Source-linked AI summary
Network Physiology reveals relations between network topology and physiological function
Amir Bashan, Ronny P. Bartsch, Jan W. Kantelhardt, Shlomo Havlin, Plamen Ch. Ivanov
TL;DR
Diverse physiologic systems interact dynamically, but their network topology and relation to physiologic function across states remain insufficiently understood. The paper develops a complex-networks framework using time delay stability and finds distinct, rapidly reorganizing interaction networks across sleep stages.
Problem
The topology of networks linking diverse physiologic systems, and its relation to function across physiologic states, had not been characterized.
Method
The study models physiologic systems as network nodes and their dynamical coupling as links, using time delay stability to quantify interactions across sleep stages.
Results
Physiologic interaction networks differ markedly across sleep stages, with connectivity highest during wake and light sleep, intermediate during REM, and lowest during deep sleep.
Takeaways & Limitations
Network topology and physiologic function show a robust interplay, with network transitions reorganizing global interconnectivity within a few minutes.
Abstract
from arXiv · showhide
The human organism is an integrated network where complex physiologic systems, each with its own regulatory mechanisms, continuously interact, and where failure of one system can trigger a breakdown of the entire network. Identifying and quantifying dynamical networks of diverse systems with different types of interactions is a challenge. Here, we develop a framework to probe interactions among diverse systems, and we identify a physiologic network. We find that each physiologic state is characterized by a specific network structure, demonstrating a robust interplay between network topology and function. Across physiologic states the network undergoes topological transitions associated with fast reorganization of physiologic interactions on time scales of a few minutes, indicating high network flexibility in response to perturbations. The proposed system-wide integrative approach may facilitate the development of a new field, Network Physiology.
RESULTS
The study quantifies interactions among diverse physiologic systems as dynamical networks, tracking topology and link-strength evolution across physiologic-state transitions. It introduces time delay stability to identify and quantify dynamic links in an integrated network of cerebral, cardiac, respiratory, ocular, and muscle activity.
- Network framework: The framework represents physiologic systems as network nodes and their dynamical interactions as network links.It quantifies network topology and the dynamics of interaction strength during a physiologic state.
- Network framework: The approach tracks multiple interconnected physiologic systems as they transition from one physiologic state to another.It uses both individual system signal outputs and interactions among systems.
- Dynamic links: Time delay stability (TDS) identifies and quantifies dynamic links among physiologic systems.TDS is introduced as a measure for characterizing these dynamic interactions.
- Analyzed systems: The analyzed physiologic network includes cerebral, cardiac, respiratory, ocular, and muscle activity.The study examines interactions among this ensemble of key integrated physiologic systems.
- Physiologic states: The framework is applied across different sleep stages to study network interactions.The supplied passage introduces sleep-stage comparisons but does not specify the individual stages.
Group average · Subj. 3
The paper characterizes physiologic interactions across wake, REM, light, and deep sleep using group-averaged time delay stability matrices and related networks. Network connectivity during light sleep more closely resembles wake than deep sleep, contrasting with individual-system dynamics.
- Group average: Group-averaged TDS matrices characterize physiologic interactions across wake, REM, light sleep, and deep sleep.Matrix elements quantify time delay stability for each pair of physiologic systems after weighted averaging across subjects.
- Group average: The interaction strength is the fraction of sleep-stage time during which time delay stability is observed.The color code represents average interaction strength across the total duration of each stage throughout the night.
- Group average: A network link is defined when a pair of systems has TDS of ≥7.The supplied passage states this threshold as the criterion for defining a network link.
- Subj. 3: The physiologic network comprises interactions among diverse systems rather than only functional connectivity within EEG networks.The passage contrasts prior EEG-focused work with the previously unstudied dynamics and topology of a network comprising diverse physiologic systems.
- Subj. 3: Individual physiologic dynamics show stronger temporal correlations and nonlinearity during wake and REM than during light and deep sleep.Non-REM sleep is described as having weaker correlations and loss of nonlinearity.
- Subj. 3: Network characteristics during light sleep are much closer to wake and very different from deep sleep.This network pattern contrasts with the individual-system dynamics described across sleep stages.
W REM LS DS … Physiologic states and network link strength
Physiologic interaction networks vary markedly across sleep stages, with wake and light sleep showing greater connectivity than REM and deep sleep. Network links are defined by stable time-delay coupling, whose strength reflects the proportion of time that stability persists.
- W REM LS DS: Stable time delays quantify how consistently modulations in one physiologic system are followed by corresponding modulations in another.Approximately constant time delays indicate stable interactions, while stronger coupling produces more persistent stability.
