investigated. As practical applications, we consider the assessment of cardiovascular regulatory mechanisms from the analysis of heart period, arterial pressure, and respiration time series, and the investigation of the information flow across brain areas from multichannel scalp electroencephalographic recordings.
In the framework of information dynamics, the temporal evolution of coupled systems can be studied by decomposing the predictive information about an assigned target system into amounts quantifying ...the information stored inside the system and the information transferred to it. While information storage and transfer are computed through the known self-entropy (SE) and transfer entropy (TE), an alternative decomposition evidences the so-called cross entropy (CE) and conditional SE (cSE), quantifying the cross information and internal information of the target system, respectively. This study presents a thorough evaluation of SE, TE, CE and cSE as quantities related to the causal statistical structure of coupled dynamic processes. First, we investigate the theoretical properties of these measures, providing the conditions for their existence and assessing the meaning of the information theoretic quantity that each of them reflects. Then, we present an approach for the exact computation of information dynamics based on the linear Gaussian approximation, and exploit this approach to characterize the behavior of SE, TE, CE and cSE in benchmark systems with known dynamics. Finally, we exploit these measures to study cardiorespiratory dynamics measured from healthy subjects during head-up tilt and paced breathing protocols. Our main result is that the combined evaluation of the measures of information dynamics allows to infer the causal effects associated with the observed dynamics and to interpret the alteration of these effects with changing experimental conditions.
The continuously growing framework of information dynamics encompasses a set of tools, rooted in information theory and statistical physics, which allow to quantify different aspects of the ...statistical structure of multivariate processes reflecting the temporal dynamics of complex networks. Building on the most recent developments in this field, this work designs a complete approach to dissect the information carried by the target of a network of multiple interacting systems into the new information produced by the system, the information stored in the system, and the information transferred to it from the other systems; information storage and transfer are then further decomposed into amounts eliciting the specific contribution of assigned source systems to the target dynamics, and amounts reflecting information modification through the balance between redundant and synergetic interaction between systems. These decompositions are formulated quantifying information either as the variance or as the entropy of the investigated processes, and their exact computation for the case of linear Gaussian processes is presented. The theoretical properties of the resulting measures are first investigated in simulations of vector autoregressive processes. Then, the measures are applied to assess information dynamics in cardiovascular networks from the variability series of heart period, systolic arterial pressure and respiratory activity measured in healthy subjects during supine rest, orthostatic stress, and mental stress. Our results document the importance of combining the assessment of information storage, transfer and modification to investigate common and complementary aspects of network dynamics; suggest the higher specificity to alterations in the network properties of the measures derived from the decompositions; and indicate that measures of information transfer and information modification are better assessed, respectively, through entropy-based and variance-based implementations of the framework.
Aim
To apply a novel human model to evaluate the morphogenesis of the mucosal attachment to implants.
Material and methods
Twenty one patients receiving implant‐supported single‐tooth replacement ...were enrolled in this study. After implant installation, a custom‐designed experimental abutment was connected to the implant. Soft tissue biopsies representing 2, 4, 8 or 12 weeks of healing were collected by the use of a circular cutting device and prepared for histological analysis.
Results
The soft tissue biopsies were retrieved, preserved and processed with a technique that was safe and reproducible. The results from the histological analysis in regards to dimensional and qualitative changes in the mucosa over time were consistent with those reported from animal experiments. At 8 weeks, the soft tissue dimension was about 3.6 mm and included a barrier epithelium of 1.9 mm and a connective tissue portion of 1.7 mm. Similar dimensions were found at 12 weeks.
Conclusion
It is suggested that the new human model provides advantages in terms of cost‐effectiveness in research as well as from ethical aspects and should be considered as an alternative to pre‐clinical in vivo studies in animals.