- W REM LS DS: The TDS method establishes a network link when time-delay stability exceeds a significance threshold.Link strength is proportional to the percentage of time for which time-delay stability is observed.
- Transitions in network topology with physiologic: Network topology can change dramatically within a few minutes during sleep-stage transitions, shifting from only a few links to many links.These transitions indicate changes in global interconnectivity between physiological systems.
- function: Stable time-delay interactions reveal characteristic network topologies for each sleep stage.Group-averaged time-delay stability matrices quantify the percentage of stable delays across all episodes of a given stage, with statistically significant elements represented as links.
- function: Brain-subnetwork topology remains unchanged across sleep stages, but its link strength varies.Links are strongest during light and deep sleep, intermediate during wake, and weakest during REM sleep.
- W REM LS DS: Wake and light sleep have higher network connectivity than REM sleep, while deep sleep has significantly fewer links.The figure reports p < 10^-3 for comparisons of REM and deep sleep with wake and light sleep, and no significant wake–light-sleep difference.
- function: Time-delay stability matrices identify separate subgroups of physiologic interactions, including brain–periphery interactions.These patterns accompany distinct physiologic dynamics during light and deep sleep and suggest additional aspects of sleep regulation.
- function: Network interactions may participate in controlling physiologic network organization during sleep.The findings indicate that previously unrecognized aspects of sleep regulation may control physiologic network interactions.
stratification
Network link strength varies systematically across sleep stages and network subnetworks. Brain-brain links are substantially stronger than other links, while individual-link strength distributions also show distinct sleep-stage patterns.
- Average link strength: Average link strength is significantly higher during wake and light sleep than during REM and deep sleep.Link strength is defined as the fraction of time when TDS is observed.
- Subnetwork differences: ≈5 times higher average link strength characterizes the brain-brain subnetwork compared with all other physiologic network links.Stronger brain-brain links during non-REM sleep are associated with stable time delays, whereas asynchronous REM activity produces weaker links.
- Subnetwork differences: Brain-brain and periphery-periphery/brain-periphery subnetworks exhibit completely different sleep-stage stratification patterns.Similar brain-brain patterns during deep and light sleep indicate sensitivity to synchronous slow-wave brain activity during non-REM sleep.
- Rank distributions: Deep sleep produces a vertically shifted rank distribution toward lower link-strength values, while REM and wake show slow smooth decay and deep and light sleep show faster decay.The deep- and light-sleep distributions include a mid-rank plateau indicating a cluster of links with similar strength.
- Rank distributions: Similar rank-distribution forms do not imply equal average link strength: deep versus light sleep and wake versus REM remain significantly different.Deep and light sleep share one distribution form, while wake and REM share another.
Local topology and connectivity of the physiologic · network
The study examines whether individual physiologic systems change their local topology and connectivity across sleep-stage transitions. The cardiac system is highly connected during wake and light sleep, lacks stable links during deep sleep, and shows changing average link strength.
- network: Sleep-stage transitions prompt examination of whether individual network nodes change their local topology and connectivity.The analysis considers each physiologic system separately.
- network: The analysis evaluates each physiologic system’s number and strength of links with the rest of the network.This treats each physiologic system as a network node.
- network: The cardiac system is highly connected to other physiologic systems during wake.This pattern is shown in Fig. 6.
- network: The cardiac system is highly connected to other physiologic systems during light sleep.This pattern is shown in Fig. 6.
- network: During deep sleep, cardiac interactions lack statistically significant time delay stability, reflected by absent cardiac links.The absence of cardiac links is shown in Fig. 6.
- network: The average strength of links connected to the cardiac system also changes across sleep-stage transitions.The supplied passage states that this average strength changes but does not provide the direction or value.
DISCUSSION · METHODS · Data
The paper introduces a TDS-based framework that identifies stable physiologic interaction networks and characterizes their transitions across physiologic states. Using continuously recorded sleep data from 36 healthy young subjects, it demonstrates how network analysis captures reorganization of interactions across the organism.
- DISCUSSION: The TDS-based framework identifies a robust network of interactions between physiologic systems that remains stable across subjects within a given physiologic state.The framework is presented as a tool for characterizing dynamics and function in heterogeneous, interdependent complex systems.
- DISCUSSION: Changes in physiologic state produce complex transitions in the network of physiologic interactions.These transitions motivate examining how network topology changes with physiologic state.
- DISCUSSION: The relation between dynamical network topology and network function has medical, clinical, and broader complex-network implications.The paper frames this relation as relevant both to applied physiology and general complex-network theory.
- Data: The study analyzes continuously recorded multi-channel physiologic data from 36 healthy young subjects during night-time sleep.The sample included 18 female and 18 male subjects, aged 20-40 years, with an average age of 29 years.
- Data: The average sleep record duration was 7.8 hours, enabling analysis across different sleep stages and sleep-stage transitions.The continuous recordings support tracking network dynamics and evolution over the night.
- Data: Sleep data demonstrate that a network approach is necessary to understand how individual-system regulation translates into organism-wide interaction reorganization.The example links modulations in individual regulatory mechanisms to changes across physiologic interactions.
Time Delay Stability (TDS) Method
The Time Delay Stability (TDS) method quantifies physiologic coupling by detecting stable time lags between output signals, with longer TDS periods indicating stronger interactions. It identifies network links using a sliding-window stability criterion and calibrates significance by comparing TDS distributions with surrogate data.
- Coupling principle: Stable time lags between two output signals indicate strong physiologic coupling, whereas fluctuating delays indicate absent stable coupling.The method is based on transient signal modulations producing corresponding changes after a stable lag.
- TDS computation: The method divides normalized signals into overlapping L = 60 sec segments with L/2 = 30 sec overlap, then estimates each segment’s delay from maximum absolute cross-correlation.For each segment, the delay τ0 is the lag maximizing the absolute cross-correlation under periodic boundary conditions.
- Stability criterion: A link is labeled stable when the delay changes by no more than ±1 sec in at least four of five consecutive segments, using a 5 × 30 sec window.The procedure scans the delay series with a sliding window whose step size is one segment.
- Link strength: Higher % TDS denotes stronger network links because it measures the fraction of time during which stable delays occur.Longer TDS periods reflect more stable interaction or coupling between physiologic systems.
- Method validation: The method is general and more reliable than traditional cross-correlation and cross-coherence for heterogeneous, nonstationary signals, whose results are affected by autocorrelation.Cross-correlation analysis showed no statistically significant differences between real and surrogate data, indicating it was not reliable for identifying physiologic interactions.
- Significance threshold: Network-wide significance is set as the TDS percentage at which all included links are statistically significant, based on TDS distributions from all 36 subjects.This threshold permits comparison of interactions that differ in strength and vary across physiologic states.
Surrogate tests
Surrogate tests show that TDS detects physiologically relevant endogenous interactions: pairing signals from different subjects removes coupling, producing near-uniform ranks and weaker links. TDS also outperforms traditional cross-correlation analysis for identifying endogenous physiologic networks.
- Surrogate tests: Pairing physiologic signals from different subjects eliminates physiologic coupling in the surrogate test.The surrogate data are used to test whether TDS captures endogenous interactions between systems.
- Surrogate tests: Surrogate data produce almost uniform rank distributions and significantly decreased link strength.These changes are attributed to the absence of physiologic interactions.
- Surrogate tests: TDS is better suited than traditional cross-correlation analysis for identifying networks of endogenous physiologic interactions.Cross-correlation rank plots show Cmax is lowest during deep sleep, higher during light sleep and REM, and highest during wake.
W REM LS DS · W REM LS DS
Sleep-stage network connectivity patterns remain robust across thresholds from 5% to 9% TDS, although higher thresholds reduce overall link counts. Light sleep and wake show the most links, REM fewer, and deep sleep the fewest, supporting network robustness.
- W REM LS DS: Surrogate tests found no statistical difference between original and cross-subject surrogate Cmax rank distributions.The surrogates abolished coupling between systems while preserving physiologic autocorrelations, suggesting cross-correlations were not physiologically informative here.
- W REM LS DS: 5% and 9% TDS thresholds were tested to assess robustness of sleep-stage network stratification.The original pattern used a 7% TDS significance threshold.
- W REM LS DS: Increasing the TDS threshold from 5% to 9% decreases the overall number of network links.This comparison spans the corresponding panels in Fig. 9.
- W REM LS DS: Light sleep and wake retain the highest network connectivity across tested thresholds.The same rank ordering is preserved around the 7% TDS threshold.
- W REM LS DS: REM retains fewer network links than light sleep and wake across the tested TDS thresholds.REM occupies the intermediate connectivity level in the sleep-stage stratification.
- W REM LS DS: Deep sleep shows a significant reduction in network connectivity across the tested thresholds.This reduction is the lowest-connectivity feature of the preserved sleep-stage pattern.