The framework of information dynamics allows the dissection of the information processed in a network of multiple interacting dynamical systems into meaningful elements of computation that quantify ...the information generated in a target system, stored in it, transferred to it from one or more source systems, and modified in a synergistic or redundant way. The concepts of information transfer and modification have been recently formulated in the context of linear parametric modeling of vector stochastic processes, linking them to the notion of Granger causality and providing efficient tools for their computation based on the state–space (SS) representation of vector autoregressive (VAR) models. Despite their high computational reliability these tools still suffer from estimation problems which emerge, in the case of low ratio between data points available and the number of time series, when VAR identification is performed via the standard ordinary least squares (OLS). In this work we propose to replace the OLS with penalized regression performed through the Least Absolute Shrinkage and Selection Operator (LASSO), prior to computation of the measures of information transfer and information modification. First, simulating networks of several coupled Gaussian systems with complex interactions, we show that the LASSO regression allows, also in conditions of data paucity, to accurately reconstruct both the underlying network topology and the expected patterns of information transfer. Then we apply the proposed VAR-SS-LASSO approach to a challenging application context, i.e., the study of the physiological network of brain and peripheral interactions probed in humans under different conditions of rest and mental stress. Our results, which document the possibility to extract physiologically plausible patterns of interaction between the cardiovascular, respiratory and brain wave amplitudes, open the way to the use of our new analysis tools to explore the emerging field of Network Physiology in several practical applications.
The growing number of people with cognitive impairment will significantly increase healthcare demand. Screening tools are crucial for detecting cognitive impairment due to a shortage of mental health ...experts aiming to improve the quality of life for those living with this condition. Eye tracking is a powerful tool that can provide deeper insights into human behavior and inner cognitive processes. The proposed Eye-Tracking-Based Trail-Making Test, ETMT, is a screening tool for monitoring a person's cognitive function. The proposed system utilizes a fuzzy-inference system as an integral part of its framework to calculate comprehensive scores assessing visual search speed and focused attention. By employing an adaptive neuro-fuzzy-inference system, the tool provides an overall cognitive-impairment score, allowing psychologists to assess and quantify the extent of cognitive decline or impairment in their patients. The ETMT model offers a comprehensive understanding of cognitive abilities and identifies potential deficits in various domains. The results indicate that the ETMT model is a potential tool for evaluating cognitive impairment and can capture significant changes in eye movement behavior associated with cognitive impairment. It provides a convenient and affordable diagnosis, prioritizing healthcare resources for severe conditions while enhancing feedback to practitioners.
Despite the widespread diffusion of nonlinear methods for heart rate variability (HRV) analysis, the presence and the extent to which nonlinear dynamics contribute to short-term HRV are still ...controversial. This work aims at testing the hypothesis that different types of nonlinearity can be observed in HRV depending on the method adopted and on the physiopathological state. Two entropy-based measures of time series complexity (normalized complexity index, NCI) and regularity (information storage, IS), and a measure quantifying deviations from linear correlations in a time series (Gaussian linear contrast, GLC), are applied to short HRV recordings obtained in young (Y) and old (O) healthy subjects and in myocardial infarction (MI) patients monitored in the resting supine position and in the upright position reached through head-up tilt. The method of surrogate data is employed to detect the presence and quantify the contribution of nonlinear dynamics to HRV. We find that the three measures differ both in their variations across groups and conditions and in the percentage and strength of nonlinear HRV dynamics. NCI and IS displayed opposite variations, suggesting more complex dynamics in O and MI compared to Y and less complex dynamics during tilt. The strength of nonlinear dynamics is reduced by tilt using all measures in Y, while only GLC detects a significant strengthening of such dynamics in MI. A large percentage of detected nonlinear dynamics is revealed only by the IS measure in the Y group at rest, with a decrease in O and MI and during T, while NCI and GLC detect lower percentages in all groups and conditions. While these results suggest that distinct dynamic structures may lie beneath short-term HRV in different physiological states and pathological conditions, the strong dependence on the measure adopted and on their implementation suggests that physiological interpretations should be provided with caution.
This work introduces a framework to study the network formed by the autonomic component of heart rate variability (cardiac process η) and the amplitude of the different electroencephalographic waves ...(brain processes δ, θ, α, σ, β) during sleep. The framework exploits multivariate linear models to decompose the predictability of any given target process into measures of self-, causal and interaction predictability reflecting respectively the information retained in the process and related to its physiological complexity, the information transferred from the other source processes, and the information modified during the transfer according to redundant or synergistic interaction between the sources. The framework is here applied to the η, δ, θ, α, σ, β time series measured from the sleep recordings of eight severe sleep apnoea-hypopnoea syndrome (SAHS) patients studied before and after long-term treatment with continuous positive airway pressure (CPAP) therapy, and 14 healthy controls. Results show that the full and self-predictability of η, δ and θ decreased significantly in SAHS compared with controls, and were restored with CPAP for δ and θ but not for η. The causal predictability of η and δ occurred through significantly redundant source interaction during healthy sleep, which was lost in SAHS and recovered after CPAP. These results indicate that predictability analysis is a viable tool to assess the modifications of complexity and causality of the cerebral and cardiac processes induced by sleep disorders, and to monitor the restoration of the neuroautonomic control of these processes during long-term treatment.
The most common approach to assess the dynamical complexity of a time series across multiple temporal scales makes use of the multiscale entropy (MSE) and refined MSE (RMSE) measures. In spite of ...their popularity, MSE and RMSE lack an analytical framework allowing their calculation for known dynamic processes and cannot be reliably computed over short time series. To overcome these limitations, we propose a method to assess RMSE for autoregressive (AR) stochastic processes. The method makes use of linear state-space (SS) models to provide the multiscale parametric representation of an AR process observed at different time scales and exploits the SS parameters to quantify analytically the complexity of the process. The resulting linear MSE (LMSE) measure is first tested in simulations, both theoretically to relate the multiscale complexity of AR processes to their dynamical properties and over short process realizations to assess its computational reliability in comparison with RMSE. Then, it is applied to the time series of heart period, arterial pressure, and respiration measured for healthy subjects monitored in resting conditions and during physiological stress. This application to short-term cardiovascular variability documents that LMSE can describe better than RMSE the activity of physiological mechanisms producing biological oscillations at different temporal scales.
In this work, we extend to the multivariate case the classical correlation analysis used in the field of network physiology to probe dynamic interactions between organ systems in the human body. To ...this end, we define different correlation-based measures of the multivariate interaction (MI) within and between the brain and body subnetworks of the human physiological network, represented, respectively, by the time series of δ, θ, α, and β electroencephalographic (EEG) wave amplitudes, and of heart rate, respiration amplitude, and pulse arrival time (PAT) variability (η, ρ, π). MI is computed: (i) considering all variables in the two subnetworks to evaluate overall brain-body interactions; (ii) focusing on a single target variable and dissecting its global interaction with all other variables into contributions arising from the same subnetwork and from the other subnetwork; and (iii) considering two variables conditioned to all the others to infer the network topology. The framework is applied to the time series measured from the EEG, electrocardiographic (ECG), respiration, and blood volume pulse (BVP) signals recorded synchronously via wearable sensors in a group of healthy subjects monitored at rest and during mental arithmetic and sustained attention tasks. We find that the human physiological network is highly connected, with predominance of the links internal of each subnetwork (mainly η-ρ and δ-θ, θ-α, α-β), but also statistically significant interactions between the two subnetworks (mainly η-β and η-δ). MI values are often spatially heterogeneous across the scalp and are modulated by the physiological state, as indicated by the decrease of cardiorespiratory interactions during sustained attention and by the increase of brain-heart interactions and of brain-brain interactions at the frontal scalp regions during mental arithmetic. These findings illustrate the complex and multi-faceted structure of interactions manifested within and between different physiological systems and subsystems across different levels of mental stress.
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